Fracture of Nano and Engineering Materials and Structures: Proceedings of the 16th European Conference of Fracture, Alexandroupolis, Greece, July 3-7, 2006 1402049714, 9781402049712

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FRACTURE OF NANO AND ENGINEERING MATERIALS AND STRUCTURES

Fracture of Nano and Engineering Materials and Structures Proceedings of the 16th European Conference of Fracture, Alexandroupolis, Greece, July 3-7, 2006

Edited by

E. E. GDOUTOS Democritus University of Thrace, Dept of Civil Engineering, Xanthi, Greece

A C.I.P. Catalogue record for this book is available from the Library of Congress.

ISBN-10 ISBN-13 ISBN-10 ISBN-13

1-4020-4971-4 (HB) 978-1-4020-4971-2 (HB) 1-4020-4972-2 ( e-book) 978-1-4020-4972-9 (e-book)

Published by Springer, P.O. Box 17, 3300 AA Dordrecht, The Netherlands. www.springer.com Cover picture Fracture and Delamination of Oxide: Fracture and delamination of 1µm (1x10–6 m) SiO2 on Si with 1µm conical probe tip. Courtesy of Hysitron Inc., Minneapolis, Minnesota, USA

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Contents Editor’s Preface............................................................................................................ xliii Organizing Committees ................................................................................................ xlv ECF16 TRACKS......................................................................................................... xlvii ECF16 SPECIAL SYMPOSIA/SESSIONS .............................................................. xlvix

A. INVITED PAPERS ........................................................................................... 1 Deformation and Fracture at the Micron and Nano Scales.............................................. 3 E. C. Aifantis

Statistical Mechanics of Safety Factors and Size Effect in Quasibrittle Fracture............ 5 Z. P. Bazant and S.-D. Pang

Nanoreliability – Fracture Mechanics on the Way from Micro to Nano ......................... 7 B. Michel

Fracture Mechanics and Complexity Sciences ................................................................ 9 A. Carpinteri and S. Puzzi

Failure of Composite Materials...................................................................................... 11 I. M. Daniel

Interactions of Constrained Flow and Size Scale on Mechanical Behavior .................. 13 W. W. Gerberich, W. M. Mook, M. J. Cordill and D. Hallman

Space Shuttle Columbia Post-Accident Analysis and Investigation ............................. 15 S. McDanels

The Role of Adhesion and Fracture on the Performance of Nanostructured Films....... 17 N. Moody, M. J. Cordill, M. S. Kennedy, D. P. Adams, D. F. Bahr and W. W. Gerberich

Assessment of Weldment Specimens Containing Residual Stress ................................ 19 K. M. Nikbin

MEMS: Recent Advances and Current Challenges ....................................................... 21 R. J. Pryputniewicz

Fracture, Aging and Disease in Bone and Teeth ............................................................ 23 R. O. Ritchie and R. K. Nalla

Laboratory Earthquakes ................................................................................................. 25 A. J. Rosakis, K. Xia and H. Kanamori

A Historical Retrospective of the Beginnings of Brittle Fracture Mechanics The Period 1907-1947.................................................................................................... 27 H. P. Rossmanith

Dynamic Crack Propagation in Particle Reinforced Nanocomposites and Graded Materials......................................................................................................................... 29 A. Shukla

Spatial and Temporal Scaling Affected by System Inhomogeneity: Atomic, Microscopic and Macroscopic. ...................................................................................... 31 G. C. Sih

Contents

vi

B. TRACKS B1. Nanomaterials and Nanostructures ........................................................ 33 1T1. Fracture and Fatigue of Nanostuctured Materials .......................................... 35 Channeling Effect in Fracture of Materials with Nanostructured Surface Layers......... 35 V. E. Panin and A. V. Panin

Atomistics and Configurational Forces in Gradient Elasticity ...................................... 37 P. Steinmann and E. C. Aifantis

Tensile Behavior and Fracture of Carbon Nanotubes Containing Stone-Wales Defects 39 K. I. Tserpes and P. Papanikos

Atomic-Scale Investigation on Fracture Toughness in Nano-Composite Silicon Carbide............................................................................................................... 41 M. Ippolito, A. Mattoni, L. Colombo and F. Cleri

Multiscale Modeling and Computer Simulation of Stress-Deformation Relationships in Nanoparticle-Reinforced Composite Materials ......................................................... 43 L. V. Bochkaryova, M. V. Kireitseu, G. R. Tomlinson, V. Kompis and H. Altenbach

The Mechanical Parameters of Nanoobjects (Theory and Experiment) ........................ 45 E. Ivanova, N. Morozov and B. Semenov

Advanced Manufacturing Design Concepts and Modelling Tools of the Next Generation Nanoparticle-Reinforced Damping Materials ............................................ 47 M. V. Kireitseu, G. R. Tomlinson, R. A. Williams and V. Kompis

Fracture of Nanostructured Ionomer Membranes.......................................................... 49 Yue Zou, X. Huang and K. L. Reifsnider

1T2. Failure Mechanisms ............................................................................................ 51 Deformation and Limit States of Carbon Nanotubes under Complex Loading............. 51 A. V. Chentsov and R. V. Goldstein

Interaction of Domain Walls with Defects in Ferroelectric Materials ........................... 53 D. Schrade, R. Mueller, D. Gross, T. Utschig, V. Ya. Shur, D. C. Lupascu

Microstructure and Internal Stresses in Cyclically Deformed Al and Cu Single Crystals........................................................................................................................... 55 M. E. Kassner

Determination of Equilibrium Configurations of Atomic Lattices at Quasistatic Deformation ................................................................................................................... 57 S. N. Korobeynikov

Multiscale Mechanics of Carbon Nanotubes and their Composites .............................. 59 X.-Q. Feng

1T4. Fatigue and Fracture of MEMS and NEMS..................................................... 61 In-Situ Scanning Electron Microscope Indentation of Gallium Arsenide ..................... 61 C. Pouvreau, K. Wasmer, J. Giovanola, J. Michler, J. M. Breguet and A. Karimi

Fracture of Nanostructured Lithium Batteries ............................................................... 63 K. E. Aifantis, J. P. Dempsey and S. A. Hackney

Analytical and Experimental Characterization of a Micromirror System ..................... 65 E. J. Pryputniewicz, C. Furlong and R. J. Pryputniewicz

Contents

vii

A Metal Interposer for Isolating MEMS Devices from Package Stresses ..................... 67 R. J. Pryputniewicz, T. F. Marinis, J. W. Soucy, P. Hefti and A. R. Klempner

Computational Modeling of Nanoparticles in Biomicrofluidic Devices ....................... 69 R. J. Pryputniewicz, Z. Sikorski, M. Athavale, Z. J. Chen and A. J. Przekwas

Characterization of a MEMS Pressure Sensor by a Hybrid Methodology .................... 71 R. J. Pryputniewicz and C. Furlong

New Approach to Synthesis of Laser Microwelding Processes for Packaging ............. 73 R. J. Pryputniewicz, W. Han and K. A. Nowakowski

Thermal Management of RF MEMS Relay Switch....................................................... 75 R. J. Pryputniewicz

1T7. Thin Films ............................................................................................................ 77 Buckling and Delamination of Thin Layers on a Polymer Substrate ............................ 77 A. A. Abdallah, D. Kozodaev, P. C. P. Bouten, J. M. J. den Toonder and G. De With

Carbide Coated Cutting Tool Properties Investigation by Nano-Mechanical Measurements under 250-500°C.................................................................................... 79 B. Vasques, D. Joly, R. Leroy, N. Ranganathan and P. Donnadieu

Diamond Coating Debounding in Tool Application ...................................................... 81 D. Moulin, P. Chevrier, P. Lipinski and T. Barré

Interfacial Strength of Ceramic Thin Film on Polymer Substrate ................................. 83 M. Omiya and K. Kishimoto

Delaminate Behavior of PVD/CPVD Thin Film ........................................................... 85 S. Doi and M. Yasuoka

Experimental Study of Microhardness and Fracture of Implanted Gállium Nitride Films .................................................................................................................. 87 P. Kavouras, M. Katsikini, E. Wendler, W. Wesch, H. M. Polatoglou, E. C. Paloura, Ph. Komninou and Th. Karakostas

1T9. Failure of Nanocomposites ................................................................................. 89 Crack Tip Strain Field and its Propagation Characteristics in a Polymer Foam............ 89 F.-P. Chiang, S. Chang and Y. Ding

How to Toughen Ceramics – Nanocomposites .............................................................. 91 H. Awaji and S.-M. Choi

Deformation and Fracture Behaviour of Nanocomposites ............................................ 93 S. Dunger, J. K. W. Sandler, K. Hedicke and V. Altsadt

Fracture Mechanisms in Carbon Nanotube-Reinforced Composites ............................ 95 E. T. Thostenson and T.-W. Chou

Contents

viii

B. TRACKS B2. Engineering Materials and Structures .................................................. 97 2T1. Physical Aspects of Fracture .............................................................................. 99 Fractal Approach to Crack Problems with Non-Root Singularity ................................. 99 A. Kashtanov

New Method for Analysing the Magnetic Emission Signals During Fracture ............ 101 Gy. B. Lenkey, N. Takacs, F. Kun and D. L. Beke

Electromagnetic Radiation Method for Identification of Multi-Scale Fracture .......... 103 Yu. K. Bivin, A. S. Chursin, E. A. Deviatkin and I. V. Simonov

Micromechanical Modeling of Grain Boundary Resistance to Cleavage Fracture Propagation .................................................................................................................. 105 M. Stec and J. Faleskog

Microstructure of Reactor Pressure Vessel Steel Close to the Fracture Surface.......... 107 M. Karlik, P. Hausild and C. Prioul

2T2. Brittle Fracture.................................................................................................. 109 Brittle Fracture in Heat-Affected Zones of Girth Welds of Modern Line Pipe Steel (X100) .......................................................................................................................... 109 A. S. Bilat, A. F. Gourgues-Lorenzon, J. Besson and A. Pineau

Cleavage Fracture of Steels at Very Low Temperatures .............................................. 111 R. Rodriguez-Martin, I. Ocana and A. Martin-Meizoso

New formulation of the Ritchie, Knot and Rice Hypothesis ....................................... 113 A. Neimitz, M. Graba and J. Galkiewicz

The Effect of the Rate of Displacement on Crack Path Stability............................... 115 D. A. Zacharopoulos and P. A. Kalaitzidis

Scratching and Brittle Fracture of Semiconductor In-Situ Scanning Electron Microscope................................................................................................................... 117 K. Wasmer, C. Pouvreau1, J. Giovanola and J. Michler

Cracks in Thin Sheets: when Geometry Rules the Fracture Path ................................ 119 P. M. Reis, B. Audoly and B. Roman

Cleavage Mechanisms in a Ship Plate Steel ................................................................ 121 R. Cuamatzi, I. C. Howard and J. Yates

2T3. Ductile Fracture................................................................................................. 123 Failure Behavior of Hybrid-Laser Welds..................................................................... 123 A. Bajric and W. Dahl

Fracture of Plastic Bodies. Deformations Concentrators............................................. 125 A. I. Khromov, A. A. Bukhanko, S. L. Stepanov and E. P. Kocherov

3D Ductile Tearing Analyses of Bi-Axially Loaded Pipes with Surface Cracks ........ 127 A. Sandvik, E. Ostby and C. Thaulow

New Model Materials for Ductile Fracture Studies .................................................... 129 A. Weck and D. S. Wilkinson

Fatigue Threshold Computation Model Based on the Shakedown Analysis .............. 131 M. A. Belouchrani, D. Weichert and A. Hachemi

Void Coalescence in Metals Involving Two Populations of Cavities .......................... 133 D. Fabregue and T. Pardoen

Contents

ix

Effects of Characteristic Material Lengths on Ductile Crack Propagation.................. 135 E. Radi

Ductile Fracture by Void Nucleation at Carbides ........................................................ 137 J. Giovanola, D. Cannizzaro, R. Doglione and A. Rossol

The Significance of Maximum Load on a Load-Displacement Curve with Stable Crack Extension ........................................................................................................... 139 J. R. Donoso and J. D. Landes

3D Visualization of Ductile Fracture using Synchrotron X-Ray Computer Tomography ................................................................................................................ 141 L. Qian, H. Toda, T. Ohgaki, K. Uesugi, M. Kobayashi and T. Kobayashi

Non-Local Plastic-Damage Model for Failure Analysis of Sheet-Metals ................... 143 M. Brunet, F. Morestin and H. Walter-Leberre

A Novel Technique for Extracting Stretch Zone Features From Fractographs ........... 145 M. Tarafder, Swati Dey, S. Sivaprasad and S. Tarafder

Simulation of Fatigue Crack Growth by Crack Tip Blunting ...................................... 147 P. Hutar and M. Sauzay

Loading Rate Effect on Ductile Fracture ..................................................................... 149 R. Chaouadi

Experimental Investigation of Slant Crack Propagation in X100 Pipeline Steel......... 151 S. H. Hashemi, I. C. Howard, J. R. Yates, and R. M. Andrews

2T4. Nonlinear Fracture Mechanics......................................................................... 153 Esis TC8 – Numerical Round Robin on Micro Mechanical Models : Results of Phase III for the Simulation of the Brittle to Ductile Transition Curve....................... 153 C. Poussard and C. Sainte Catherine

Closure of a Rectangular Skin Defect via the Advancement Flap............................... 155 C. Antypas, C. Borboudaki, V. Kefalas and D. A. Eftaxiopoulos

Similarity Solutions of Creep – Damage Coupled Problems in Fracture Mechanics.. 157 L. V. Stepanova and M. E. Fedina

Impact Fracture Toughness Determination of Ductile Polymers by SPB Method ...... 159 J. Wainstein , L. A. Fasce and P. M. Frontini

A Micro-Toughness Model for Ductile Fracture ......................................................... 161 K. Srinivasan, T. Siegmund and O. Kolednik

2T5. Fatigue and Fracture......................................................................................... 163 Crack Coalescence Modelling of FSW Joints.............................................................. 163 A. Ali, M. W. Brown and C. A. Rodopoulos

Fatigue Crack initiation in a Two Phase B-Metastable Titanium Alloy: Influence of Microstructural Parameters..................................................................................... 165 A. Lenain, P. J. Jacques and T. Pardoen

Effects of Specimen Type, Size and Measurement Techniques on FCGR .................. 167 B. Kumar and J. E. Locke

The Effect of Stress Ratio on Fatigue Short Cracking ................................................. 169 C. A. Rodopoulos and S.-H. Han

Dwell-fatigue Behaviour of a Beta-Forged Ti 6242 Alloy .......................................... 171 P. Lefranc, C. Sarrazin-Baudoux and V. Doquet

Investigation into Fatigue Life of Welded Chemical Pipelines ................................... 173

Contents

x Cz. Goss and L. Sniezek

Different Analytical Presentations of Short Crack Growth under Rotation-Bending Fatigue ......................................................................................................................... 175 D. Angelova and A. Davidkov

Variable Amplitude Load Interaction in Fatigue Crack Growth for 2024-T3 Aluminium Alloy ........................................................................................................ 177 D. Kocanda, S. Kocanda and J. Torzewski

An Investigation on the Fatigue Performance of Hydraulic Gate Wheels................... 179 D. Polyzois and A. N. Lashari

A Micromechanical Model for Crack Initiation in High Cycle Fatigue of Metallic Materials ...................................................................................................................... 181 V. Monchiet, E. Charkaluk and D. Kondo

Comparative Analysis of Two Models for Evaluating Fatigue Data ........................... 183 E. Castillo, A. Ramos, M. Lopez-Aenlle, A. Fernandez-Canteli and R. Koller

Assessment of Damage at Notch Root of Thick Plates ............................................... 185 E. C. G. Menin and J. L. de A. Ferreira

Fatigue Strength Prediction of Spot-Welded Joints Using Small Specimen Testing... 187 E. Nakayama, M. Fukumoto, M. Miyahara, K. Okamura, H. Fujimoto and K. Fukui

A Thermo-Mechanical Model for Random Braking of Machine Components ........... 189 F. Loibnegger, H. P. Rossmanith and R. Huber

Lifetime Calculation of Railway Wheel Steels Based on Physical Data ..................... 191 F. Walther and D. Eifler

Fatigue Crack Propagation of Super-Duplex Stainless Steel at Different Temperatures ................................................................................................................ 193 G. Chai and S. Johansson

Transitions of Fatigue Crack Initiation From Surface, Subsurface to SNDFCO......... 195 G. Chai

Surface Fatigue of Gear Teeth Flanks.......................................................................... 197 G. Fajdiga, M. Sraml and J. Flasker

Fatigue and Fracture Processes in High Performance PM Tool Steels ........................ 199 G. Jesner, S. Marsoner, I. Schemmel and R. Pippan

Notch and Defect Sensitivity of ADI in Torsional Fatigue.......................................... 201 B. Atzori and G. Meneghetti

Multi Axial Fatigue in Welded Components ............................................................... 203 G. Mesmacque, B. Wu, C. Robin, D. Zakrzewski and X. Decoopman

Enhanced Fatigue Life by Mechanical Surface Treatments – Experiment and Simulation .................................................................................................................... 205 H. P. Gaenser, I. Goedor, H. Leitner and W. Eichlseder

Analysis of Repaired Aluminum Panels in General Mixed-Mode Conditions............ 207 H. Hosseini-Toudeshky, M. Saber and B. Mohammadi

Effect of Strain Rate on Fatigue Behavior of Ultrafine Grained Copper..................... 209 P. Gabor, H. J. Maier and I. Karaman

Lubricant Effects on Propagation of Surface-Breaking Cracks under Rolling Contact Loading........................................................................................................... 211 J. Lai and S. Ioannides

Contents

xi

Computational Modelling of Crack Initiation in a Mixing Tee Subjected to Thermal Fatigue Load ................................................................................................................ 213 I. Varfolomeyev

Estimation of Critical Stress Intensity Factor in Steel Cracked Wires......................... 215 J. Toribio, F. J. Ayaso, B. Gonzalez, J. C. Matos and D. Vergara

Low-Cycle Fatigue of Din 1.2367 Steels in Various Treatments................................. 217 C. C. Liu, J. H. Wu and C. C. Kuo

Impact Testing a Capable Method to Investigate the Fatigue Resistance.................... 219 K. David, P. Agrianidis, K. G. Anthymidis and D. N. Tsipas

Comparative Assessment of Fatigue-Thresholds Estimated by Short and Long Cracks ................................................................................................................. 221 K. K. Ray, N. Narasaiahb and S. Tarafderb

Scanning Electron Microscope Measurements of Crack-Opening Stress on Fatigue Cracks Exposed to Overloads ...................................................................................... 223 L. Jacobsson and C. Persson

Propagation Path and Fatigue Life Predictions of Branched Cracks under Plane Strain Conditions.......................................................................................................... 225 M. A. Meggiolaro, A. C. O. Miranda, J. T. P. Castro and L. F. Martha

Short Crack Equations to Predict Stress Gradient Effects in Fatigue .......................... 227 M. A. Meggiolaro, A. C. O. Miranda, J. T. P. Castro and J. L. F. Freire

Fatigue Behaviour of Pre-Strained Type 316 Stainless Steel...................................... 229 M. Akita, M. Nakajima, K. Tokaji and Y. Uematsu

The Influence of Constraint on Fitting Fatigue Crack Growth Data ........................... 231 M. Carboni and M. Madia

Atomic Force Microscopy of Local Plastic Deformation for Tempered Martensite ... 233 M. Hayakawa, S. Matsuoka and Y. Furuya

Improvement of Fatigue Strength due to Grain Refinement in Magnesium Alloys .... 235 M. Kamakura, K. Tokaji, H. Shibata and N. Bekku

A Unified Fatigue and Fracture Model Applied to Steel Wire Ropes ......................... 237 M. P. Weiss, R. Ashkenazi and D. Elata

Correlation Between Paris’ Law Parameters Based on Self-Similarity and Criticality Condition...................................................................................................................... 239 A. Carpinteri and M. Paggi

Thermo-Mechanical Fatigue Lifetime Assessment with Damage-Parameters, Energy-Criterions and Cyclic-J-Integral Concepts ...................................................... 241 M. Riedler, R. Minichmayr, G. Winter and W. Eichlseder

Predicting Fatigue Crack Retardation Following Overload Cycles............................. 243 M. V. Pereira, F. A. Darwish, A. F. Camarao and S. H. Motta

Fatigue Crack Growth at Notches Considering Plasticity Induced Closure ................ 245 J. Bruening, O. Hertel, M. Vormwald and G. Savaidis

Influence of Microstructure on Fatigue Properties of Ni-Base Superalloy at Elevated Temperature .................................................................................................. 247 Qy. Wang , Y. Matsuyama, N. Kawagoishi, M. Goto and K. Morino

Moddelling Fatigue Crack Closure using Dislocation Dipoles ................................... 249 P. F. P. de Matos and D. Nowell

Comparison Between Fatigue Crack Growth Modelled by Continous Dislocation Distributions and Discrete Dislocations ...................................................................... 251

Contents

xii

P. Hansson, S. Melin and C. Persson

Fatigue Evaluation Considering the Environmental Influence Using a Monitoring System.......................................................................................................................... 253 R. Cicero, I. Gorrochategui and J. A. Alvarez

Thermal Fatigue Crack Initiation and Propagation Behavior of Steels for Boiler....... 255 S. Aoi, T. Marumiya, R. Ebara , T. Nishimura and Y. Tokunaga

Recent Developments in Fatigue Crack Growth ......................................................... 257 R. Jones , S. Pitt, and E. Siores

Crack Closure Effects in a Cracked Cylinder under Pressure...................................... 259 J. Zhao, R. Liu, T. Zhang and X. J. Wu

An Experimental Study of Tearing-Fatigue Interaction............................................... 261 P. Birkett, M. Lynch and P. Budden

Sif Solutions for Cracks in Railway Axles under Rotating Bending........................... 263 S. Beretta, M. Madia, M. Schode and U. Zerbst

Mechanical Characterization of Single Crystal Bars with Capacitor Discharge Welding and Laser Cladding........................................................................................ 265 S. Chiozzi, V. Dattoma and F.o W. Panella

Fractal Dimension Analysis of Fracture Toughness Used High Strength Cast Iron.... 267 S. Doi and M. Yasuoka

Investigating Gap Effects in Fatigue Life of Spot Welded Joints ................................ 269 M. Zehsaz and S. Hasanifard

Fatigue of Pmma Bone Cement ................................................................................... 271 S. L. Evans

Influence on Thermal Barrier Coating Delamination Behaviour of Edge Geometry .. 273 H. Brodin, X. H. Li and S. Sjoestroem

Low Cycle Fatigue and Fracture of a Coated Superalloy CMSX-4 ............................ 275 S. Stekovic

Thermomechanical Fatigue of Open-Cell Aluminium Sponge ................................... 277 T. Guillen, A. Ohrndorf, U. Krupp, H. J. Christ, S. Derimay, J Hohe and W Becker

The Influence of Alternate Block Loading on the Fatigue Lifetime............................ 279 M. Kohut and T. Lagoda

Fatigue Design and Inspection Planning of Welded Joints Based on Refined Physical Modelling ..................................................................................................... 281 T. Lassen and N. Recho

A Mixed Mode Fatigue Crack Growth Model Including the Residual Stress Effect Due to Weld.................................................................................................................. 283 S. Ma, X. B. Zhang, N. Recho and J. Li

Effects of Shot Peening on Fatigue Property in SICP/Al-MMC ................................. 285 Y. Ochi, K. Masaki , T. Matsumura and T. Hamaguchi

Fatigue Behaviour of Friction Stir Welded 6061-T6 Aluminium Alloy...................... 287 Y. Uematsu, K. Tokaji, Y. Tozaki and H. Shibata

Transformation of a Nonproportional Multiaxial Loading to an Equivalent Proportional Multiaxial Loading.................................................................................. 289 A. Chamat, Z. Azari, M. Abbadi and F. Cocheteux

2T8. Polymers and Composites................................................................................. 291

Contents

xiii

Acoustic Emission Monitoring of Delamination Growth in Fiber-Reinforced Polymer-Matrix Composites ........................................................................................ 291 A. J. Brunner and M. Barbezat

Fracture Mechanics Versus Strength Concepts for Evaluation of Adhesion Quality

293

B. Lauke

Alternative Approaches for the Evaluation of the Slow Crack Growth Resistance of Polyethylene Resins Used in the Production of Extruded Water Pipes................... 295 F. M. Peres and C. G. Schon

A Stereoscopic Method for Fractographic Investigations of Ordinary Ceramics........ 297 C. Manhart and H. Harmuth

Modelings of Fiber Deformation During Machining Aramid-FRP ............................. 299 E. Nakanishi, M. Fukumori, Y. Sawaki and K. Isogimi

Quality Control and the Strength of Glass ................................................................... 301 F. Veer, C. Louter and T. Romein

Experimental Study of Cracked Laminate Plates by Caustics ..................................... 303 G. A. Papadopoulos and E. Sideridis

Fracture of Composites in Military Aircraft ................................................................ 305 R. Pell, N. Athiniotis and G. Clark

Analysis of 7005/AL2O3/10P MMC Sheets Joined by FSW by Thermoelasticity..... 307 P. Cavaliere, G. L. Rossi, R. di Sante and M. Moretti

Surface Modification of Lightweight Aggregate and Properties of the Lightweight Aggregate Concrete...................................................................................................... 309 T. Y. Lo and H. Z. Cui

Finite Element Based Prediction of Failure in Laminated Composite Plates .............. 311 H. Hosseini-Toudeshky, B. Hamidi, B. Mohammadi and H. R. Ovesi

An Embedded Cylindrical PZT with Electroded Imperfect Interface ......................... 313 H. M. Shodja and S. M. Tabatabaei

Characterization of Composites for the Maeslant Storm Surge Barrier ...................... 315 J. Degrieck, W. van Paepegem, L. van Schepdael, P. Samyn, P. de Baets, E. Suister and J. S. Leendertzc

Weight Function, J-Integral and Material Forces Approach to Ceramic Multilayers.. 317 J. Pascual, C. R. Chen, O. Kolednik, F. D. Fischer, R. Danzer and T. Lube

Assessment of Matrix Fatigue Damage in CFRP ........................................................ 319 K. J. Cain and A. Plumtree

Progressive Failure of Composite Materials under Dynamic Loading........................ 321 L. Xing, X. Huang and K. Reifsnider

Aging Aircraft Transparencies: A Case History from Italian Air Force Fleet............. 323 C. M. Bernabei, D. Caucci and C. L. Aiello

Fatigue Crack Growth in Quenched Amorphous Polymers PC and PET.................... 325 M. Kitagawa and D. Nishi

Thermo-Mechanical State of Bimaterial with an Interface Crack ............................. 327 R. Martynyak, M. Matczynski and K. Honchar

Thermo-Mechanical State of Bimaterial with an Interface Crack ............................... 329 M. Tarfaoui, S. Choukri, A. Neme and M. Mliha-Touati

Indentation Response of Fibre Reinforced Composite Laminates............................... 331 P. Bourke and I. Horsfall

Analysis of Tubular Composite Cylindrical Shells...................................................... 333 R. M. Gheshlaghi and M. H. Hojjati and H. R. M. Daniali

Contents

xiv

Analysis of Composite Pressure Vessels...................................................................... 335 R. M. Gheshlaghi, M. Hassan H. and H. R. M. Daniali

Gradients Influence on Damage and Cracking in Crystalline Polymers ..................... 337 S. Castagnet and J.-C. Grandidier

An Elasto-Plastic Shear-Lag Model for Single Fiber Composite ................................ 339 S. Kimura, J. Koyanagi and H. Kawada

Progressive Failure of Composite Laminates; Analysis vs Experiments .................... 341 V. Skytta, O. Saarela and M. Wallin

A Temperature Dependent Viscoelastic-Damage Model for Ceramics Failure........... 343 V. P. Panoskaltsis, L. M. Powers and D. A. Gasparini

2T11. Fracture Mechanics Analysis ......................................................................... 345 Avalanche Mechanics: Lefm vs. Gradient Model........................................................ 345 A. Konstantinidis, N. Pugno, P. Cornetti and E. C. Aifantis

Influence of Austempering on Fracture Mechanics Parameters of 65 Si 7 Steel......... 347 D. Pustai, F. Cajner and M. Lovreni

Modelling the Evolution of Elastic Symmetries of Growing Mixed-Mode Cracks .... 349 H. Schutte and K. M. Abbasi

Effect of Aging on the Microstructure and Fracture of Aluminum-Lithium ............... 351 J. M. Fragomeni

Buckling of Multicracked Columns............................................................................. 353 C. Carloni, C. Gentilini and L. Nobile

Experimental and Numerical Analysis of Interactions Between Stress Corrosion Cracks.......................................................................................................... 355 M. Lamazouade, M. Touzet and M. Puiggali

An Improved Upper Bound Limit Load Solution for Weld Strength anisotropic Overmatched Cracked Plates in Pure Bending ............................................................ 357 N. Kontchakova and S. Alexandrov

Fracture Parameter Estimation of Alloy Steel Reinforced with Maraging Steel ......... 359 S. Bhat, V. G. Ukadgaonker, M Jha and S. M. Nirgude

Incorporation of Length Scales in Plane Stress Fracture Analysis .............................. 361 V. P. Naumenko

Mode III Crack in a Functionally Graded Piezoelectric/Piezomagnetic Half Plane.... 363 W.-H. Hsu and C.-H. Chue

Electro-Mechanical Field of a Piezoelectric Finite Wedge under Antiplane Loading. 365 W.-J. Liu and C.-H. Chue

Sensitivity of Crack Nucleation Parameters to the Geometric Imperfection............... 367 V. P. Naumenko and Yu. D. Skrypnyk

2T13. Probabilistic approaches to Fracture Mechanics ......................................... 369 An Experimental Evaluation of a Local Approach Model for Graded Materials........ 369 B. Bezensek, J. Flasker and J. W. Hancock

A Stochastic Model for Crack Growth......................................................................... 371 C.-R. Chiang

Stochastic Evaluation of Fatigue Crack Initiation and Propagation ............................ 373 G. S. Wang

Contents

xv

A Weibull-Based Method to Predict the Strength of Adhesively Bonded Joints of Pultruded FRPS............................................................................................................ 375 T. Vallée, J. R. Correia and T. Keller

2T14. Computational Fracture Mechanics.............................................................. 377 The Lateral Constraint Index as a New Factor to Assess the Influence of the Specimen Thickness..................................................................................................... 377 A. Fernandez-Canteli, D. Fernandez-Zuniga and E. Castillo

Analysis of Crack Propagation in Alumina-Glass Functionally Graded Materials ..... 379 V. Cannillo, L. Lusvarghi, T. Manfredini, M. Montorsi, C. Siligardi and A. Sola

Numerical Solution of Integro-Differential Equations for Fracture Mechanics Problems....................................................................................................................... 381 A. V. Andreev

Analytical Method of Generating DA/DN Curve for Aerospace Alloys..................... 383 B. Farahmand

Thermo-Elastic Fracture of Edge Cracked Plate under Surface ‘Shock’ Loading ...... 385 B. P. Fillery, X. Hu and G. Fisher

Failure Prediction of IC Interconnect Structures Using Cohesive Zone Modelling .... 387 B. A. E. van Hal, R. H. J. Peerlings, M. G. D. Geers and G. Q. Zhang

Non-Local Damage Simulation in Composites Using Crack Propagation and Mesh Adaptivity..................................................................................................................... 389 F. Reusch, C. Hortig and B. Svendsen

Elastic Wave Motion in a Cracked, Multi-Layered Geological Region under Transient Conditions .................................................................................................... 391 P. S. Dineva, T. V. Rangelov and G. D. Manolis

Wood Beam Strengthened with Glass/Epoxy Composite Sheets ............................... 393 G. E. Papakaliatakis, G-S. P. Diamantopoulos, P.A. Kalaitzidis and E. M. Marinakis

Computation of Dynamic Stress Intensity Factors Using Enriched Finite Elements .. 395 M. Saribay and H. F. Nied

Partly Cracked Xfem Interface for Intersecting Cracks............................................... 397 J. L. Asferg, T. Belytschko, P. N. Poulsen and L. O. Nielsen

On the Evaluation of Elastic Compliance Tensor Due to Growing Mixed-Mode Microcracks.................................................................................................................. 399 K. M. Abbasi and H. Schutte

On the Problem of Determination of Safety Factors for Machine-Building Parts Using the Finite Element Computations ...................................................................... 401 L. B. Getsov, B. Z. Margolin and D. G. Fedorchenko

Dynamic Explicit Cell Model Simulations in Porous Ductile Metals ......................... 403 L. Siad and M. O. Ouali

Numerical Evaluation of Energy Release Rates for Bimaterials Interface Cracks...... 405 M. Belhouari, B. B. Bouiadjra, B. Boutabout and K. Kaddouri

Inclusion Effect on the Plastic Zone Size in Confined Plasticity................................. 407 M. Benguediab, M. Elmegueni, M. Nait-Abdelaziz and A. Imad

Modified Key-Curve-Method for Determination of Dynamic Crack Resistance Curves .......................................................................................................................... 409

Contents

xvi

U. Muhlich, A. Emrich and M. Kuna

A Coupled Computational Framework for Ductile Damage and Fracture .................. 411 R. H. J. Peerlings, J. Mediavilla and M. G. D. Geers

Marble Discs under Distributed Loading: Theoretical, Numerical and Experimental Study ........................................................................................................................... 413 Ch. Markides, E. Sarris, D. N. Pazis, Z. Agioutantis and S. K. Kourkoulis

Simulation of the Mechanical Behaviour of the Lumbar Intervertebral Disc.............. 415 M. Satraki, E. A. Magnissalis, G. Ferentinos and S. K. Kourkoulis

The Pull-Out Strength of Transpedicular Screws in Posterior Spinal Fusion.............. 417 P. Chazistergos, G. Ferentinos, E. A. Magnissalis and S. K. Kourkoulis

Mechanical Behavior Simulation of Hip Prostheses Stress Distributions Analysis .... 419 M. Kadi, R. Boulahia, K. Azouaoui, N. Ouali, A. Ahmed-Benyahia and T. Boukharouba

Dbem Analysis of Axisymmetric Crack Growth in a Piston Crown .......................... 421 T. Lucht

Residual Shear Stresses and KII Computation ............................................................. 423 W. Cheng and I. Finnie

2T15. Experimental Fracture Mechanics ................................................................ 425 Quantitative Interpretation of Crack Tip Strain Field Measurements.......................... 425 A. M. Korsunsky

Mixed Mode (I+II) Stress Intensity Factor Measurement Using Image Correlation... 427 A. Shterenlikht, P. López-Crespo, P. J. Withers, J. R. Yates and E. A. Patterson

Fracture of Turbine Blades under Self-Exciting Modes .............................................. 429 C. A. Sciammarella, C. Casavola, L. Lamberti and C. Pappalettere

Predicting Crack Arrest Behaviour of Structural Steels Using New Procedures......... 431 C. Gallo, J. A. Alvarez, F. Gutierrez-Solana and J. A. Polanco

Mechanical Properties of Large Plastic-Mold Steel Blooms. ...................................... 433 M. Chiarbonello, D. Firrao, R. Gerosa, A. Ghidini, M. G. Ienco, P. Matteis, G. Mortarino, A. Parodi, M. R. Pinasco, B. Rivolta, G. Scavino, G. Silva, E. Stagno and G. Ubertalli

Non-Linear Photoelastic Method for Study Fracture Problems................................... 435 G. Albaut

Fatigue Crack Length Measurement Method with an Ion Sputtered Film .................. 437 G. Deng, K. Nasu, T. D. Redda and T. Nakanishi

Individual Fracture Events in Cellular Foods .............................................................. 439 H. Luyten, E. M. Castro-Prada, E. Timmerman, W. Lichtendonk and T. van Vliet

Exfoliation Fracture Mode in Heavily Drawn Pearlitic Steels..................................... 441 J. Toribio and F. J. Ayaso

Investigation of Crack Closure by Using Thermoeastic Stress Analysis..................... 443 L. Marsavina, R. A. Tomlinson, E. A. Patterson and J. R. Yates

Fracture Toughness Investigations of Severe Plastic Deformed Tungsten Alloys ...... 445 M. Faleschini, W. Knabl and R. Pippan

Photoelastic Analysis of Mode I Stress Intensity Factor in Beams with Angular Notches......................................................................................................................... 447 M. Tabanyukhova and V. Pangaev

Contents

xvii

Full-Scale Experimental Investigations on Pressure Tubes Rupture of RBMK .......... 449 N. Yu. Medvedeva, A. V. Andreev, S. V. Timkin, I. A. Peshkov, V. N. Zhilko, D. Ye. Martsiniouk and O. A. Poshtovaya

Study of Fracture Mechanism of Composite Material Buildings by Photoelasticity and Photoelasitc Coating Methods............................................................................... 451 O. Ivanova, G. Albaut, V. Mitasov, V. Nikiforovskij and M. Tabanyukhova

Fracture Energy in Mode I and Mode II of Textile Reinforced Wood......................... 453 R. Putzger and P. Haller

Measurement Based Performance Prediction of the Europabrucke Against Traffic Loading ....................................................................................................................... 455 R. Veit and H. Wenzel

The Effect of the Laboratory Specimen on Fatigue Crack Growth Rate..................... 457 S. C. Forth, W. M. Johnston and B. R. Seshadri

Validity of the Caustics Method for Plates with Circular Hole.................................... 459 P. Tsirigas, G. Kontos, D. N. Pazis, S. K. Kourkoulis and Z. Agioutantis

An Enhanced Normalization Method for Dynamic Fracture Toughness Testing ........ 461 S. M. Graham and D. J. Stiles

The Potential Drop Technique for Measuring Crack Growth in Shear........................ 463 V. Spitas and P. Michelis

A Modified DCB Geometry for CTOA Measurement in Thin Sheet 2024-T3 Aluminium Alloy ........................................................................................................ 465 Y. H. Tai, S. H. Hashemi, R. Gay, I. C. Howard and J. R. Yates

Could Cod Serve as Fracture Criterion in Case of Marble? ....................................... 467 A. Marinelli, S. K. Kourkoulis and I. Vayas

2T16. Creep Fracture ................................................................................................ 469 Creep Rupture of a Lead-Free Sn-Ag-Cu Solder......................................................... 469 C.-K. Lin and D.-Y. Chu

Quantitative Evaluation of Acceleration Creep in Magnesium-Aluminum Alloys at 0.65tm........................................................................................................... 471 H. Sato

Long-Term Creep Rupture Prediction in Unidirectional Composites ........................ 473 J. Koyanagi, F. Ogawa and H. Kawada

A Computational Model for Cardboard Creep Fracture ............................................. 475 J. Schonwalder, G. P. A. G. van Zijl and J. G. Rots

Creep Fracture of Binary and Ternary Commercial Aluminum Alloys....................... 477 K. Ishikawa

Analysis of Creep Crack initiation and Growth in Laboratory Specimens.................. 479 K. Wasmer

Temperature Gradient Effects on the Creep Behaviour of Structures.......................... 481 F. Vakili-Tahami and S. Hasanifard

2T17. Environment Assisted Fracture ..................................................................... 483 A Surgical Implant Crevice-Assisted Corrosion Fatigue In-Body Failure .................. 483 H. Amel-Farzad, M.-T. Peivandi and S. M.-R. Yosof-Sani

Asymptotically Stable Growth of Delaminations under Hydrogen Embrittlement Conditions .................................................................................................................... 485

Contents

xviii A. V. Balueva

Corrosion and Mechanical Strength of Russian Light Water Reactors ....................... 487 B. T. Timofeev

Corrosion Fatigue Characteristics of CF8A Steel Degraded at High Temperature ..... 489 S.-C. Jang, D.-H. Bae, G.-Y. Lee, and S.-Y. Baek

Modeling Environment-Assisted Fatigue Crack Propagation ..................................... 491 J.-A. Ruiz-Sabariego and S. Pommier

2T18. Dynamic, High Strain Rate, or Impact Fracture ......................................... 493 Measuring the Fracture Resistance of Composites and Adhesively Bonded Joints at High Test Rates. ....................................................................................................... 493 B. R. K. Blackman, D. D. R. Cartie, A. J. Kinloch, F. S. Rodriquez-Sanchez and W. S. Teo

Quasistatic and Dynamic Fracture of Pearlitic Steel.................................................... 495 B. Strnadel, P. Hausild and M. Karlik

Fragmentation in the Expanding Ring Experiment...................................................... 497 H. Zhang and K. Ravi-Chandar

Influence of Friction on Results of an Instrumented Impact Test ............................... 499 I. V. Rokach

Influence of Moisture Content on the Dynamic Behaviour of Concrete ..................... 501 I. Vegt and J. Weerheijm

Strength and Toughness Properties of Steels under Dynamic Loading ....................... 503 J. Fang

Rubber Particle Size Effect on Impact Characteristics of PC/ABS (50/50) Blends .... 505 M. Nizar Machmud, Masaki Omiya, Hirotsugu Inoue and Kikuo Kishimoto

Effect of Strain Rate on Mechanical Properties of Reinforced Polyolefins................. 507 M. Schossig, C. Bieroegel, W. Grellmann, R. Bardenheier and T. Mecklenburg

Fracture Related Mechanical Properties of Aircraft Cast Aluminum Alloy A357...... 509 N. D. Alexopoulos

Shear Failure of TI-6AL-4V by Direct Impact and analyse of the Process of Elastic and Plastic Wave Propagation ......................................................................... 511 P. Chwalik, A. Rusinek and J. R. Klepaczko

Evaluating of Fracture Mechanics Properties at Intermediate Strain Rates, Transferable to Components ........................................................................................ 513 P. Trubitz, A. Ludwig, G. Pusch and H.-P. Winkler

Crack Resistance Determination From the Charpy Impact Test.................................. 515 R. Chaouadi

A Stochastic Interface Model for the Fracture of Bars ................................................ 517 S. Nagy and F. Kun

The Anti-Penetration Properties of Space Armor ....................................................... 519 Tso-Liang Teng, Cho-Chung Liang and Cheng-Chung Lu

Key Curve Methods for Dynamic Fracture Mechanics of Cast Iron ........................... 521 W. Baer

Dynamic Tensile Behavior of Aramid Frp Using Split Hopkinson Bar Method......... 523 Y. Sawaki, J. Watanabe, E. Nakanishi and K. Isogimi

2T19. Damage Mechanics.......................................................................................... 525

Contents

xix

Detection of Low-Velocity Impact Damage in Carbon-Epoxy Plates using NDT ..... 525 A. M. Amaro, M. F. M. S. de Moura and P. N. B. Reis

Damage Accumulation at High Temperature Creep of a Single-Crystal Superalloy... 527 A. Staroselsky and B. Cassenti

Asymptotic Homogenisation for Heterogeneous Media with Evolving Microcracks 529 E. K. Agiasofitou, C. Dascalu and J. L. Auriault

On the Analysis of Damage Localization as Precursor of Macro-Cracks ................... 531 H. Stumpf and K. Hackl

Fatigue Assessment Based on Statistical Analysis of Theoretical Parameters ............ 533 J. Cacko

Determination of Ductile Damage Parameters by Local Deformation Fields ............. 535 M. Kuna and M. Springmann

Fracture of Concrete Due to Corrosion........................................................................ 537 N. Thanh, A. Millard, Y. Berthaud, S. Care and V. L’Hostis

2T21. Concrete and Rock .......................................................................................... 539 Experimental Study of Sprayed Concrete Strength Using Marble Aggregates ........... 539 A. Sotiropoulou and Z. G. Pandermarakis

Analysis of the Behaviour of Interface Cracks in Gravity Dam ................................. 541 B. B. Bouiadjra, A. B. Bouiadjra, M. Belhouari and B. Serier

Application of Composite Mechanics to Composites Enhanced Concrete Structures 543 C. C. Chamis and P. K. Gotsis

Initiation and Coalescence of Locals Damages on Blanco de Macael Marble............ 545 K. Mehiri, P. Vieville, P. Lipinski, A. Tidu and V. Tijeras

Influence of Concrete´s Mineralogical Components on Fracture Compressive and Tractive ........................................................................................................................ 547 M. P. Morales Alfaro and F. A. I. Darwish

Constitutive Model for Description of High-strain Rate Behavior of Concrete ......... 549 I. R. Ionescu and O. Cazacu

Hydraylic Fracturing in Weak Rocks .......................................................................... 551 P. Papanastasiou

Application of Fracture Mechanics on Unreinforced Concrete Walls ......................... 553 T. Eck, B.-Gu Kang and W. Brameshuber

Subcritical Crack Growth in Rocks under Water Environment ................................... 555 Y. Nara, H. Kurata and K. Kaneko

2T22. Sandwich Structures ....................................................................................... 557 Stress Analysis and Prediction of Failure in Structurally Graded Sandwich Panels ... 557 A. Lyckegaard, E. Bozhevolnaya and O. T. Thomsen

Debonding and Kinking in Foam-Core Sandwich Beams ........................................... 559 D. A. Zacharopoulos, V. D. Balopoulos, Z. S. Metaxa, P. A. Kalaitzidis and E. E. Gdoutos

Modeling Core Failure by the Tsai–Wu Criterion in the Design of Foam-Core Sandwich Beams .......................................................................................................... 561 E. E. Gdoutos, V. D. Balopoulos, P. A. Kalaitzidis and M. Konsta

Numerical Investigation of Crack Propagation in Sandwich Structures...................... 563 E. E. Theotokoglou

Contents

xx

Local Effects in Sandwich Beams: Modelling and Experimental Investigation.......... 565 M. Johannes, J. Jakobsen, V. Skvortsov, E. Bozhevolnaya and O. T. Thomsen

Typical In-Plane Response Surfaces for Prismatic Foam-Core Sandwich Beams ...... 567 V. D. Balopoulos, P. A. Kalaitzidis, D. A. Zacharopoulos and E. E. Gdoutos

2T23. Novel Testing and Evaluation Techniques.................................................... 569 Non-Destructive Evaluation of Yield Strength Using a Novel Miniature Dumb-Bell Specimen-An Empirical Approach ............................................................................. 569 G. Partheepan, D. K. Sehgal and R. K. Pandey

3D Measurement of the Strain Field Surrounding Crack Tip ...................................... 571 D. Vavrik, J. Bryscejn, J. Jakubek and J. Valach

Radiographic Observation of Damage Zone Evolution in High Ductile Specimen .... 573 D. Vavrik, T. Holy, J. Jakubek, M. Jakubek and Z. Vykydal

Calibration of Fracture Parameters by Instrumented Indentation and Test Simulation .................................................................................................................... 575 M. Bocciarelli, G. Bolzon and G. Maier

Internal Crack Detection and Analysis Using Thermoelastic Stress Analysis ............ 577 N. Sathon and J. M. Dulieu-Barton

Ultrahigh-Resolution Transversal Polarization-Sensitive Optical Coherence Tomography: Structural Analysis and Strain-Mapping ............................................... 579 K. Wiesauer, M. Pircher, R. Engelke, G. Ahrens, G. Grutzner, R. Oster, C. K. Hitzenberger and D. Stifter

Application of Digital Shearography in Determining Opening Mode SIF in Edge Cracks ................................................................................................................. 581 M. Ghassemieh, A. Ghazavizadeh and N. Soltani

Finite Element Modeling of Pulse Transient IR Thermography.................................. 583 M. Krishnapillai, R. Jones, I. H. Marshall, M. Bannister and N. Rajic

A New Technique for the Machining of Natural Cracks ............................................. 585 N. P. Andrianopoulos and A. Pikrakis

Displacements Measurement in Irregularly Bounded Plates Using Mesh Free Methods........................................................................................................................ 587 N. P. Andrianopoulos and A. P. Iliopoulos

Biaxial Strength Testing on Mini Specimens............................................................... 589 R. Danzer, P. Supancic, W. Harrer, T. Lube and A. Borger

Numerical Simulation of a Fracture Test for Brittle Disordered Materials ................. 591 T. Auer and H. Harmuth

2T26. Structural Integrity ......................................................................................... 593 Unification of the Out-of-Plane Constraint Loss in Centre-Cracked Panels ............... 593 B. Bezensek, A. Baron and J. W. Hancock

High Temperature Failure Assessment of Weldments ................................................ 595 B. Dogan, B. Petrovski and U. Ceyhan

Post-Tensioned Glass Beams ....................................................................................... 597 C. Louter, J. van Heusden, F. Veer, J. Vambersky, H. de Boer and J. Versteegen

Contents

xxi

Structural Integrity of a NPP Using the Master Curve Approach................................ 599 D. Ferreno, I. Gorrochategui, M. Scibetta, R. Lacalle, E. van Walle and F. Gutierrez-Solana

FRP Consolidation for Masonry Arches by Using Bridged Crack Model .................. 601 G. Ferro, M. Ipperico, V. Pignata and A. Carpinteri

Structural Reliability Analysis of Pipe Subjected to Reeling ...................................... 603 H. A. Ernst, R. E. Bravo and F. Daguerre

Network Seismic Capability Assessment of Power High Voltage Electric Equipment....................................................................................................... 605 I. Manea, C. Diaconu, C. Radu and M. Negru

FKM Guideline “Fracture Mechanics Proof of Strength for Engineering Components” – Overview and Extension topics.......................................................... 607 B. Pyttel, I. Varfolomeyev and M. Luke

Static and Dynamic Behavior of a 3D-Periodic Structure ........................................... 609 J. Rishmany, L. Renault, C. Mabru, R. Chieragatti and F. Rezaï Aria

Environmental Effect on Pipeline Steels: A Fitness for Service Perspective .............. 611 J. A. Alvarez, F. Gutierrez-Solana and S. Cicero

Finding the Australian Railway Load Spectrum Design and Assessment of Light Weight & Durable Railway Structural Components .................................................... 613 R. Jones and J. Baker

Structural Integrity Assessment of Componets with Low Constraint.......................... 615 S. Cicero, F. Gutierrez-Solana and J. A. Alvarez

Life Assessment of Superheater Tubes Fabricated From 2.25CR-1MO Steel ............ 617 S. Fujibayashi

Predicting Cleavage Fracture in Presence of Residual Stresses; A Numerical Case Study.................................................................................................................... 619 S. Hadidi-Moud, C. E. Truman and D. J. Smith

A Necessary Condition for Cleavage on Laboratory Specimens and Structures......... 621 V. le Corre, S. Chapuliot, S. Degallaix and A. Fissolo

Safety Assessment of Components with Crack-Like Defects .................................... 623 Yu. G. Matvienko and O. A. Priymak

Numerical Analysis of Surface Cracks in Steam Generator Tubes ............................. 625 Z. Tonkovi, I. Skozrit and J. Sori

2T28. Mesofracture Mechanics................................................................................. 627 Tensile Simulation of Polymeric Material Considering the Meso-Scale Structure .... 627 A. Shinozaki, K. Kishimoto and I. Hirotugu

Microfracture and Strain Localization: A Computational Homogenization Approach 629 C. Dascalu, G. Bilbie and R. Chambon

Strain and Fracture at Mesoscale of Coated Materials ................................................ 631 S. Panin

2T32. Micromechanisms in Fracture and Fatigue.................................................. 633 Relating Cleavage Crack Nucleation to Cracked Carbides in A533B Steel................ 633 A. Kumar and S. G. Roberts

Contents

xxii

Micro-Energy Rates for Damage Tolerance and Durability of Composite Structures 635 C. C. Chamis and L. Minnetyan

Micromechanical Observation of Fracture Process in Mortars ................................... 637 E. Schlangen and O. Copuroglu

Micro-fracture Maps in Progressively Drawn Pearlitic Steels .................................... 639 J. Toribio and F. J. Ayaso

A Brief History of Fractography.................................................................................. 641 S. P. Lynch and S. Moutsos

C. SPECIAL SYMPOSIA/SESSIONS C1. Nanomaterials and Nanostructures ..................................................... 643 1. Fracture and Fatigue at the Micro and Nano Scales .......................................... 645 Size Effects in Lead Free Solder-joints........................................................................ 645 A. Betzwar-Kotas, G. Khatibi, A. Ziering, P. Zimprich, V. Groeger, B. Weiss and H. Ipser

Micro-Scale Simulation of Impact Rupture in Polysilicon MEMS ............................. 647 A. Corigliano, F. Cacchione, A. Frangi and B. de Masi

Nanoindentation of CNT Reinforced Epoxy Nanocomposites.................................... 649 D. C. Lagoudas, P. R. Thakre and A. A. Benzerga

Diffusion Kinetics and Multivariant Phase Transformation in Shape Memory Alloys 651 D. R. Mahapatra and R. V. N. Melnik

3. Nanoscale Deformation and Failure..................................................................... 653 EBSD Analysis on Deformation of Nanocrystals in ECAP-Processed Copper .......... 653 H. Kimura, Y. Akiniwa, K. Tanaka and T. Ishida

The Effect of Extensional Strains on Molecular Orientation, Polymer Free Volume Distribution and Crystallization ................................................................................... 655 H. Dong, R. Guo and K. I. Jacob

Microrotation-augmented Energy-Minimization for 3D Nanocrystalline Cu Structures ..................................................................................................................... 657 M. A. Tschopp and D. L. McDowell

Mechanics and Electromechanics of Single Crystalline Piezoelectric Nanowires ...... 659 M.-F. Yu, Z. Wang, J. Hu and A. Suryavanshi

Multiscale Simulation for High Spped Propagation of Disordered Regions .............. 661 W. Yang, X. Li and Z. Guo

Surface-Stress-Driven Pseudoelasticity and Shape Memory Effect at the Nanoscale. 663 W. Liang and M. Zhou

Thermomechanical Behavior of Zinc Oxide Nanobelts .............................................. 665 A. Kulkarni and M. Zhou

Natural Modes of C60 Cage via Carbon-Carbon Bonding Element............................ 667 P. Zeng, X.-G. Y. and J. Du

11. Deformation and Fracture at the Nano Scale.................................................... 669 Fracture of Nanocrystalline Aluminum ....................................................................... 669

Contents

xxiii

C. San Marchi, S. L. Robinson, N. Y. C. Yang and E. J. Lavernia

Wear and Fatigue in Silicon Structural Films for MEMS Applications ...................... 671 D. H. Alsem, R. Timmerman, E. A. Stach, C. L. Muhlstein, M. T. Dugger and R. O. Ritchie

Indentation Induced Through Thickness Film Fracture on Engineering Alloys ......... 673 D. F. Bahr, K. R. Morasch and A. Alamr

Surface Nanostructured Aluminum by Severe Plastics Deformation.......................... 675 E. I. Meletis, K. Y. Wang and J. C. Jiang

Contribution of Localized Deformation to IGSCC and IASCC in Austenitic Stainless Steels ............................................................................................................. 677 G. S. Was, Z. Jiao and J. T. Busby

A Study of Crack-Dislocations Interaction with 3D Discrete Dislocation Dynamics . 679 I. N. Mastorakos and H. M. Zbib

Numerical Simulations and Measurements of Cracks Parallel and Near Interfaces in Graded Structures..................................................................................................... 681 I. Reimanis, K. Rozenburg, J. Berger, M. Tilbrook and M. Hoffmann

Deformation and Failure Processes Operating in Ultra-Fine Grain Metals................. 683 K. Hattar, I. M. Robertson, J. Han, T. Saif, S. J. Hearne and D. Follstaedt

Simulation of Cross-Sectional Nanoindentation in Interconnect Structures with Cohesive Elements....................................................................................................... 685 D. Gonzalez, J. Molina, I. Ocana, M. R. Elizalde, J. M. Sanchez. J. M. Martinez-Esnaol, J. Gil-Sevillano, G. Xu, D. Pantuso, T. Scherban, B. Sun, B. Miner, J. He and J. Maiz

Fracture Between Two Self-Assembled Monolayers .................................................. 687 K. M. Liechti and D. Xu

Nanotube Nanoactuator................................................................................................ 689 M.-F. Yu, J. Hu, Z. Wang and A. Suryavanshi

Nanocrack Detection in Vibrating Nanowires ............................................................. 691 R. Ruoff, L. Calabri, N. Pugno, X. Chen, W. Ding and K. Kohlhaas

Fracture of atomic Layer Deposited Nanolaminate Films ........................................... 693 N. R. Moody, J. M. Jungk, T. M. Mayer, R. A. Wind, S. M. George and W. W. Gerberich

Influence of Microstructure, Strength and Adhesion on Au Electrodeposits ............. 695 N. Yang, J. Kelly, T. Headley and C. S. Marchi

Fracture of Submicron Thin Metal Films During Cyclic Loading .............................. 697 S. Eve, D. Wang, C. Volkert, N. Huber and O. Kraft

Micromechanics of Damage Evolution in Solid Propellants ....................................... 699 N. Aravas, F. Xu and P. Sofronis

Deformation and Failure Mechanisms in Metallic Nanolayered Composites ............. 701 R. G. Hoagland, J. P. Hirth, and A. Misra

Dislocation Source Sensitivity of Plasticity and Fracture in Tungsten........................ 703 J. E. Talia and R. Gibala

Delamination of Thin Metal Films on Polymers ......................................................... 705 A. Pundt, E. Nikitin, and R. Kirchheim

Fracture Mechanics of One-Dimensional Nanostructures ........................................... 707 W. Ding, L. Calabria, K. M. Kohlhaas, X. Chen and R. S. Ruoff

Effects of Structure and Bonding at Surfaces and Interfaces on Fracture .................. 709 S. P. Lynch, S. Moutsos, B. Gable, S. Knight, D. P. Edwards

Contents

xxiv and B. C. Muddle

29. Reliability and Failure Analysis of Electronics and Mechanical Systems ...... 711 Application of the New Static Photoelastic Experimental Hybrid Method with New Numerical Method to the Plane Fracture Mechanics................................................... 711 J.-S. Hawong , J.-H. Nam, O.-S. Kwon and K. Tche

Risk Analysis of Buried Pipeline using Probabilistic Method..................................... 713 O. S. Lee, D. H. Kim and N. H. Myoung

Reliability Estimation of Solder Joint by Accelerated Life Tests ................................ 715 O. S. Lee, N. H. Myoung and D. H. Kim

Analysis of Engineering Plastic Behaviors in Thermal Stress Condition.................... 717 S. I. Ham, D. J. Choi and S. D. Park

A Mechanistic Model for the Thermal Fatigue Behavior of the Lead-Free Solder Joints................................................................................................................. 719 I. Kim, T.-S. Park and S.-B. Lee

Mechanical Behavior of Metallic Thin Film on Polyimide Substrate ......................... 721 D.-C. Baek, S.-Y. Kim and S.-B. Lee

31. Multiscaling in Molecular and Continuum Mechanics - Scaling in Time and Size From Macro to Nano .................................................................................. 723 Macro-, Meso- and Micro-damage Model Based on Singularity Representation for Anti-plane Deformation ......................................................................................... 723 G. C. Sih and X. S. Tang

Multiscaling Effects in Trip Steels............................................................................... 725 G. N. Haidemenopoulos and N. Aravas

A Hyper-Surface for the Combined Rate and Size Effects on the Material Properties 727 Z. Chen, L. Shen, Y. Gan and H. E. Fang

34. Cracks in Micro- and Nanoelectronics............................................................... 729 A New Method for Local Strain Field Analysis Near Cracks in Micro- and Nanotechnology Applications...................................................................................... 729 B. Michel, D. Vogel, N. Sabate and D. Lieske

Experimental Investigations for Fracture Analysis of Solder Joints in Microelectronic and MEMS Applications ................................................................... 731 H. Walter, C. Bombach, R. Dudek, W. Faust and B. Michel

Simulation of Interface Cracks in Microelectronic Packaging .................................... 733 J. Auersperg, B. Seiler, E. Cadalen, R. Dudek and B. Michel

AFM Based Fracture Analysis in Micro- and Nanomaterials...................................... 735 J. Keller, A. Gollhardt, D. Vogel and B. Michel

Simulation of Deformation and Fracture Behaviour in Microelectronic Packaging ... 737 O. Wittler, H. Walter, J. Keller, R. Dudek, D. Vogel and B. Michel

43. Interfacial Fracture in Composites and Electronic Packaging Materials ...... 739 Mixed-Mode Fracture Modeled Through a Discrete Cohesive Zone Model-DCZM.. 739 D. Xie and A. M. Waas

Signifince of K-Dominance in Delamination Cracking in Composite Laminates....... 741 C. T. Sun and Z. Yang

Contents

xxv

Evaluation of Interface Toughness Between Submicron Island and Substrate............ 743 H. Hirakata, T. Kitamura, S. Matsumoto and Y. Takahashi

Three-Dimensional Thermal Stress Analysis Considering the Stress Singularity for Bonded Structures ........................................................................................................ 745 H. Koguchi

Center of Dilatation and Penny-Shaped Crack in Viscoelastic Bimaterial .................. 747 K. T. Chau, R. C. K. Wong and Y. Z. Sun

Fracture Analysis on Popcorning of Plastic Packages During Solder Reflow ............ 749 S. W. R. Lee and D. C. Y. Lau

Delamination of PB-Free Flip Chip Underfill During 2nd Level Interconnect Reflow.......................................................................................................................... 751 S. Chung, Z. Tang and S. Park

Reliability of Interfaces Between Components in Advanced Electronic Packages under Solder Reflow Process ....................................................................................... 753 T. Ikeda and N. Miyazaki

Three-Dimensional Stress Intensity Factors Analyses of Interface Cracks Between Dissimilar Anisotropic Materials ................................................................................. 755 M. Nagai, T. Ikeda, N. Miyazaki

Molecular Dynamics of Interfacial Fracture................................................................ 757 T. E. Tay, V. B. C. Tan and M. Deng

C. SPECIAL SYMPOSIA/SESSIONS C2. Engineering Materials and Structures................................................ 759 4. Fracture and Fatigue of Elastomers..................................................................... 761 Nucleation, Growth and Instability of the Cavitation in Rubber ................................. 761 E. Bayraktar, K. Bessri and C. Bathias

Engineering Fracture Mechanics for Crack Toughness Characterisation of Elastomers.................................................................................................................... 763 K. Reincke, W. Grellmann and G. Heinrich

Multiaxial Fatigue Crack Initiation on Filled Rubbers : Statistical Aspects................ 765 L. Laiarinandrasana, A. Bennani and R. Piques

Fracture Criteria of Rubber-like Materials under Plane Stress Loadings .................... 767 A. Hamdi, M. Nait-Abdelaziz, N. Ait Hocine and P. Heuillet

Prediction of Rubber Fatigue Life under Multiaxial Loading ..................................... 769 A. Zine, N. Benseddiq, M. Nait-Abdelaziz and N. Ait Hocine

Modeling of Biaxial Fatigue of Natural Rubber ........................................................ 771 S. Dong, C. Bathias, K. le Gorjo, F. Hourlier and J. F. Vitorri

Modeling of Crack Propagation in Elastomeric Materials Using Configurational Forces ........................................................................................................................... 773 T. Horst and G. Heinrich

Determination of Inter-Fibre-Failure in Complex, Reinforced Composites................ 775 V. Trappe and H. Ivers

The Test Frequency Dependence of the Fatigue Behavior of Elastomers ................... 777 Z. Major, Ch. Feichter, R. Steinberger and R. W. Lang

Contents

xxvi

5. Integrity of Dynamical Systems ............................................................................ 779 Nonlinear Model for Reinforced Concrete Frames Loaded by Seismic forces ........... 779 D. Kovacevic

Monitoring the Durability Performances of Concrete and Masonry Structures by Acoustic Emission Technique ..................................................................................... 781 A. Carpinteri and G. Lacidogna

Bifurcation Control of Parametric Resonance in Axially Excited Cantilever Beam .. 783 H. Yabuno and M. Hasegawa

Adaptive Properties of Dynamic Objects..................................................................... 785 I. I. Blekhman and L. A. Vaisberg

Influence of Addendum Modification Coefficient on the Gear's Load Capacity ........ 787 I. Atanasovska and V. Nikoli-Stanojevi

Micromechanical Modelling of Fracture-induced Anisotropy and Damage in Orthotropic Materials .................................................................................................. 789 V. Monchiet, I.-C. Gruescu, D. Kondo and O. Cazacu

Vibration Control Devices and their Application ....................................................... 791 K. Nagaya

Measurements of Dynamical System Integrity and Fracture Mechanics .................... 793 K. S. Hedrih

Modeling of the Surface Cracks and Fatigue Life Estimation..................................... 795 K. Maksimovic, S. Maksimovic and V. Nikolic-Stanojevic

Structural Damage Detection via the Subspace Identification Method ....................... 797 M. Trajkovic, D. Sumarac and M. Mijalkovic

Clock Mechanism as Base of Artillery Safety and Arming Devices........................... 799 M. Ugrci c

Twisting Deformation Evolution of Drilling Ropes .................................................... 801 N. P. Puchko

Hereditary Strain Theory of Syntetic and Steel Ropes ................................................ 803 O. O. Goroshko

Brittle and Ductile Failure in Thermoviscoplastic Solids under Dynamic Loading.... 805 R. C. Batra and B. M. Love

Some Aspects of Dynamic interfacial Crack Growth ................................................. 807 R. R. Nikolic and J. M. Veljkovic

On Stability Problems of Periodic Impact Motions ..................................................... 809 S. Mitic

Dynamical Integrity of Nonlinear Mechanical Oscillators .......................................... 811 S. Lenci and G. Rega

8. Modelling of Material Property Data and Fracture Mechanisms..................... 813 Fatigue Crack initiation and Propagation at High Temperature in a Softening Martensitic Steel ......................................................................................................... 813 B. Fournier, M. Sauzay, M. Mottot, V. Rabeau, A. Bougault and A. Pineau

Transferability of Cleavage Fracture Parameters Between Notched and Cracked Geometries ................................................................................................................... 815 C. Bouchet, B. Tanguy, J. Besson, A. Pineau and S. Bugat

Relation Between Crack Velocity and Crack Arrest .................................................... 817 M. Hajjaj, C. Berdin, P. Bompard and S. Bugat

Contents

xxvii

Mechanisms of Damage and Fracture in Trip Assisted Multiphase Steels.................. 819 G. Lacroix, Q. Furnemont, P. J. Jacques and T. Pardoen

The Role of Sub-Boundaries in the Brittle Fracture of Polycrystalline Materials....... 821 G. Hughes, P. Flewitt, F. Sorbello, G. Smith and A. Crocker

Three-Dimensional Modelling of Fracture in Polycrystals.......................................... 823 G. Smith, A. Crocker, G. Hughes and P. Flewitt

Anti-Wing Crack Growth from Surface Flaw in Real Rock under Uniaxial Compression................................................................................................................. 825 R. H. C. Wong, Y. S. H. Guo , L. Y. Li, K. T. Chau , W. S. Zhu and S. C. Li

Mechanical Behavior Modeling in the Presence of Strain Aging................................ 827 J. Belotteau, C. Berdin, S. Forest, A. Parrot and C. Prioul

On the Local Conditions for Cleavage Initiation in Ferritic Steels.............................. 829 J. Hohe, V. Friedmann and D. Siegele

Unified Constitutive Equations to Describe Elastoplastic and Damage Behavior of X100 Pipeline Steel...................................................................................................... 831 T. T. Luu, B. Tanguy, J. Besson, A. Pineau and G. Perrin

Estimation of Lower Bound Engineering Fracture Toughness in the Ductile to Brittle Transition Regime......................................................................................... 833 R. Moskovic and R. A. Ainsworth

Cleavage Fracture Micromechanisms Related to WPS Effect in RPV Steel............... 835 S. R. Bordet, B. Tanguy, S. Bugat, D. Moinereau and A. Pineau

Modelling of Fatigue Damage in Aluminum Cylinder Heads..................................... 837 R. Salapete, B. Barlas, E. Nicouleau, D. Massinon, G. Cailletaud and A. Pineau

Local Approach to High Temperature Ductility Modeling in 6XXX Aluminium Alloys ........................................................................................................................... 839 D. Lassance, D. Fabregue, F. Delannay and T. Pardoen

9. Micromechanisms in Fracture and Fatigue......................................................... 841 Small Fatigue Crack Growth in Steel-Compressor Disks of Aircraft Engines............ 841 A. A. Shanyavskiy and A. Yu. Potapenko

Micromechanisms of Damage in Multiaxial Fatigue of an Austenitic-Ferritic Stainless Steel............................................................................................................... 843 A. el Bartali, V. Aubin, S. Degallaix and L. Sabatier

Multiscale Modeling of Fracture and Plasticity in Layered Structures........................ 845 A. Hartmaier, N. Brodling and H. Gao

Critical and Fracture Planes of 18G2A Steel under Non-Proportional Combined Bending and Torsion .................................................................................................... 847 A. Karolczuk and E. Macha

Slip Processes and Fracture in Iron Crystals................................................................ 849 V. Pelikan, P. Hora, A. Machova1 and M. Landa

A Discussion of the Applicability of DK-Values to Explain the Fatigue Crack Growth Behaviour of Short Cracks.............................................................................. 851 A. Tesch, H. Doker, K. H. Trautmann, R. Pippan and C. Escobedo

Simulation of Crack Growth under Low Cycle Fatigue at High Temperature in a Single Crystal Superalloy............................................................................................. 853 B. Fedelich, Y. Kiyak, T. May and A. Pfennig

Contents

xxviii

Fatigue Crack Growth for Different Ratios of Bending to Torsion in ALCU4MG1 .. 855 D. Rozumek and E. Macha

Ductile Damage Models Applied to Anisotropic Fracture of Al2024 T351 ............... 857 D. Steglich, W. Brocks and T. Pardoen

Fatigue and Fracture Processes in Severe Plastic Deformed Rail Steels .................... 859 F. Wetscher, R. Pippan and R. Stock

Damage Evolution in Torsion Specimens Deformed at Forging Temperatures .......... 861 G. Trattnig, R. Pippan and S. Kleber

Microstructural Effects on Short Fatigue Crack Propagation and their Modelling ..... 863 H. J. Christ, O. Duber, W. Floer, U. Krupp, C. P. Fritzen, B. Kunkler and A. Schick

Micromechanical Aspects of Transgranular and Intergranular Failure Competition .. 865 I. Dlouhy and M. Holzmann

Defect in Ultra-fine Grained Mg-based Alloys Deformed by High-Pressure Torsion 867 J. Cizek, I. Prochazka, B. Smola, I. Stulikova, R. Kuzel, Z. Matej and V. Cherkaska

Modelling Crack-Tip Shielding Effects in Particle Reinforced Composites .............. 869 J. Hornikova, P. Sandera and J. Pokluda

Early Stages of Fatigue Damage in 316l Steel............................................................. 871 J. Man, K. Obrtlik, J. Polak and P. Klapetek

AB Initio Study of Elasticity and Strength of Nano-Fibre Reinforced Composites .... 873 M. Cerny and J. Pokluda

Strength and Fracture of Ultra-Fine Grained Aluminum 2024 ECAP Metal .............. 875 K. B. Yoon, Y. W. Ma, J. W. Choi and S. H. Kim

Fatigue Lifetime of Bearing Steel in Ultra-High-Cycle Region .................................. 877 L. Kunz, P. Lukas, M. Cincala and G. Nicoletto

Calculation of K-Factor and T-Stress for Crack at Anisotropic Bimaterials .............. 879 M. Kotoul, T. Profant and O. Sevecek

Interaction of Microcracks with Grain Boundaries: Systematical Investigation of the Mechanisms............................................................................................................ 881 M. Marx, W. Schaf and H. Vehoff

Dislocation Arrangements in Cyclically Strained Inconel 713LC............................... 883 M. Petrenec, K. Obrtlik and J. Polak

Crack Initiation and Fracture of Metal Matrix Composites......................................... 885 K. Unterweger and O. Kolednik

Mechanical Behaviour of Ultra-Fine Grained Austenitic Stainless Steel .................... 887 S. Brochet, A. Poulon-Quintin, J.-B. Vogt , J.-C. Glez and J.-D. Mithieux

Tribological Properties and Wear Mechanisms of Wear Resistant Thermally Sprayed Coatings........................................................................................ 889 Sa. Houdkova, F. Zahalka and R. Enzl

Crack Propagation Resistance and Damage Mechanisms in Nuclear Graphite........... 891 A. Hodgkins, J. Marrow, P. Mummery, A. Fok and B. J. Marsden

Environment-assisted Cracking of High-Strength Magnesium Alloys WE43-T6....... 893 A. Ahmad and T. J. Marrow

Effects of Surface Finish on the Fatigue Limit in Austenitic Stainless Steels (Modelling and Experimental Observations) ............................................................... 895 M. Kuroda, T. J. Marrow and A. Sherry

Contents

xxix

Intergranular Stress Corrosion Crack Propagation in Sensitised Austenitic Stainless Steel (Microstructure Modelling and Experimental Observation)................ 897 T. J. Marrow, L. Babout, A. P. Jivkov, P. Wood, D. Engelberg, N. Stevens, P. J. Wither and R. C. Newman

Ideal Strength of Nanoscale Thin Films ...................................................................... 899 T. Kitamura, Y. Umeno and A. Kushima

Toughness Variability................................................................................................... 901 R. Bouchard, G. Shen and W. R. Tyson

Thermo-Mechanical Behaviour of Nanostructured Copper......................................... 903 C. Duhamel, S. Guerin, M. J. Hytch and Y. Champion

Some Insights into Fatigue Crack Initiation Stage....................................................... 905 H. Alush and Y. Katz

Fatigue Behaviour of Metallic Materials Exposed to High Pressure Hydrogen Environments ............................................................................................................... 907 Y. Mine, S. Matsuoka, Y. Murakami C. Narazaki and T. Kanezaki

In-Situ Investigations of the Fracture Mechanisms at Various Length Scales............. 909 Z. Pakiela, W. Zielinski and K. J. Kurzydlowski

12. Interface Fracture and Behavior of Joints ........................................................ 911 Environmental Attack at Polymer/Metal Interfaces..................................................... 911 A. J. Kinloch, D. Bland, K. T. Tan and J. F. Watts

Modelling of Elastic-Plastic Peel Tests for Structural Adhesives................................ 913 A. J. Kinloch, H. Hadavinia, L. Kawashita, D. R. Moore and J. G. Williams

An Alternating Crack Growth in Adhesively Bonded Joints ...................................... 915 A. R. Akisanya

Measurements of Interface Fracture and Mechanical Properties of Low-K Dielectric Thin Films ................................................................................................................... 917 F. Atrash and D. Sherman

Initiation of Fracture Mechanisms at the Fibre/Matrix interface................................. 919 E. Martin, B. Poitou and D. Leguillon

Effects of Plasticity and Residual Stress for Cracks Near Interfaces........................... 921 I. Reimanis, K. Rozenburg, M. Tilbrook and M. Hoffmann

Toughness of a ±45o Interface ..................................................................................... 923 L. Banks-Sills, Y. Freed, R. Eliasi and V. Fourman

Residual Stress Influence on Dissimilar Material Weld Junction Fracture.................. 925 P. Gilles and M.-F. Cipiere

Fracture Mechanisms of a Thin Elastic Plastic Laminate............................................ 927 C. Bjerken, S. Kao-Walter and P. Stahle

Crack-Tip Parameters in Polycrystalline Plates with Compliant Grain Boundaries.... 929 R. Ballarini and Y. Wang

Extended Fe Simulations of Crack Growth in Layered and Functionally Graded Materials....................................................................................................................... 931 C. Comi and S. Mariani

13. Computational Fracture Mechanics................................................................... 933 Simulation of Plastic Fatigue Crack Growth by a Two Scale Extended Finite Element Method........................................................................................................... 933

Contents

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A. Gravouil, T. Elguedj and A. Combescure

Accurate Determination of Cohesive Crack Tip Fields using Xfem and Admissible Stress Recovery............................................................................................................ 935 B. L. Karihaloo, Q. Z. Xiao and X. Y. Liu

A New Generation of Boundary Element Method for Damage Tolerance Assessment of Aerostructures...................................................................................... 937 M. H. Aliabadi

Robust Stress Intensity Factors Evaluation for 3D Fracture Mechanics with X-FEM ....................................................................................................................... 939 H. Minnebo, E. Bechet and N. Moes

A Micro-Macro Partition of Unity Method for Crack Propagation ............................. 941 P. A. Guidault, O. Allix, L. Champaney and C. Cornuault

A Dynamic Crack Propagation Criteria for XFEM, Based on Path-Independent Integral Evaluation....................................................................................................... 943 I. Nistor, S. Caperaa and O. Pantale

Truss Model as Simple Computational Tool in Fracture Mechanics ........................... 945 P. G. Papadopoulos, D. Plasatis and P. Lambrou

Finite Element Modeling of Cohesive Cracks by Nitsche’s Method........................... 947 P. Hansbo and P. Heintz

Computing Crack Growth in Quasiperiodic Alloys..................................................... 949 P. M. Mariano and F. L. Stazi

X-FEM for 3D Cracks in Shaft with Contact .............................................................. 951 S. Geniaut, P. Massin and N. Moes

Some Improvements for Extended Finite Element Methods in Fracture Mechanics .. 953 P. Laborde, J. Pommier, Y. Renard and M. Salaun

14. Cohesive Models of Fracture .............................................................................. 955 Failure Prediction of Adhesively Bonded T-Peel Joints .............................................. 955 A. Pirondi

An Approach for the Determination of Mixed Mode Cohesive Laws......................... 957 B. F. Sorensen and T. K. Jacobsen

The Use of CZM for Coupled Fatigue/Plasticity Crack Propagation Simulation........ 959 Jl. Bouvard, F. Feyel and Jl. Chaboche

Dynamic Crack Growth : Analytical and Numerical CZM Approaches ..................... 961 G. Debruyne, J. Laverne and P. E. Dumouchel

Simulation of Pre-Critical Cracking in Concrete Using 3D Lattice Model................. 963 H.-K. Man and J. G. M. Van Mier

Effect of Cohesive Law and Triaxiality Dependence of Cohesive Parameters in Ductile Tearing............................................................................................................. 965 I. Scheider, F. Hachez and W. Brocks

Modeling Quasibrittle Material Cracking with Cohesive Cracks: Experimental and Computational Advances ...................................................................................... 967 J. Planas, J. M. Sancho, A. M. Fathy, D. A. Cendon and J. C. Galvez

Pinwheel Meshes and Branching of Cohesive Cracks................................................. 969 P. Ganguly and K. D. Papoulia

A Dynamic Crack Growth Simulation Using Cohesive Elements .............................. 971 M. Anvari and C. Thaulow

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xxxi

A New Cohesive Zone Model for Mixed-Mode Decohesion ...................................... 973 M. J. van Den Bosch , P. J. G. Schreurs and M. G. D. Geers

Cohesive-Zone Modeling of Crack Growth in Specimens with Different Constraint Conditions .................................................................................................................... 975 C. R. Chen, O. Kolednik and F. D. Fischer

Effect of Anisotropic Plasticity on Mixed Mode Interface Crack Growth .................. 977 V. Tvergaard and B. N. Legarth

16. Environment Assisted Fracture.......................................................................... 979 Characterisation of TG-SCC in Pure Magnesium and AZ91 Alloy ............................ 979 N. Winzer, G. Song, A. Atrens, W. Dietzel and C. Blawert

Hydrogen Embrittlement and Cracking of 18MN-4CR Steels .................................... 981 A. Balitskii

Transient Stress and EAC of Steam Turbine Disc Steel .............................................. 983 A. Turnbull and S. Zhou

Irreversible Hydrogen Trapping in Welded Beta-21S Titanium Alloy ........................ 985 D. Eliezer, E. Tal-Gutelmacher, C. E. Cross and Th. Boellinghaus

EAC in High Strength Steels for Gas Transportation .................................................. 987 G. Gabetta and R. Bruschi

High Temperature Fatigue Crack Growth in Titanium Microstructures...................... 989 H. Ghonem

Corrosion Damaging and Corrosion Fatigue Assessment in Three-Layered Metallic Material.......................................................................................................... 991 I. M. Dmytrakh and V. V. Panasyuk

Simulation of Hydrogen Assisted Stress Corrosion Cracking Using a Time Dependent Cohesive Model ......................................................................................... 993 I. Scheider, M. Pfuff and W. Dietzel

Environmental Stress Cracking of Polyethylene Pipes in Water Distribution Networks ...................................................................................................................... 995 J. P. Dear, N. S. Mason and M. Poulton

Fatigue Crack Propagation in 2XXX Aluminium Alloys at 223K .............................. 997 C. Gasqueres, C. Sarrazin-Baudoux, D. Dumont and J. Petit

Hydrogen Assisted Cracking Paths in Oriented Pearlitic Microstructures .................. 999 J. Toribio and E. Ovejero

Effect of Residual Stress-Strain Profile on Hydrogen Embrittlement Susceptibility of Prestressing Steel Wires......................................................................................... 1001 J. Toribio and V. Kharin

Hydrogen Embrittlement of Austenitic Stainless Steels at Low Temperatures ......... 1003 L. Zhang, M. Wen, M. Imade, S. Fukuyama and K. Yokogawa

Hydrogen Diffusion and EAC of Pipeline Steels under Cathodic Protection .......... 1005 M. Cabrini and T. Pastore

Initiation of Environmentally Assisted Cracking in Line Pipe Steel ......................... 1007 M. Elboujdaini

Fatigue Crack Growth Behaviour Depending on Environment in Magnesium Alloys ........................................................................................................................ 1009 M. Nakajima, K. Tokaji, Y. Uematsu and T. Shimizu

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xxxii

Assessment of High-Temperature Hydrogen Degradation of Power Equipment Steels .......................................................................................................................... 1011 H. M. Nykyforchyn and O. Z. Student

Stress Corrosion Cracking of 18MN-4CR Generator Rotor End-retaining Ring Steel............................................................................................................................ 1013 N. Mukhopadhyay and U. K. Chatterjee

17. SIM, Philosophy, Instrumentation and Analysis ............................................ 1015 Non Contacting Stress Monitoring ............................................................................ 1015 W. D. Dover, R. F. Kare and N. Stone

Rapid Calculation of Stress Intensity Factors ............................................................ 1017 A. J. Love and F. P. Brennan

Variable Amplitude Corrosion Fatigue of High Strength Weldable Steel ................. 1019 S. S. Ngiam and F. P. Brennan

Crack Monitoring using ACFM................................................................................. 1021 R. F. Kare

18. Fracture of Biomaterials ................................................................................... 1023 Fatigue Behaviour of Fiber Reinforced Bone Cement .............................................. 1023 B. Kumar and F. W. Cooke

Fracture and Fatigue of Bone and Bone Cement: The Critical Distance Approach .. 1025 D. Taylor, D. Hoey, L. Sanz and P. O’Reilly

Fatigue Failure in Reconstracted Acetabula – a Hip Simulator Study....................... 1027 J. Tong, N. P. Zant and P. Heaton-Adegbile

Deformation and Fracture of Bioactive Particulate Composites Developed for Hard Tissue Repair..................................................................................................... 1029 M. Wang

Failure of Biomaterials in Implant Fixation............................................................... 1031 P. J. Prendergast, J. R. Britton, P. T. Scannell and A. B. Lennon

19. Structural integrity Assessment in Theory and Practice ............................... 1033 Stress Analisys of High Pressure Steamlines in Thermal Power Plants .................... 1033 A. Jakovljevic

Laminar Composite Materials Damage Monitoring by Embedded Optical Fibers ... 1035 A. Kojovi, I. Zivkovi, L. Brajovi, D.Mitrakovi and R. Aleksi

SOL GEL Synthesis and Structure of Hybrid Nanomaterials with Strong Chemical Bonds ......................................................................................................................... 1037 B. Samuneva, P. Djambaski, E. Kashchieva and G. Chernev

An Alternative Approach to Conventional Data Presentation of Fatigue.................. 1039 D. Angelova

Absorbers of Seismic Energy for Damaged Masonary Structures............................. 1041 D. Sumarac, Z. Petraskovi, S. Miladinovic, M. Trajkovi, M. Andjelkovic and N. Trisovic

Numerical Analysis of Tensile Specimen Fracture with Crack in HAZ ................... 1043 G. Adziev, A. Sedmak and T. Adziev

Determination of JR-Curve by Two Points Method .................................................. 1045 I. Blacic and V. Grabulov

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xxxiii

Monitoring of Stress-Strain State of Boiler During Pessure Test ............................. 1047 J. Kurai, Z. Burzic, N. Garic, M. Zrilic and B. Aleksic

Local Variation of Crack Driving Force in a Mismatched Weld ............................... 1049 J. Predan, N. Gubeljak and O. Kolednik

Strength Recovery of Machined Alumina by Self Crack Healing............................. 1051 K. Ando, K. Takahashi, W. Nakao, T. Osada and S. Sato

Crack Initiation and Growth in HAZ of Microalloyed Steel ..................................... 1053 K. Geric and S. Sedmak

Structural Integrity at Elevated Temperatures - Residual Service Life Evaluation ... 1055 L. Milovic and S. Sedmak

The Analysis of Supporting Structure of Planetary Gear Box Satellite .................... 1057 M. Arsi, V. Aleksi and Z. Anelkovi

Failure Probability of Gear Teeth Wear ..................................................................... 1059 M. Ognjanovic

Some Aspects of Engineering Approach to Structural Integrity Assessment............ 1061 M. Kiric and A. Sedmak

Structural Integrity Assessment Applying Ultrasonic Testing................................... 1063 M. Kiric

(Crack-Healing + Proof-Test): Methodology to Guarantee the Reliability of Ceramics..................................................................................................................... 1065 M. Ono, W. Nakao, K. Takahashi, K. Ando and M. Nakatani

Risk Based Integrity Assessment of Concrete Structures .......................................... 1067 M. Pavisic

Structural Integrity Assessment by Local Approach to Fracture ............................... 1069 M. Zrilic, M. Rakin, Z. Cvijovic, A. Sedmak and S. Sedmak

Brittle and Ductile Fracture in Service of Pressure Vessels....................................... 1071 N. Filipovic and K. Geric

Mechanisms of Fracture in Medium Carbon Vanadium Microalloyed Steels ........... 1073 N. Radovic, Dj. Drobnjak and H. Hraam

Computation and Experimental Investigations of Notched Components Fatigue Life Estimation .......................................................................................................... 1075 S. Maksimovic, Z. Burzic and K. Maksimovic

Failure Analysis of Layered Composite Structures: Computation and Experimental Investigation............................................................................................................... 1077 S. Maksimovic

Loading Rate Effect on HSLA Steel Welded Joints Fracture Resistance ................. 1079 V. Grabulov, I. Blai, A. Radovi and S. Sedmak

Case Study of Supporting Tubes Failure.................................................................... 1081 V. S. Zeravcic, M. Djukic, G. Bakic, B. Andjelic and B. Rajicic

Structure Integrity of Pressure Vesels Repair Welding Joints.................................... 1083 V. S. Zeravcic, G. Bakic, M. Djukic and B. Rajicic

Effect of Microalloyed Steel Welding Procedure on Fatigue Crack Growth ............ 1085 Z. Burzic, V. Grabulov, M. Burzic, M. Manjgo, V. Gliha and T. Vuherer

Fracture Resistance of High-Strength 7000 Forging Alloys...................................... 1087 Z. Cvijovic, M. Rakin and M. Vratnica

20. Critical Distance Theories of Fracture............................................................. 1089

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xxxiv

Does a Characteristic Crack-Tip Distance Imply Discontinuous Crack Propagation?............................................................................................................... 1089 A. P. Kfouri

A Multiaxial Criterion for Notch Fatigue Using a Critical-Distance Method .......... 1091 A. Carpinteri, A. Spagnoli, S. Vantatori and D. Viappiani

Size Effects for Crack Initiation at Blunt Notches or Cavities in Brittle Materials... 1093 D. Leguillon, E. Martin, D. Picard and C. Putot

The Theory of Critical Distances ............................................................................... 1095 D. Taylor

Strength Analysis of Composite Pinned Joints .......................................................... 1097 H. A. Whitworth, O. Aluko and N. Tomlinson

Application of the Theory of Critical Distance to Fretting Fatigue .......................... 1099 J. A. Araujo, L. Susmel, D. Taylor and L. H. M. Lopes

The Theory of Critical Distances: Applications in Fatigue ....................................... 1101 L. Susmel

Fatigue Assessment using an Integrated Threshold Curve Method - Applications... 1103 M. D. Chapetti

Anaytical Approaches vs Atomistic Simulations in Fracture ................................... 1105 N. Pugno, A. Carpinteri, M. Ippolito, A. Mattoni and L. Colombo

A Coupled Stress and Energy Criterion within Finite Fracture Mechanics............... 1107 P. Cornetti, N. Pugno, A. Carpinteri and D. Taylor

Local Strain Energy Density and Fatigue Strength of Welded Joints ........................ 1109 P. Lazzarin, P. Livieri and F. Berto

An Implicit Gradient Application to Fatigue of Notches and Weldments .................. 1111 R. Tovo and P. Livieri

Use of JVR to Predict Static Failures in Notched Components................................. 1113 P. Livieri

Standardization of Strength Evaluation Methods Using Critical Distance Stress ..... 1115 T. Hattori, N. Nishimura and M. Yamashita

Application of Point Stress Method to Hydro-Fracturing Tectonic Stress Measurement.............................................................................................................. 1117 T. Ito

A Unified Failure Criterion for Brittle or Quasi-Brittle Materials under Arbitrary Stress Concentration .................................................................................................. 1119 J. Li and X. B. Zhang

22. New Investigations on Very High Cycle Fatigue of Materials ....................... 1121 Morphology of Step-Wise S-N Curves Depending on Notch and Surface Roughness in High Strength Steel.............................................................................. 1121 H. Itoga, K. Tokaji, M. Nakajima and H. N. Ko

Very High Cycle Fatigue Behaviour under Cyclic Torsion Loading ......................... 1123 H. Mayer and S. Stanzl-Tschegg

Modelling of Fatigue Crack Growth From Exfoliation and Pitting Corrosion.......... 1125 G. Clark, P. K. Sharp and R. Jones

Does Copper Undergo Surface Roughening during Fatigue in the VH Regime?...... 1127 S. Stanzl-Tschegg, H. Mughrabi and R. Schuller

Crack Initiation Mechanism of Bearing Steel in High Cycle Fatigue ....................... 1129

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T. Sakai

Very High Cycle Fatigue Behavior of High Strength Steels...................................... 1131 Y. Akiniwa, N. Miyamoto, H. Tsuru and K. Tanaka

23. Deformation and Fracture of Engineering Materials..................................... 1133 Fracture Toughness of Hydrided Zircaloy-4 Experimental and Numerical Study .... 1133 C. Langlade, P. Bouffioux and M. Clavel

Crack Growth Behavior in a Highly Filled Elastomer............................................... 1135 C. T. Liu , R. Neviere and G. Ravichandran

Crack Tip Behavior in TiAl when Approaching Grain Boundary ............................. 1137 F.-P. Chiang, S. Chang and K. Wang

Effect of Loading Rate on the Energy Release Rate in a Constrained Elastomeric Disk ............................................................................................................................ 1139 H. K. Ching, C. T. Liu and S. C. Yen

Analyses of Progressive Damage and Fracture of Particulate Composite Materials Using S-FEM Technique............................................................................................ 1141 H. Okada, S. Tanaka, Y. Fukui and N. Kumazawa

Fracture Mechanics on PVDF Polymeric Material : Specimen Geometry Effects.... 1143 L. Laiarinandrasana and G. Hochstetter

Fracture Toughness of Alloyed Austempered Ductile Iron (ADI)............................. 1145 O. Eric, D. Rajnovic, Z. Burzic, L. Sidjanin and M. T. Jovanovic

Prediction of Crack Growth under Random Load in Railway Wheel ....................... 1147 R. Hamam, S. Pommier and F. Bumbieler

24. Materials Damage Prognosis and Life Cycle Engineering............................. 1149 Predicting the Evolution of Stress Corrosion Cracks From Pits ................................ 1149 A. Turnbull, L. N. Mccartney and S. Zhou

Corrosion Problems in Nuclear Industry : Lessons Learned and Perspectives.......... 1151 J. M. Boursier, F. Foct, F. Vaillant and E. Walle

Aluminium Alloys Fatigue Evaluation Method......................................................... 1153 S. Rymkiewicz

25. Mixed-Mode Fracture........................................................................................ 1155 Singular Stress Fields Situations in Mode-II and Mixed-Mode Loaded Cracks ...... 1155 D. Fernández-Zúñiga, J. F. Kalthoff, A. Blázquez and A. Fernández-Canteli

Evaluation of M-Integral for Rubbery Material Problems Containing Multiple Cracks......................................................................................................................... 1157 J.-H. Chang and D.-J. Peng

Use of a Crack Box Technique for Crack Bifurcation in Ductile Material................ 1159 D. Lebaillif, X. B. Zhang and N. Recho

Mixed Mode Fracture of Linear Elastic Materials with Cubic Symmetry ................ 1161 D. E. Lempidaki, N. P. O’Dowd and E. P. Busso

Three-Dimensional Experimental and Numerical SIFs and Crack Growth ............. 1163 D. M. Constantinescu, B. Bocaneala and L. Marsavina

An Arbitrarily Oriented Crack Near a Coated Fiber.................................................. 1165 H. M. Shodja and F. Ojaghnezhad

Simulation of the Mixed Mode Fracture of Concrete with Cohesive Models ........... 1167

Contents

xxxvi

J. C. Gálvez, D. A. Cendón, E. Reyes, J. M. Sancho and J. Planas

Micromechanical Analysis of Rupture Mechanisms in Mixed Mode Ductile Fracture ...................................................................................................................... 1169 I. Barsoum and J. Faleskog

Mode I Preloading-Mode II Fracture in Warm Pre-Stressing .................................... 1171 M. R. Ayatollahi and M. Mostafavi

Predictions of Mixed Mode I/II Fracture toughness for Soft Rocks.......................... 1173 M. R. Ayatollahi and M. R. M. Aliha

An Interface Model for Mixed-mode, Buckling-Driven Decohesion of Superficial Layers......................................................................................................................... 1175 S. Bennati and P. S. Valvo

MXED-Mode Fracture Analyss of Orthotropc Functonally Graded Materals ......... 1177 S. Dag, B. Yildirim, D. Sarikaya

New Scheme for Fea of Mixed Mode Stable Crack Growth ..................................... 1179 S. K. Maiti , S. Namdeo and A. H. I. Mourad

Numerical Simulation of Nonlinear Crack Propagation under Mixed-Mode Impact Loading ...................................................................................................................... 1181 T. Fujimoto and T. Nishioka

Elastic-Plastic Behaviour of Crack Propagation under Biaxial Cyclic Loading ....... 1183 T. Hoshide

Numerical Analysis of Mixed-Mode Cracking in Concrete Dams............................ 1185 Z. Shi

26. Fracture Mechanics Characterization of Wood.............................................. 1187 Species and Other Physical Effects on Parameters Describing a Wood Toughness Test. ............................................................................................................................ 1187 B. Thibaut and J. Beauchene

Yew and Spruce Wood: Mechanical Properties and Fracture Surface Studies .......... 1189 D. Keunecke, C. Marki and P. Niemz

Critical Crack Lengths in FRP Reinforced Glulam Beams ....................................... 1191 J. Desjarlais, W. G. Davids and E. N. Landis

Failure Analysis of Engineering Wood Products ....................................................... 1193 I. Smith, M. Snow and A. Asiz

Modelization of Slow Crack Growth in Wood Considered as a Damage Viscoelastic Material.................................................................................................. 1195 M. Chaplain and G. Valentin

Mode I Crack Propagation in Softwood, Microanalyses and Modeling.................... 1197 P. Navi and M. Sedighi-Gilani

Fracture Properties of Pine and Spruce in Mode I ..................................................... 1199 N. Dourado, S. Morel, M. F. S. F. De Moura, G. Valentin and J. Morais

Influence of the Specimen Geometry on R-Curve: Numerical Investigations. ......... 1201 C. Lespine, S. Morel, J.-L. Coureau and G. Valentin

Fracture Behaviour and Cutting of Small Wood Specimens in RT-Direction ........... 1203 S. Koponen and P. Tukiainen

Fracturing of Wood under Torsional Loading: Fracture Mechanisms and Mechanics .................................................................................................................. 1205 E. K. Tschegg and S. E. Stanzl-Tschegg

Contents

xxxvii

On the Influence of Humidity Cycling on Fracture Properties of Wood ................... 1207 S. Vasic and S. Tschegg

Determination of Cohesive Fracture Parameters for Wood ....................................... 1209 T. Astrup, J. F. Olesen, L. Damkilde and P. Hoffmeyer

The Role of Fracture Toughness in the Cutting of Wood .......................................... 1211 T. Atkins

28. Short Fatigue Crack Growth under Multi-Axial Loading Conditions ......... 1213 Short Fatigue Cracks of In-Service Fatigued Turbine Blades ................................... 1213 A. A. Shanyavskiy, M. A. Artamonov, A. L. Tushentsov and Yu. A. Potapenko

Short Crack Growth under Cyclic Torsion with Static Tension................................. 1215 I. Ohkawa, S. Hirano, T. Negishi and M. Misumi

Resistance-Curve Method for Predicting Fatigue Thresholds under Combined Loading ...................................................................................................................... 1217 K. Tanaka, Y. Akiniwa and M. Wakita

The Growth of Short Cracks From Defects under Multi-Axial Loading................... 1219 M. Endo and A. J. Mcevily

Short Fatigue Cracks in Notched and Unnotched Specimens under Non-Proportional Loading ......................................................................................... 1221 O. Hertel, T. Seeger, M. Vormwald, R. Doring and J. Hoffmeyer

Microcracks Growth in Push-Pull and Reversed Torsion in Stainless Steel.............. 1223 V. Doquet and G. Bertolino

Hydrogen and Notch Effects on Torsional Fatigue of Stainless Steel ....................... 1225 Y. Kondo, M. Kubota and K. Ohguma

30. Integrity of Gears ............................................................................................... 1227 Influence of Moving Tooth Load on Gear Fatigue Behaviour................................... 1227 D. T. Jelaska and S. Podrug

Comparison of Solid Spur Gear Face Load Factors .................................................. 1229 G. Marunic

Prediction of Contact Fatigue Internal Crack Propagation in Hypoid Gears............. 1231 M. Vimercati, M. Guagliano, L. Vergani and A. Piazza

Fatigue Crack Initiation Along Inclusion Interfaces of Contacting Mechanical Elements ................................................................................................. 1233 S. Glodez, M. Ulbin and J. Flasker

Energy Based Gear Fault Diagnostics........................................................................ 1235 S. J. Loutridis

Crack Propagation in Gear Tooth Root...................................................................... 1237 S. Pehan, B. Zafosnik and J. Kramberger

Experimental Evaluation of Stress Intensity Factors in Spur Gear Teeth .................. 1239 V. Spitas , G. Papadopoulos, Th. Costopoulos and C. Spitas

35. High Temperature and Thermomechanical Fatigue ...................................... 1241 Isothermal and Thermomechanical Fatigue Behavior of the ODS Superalloy PM1000...................................................................................................................... 1241 W. O. Ngala, G. Biallas and H. J. Maier

Contents

xxxviii

Fatigue-Creep-Environment Interactions in a Directionally-Solidified Ni-Base Superalloy .................................................................................................................. 1243 A. P. Gordon, M. M. Shenoy, R. W. Neu and D. L. McDowell

The Effects of Microstructure, Deformation Mode and Environment on Fatigue .... 1245 S. D. Antolovich and B. F. Antolovich

Comparing Fatigue Behaviour of TI6242 and Novel TIAL Intermetallics ............... 1247 T. K. Heckel, A. Guerrero-Tovar and H. J. Christ

A TBC Failure Model Based on Crack Number Density ......................................... 1249 X. Wu, Z. Zhang and R. Liu

36. Impact Failure of Laminated and Sandwich Composite Structures............. 1251 Impact Induced Composite Delamination: State and Parameter Identification via Unscented Kalman Filter ........................................................................................... 1251 A. Corigliano, A. Ghisi and S. Mariani

Modelling Impact Damage in Sandwich Concept Structures .................................... 1253 A. Johnson and N. Pentecote

Punch Shear Behavior of Composites at Low and High Rates.................................. 1255 B. A. Gama and J. W. Gillespie Jr.

Repeated Impact Behaviour and Damage Progression of Glass Reinforced Plastics 1257 G. Belingardi, M. P. Cavatorta and D. S. Paolino

Impact Behaviour Modelling of a Composite Leading Edge Structure..................... 1259 G. Labeas and Th. Kermanidis

Bending Strength of Sandwich Panels with Different Cores After Impact ............... 1261 W. Goettner and H. G. Reimerdes

Energy Absorbing Ability of Sandwich Composite Structures ................................. 1263 J. P. Dear, W. Maruszewska, S. T. Oh and H. Lee

Impact Behaviour of Metal Foam Cored Sandwich Beams....................................... 1265 S. Mckown and R. A. W. Mines

37. Mesofracture and Transferability .................................................................... 1267 Stress Gradient at Notch Roots Using Volumetric Method ....................................... 1267 H. Adib and G. Pluvinage

Local Approach Use at Solution of Fracture Parameters Transferability .................. 1269 L. Jurasek, M. Holzmann and I. Dlouhy

Damage in Rubber-Modified Polymers : Experimental, Modelling and Computational Aspects .............................................................................................. 1271 N. Belayachi, F. Zaïri, N. Benseddiq and M. Naït Abdelaziz

Failure Assessment Diagrams Based on the Criterion of Average Stress ................. 1273 Y. G. Matvienko

38. Damage in Composites - Damage Development in Composite Materials & Structures - Models of Prediction ............................................................... 1275 Material Models for Damaged Composite Laminates ............................................... 1275 J. Varna

Raman Spectroscopy Assessment of Stiffness Reduction and Residual Strains due to Matrix Cracking in Angle – PLY Laminates .................................................. 1277 P. Lundmark, D. G. Katerelos, J. Varna and C. Galiotis

Contents

xxxix

Physical Modelling of Failure Processes in Composite Materials............................. 1279 P. W. R. Beaumont

NCF Cross-PLY Laminates: Damage Accumulation and Degradation of Elastic Properties ................................................................................................................... 1281 R. Joffe and D. Mattsson

Matrix Crack Initiation and Propagation in Laminates with Off-Axis PLIES........... 1283 N. Vrellos, S. L. Ogin and P. A. Smith

Stress Oscillation and Instability of Yielding in Polymers and Nanocomposites...... 1285 D. E. Mouzakis, G. Kandilioti, S. Tzavalas and V. Gregoriou

Prediction of Cyclic Durability of Woven Composite Laminates ............................. 1287 V. Tamuzs and K. Reifsnider

39. Aging Aerostructures......................................................................................... 1289 Repair of Corroded Aerospace Aluminium Panels Using Ultrasonic Impact Treatment ................................................................................................................... 1289 C. A. Rodopoulos, S. Pantelakis, M. Liao and E. Statnikov

Fatigue Crack Initiation in Stress Concentration Areas............................................. 1291 C. Schwob, F. Ronde-Oustau and L. Chambon

Hydrogen Trapping: Deformation and Heat Treatment Effects in 2024 Alloy ......... 1293 H. Kamoutsi, G. N. Haidemenopoulos, V. Bontozoglou , P. V. Petroyiannis and Sp. G. Pantelakis

An Integrated Methodology Assessing the Aging Behaviour of Aircraft Structures 1295 G. Labeas and I. Diamantakos

Numerical Investigation on the Tensile Behaviour of Pre-Corroded 2024 Aluminium Alloy ....................................................................................................... 1297 P. V. Petroyiannis, G. Labeas, Sp. G. Pantelakis, E. Kamoutsi, V. Bontozoglou and G. N. Haidemenopoulos

40. Residual Stress and its Effects on Fatigue and Fracture................................ 1299 Assessment of Defects under Combined Primary and Residual Stresses .................. 1299 A. H. Sherry and M. R. Goldthorpe

Effect of Residual Stresses on the Crack Growth in Aluminum ............................... 1301 B. Kumar and J. E. Locke

Effect of the Cryogenic Wire Brushing on the Surface Integrity and the Fatigue Life Improvement of the AISI 304 Stainless Steel Ground Components ................. 1303 N. B. Fredja, H. Sidhoma and C. Brahamb

Interaction of Residual Stress with Mechanical Loading in Ferritic Steels ............... 1305 A. Mirzaee-Sisan, C. E. Truman and D. J. Smith

Evaluation of Novel Post Weld Heat Treatment in Ferritic Steel Repair Welds Based on Neutron Diffraction .................................................................................... 1307 C. Ohms, D. Neov, R. C. Wimpory and A. G. Youtsos

Surface Crack Development in Transformation Induced Fatigue of SMA Actuators 1309 D. C. Lagoudas, O. W. Bertacchini and E. Patoor

Finite Element Simulation of Welding in Pipes: a Sensitivity Analysis.................... 1311 D. Elias Katsareas , C. Ohms and A. G. Youtsos

Residual Stress Prediction in Letterbox-Type Repair Welds ..................................... 1313 L. Keppas, N. K. Anifantis, D. E. Katsareas and A. G. Youtsos

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Effect of Reflection Shot Peening and Fine Grain Size on Improvement of Fatigue Strength for Metal Bellows ....................................................................................... 1315 H. Okada, A. Tange and K. Ando

Viscosity Effect on Displacements and Stresses of a Two-Pass Welding Plate ........ 1317 W. El Ahmar and J. F. Jullien

Surface Integrity in High Speed Machining of TI-6WT.%Al-4WT.%V Alloy ......... 1319 J. D. P. Velasquez, B. Bolle, P. Chevrier and A. Tidu

Phase Transformation and Damage Elastoplastic Multiphase Model for Welding Simulation .................................................................................................................. 1321 T. Wu, M. Coret and A. Combescure

The Present Sans Instrument and the New HFR-Petten Sans Facility Based on a Cold Neutron Source.......................................................................................... 1323 O. Ucaa,B, C. Ohmsa, D. Neova and A. G. Youtsosa

Residual Stress Numerical Simulation of Two Dissimilar Material Weld Junctions. 1325 P. Gilles, L. Nouet and P. Duranton

Identification of Weld Residual Stress Length Scales for Fracture Assessment ....... 1327 P. J. Bouchard and P. J. Withers

High-Resolution Neutron Diffraction for Phase and Residual Stress Investigations 1329 P. Mikula and M. Vrana

Sensitivity of Predicted Residual Stresses to Modelling Assumptions...................... 1331 S. K. Bate, R. Charles, D. Everett, D. O’Gara1, A. Warren and S. Yellowlees

Welding Effects on Thin Stiffened Panels ............................................................ 1333 T. T. Chau

Evaluation of Residual Stresses in Ceramic Polymer Matrix Composites Using Finite Element Method............................................................................................... 1335 K. Babski, T. Boguszewski, A. Boczkowska, M. Lewandowska, W. Swieszkowski and K. J. Kurzydlowski

41. Computational Modeling of Multiphysics Degrading Systems (CMMDS) .. 1337 Towards Data-Driven Modeling and Simulation of Multiphysics Degrading Systems ..................................................................................................................... 1337 J. G. Michopoulos and C. Farhat

Mathematical Modelling of Piezoceramic Transducer Performance in the Presence of Material Defects ..................................................................................... 1339 T. A. Christensen, N. L. Andersen, and M. Willatzen

A Continuum Approach for Identifying Elastic Moduli of Composites.................... 1341 J. G. Michopoulos and T. Furukawa

Regularized Identification of Material Constants Using Multi-Objective Gradient-Based Method ............................................................................................. 1343 T. Furukawa and J. G. Michopoulos

Loading and Material Features Influence on Piezoelectric Material Performance.... 1345 V. G. Degiorgi and S. A. Wimmer

Modeling of Plasma Chemical Deposition and Degradation of Silicon Thin Films . 1347 V. V. Krzhizhanovskaya, P. M. A. Sloot and Y. E. Gorbachev

42. Scaling and Size Effects ..................................................................................... 1349

Contents

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A Fractal Approach Interpretation for the Indentation Size Effect............................ 1349 A. Carpinteri and S. Puzzi

Description of Multi-Scaling Power Laws in Fracture and Strength......................... 1351 A. M. Korsunsky

The Spalling Failure Around Deep Excavations in Rock Masses ............................ 1353 A. P. Fantilli and P. Vallini

Scaling in Multiaxial Compressive Fracture.............................................................. 1355 A. S. Elkadi and J. G. M. van Mier

Fracture of Antarctic FY Sea Ice ............................................................................... 1357 J. P. Dempsey, S. Wang and D. M. Cole

Mixed Mode Fracture of Brickwork Masonry........................................................... 1359 J. C. Galvez, E. Reyes, M. J. Casati, J. M. Sancho, J. Planas and D. A. Cendon

Geometric Scaling and Instability in FRP-Concrete Debonding ............................... 1361 K. V. Subramaniam, M. Ali-Ahmad and C. Carloni

A Simplified MCFT for Shear Capacity Scaling of R/C Beams ............................... 1363 M. T. Kazemi and V. Broujerdian

Interplay of Sources of Size Effects in Concrete Specimens..................................... 1365 M. Vorechovsky and D. Matesova

Scale Effect in Elastic and Strength Properties of Nanostructures ............................ 1367 O. S. Loboda , A. M. Krivtsov and N. F. Morozov Fracture Toughness Assessment of a C-MN Steel Using Miniature Specimens ....... 1369 P. J. Apps, W. Geary, J. W. Hobbs and G. Wardle

Size Effect in the Bonding of Smooth and Deformed Bars: NSC versus HPC ......... 1371 P. Bamonte, D. Coronelli and P. G. Gambarova

Size Effect in the Cracking of Drying Soil ................................................................ 1373 P. C. Prat, A. Ledesma, and M. R. Lakshmikantha

Modelling of the Volume Effects Related to the Unixial Behaviour of Concrete. From a Discontinuous to a Macroscopic Approach................................................... 1375 P. Rossi, J. L. Tailhan, J. Lombart and A. Deleurence

Size Effect and R-Curve in Quasibrittle Fracture ...................................................... 1377 S. Morel, E. Bouchaud and G. Valentin

Bifurcation and Size Effect in a Viscoelastic Non-Local Damageable Continuum... 1379 Th. Baxevanis, G. Pijaudier-Cabot and F. Dufour

Ultiscale Necessary and Sufficient Strength Criteria................................................. 1381 V. M. Kornev

Size Effects: Moving forwards................................................................................... 1383 X. Hu and K. Duan

An Experimental Study on Rapid Setting Concrete Repair Materials....................... 1385 J. P. Richards and Y. Xi

44. Multiple Cracking and Delamination .............................................................. 1387 Hierarchical Failure Modeling and Related Scale-Invariant Probability Distributions of Strength ............................................................................................ 1387 D. A. Onishchenko

Interaction of Two Adhesively Bonded Weak Zones .............................................. 1389 I. V. Simonov and B. L. Karihaloo

Contents

xlii

Multiple Cracking in Surface-Hardened Tensile Specimens and their Fracture Mechanisms ............................................................................................................... 1391 L. S. Derevyagina, V. E. Panin, R. V. Goldstein, N. A. Antipina and I. L. Strelkova

Fracture Criterion of Cracks Initiation and Growth................................................... 1393 M. Perelmuter

Interfacial Cracks Emanating from Partially Debonded Subsurface Circular Elastic Inclusions ................................................................................................................... 1395 P. B. N. Prasad

Mechanics of Block Structures and its Applications to Geodynamics ...................... 1397 P. V. Makarov

Static and Dynamic Response of Multiple Delaminations ........................................ 1399 M. G. Andrews and R. Massabo

Modeling Crack Growth in Structure- Nonhomogeneous Medium under Complex Stress State ................................................................................................................. 1401 R. V. Goldstein, Y. V. Zhitnikov and N. M. Osipenko

Nonideal Interface of a Bimaterial with Defects under Thermal Load...................... 1403 V. E. Petrova and K. P. Herrmann

Multiple Cracking Development at the Prefructure Stage of Ion Crystals ................ 1405 Y. Y. Deryugin, V. E. Panin, V. Hadjicontis, K. Mavromatou

Author Index ............................................................................................................ 1407

Editor’s Preface This volume contains two-page abstracts of the 698 papers presented at the “16th European Conference of Fracture,” (ECF16) held in Alexandroupolis, Greece, July 3-7, 2006. The accompanying CD attached at the back cover of the book contains the full length papers. The abstracts of the fifteen plenary lectures are included in the beginning of the book. The remaining 683 abstracts are arranged in 25 tracks and 35 special symposia/sessions with 303 and 380 abstracts, respectively. The papers of the tracks have been contributed from open call, while the papers of the symposia/sessions have been solicited by the respective organizers. Both tracks and symposia/sessions fall into two categories, namely, fracture of nanomaterials and structures and engineering materials and structures with 88 and 595 papers, respectively. Started in 1976, the European Conference of Fracture (ECF) takes place every two years in a European country. Its scope is to promote world-wide cooperation among scientists and engineers concerned with fracture and fatigue of solids. ECF16 was under the auspices of the European Structural Integrity Society (ESIS) and was sponsored by the American Society of Testing and Materials, the British Society for Stain Measurement, the Society of Experimental Mechanics, the Italian Society for Experimental Mechanics, and the Japanese Society of Mechanical Engineers. ECF16 focused in all aspects of structural integrity with the objective of improving the safety and performance of engineering structures, components, systems and their associated materials. Emphasis was given to the failure of nanostructured materials and nanostructures and micro and nanoelectromechanical systems (MEMS and NEMS). The technical program of ECF16 was the product of hard work and devotion of more than 150 world leading experts to whom I am greatly indebted. The success of ECF16 relied solely on the dedication and titanic work of the members of the Scientific Advisory Board, the pillars of ECF16. As chairman of ECF16 I am honored to have them on the Board and have worked closely with them for a successful conference. Fracture mechanics analysis has been successful for many years in the prevention of failures of engineering materials and structures. It is based on the realistic assumption that all materials contain crack-like defects from which failure initiates. New technological developments, however, raise new challenges for fracture mechanics research and development. Quasi-brittle materials including concrete, cement pastes, rock, soil, etc. are being extensively used in engineering applications. Layered materials and especially thin film/substrate systems are becoming important in small volume systems used in micro and nanoelectromechancial systems (MEMS and NEMS). Nanostructured materials are being introduced in our every day life. In all these problems fracture mechanics plays a major role for the prediction of failure and safe design of materials and structures. Failure of materials and structures at the micro and nano scale levels are adequately addressed at ECF16 with 93 papers referred to in this area.

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Editor’s Preface

More than nine hundred participants attended ECF16, while more than eight hundred fifty papers were presented, far more than any other ECF over a thirty year period. The participants of ECF16 came from 49 countries. Roughly speaking 66% came from Europe, 17% from the Americas, 8% from the Far East and 9% from other countries. I am happy and proud to have welcomed in Alexandroupolis well-known experts who came to discuss problems related to the analysis and prevention of failure in structures. The tranquility and peacefulness of this small town provided an ideal environment for a group of scientists and engineers to gather and interact on a personal basis. Presentation of technical papers alone is not enough for effective scientific communication. It is the healthy exchange of ideas and scientific knowledge, formal and informal discussions, together with the plenary and contributed papers that make a fruitful and successful meeting. Informal discussions, personal acquaintance and friendship play an important role. I am proud to have hosted ECF16 in the beautiful town of Alexandroupolis, site of the Democritus University of Thrace and I am pleased to have welcomed colleagues, friends, and old and new acquaintances. I very sincerely thank the authors who have contributed to this volume, the symposia/ sessions organizers for their hard work and dedication and the referees who reviewed the quality of the submitted contributions. Our sponsors’ support, give in various forms, is gratefully acknowledged. The tireless effort of the members of the Organizing Committee as well as of other numerous individuals, and people behind the scenes is appreciated. I am deeply indebted to the senior students of the Department of Electrical and Computer Engineering of the Democritus University of Thrace Messrs. N. Tsiantoulas and S. Siailis for their hard work and dedication in the preparation of the ECF16 website in a timely and efficient manner and the organization of the conference, and for their efforts in helping me compile this volume. Finally, a special word of thanks goes to Mrs. Nathalie Jacobs of Springer for the nice appearance of this book and her kind and continuous collaboration and support.

January 2006 Xanthi, Greece

Emmanuel E. Gdoutos Editor

ORGANIZING COMMITTEES Scientific Advisory Board Emmanuel E. Gdoutos (Chairman) Track 1 (Nanomaterials and Nanostructures) Awaji, H. (Japan), Bahr, D., (USA), Ballarini, R., (USA), Batra, R. (USA), Belytschko, T. (USA), Berndt, C. (USA), Bhushan, B. (USA), Espinosa, H. (USA), Friedrich, K. (Germany), Karimi, A. (Switzerland), Kouris, D. (USA), Lagoudas, D. (USA), Meletis, E.I. (USA), Michel, B. (Germany), Moody, N. (USA), Plumbridge, W.J. (UK), Pluvinage, G. (France), Ruoff, R. (USA), Sih, G.C. (China), Zhang, Z. (Germany), Zhou, M. (USA). Track 2 (Engineering Materials and Structures) Akid, R. (UK), Aliabadi, M.H. (UK), Andrianopoulos, N. (Greece), Angelova, D. (Bulgaria), Aravas, N. (Greece), Atkins, A.G. (UK), Banks-Sills, L. (Israel), Bartolozzi, F. (Italy), Barton, J. (UK), Bartzokas, D. (Greece), Bathias, C., (France), Bazant, Z. (USA), Beaumont, P. (UK), Beretta, S. (Italy), Blackman, B. (UK), Brocks, W. (Germany), Bunch, J. (USA), Cacko, J. (Slovakia), Carpinteri, Alberto (Italy), Carpinteri, Andrea (Italy), Chona, R. (USA), Daniel, I.M. (USA), Danzer, R. (Austria), Dietzel, W. (Germany), Dover, B. (UK), Exadaktylos, G. (Greece), Fernando, U.S. (UK), Ferro, G. (Italy), Finnie, I. (USA), Fischer, F.D. (Austria), Fleck, N. (UK), Freitas, M.J.M. (Portugal), Gabetta, G. (Italy), Galiotis, C. (Greece), Georgiadis, H.G. (Greece), Goldstein, R. (Russia), Gosz, M. (USA), Gubeljack, N. (Slovenia), Hawong, J.S. (Korea), Hedrich, K. (Republic of Serbia), Hopkins, S. (USA), Ingraffea, A. (USA), Isogimi, K. (Japan), Jelaska, D. (Croatia), Jirasek, M. (USA), Johnson, E. (Sweden), Jones, R. (Australia), Kalluri, S. (USA), Kalthoff, J.F. (Germany), Karalekas, D. (Greece), Karihaloo, B. (UK), Kassner, M. (USA), Kermanidis, Th. (Greece), Kienzler, R. (Germany), Kocanda, D. (Poland), Konsta-Gdoutos, M. (Greece), Kostopoulos, V. (Greece), Kourkoulis, S. (Greece), Landes, J. (USA), Lee, B-L (USA), Lee. O.S. (Korea), Lee, S.B. (Korea), Liolios, A. (Greece), Liu, C.T. (USA), Luxmoore, A.R. (UK), MacGillivray, H. (UK), Mai, Y.W. (Australia), Maier, H.J. (Germany), MarioliRiga, Z. (Greece), Markenskoff, X. (USA), Massabo, R. (Italy), Matczynski, M. (Poland), Matysiak, S. (Poland), Mayer, H.R. (Austria), McEvily, A. (USA), Michopoulos, J. (USA), Mines, R. (UK), Mitchell, M. (USA), Moscovic, R. (UK), Murakami, Y. (Japan), Needleman, A. (USA), Neimitz, A. (Poland), Neu, R. (USA), Nied, H. (USA), Nilsson, F. (Sweden), Nurse, A. (UK), Nykyforchyn, H. (Ukraine), Paipetis, S.A. (Greece), Panoskaltsis, V. (USA), Pantelakis, S. (Greece), Papadopoulos, G. (Greece), Papakaliatakis, G. (Greece), Pappalettere, C. (Italy), Patterson, E. (UK), Pavan, A. (Italy), Petit, J. (France), Pineau, A. (France), Pokluda, J. (Czech Republic),

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Organizing Committees

Pook, L. (UK), Prakash, V. (USA), Prassianakis, J. (Greece), Rajapakse, Y.D.S. (USA), Ravi-Chandar, K. (USA), Ravichandran, R. (USA), Rodopoulos, Chr. (UK), Rosakis, A. (USA), Rossmanith, H.P. (Austria), Saxena, A. (USA), Sciammarella, C. (Italy), Sedmak, S. (Republic of Serbia), Shah, S. (USA), Shukla, A. (USA), Soboyejo, W. (USA), Sotiropoulos, D. (Greece), Spyropoulos, C. (Greece), Stanzl-Tschegg, S. (Austria), Staszewski, W.J. (UK), Steen, M. (Netherlands), Subhash, G. (USA), Sumarac, D. (Republic of Serbia), Sun, C.T. (USA), Sutton, M. (USA), Tamuzs, V. (Latvia), Taylor, D. (Ireland), Theotokoglou, S. (Greece), toor, P. (USA), toth, L. (Hungary), Tsamasphyros, G. (Greece), Tvergaard, V. (Denmark), Unger, D. (USA), van Mier, J.G.M. (Switzerland), Vardoulakis, Y. (Greece), Vodenicharov, S. (Bulgaria), Wallin, K. (Finland), Wardle, G. (UK), Williams, J.G. (UK), Withers, P. (UK), Yates, J. R. (UK), Youtsos, A.G. (Netherlands), Zacharopoulos, D.A. (Greece).

LOCAL ORGANIZING COMMITTEE Emmanuel E. Gdoutos (Chairman) Z. Adamidou, P. Kalaitzidis, M.S. Konsta-Gdoutos, G. Papakaliatakis, S. Sailis, N. Tsiantoulas, D.A. Zacharopoulos

ECF16 TRACKS

B: TRACKS B1: Nanomaterials and Nanostructures 1T1. Fracture and Fatigue of Nanostuctured Materials 1T2. Failure Mechanisms 1T4. Fatigue and Fracture of MEMS and NEMS 1T7. Thin Films 1T9. Failure of Nanocomposites

B2: Engineering Materials and Structures 2T1. Physical Aspects of Fracture 2T2. Brittle Fracture 2T3. Ductile Fracture 2T4. Nonlinear Fracture Mechanics 2T5. Fatigue and Fracture 2T8. Polymers, Ceramics and Composites 2T11. Fracture Mechanics Analysis 2T13. Probabilistic Approaches to Fracture Mechanics 2T14. Computational Fracture Mechanics 2T15. Experimental Fracture Mechanics 2T16. Creep Fracture 2T17. Environment Assisted Fracture 2T18. Dynamic, High Strain Rate, or Impact Fracture 2T19. Damage Mechanics 2T21. Concrete and Rock 2T22. Sandwich Structures 2T23. Novel Testing and Evaluation Techniques 2T26. Structural Integrity 2T28. Mesofracture Mechanics 2T32. Micromechanisms in Fracture and Fatigue

ECF16 SPECIAL SYMPOSIA/SESSIONS

C: SPECIAL SYMPOSIA/SESSIONS C1: Nanomaterials and Nanostructures 1. Fracture and Fatigue at the Micro and Nano Scales (Organized by H.D. Espinosa and I.M.Daniel) 3. Nanoscale Deformation and Failure (Organized by M. Zhou) 29. Reliability and Failure Analysis of Electronics and Mechanical Systems (O.S. Lee) 31. Multiscaling in Molecular and Continuum Mechanics – Scaling in Time and Size from Macro to Nano (Organized by G.C. Sih) 34. Cracks in Micro- and Nanoelectronics (Organized by B. Michel) 43. Interfacial Fracture in Composites and Electronic Packaging Materials (Organized by C.T. Sun and T. Ikeda)

C2: Engineering Materials and Structures 4. Fracture and Fatigue of Elastomers (Organized by C. Bathias and E. Bayraktar) 5. Integrity of Dynamical Systems (Organized by K. Hedrih) 8. Modelling of Material Property Data and Fracture Mechanisms (Organized by R. Moskovic) 9. Micromechanisms in Fracture and Fatigue (Organized by J. Pukluda and R. Pippan) 12. Interface Fracture and Behavior of Joints (Organized by L. Banks-Sills) 13. Computational Fracture Mechanics (Organized by T. Belytschko and A. Gravouil) 14. Cohesive Models of Fracture (Organized by W. Brocks) 16. Environment Assisted Fracture (Organized by G. Gabetta, W. Dietzel and H. Nykyforchyn) 17. SIM, Philosophy, Instrumentation and Analysis (Organized by W. D. Dover) 18. Fracture of Biomaterials (Organized by J. tong) 19. Structural Integrity Assessment in Theory and Practice (Organized by S. Vodenitsarov and S. Sedmak) 20. Critical Distance Theories of Fracture (Organized by D. Taylor) 22. New Investigations on Very High Cycle Fatigue of Materials (Organized by H. Mayer and S. Stanzl-Tschegg) 23. Deformation and Fracture of Engineering Materials (Organized by C.T. Liu) 24. Materials Damage Prognosis and Life Cycle Engineering (Organized by R. P. Wei, G. Harlow, A. Ingraffea and J. Larsen) 25. Mixed-Mode Fracture (Organized by M. Gosz)

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ECF16

26. Fracture Mechanics Characterization of Wood (Organized by S. Stanzl-Tschegg) 28. Short Fatigue Crack Growth under Multi-axial Loading Conditions (Organized by Y. Murakami and A.J. McEvily) 30. Integrity of Gears (Organized by D. Jelaska) 33. Fracture and Failure of Natural Building Stones Applications in the Restoration of Ancient Monuments (Organized by S. Kourkoulis) 35. High Temperature and Thermomechanical Fatigue (Organized by R.W. Neu, S. Kalluri and H.J. Maier) 36. Impact Failure of Laminated and Sandwich Composite Structures (Organized by R. Mines) 37. Mesofracture and Transferability (Organized by G. Pluvinage) 38. Damage in Composites - Damage Development in Composite Materials & Structures - Models of Prediction (Organized by C. Galiotis) 39. Aging Aerostructures (Organized by S. Pantelakis) 40. Residual Stress and its Effects on Fatigue and Fracture (Organized by A.G. Youtsos and P.J. Withers) 41. Computational Modeling of Multiphysics Degrading Systems (CMMDS), (Organized by J. Michopoulos) 42. Scaling and Size Effects (Organized by Z.P. Bazant and M. Jirasek) 44. Multiple Cracking and Delamination (Organized by R. Goldstein and R. Massabo)

A. INVITED PAPERS

Invited Papers

3

DEFORMATION AND FRACTURE AT THE MICRON AND NANO SCALES E. C. Aifantis Laboratory of Mechanics and Materials, Polytechnic School, Aristotle University of Thessaloniki, 54124, Thessaloniki, Greece [email protected] The progressively increasing demands of new science and technology to understand the behavior of materials/components and processes at the micrometer and nanometer regimes has led in the mid seventies to the development of micromechanics. In the mid nineties a new term nanomechanics was used by the author to indicate the forthcoming excessive activity in this field and point out to the need for new constitutive equations and mechanics tools to be developed in relation to the emerging fields of nanotechnology. In fact, it was only a few years earlier, that the first carbon nanotubes were produced in Japan - a unique example for the use of elasticity theory at the nanoscale - and the first bulk nanopolycrystals were produced in Russia. At the same time the first experimental observations on deformation and fracture mechanisms of nanopolycrystalline thin films were reported by the author and his co-workers in US. It was reported, among other things, that plastic deformation at the nanoscale does not take place through lattice dislocation activity but through grain boundary processes including material rotation and mass diffusion. Moreover, fracture processes occur through nanovoid nucleation and coalescence. Some of these experimental observations were numerically verified a few years later through molecular dynamics (MD) multimillion atom simulations. A first attempt to develop constitutive equations for describing deformation and fracture at the nanoscale is outlined by the author and co-workers with two specific concepts being advanced: the use of a mixture argument for “bulk” and “grain boundary” states and the resort to non-locality for describing the state of stress and strain at the nanoscale. In very recent years, due to the most promising developments in nanosciences/nanotechnologies in conjunction with the rapidly evolved computational advances, coupled ab initio/atomistic/molecular dynamics/finite element calculations have been employed to simulate the mechanical response of matter at the nanoscale in thin film and bulk configurations within the so-called multiscale modeling approach. A variety of nano-objects, including multilayered films, nanocomposites, proteins, as well as other metal or non-metal and biological nanostructures are modeled within such multiscale modeling framework and new nano-testing procedures and nano-apparatuses have been developed to capture this response experimentally. HRTEM, STM, AFM, micro/nano tensile machines and micro/nano indenters are among some of the new experimental tools for probing the mechanical response of materials and structures at the micro/nano scale and designing MEMS/NEMS devices for a variety of electromechanical and biomedical applications. In an effort to have a general micro/nano mechanics framework as useful as the continuum mechanics model that has been employed so successfully for the understanding of the mechanical behavior at the macroscale and the design of macroscopic components and structures, a proposal will be presented by a straightforward extension/generalization of the macroscopic continuum model. This generalization is based on the concept of a micro/nano continuum which is capable of exchanging mass, momentum and energy with its bounding surface. While such a model has been suggested by the author more than twenty five years ago, it was not until recently that its implications to elasticity, plasticity, and other continuum theories of structural defects was fully explored. The two new basic ingredients of the model are: a) the appearance of deterministic higher order spatial and time derivatives in the governing equations of mechanical fields; and b)

E. C. Aifantis

4

the appearance of stochastic terms due to random effects associated with the nucleation and evolution of deformation events at the micron/nano scale regime. Several benchmark problems are considered to illustrate the applicability of the proposed framework, as follows: (i) Elimination of Singularities. Gradient elasticity models are shown to eliminate the strain and stress singularities form dislocation/disclination lines and crack tips. On the basis of these solutions new relations can be obtained for the strength, energy and interaction of defects in nanocrystals and new fracture criteria can be derived at the nanoscale. (ii) Internal Stress, Elastic Constants and Yield Strength: Size Effects. Gradient elasticity and gradient plasticity are shown to produce new formulas for the determination of internal stress and elastic moduli in micro/nano multilayers and micro/nano plates under bending. A modification of the well-known Stoney formula is an example. Also the dependence of the elastic modulus on the nanoplate thickness is another interesting example. In this connection, it is pointed out that the size dependence of yield strength of micro/nano columns and the dependence of Young’s modulus/ failure stress on nanotube diameter has also been documented. (iii) Micro/Nano Indentation. Various basic formulas that have been used for determining material properties at the macroscale during indentation are revisited by employing gradient elasticity/plasticity with or without stochastic terms. Displacement bursts, load-depth serrations, and size-dependent hardness are all phenomena that are often observed during micro/nano indentation and their proper interpretation can assist in the determination of deformation and fracture properties at these scales. (iv) Localization of Deformation and Multiple Shear Banding. The interesting features of deformation and fracture at the micro/nano scale are concerned with the determination of the critical grain sizes where a plasticity transition mechanism takes place. At the nanoscale (1-100 nm) the critical grain size determines the transition from grain rotation/sliding to massive dislocation motion, which often manifests itself by the appearance of an inverse Hall-Petch behavior. At the ultra-fine grain size regime (100-1000 nm) another plasticity mechanism that occurs is the so-called multiple shear banding which often manifests itself by the appearance of a perfectly plastic behavior in the corresponding stress-strain curve. These two plasticity mechanism transitions will be discussed within the proposed unified material micro/nano mechanics framework. In concluding, it will be pointed out why new techniques such as fractals, wavelets and timeseries are often necessary for capturing details and additional features of micro/nano deformation and fracture. Information on some of the above topics can be found in references [1]-[3] and articles quoted therein.

References 1.

Aifantis, E.C., In Recent Advances in Applied Mechanics (Honorary Volume for Academician A.N. Kounadis), edited by T. Katsikadelis, D.E. Beskos and E.E. Gdoutos, NTUA, Athens, 2000, 243-254.

2.

Aifantis, E.C., Mech. Mat., vol. 35, 259-280, 2003.

3.

Konstantopoulos, I., Tragoudaras, D., Mokios, G., Konstantinidis, A., Zaiser, M. and Aifantis, E.C., Research in Progress.

Invited Papers

5

STATISTICAL MECHANICS OF SAFETY FACTORS AND SIZE EFFECT IN QUASIBRITTLE FRACTURE Z. P. Bazant and S.-D. Pang McCormick Institute Professor and W.P. Murphy Professor of Civil Engineering and Materials Science, Northwestern University, Graduate Research Assistant [email protected] Throughout most of the 20th century, it was widely believed that the size effect on structural strength has a purely statistical origin, explained by extreme value statistics based on the weakest link model, and described by Weibull statistical theory of random strength. However, beginning with the first suggestions made already in the early 1970s, it gradually transpired that, in quasibrittle materials (i.e. heterogeneous brittle materials with a non-negligible fracture process zone), the mean size effect is essentially deterministic, stemming from energy release caused by stress redistribution in a structure prior to maximum load. The quasibrittle energetic scaling bridges three simple asymptotic power-law scalingsthose of linear elastic fracture mechanics, plasticity, and Weibull theory. Renormalization group transformation does not suffice to handle the transitional nature of this quasibrittle size effect, often spanning several orders of magnitude of size. As is now widely accepted, quasibrittle materials including concrete, rock, tough ceramics, sea ice, snow slabs and composites exhibit major size effects on the mean structural strength that are largely or totally deterministic in nature, being caused by stress redistribution and energy release associated with stable propagation of large fractures or with formation of large zones of distributed cracking. The lecture begins by reviewing the general asymptotic properties of size effect implied by the cohesive crack model or crack band model, and highlights the use of asymptotic matching techniques as a means of obtaining scale-bridging size effect laws representing a smooth transition between two power laws. Asymptotic matching is a range of diverse techniques widely used in fluid mechanics, but overlooked in solid mechanics. Presented is a method of asymptotic matching which is suitable for structural strength problems. The method is based on power series expansion of the governing equation written as a function of dimensionless variables. The key idea is to choose these variables in such a way that, at each asymptotic state, all of them vanish except one. Attention is then focused on the size effects observed in fiber-polymer composites failing either by tensile fracture or by propagation of compression kink bands with fiber micro-buckling. The size effects in polymeric foams and sandwich structures are also discussed. Nonlocal probabilistic analysis of the size effect on the statistical distribution of nominal strength of structures is outlined and discussed from the viewpoint of the extreme value statistics. Implications for the design of hulls, bulkheads, decks, masts and antenna covers for very large ships, and for the design of large load-bearing aircraft fuselage panels, are pointed out. The problem of estimating loads of extremely small failure probability, such as 10-7, required for design is investigated. Attention is focused on the type 1 size effect, occurring in structures failing at crack initiation, which is the only type for which material randomness affects not only the scatter but also the mean of nominal strength. It is shown that a reform of structural reliability concepts is necessary because of a strong effect of structure size (or brittleness) on failure probability in the far-out tail of the cumulative probability distribution function (cdf) of structural strength. The cdf is modeled by a chain of representative volume element (RVE) of the material, each of which is represented by a hierarchical hybrid series-parallel coupling model. Each micro-

Z. P. Bazant and S.-D. Pang

6

element of this model simulates one of the micro-bonds within the RVE. From MaxwellBoltzmann distribution of thermal energies of atoms and the effect of applied stress on the activation energy, it is deduced that the left tail of cdf of a RVE (for failure probabilities < 0.0001 to 0.01) must be a power law, while there must be a broad Gaussian core because of parallel couplings within the RVE. The amplitude of the power law tail is obtained as a function of temperature and load duration. A chain-of-RVEs model is proposed to model a gradual transition of strength cdf from a mostly Gaussian pdf with a short Weibull tail for small structures to a purely Weibull cdf for very large structures. The equivalent number of RVEs for which the chain represents the cdf of strength of a structure with nonuniform stress field is expressed in terms of Weibull integral according to nonlocal Weibull theory. The center of the Weibull-Gaussian transition moves along the cdf from left to right as a function of the equivalent number Neq of RVEs in the chain-of-RVEs model. Matching of this model serves to calibrate a smooth analytical expression for the transitional cdf, varying from purely Gaussian for zero size (or zero brittleness) to purely Weibull for infinite size (or perfect brittleness) as a function of the structure size as well as geometry. The distance from the mean to a point of a tolerable failure probability such as 10-7 or 10-6 on this transitional cdf is shown to be strongly size and geometry dependent, and nearly doubles while passing from very small to very large structures. To capture this major effect, it is necessary to introduce a correction into Cornell's and Hasofer-Lind's reliability indices (known from the classical first-order reliability method, or FORM). To make reliability assessments realistic, it is further necessary that the 'covert' understrength factors implied in brittle failure provisions of concrete design codes be made overt, and that a 'covert' size effect implied by excessive load factor for self-weight acting alone be eliminated. Adaptation of the stochastic finite element method to cope with extreme value statistics of energetic-statistical size effect is described, and its importance is demonstrated by analysis of some famous disasters, particularly Malpasset Dam. To improve design safety and efficiency, experts in statistical reliability and fracture mechanics will need to collaborate to tackle these problems in a comprehensive manner To improve design safety and efficiency, experts in statistical reliability and fracture mechanics will need to collaborate to tackle these problems in a comprehensive manner

References 1.

Bažant, Z.P., "Scaling theory for quasibrittle structural failure." Proc., National Academy of Sciences, 101 (37), 13397-13399, 2004.

2.

Bažant, Z.P., Scaling of Structural Strength. Hermes Penton Science, London, 2002. (French translation, Hermes, Paris 2004); 2nd ed., Elsevier 2005, in press.

3.

Bažant, Z.P., "Probability distribution of energetic-statistical size effect in quasibrittle fracture." Probabilistic Engineering Mechanics, 19(4), 307-319, 2004.

Invited Papers

7

“NANORELIABILITY” – FRACTURE MECHANICS ON THE WAY FROM MICRO TO NANO B. Michel Fraunhofer Micro Materials Center at IZM Berlin Gustav-Meyer-Allee 25, D-13355 Berlin, Germany [email protected] “Thermo-mechanical compatibility” (TMC) of different micro- and nanomaterials in electronic and mechatronic systems is one mayor reason for troubles in the field of reliability and life-time of “high-tech” applications. Problems of thermal misfit (or mismatch) have become more and more important in the recent years because more than 60 percent of failure events in modern microelectronics are more or less directly connected with thermal misfit problems. The interface regions between the different materials, e.g. of a chip interconnection layer within a microsensor or a microactuator, is very important for the reliability of the component and of the whole system. Interface cracks, therefore, have to be dealt with in details in modern microsystem and nanotechnology as well. The author is going to present a survey on modern crack, fracture and reliability concepts of Microsystems in the chip interconnection region, where a lot of very different materials are “playing the concert”. Polymers, metals, ceramic materials and composites of very different kind will be shown to excert their specific influence on the local deformation and crack behaviour. Fatigue, creep and moisture effects and their complicated interactions have to be taken into account for reliable lifetime prognoses. The author presents some new experimental techniques based on modern digital image correlation techniques (DIC) which enable to take into account local and global effects as well. The so-called microDAC and nanoDAC deformation analyses provide very good means for local crack field analysis. These methods are combined with numerical field calculation and advanced reliability and lifetime concepts and lead to very good results for time-dependent failure analysis of Microsystems. In electronic packaging of MEMS and sensor components nanomechanics effects have been shown to become more and more important. The author presents recent results of his group to include focus ion beam technique (FIB), AFM analysis and advanced methods of materials testing (e.g. nanoindentation, nanoDMA, local stress and strain analysis) into the crack evaluation procedure in the micro-nano interface regions. Besides the above mentioned techniques the author also is going to outline his opinion about the perspectives of modern fracture mechanics in the field of micro- and nanotechnologies applied to the electronics, automotives and above all IT branches.

References 1.

Michel, B., Testing at Micro and Nanoscale, EuroSIME, European Conf. On Thermal, Mechanical and Multiphysics Simulation and Experiments in Microelectronics, Berlin, 18-20 April 2005.

2.

Michel, B., Keller, J., NanoDAC – A New Technique for Micro- and Nanomechanical Reliability Analysis of Lead-free Solder Interconnects, Int. Conf. on Lead-free Soldering, Toronto, Canada, 24-26 May 2005.

3.

Walter, H., Dudek, R., Michel, B., Fracture and Fatigue Behaviour of MEMS Related Micro Materials, Int. Conf. on Fracture (ICF 11), Turin, Italy, 20-25 March 2005.

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B. Michel

4.

Michel, B., Fracture Electronics and Thermo-Mechanical Compatibility (TMC) of Microcomponents in High-Tech Systems, Int. Conf. Micro Materials 2000, Berlin, 17-19 April 2000.

5.

Michel, B., Experimental Mechanics on the Way from Micro to Nano, Exp. Technique 29 (2005) 2, 3-5.

Invited Papers

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FRACTURE MECHANICS AND COMPLEXITY SCIENCES A. Carpinteri and S. Puzzi Politecnico di Torino, Department of Structural and Geotechnical Engineering Corso Duca degli Abruzzi 24, 10129 Torino, Italy [email protected] The so-called Complexity Sciences are a topic of fast growing interest inside the scientific community. Actually, researchers did not come to a definition of complexity, since it manifests itself in so many different ways [1]. This field itself is not a single discipline, but rather a heterogeneous amalgam of different techniques of mathematics and science. In fact, under the label of Complexity Sciences we comprehend a large variety of approaches: nonlinear dynamics, deterministic chaos theory, nonequilibrium thermodynamics, fractal geometry, intermediate asymptotics, complete and incomplete similarity, renormalization group theory, catastrophe theory, self-organized criticality, neural networks, cellular automata, fuzzy logic, etc. Complex systems lie somehow in between perfect order and complete randomness –the two extreme conditions that are likely to occur only very seldom in nature– and exhibit one or more common characteristics, such as: sensitivity to initial conditions, pattern formation, spontaneous self-organization, emergence of cooperation, hierarchical or multiscale structure, collective properties beyond those directly contained in the parts, scale effects. Aim of this paper is to provide an insight into the role of complexity in the field of Materials Science and Fracture Mechanics. The included examples will be concerned with the snap-back instabilities in the structural behaviour of composite structures (Carpinteri [2-3]), the occurrence of fractal patterns and self-similarity in material damage and deformation of heterogeneous materials, and the apparent scaling on the nominal mechanical properties of disordered materials (Carpinteri [4,5]). Further examples will deal with criticality in the acoustic emissions of damaged structures and with scaling in the time-to-failure (Carpinteri et al. [6]). Eventually, results on the transition towards chaos in the dynamics of cracked beams will be reported (Carpinteri and Pugno [7]).

References 1.

Garrido, M.S. and Vilela Mendes, R., Complexity in physics and technology, World Scientific, Singapore, 1992.

2.

Carpinteri, A., In Application of Fracture Mechanics to Cementitious Composites (Proceedings of a NATO Advanced Research Workshop, Evanston, USA, 1984), edited by S.P. Shah, Martinus Nijhoff Publishers, Dordrecht, 1985, 287-316.

3.

Carpinteri, A., J. Mech. Phys. Solids, vol. 37, 567-582, 1989.

4.

Carpinteri, A., Mech. Mater., vol. 18, 89-101, 1994.

5.

Carpinteri, A., Int. J. Solids Struct., vol. 31, 291-302, 1994.

6.

Carpinteri, A., Lacidogna, G. and Pugno, N., In Fracture Mechanics of Concrete and Concrete Structures (Proceedings of the 5th International FraMCoS Conference, Vail, Colorado, USA, 2004), edited by V.C. Li et al., 2004, vol. 1, 31-40.

7.

Carpinteri, A. and Pugno, N., J. Appl. Mech., in print.

Invited Papers

11

FAILURE OF COMPOSITE MATERIALS I. M. Daniel Robert R. McCormick School of Engineering and Applied Science Northwestern University, Evanston, IL 60208, USA [email protected] The failure of composites has been investigated extensively from the micromechanical and macromechanical points of view. On the micromechanical scale, failure mechanisms and processes vary widely with type of loading and are intimately related to the properties of the constituent phases, i. e., matrix, reinforcement, and interface-interphase. Failure predictions based on micromechanics, even when they are accurate with regard to failure initiation at critical points, are only approximate with regard to global failure of a lamina and failure progression to ultimate failure of a multi-directional laminate. For these reasons a macromechanical approach to failure analysis is preferred. Numerous failure theories have been proposed and are available to the composite structural designer[1].They are classified into three groups, limit or noninteractive theories (maximum stress, maximum strain); interactive theories (Tsai-Hill, Tsai-Wu); and partially interactive or failure mode based theories (Hashin-Rotem, Puck). The validity and applicability of a given theory depend on the convenience of application and agreement with experimental results. The plethora of theories is accompanied by a dearth of suitable and reliable experimental data, which makes the selection of one theory over another rather difficult. Considerable effort has been devoted recently to alleviate this difficulty. The problem can be divided in two parts, one being the prediction of failure of a single lamina and the second dealing with prediction of first-ply-failure and damage progression leading to ultimate failure of a multi-directional laminate. C. T. Sun [2] reviewed six failure theories and showed comparisons of theoretical predictions with experimental results for six different composite material systems and various loading conditions. A round robin exercise was initiated by Hinton, Soden, and Kaddour for the purpose of assessing the predictive capabilities of current failure theories [3]. The difficulty in evaluating failure theories is much greater in the case of a multidirectional laminate. The scope of the proposed laminate failure analysis comprises the following [1]: 1

A selected or adapted lamina failure theory for prediction of failure initiation, i.e., first-ply failure (FPF) in the laminate.

2

A failure mode discrimination rule and a scheme of ply discounting and failure progression in the laminate after FPF.

3

A criterion or definition of ultimate laminate failure (ULF).

In general, a wide variation has been observed in the prediction of laminate failures by the various theories. The divergence in the predictions is greater for FPF than for ULF; also is greater for matrix dominated failures than for fiber dominated ones. The divergence observed may be attributed primarily to the following factors: 1

The different ways in which curing residual stresses are introduced in the predictions, especially in the case of first-ply-failure.

2

The concept of in-situ behavior of a lamina within the laminate which is still debated.

3

The different methods of modeling the progressive failure process and the definition of ultimate laminate failure.

I. M. Daniel

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The nonlinear behavior of matrix-dominated laminates, e.g., angle-ply laminates.

Under uniaxial loading of a laminate the deciding factor in predicting ultimate failure is whether it is fiber or matrix dominated. In the case of matrix dominated angle-ply laminates, predictions by the limit or interactive theories are not usually in agreement with each other and with experimental results. Failure is governed by the lamina transverse normal stress V 2 and the in-plane shear stress W 6 . When V 2 ! 0 , as in the case of [r45]s and the limit theories predict higher strengths in agreement with the experiment [1]. When V 2  0 , as in the case of the [r20]2 s laminate under tension, the Tsai-Wu criterion comes closer to the experimental results [1]. In the more general cases of biaxial loading it is not easy to establish fiber or matrix dominance in failure as that varies with the loading biaxiality. In view of the multitude of failure theories, the divergence of their predictions and the lack of definitive general conclusions regarding their applicability, a practical approach is recommended as follows [1]: 1

Select a classical representative theory from each category, i.e., non-interactive (maximum stress), fully interactive (Tsai-Wu), and partly interactive (Hashin-Rotem).

2

Compute and plot stress-strain relations of the laminate under representative mechanical and hygrothermal loading.

3

Use a newly proposed failure mode discrimination rule and define ULF

4

Compute safety factors for FPF and ULF and compute and plot failure envelopes for the selected failure theories for the two failure levels (FPF and ULF).

5

Select prediction according to degree of conservatism desired. For the most conservative approach, limit the state of stress (loading) to within the common domain of the selected failure envelopes.

All computations and plots can be performed by a newly developed computer program [4]. The approach above is adequate for conservative structural design. More sophisticated theories and approaches exist as discussed before incorporating nonlinear behavior and in-situ effects.

References 1.

I.M. Daniel and O. Ishai, Engineering Mechanics of Composite Materials, Second Edition, Oxford University Press, 2005.

2.

C.T. Sun, “Strength Analysis of Unidirectional Composites and Laminates,” in Comprehensive Composite Materials, ed. by A. Kelly and C. Zweben, Ch. 1.20, Elsevier Science, Ltd., Oxford, UK, 2000.

3.

M.J. Hinton, P.D. Soden, and A.S. Kaddour, Failure Criteria in Fibre-Reinforced-Polymer Composites, Elsevier, Oxford, 2004.

4.

J.J. Luo and I.M. Daniel, “Webcomp: Stress and Failure Analysis of Laminate Composites,” http:www.composites.northwestern.edu/awebcomp, 2004.

Invited Papers

13

INTERACTIONS OF CONSTRAINED FLOW AND SIZE SCALE ON MECHANICAL BEHAVIOR W. W. Gerberich, W. M. Mook, M. J. Cordill and D. Hallman Chemical Engineering and Materials Science Department University of Minnesota 421 Washington Ave SE Minneapolis, MN 55455 [email protected] Coupled effects between constrained flow, increased strength as a function of decreased sample size, and resulting high stresses affect both modulus and fracture toughness. For submicron size crystalline spheres [1,2], boxes [3], and cubes [4], we have recently shown that dislocation by dislocation events can be followed using a combination of AFM/nanoindentation. This has led to at least three proposed strengthening mechanisms for hardening of small constrained volumes under compression[4]. With the increased stresses, this can produce increased moduli of elasticity in confined volumes small in three dimensions. With increased constrained plasticity this produces increased strength in volumes small in three, two or one dimensions. Hardening mechanisms for the gigapascal strengths observed in small volumes are addressed. These are explored for Si and Ti nanospheres as well as Ni, Co, and Ni80Fe20 (permalloy) thin films in the 10-40 nm particle radius or thin film thickness[4,5] regime. Because of trapped dislocations between the upper and lower loading surfaces being typically diamond or sapphire, strengths approaching theoretical are often reached with deformation of only tens of nanometers or less. Of course, this is highly dependent upon the length scale of the confining structure. For oxide-covered nanospheres, the length scale can be taken as the volume to contact surface area as given elsewhere[5] by (2/3)r3/a2 where r is the sphere radius and a is the contact radius at the upper and lower platen. Alternatively, from contact geometry this length scale is (2/3)r2/G. For deposited thin films, it was previously shown that a measured volume of plastic deformation to contact surface area was empirically given by Dh2/a where h is the film thickness and a is the contact radius[6]. These two measures of length scale show that the flow strength of the nanospheres and the hardness of the thin films scale with G1/2/r and G1/4/h, respectively. Here, G is the displacement the sphere has been squeezed or the penetration depth of the indenter into the film. It is significant that both of these show strength to be inversely proportional to the smallest dimension of the volume. Additionally, it is interesting that the more constrained nanosphere has strength increasing as G1/2 compared to film hardness, small in only one dimension, increasing as G1/4. With this same length scale approach we have shown that the fracture toughness of a delaminating thin film conforms to R-curve behavior with GR representing the resistance equivalent to the strain energy release rate at fracture. This has been given by[6] f R

G ~

DV ys2 h § ' b · E

¸¸ ¨¨ © bo ¹

1/ 2

(1)

where Vys/E is the strength to modulus ratio, 'b/bo is the incremental growth to initial crack size and D is a constant on the order of 10. In the present paper we use the same approach by equating

I. M. Daniel

14

the local deformation length scale to the fracture process zone length scale. This gives the fracture resistance for the sphere to be

G RS ~

6V ys2 r § t ox · 1 / 2 ¨ ¸ E ©G ¹

(2)

Here tox is the oxide film thickness on the sphere, and G is the vertical displacement the sphere has been squeezed to the point of fracture. Note that the triggering event is assumed to be a crack nucleated in the less robust oxide film around the sphere such that the defect size is tox. In both cases for Eqs. (1) and (2), the leading term is the strain energy density times the smallest dimension of the constrained volume. We also discuss relationships such as Eq. (2) in terms of the overall size dependence if Vys obeys a Hall-Petch type relation giving strength proportional to G1/2/r for the nanosphere. It is emphasized that this is an evolutionary length scale which decreases with increasing displacement, i.e., (2/3)r2/G. Incorporating the length scale dependence of yield strength actually gives Gg’ proportional to G1/2/r so that both strength and fracture resistance scale with G1/2/r for very small volumes. Due to the first term in the Hall-Petch relation dominating at very large volumes for both thicker films and larger spheres, this trend would be predicted to reverse. That is, at larger volumes one should find an increase in fracture resistance with scale according to Eqs. (1) and (2) as Vys becomes more nearly constant. Most of these relationships are still in their formative stages but have some corroboration with respect to Cu and Au film delamination studies. Regarding fracture experiments on nanospheres, we have only recently fractured a silicon particle in situ in the transmission electron microscope. However, this corroborates some previous indirect analysis using atomic force microscopy based nanoindentation to determine the fracture toughness of silicon nanospheres with radii in the range of 20 to 110 nm. In the full paper we will derive the above relationships and discuss increased strength and fracture resistance of constrained volumes under compression or pressure as having ramifications to friction, wear, and microelectromechanical systems.

REFERENCES 1.

Gerberich, W.W., Cordill, M.J., Mook, W.M., Moody, N.R., Perrey, C.R., Carter, C.B., Mukherjee, R., and Girshick, S.L., Acta Mater., vol. 53, 2215-2229, 2005.

2.

Gerberich, W.W., Jungk, J.M., Cordill, M.J., Mook, W.M., Boyce, B., Friedmann, T., Moody, N.R. and Yang, D., Intern. J. Fracture, 2005 (accepted).

3.

Mook, W.M., Jungk, J.M., Cordill, M.J., Moody, N.R., Sun, Y., Xia, Y., and Gerberich, W.W., Z. Metallkd., vol. 95, 416-424, 2004.

4.

Cordill, M.J., Chamber, M.M., Hallman, D., Lund, M., Perrey, C.R., Carter, C.B., Kortshagen, U. and Gerberich, W.W., “Plasticity Responses in Ultra-Small Confined Cubes and Films,” 2005 (in preparation).

5.

Gerberich. W.W., Mook. W.M., Perrey. C.R., Carter. C.B., Baskes. M.I., Mukherjee. R., Gidwani. A., Heberlein. J., McMurry. P.H. and Girshick. S.L., J. Mech. Phys. Solids, vol. 51, 979-992, 2003.

6.

Gerberich. W.W., Jungk, J.M., Li, M., Volinsky, A.A., Hoehn, J. W. and Yoder, K., Intern. J. Fracture vol. 119/120, 287-405, 2003.

Invited Papers

15

SPACE SHUTTLE COLUMBIA POST-ACCIDENT ANALYSIS AND INVESTIGATION S. McDanels NASA YA-F1 Kennedy Space Center, FL, 32899 USA [email protected] Although the loss of the Space Shuttle Columbia and its crew was tragic, the circumstances offered a unique opportunity to examine a multitude of components which had experienced one of the harshest environments ever encountered by engineered materials: a break up at a velocity in excess of Mach 18 and an altitude exceeding 200,000 feet (63 KM), resulting in a debris field 645 miles/1,038 KM long and 10 miles/16 KM wide. Various analytical tools were employed to ascertain the sequence of events leading to the disintegration of the Orbiter and to characterize the features of the debris. The testing and analyses all indicated that a breach in a left wing reinforced carbon/carbon composite leading edge panel was the access point for hot gasses generated during re-entry to penetrate the structure of the vehicle and compromise the integrity of the materials and components in that area of the Shuttle. The analytical and elemental testing utilized such techniques as X-Ray Diffraction (XRD), Energy Dispersive X-Ray (EDX) dot mapping, Electron Micro Probe Analysis (EMPA), and XRay Photoelectron Spectroscopy (XPS) to characterize the deposition of intermetallics adjacent to the suspected location of the plasma breach in the leading edge of the left wing, Fig.1.

FIGURE 1. Micrograph of a Left Wing Carrier Panel Slag Deposit. Cummings [1] Fractographic and metallographic analyses of several pieces of debris, Fig. 2, were performed to evaluate such fracture characteristics as broomstrawing and feathering of aluminum alloys, suspected stress-assisted grain boundary oxidation (SAGBO) of Inconel components, and intergranular high temperature fracture features observed on several A286 stainless steel spar fittings from the left wing structure of the Orbiter. Likewise, depositional characteristics such as composition, directionality and orientation, and the sequence and order of layering, were evaluated to assist in re-tracing the path of the plasma flow into the wing structure.

S. McDanels

16

FIGURE 2. Interior view of aluminum drag chute canister. Parker [2] The examination of the debris’ fracture surfaces, and of metallographically-prepared specimens harvested from the debris, was performed via scanning electron microscope. The resultant features and characteristics were compared to those of laboratory exemplars of similar base materials. The observed features, along with the results from the elemental analytical testing, helped the Space Shuttle Columbia accident investigation team reconstruct the mishap and determine the sequence of events which ultimately led to the loss of the vehicle. The debris from the Columbia accident now resides in the Vehicle Assembly Building (VAB) at the Kennedy Space Center. A portion of the debris is on display, while the majority is in storage in the VAB. A process is in place whereby universities and professional societies can request pieces of debris for educational and research purposes, Fig.3.

FIGURE 3. Debris sample loaned out for educational purposes.

References 1.

Cummings, V. J., XPS, Metallographic and SEM X-Ray elemental Dot Map Analysis of STS107 Debris Sample 24543-1, National Aeronautics and Space Administration, KSC-MSL2003-149, 2003.

2.

Parker, D. S., Optical and SEM/EDS Analysis of STS-107 Debris Sample 58693-1, National Aeronautics and Space Administration, KSC-MSL-2003-208, 2003.

Invited Papers

17

THE ROLE OF ADHESION AND FRACTURE ON THE PERFORMANCE OF NANOSTRUCTURED FILMS Neville Moody, Megan J. Cordill1, Marian S. Kennedy2, David P. Adams3, David F. Bahr2 and William W. Gerberich1 Sandia National Laboratories, Livermore, CA 94550 1University of Minnesota, Minneapolis, MN 55455 2Washington State University, Pullman, WA 99164 3Sandia National Laboratories, Albuquerque, NM 87185 [email protected] Nanostructured materials are the basis for emerging technologies, such as MEMS, NEMS, sensors, and flexible electronics, that will dominate near term advances in nanotechnology. These technologies are often based on devices containing layers of nanoscale polymer, ceramic and metallic films and stretchable interconnects creating surfaces and interfaces with properties and responses that differ dramatically from bulk counterparts. The differing properties can induce high interlaminar stresses that lead to wrinkling, delamination, and buckling in compression [1,2], and film fracture and decohesion in tension. [3] However, the relationships between composition, structure and properties, and especially adhesion and fracture, are not well-defined at the nanoscale. These relationships are critical to assuring performance and reliability of nanostructured materials and devices. They are also critical for building materials science based predictive models of structure and behavior. Gold films are of special interest in applications from MEMS mirrors to nanoscale interconnects. In these applications, the need to minimize stress effects requires deposition of very thin films. Figure 1 shows that the fracture energies for these films decrease to work of adhesion values as the films become very thin. [2] While these fracture energies are fully capable of forming plastic zones, there is no evidence of deformation or ductile fracture processes on the fracture surfaces. This strongly suggests that dislocations were not emitted from the crack tips during interfacial fracture. This is a concept supported by elastic strip and dislocation free zone models where the only requirement for fracture is for the energy release rate to attain the true work-ofadhesion. It also shows that adhesion controls performance and reliability of nanoscale films through its effect on fracture. The composition of gold-on-oxidized silicon can change markedly with increases in temperature from any post-deposition processing. The changes can be even more dramatic for films such as scandium, where strong reactions during deposition markedly alter composition, structure and functionality (Figure 2). For nanoscale films, any film-substrate interactions, or when using adhesion promoting interlayers, any film-film interactions lead to a complete change in film composition and properties. Understanding these interactions is therefore critical for assuring performance and reliability as there are no plastic energy dissipative processes to mitigate the effects of low adhesive energies. These interactions and their effect on adhesion and fracture are the focus of current work and of this presentation.

S. McDanels

18

Figure 1. (a) Steady state, *ss, and mode I, *I, fracture energies for thin gold films on sapphire. Gold-on-oxidized silicon values are superimposed for comparison. The shaded region corresponds to measured gold-on-sapphire work of adhesion values.

(a)

(b)

Figure 2. The composition of gold-on-oxidized silicon can change markedly with post-deposition processing as shown for (a) as deposited and (b) 300C/1hr annealed films.

References 1.

R. Huang, Z. Suo, Journal Applied Physics, 91, 1135, 2002.

2.

N. Moody, D. Adams, A. Mudd, M. Cordill, D. Bahr, Plasticity Effects on Interfacial Fracture of Thin Gold Films, Proceedings ICM9, Geneva, Switzerland 2003 (SAND2003-8146)

3.

T. Ye, Z. Suo, A. G. Evans, Int. J. Solids Structures, 29, 2639, 1992.

This work is supported by Sandia National Laboratories, a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Invited Papers

19

ASSESSMENT OF WELDMENT SPECIMENS CONTAINING RESIDUAL STRESS K. M. Nikbin Mechanical Engineering Department, Imperial College, Lonndon SW7 2BX., UK [email protected] Weldments in components are regions where failures are most likely to occur either by fast fracture, creep or fatigue. These regions could exhibit microstructural inhomogeneity as well as the presence of micro-cracks and residual stresses. Understanding their behaviour is of major source of interest for a range of industries. Creep and creep/fatigue crack growth models as well as residual defect assessment codes need reliable and verifiable material properties data and validated fracture mechanics parameters for use in their predictive methodologies. The research to develop an overall methodology for deriving acceptable data and validated parameters for life assessment analysis has been developing in Europe through a number of collaborative European projects. These have covered both parent as well as weld material of a range of alloys and conditions. Although there is substantial information and data on weld tests available, due to an absence of validated information the industrial community cannot easily use this information with confidence. The present standards, also, do not deal directly with testing of welded specimens and therefore. The Analysis of the results from these projects have been continuing and furthermore have been used to assist in the development of testing standards as well as life assessment codes of practice. As a result a VAMAS (Versailles Agreement for Materials And Standards) Round Robin weld testing programme has been initiated to address the issues of testing and analysis of weld related materials. The paper presents the methodology that will lead to recommendations for a code of practice (CoP) of welded materials. The overall aims are presented below;

Objectives The following are the objectives of the new programme which adds emphasis on both the Round Robin testing as well as the predictive modelling, and measuring of residual stresses in components. •

Undertake a review of the information available on cracking of weld specimens and components at high temperatures.

•

Partners to link this initiative to their own projects

•

Initiate a Round Robin testing programme of welded specimens within the TWA collaboration based on the available information from the review. The round robin will cover four different steels namely (347 weld, 316H stainless, P22, P91 and P92) steels which have been offered for testing by partners in UK, Germany and Japan.

•

The tests to be carried out will consist of mainly Compact Tension (CT) specimens of parent, weld, and x-weld crack growth tests. The testing and analysis will be performed on a Round Robin basis. Details will be set out at the kick-off meeting

•

FE Modelling of residual stresses and identifying the role of stress relaxation during the testing of the component at elevated temperatures.

•

Measurement of residual stresses in a number of CT crack growth tests before and after crack initiation using deep-hole drilling, neutron and X-ray diffraction of a number of tests

K. M. Nikbin

20

from the Round Robin. In addition collection of information on residual stress measurements from partners involved in other research in this field. •

Identify the appropriate fracture mechanics parameters and materials and weld conditions for different geometries, to cover the majority of cases for testing of weldments.

•

Provide recommendations on weld testing and analysis plus the effects of stress relaxation at high temperatures.

Pre-standardisation Needs At present there is excessive conservatism in treating weldments and residual stresses. Therefore it is envisaged that the results from this collaboration can be incorporated quickly into existing or planned standards so that •

Relevant existing standards such as ASTM E1457 and the industrial codes of practice such as R5, BS7910, ASME and API are likely to be improved as a result of this work.

•

The recommendations from the work will improve predictive methods in High Temperature Life Assessment procedures.

•

The range of industries using this will be the power, aerospace, chemical and the electrical industries

•

Collaboration and sharing of information with active standardisation committees such as ASTM, ‘ESIS TC11: HTMT Working Group On High Temperature Testing of Weldments' and the 'Net European Network: Network On Neutron Techniques Standardization For Structural Integrity'.

Deliverables •

Define the criteria and methodology for dealing with weldment testing and analysis.

•

Provide relevant crack growth data from available tests of specimens and feature tests and provide residual stress measurements and relaxation data from these tests.

•

Using the appropriate fracture mechanics parameters analyse the crack growth data and identify the effects of residual stresses.

•

Make recommendations of welded component testing and analysis in the draft Code of Practice for dealing with component creep crack growth testing and analysis of industrial feature specimens derived from the initial phase of VAMAS TWA 25.

•

Dissemination of results to the wider industrial audience and future implementation of results in an ISO document.

Invited Papers

21

MEMS: RECENT ADVANCES AND CURRENT CHALLENGES R. J. Pryputniewicz Worcester Polytechnic Institute, Mechanical Engineering Department / CHSLT-NEST [email protected] Recent advances in MEMS technology have led to development of a multitude of new devices. However applications of these devices are hampered by challenges posed by their integration and packaging (Wei et al., 2005). Current trend in micro/nanosystems is to produce ever smaller, lighter, and more capable devices at a lower cost than ever before. In addition, the finished products have to operate at very low power and in very adverse conditions while assuring durable and reliable performance (Pryputniewicz et al., 2001). Some of the new devices were developed to function at high rotational speeds, others to make accurate measurements of operating conditions of specific processes. Regardless of their application, the devices have to be packaged to facilitate their use. MEMS packaging, however, is application specific and, usually, has to be developed on a case by case basis (Pryputniewicz et al., 2006). To facilitate advances of MEMS, educational programs have been introduced addressing all aspects in their development (Pryputniewicz et al., 2003). This presentation will address various aspects in a development of MEMS including, but not limited to, design, analysis, fabrication, characterization, packaging, and testing. The presentation will be illustrated with selected examples, Figs 1 to 5.

R. J. Pryputniewicz

22

References 1.

Pryputniewicz, R. J., T. F. Marinis, D. S. Hanson, and C. Furlong, 2001, “New approach to development of MEMS packaging for inertial sensors,” Paper No. IMECE2001/MEMS22906, Am Soc. Mech. Eng., New York, NY.

2.

Pryputniewicz, R. J., E. Shepherd, J. J. Allen, and C. Furlong, 2003, “University – National Laboratory alliance for MEMS education,” Proc. 4th Internat. Symp. on MEMS and Nanotechnology (4th-ISMAN), Charlotte, NC, pp. 364-371.

3.

Pryputniewicz, R. J., T. F. Marinis, J. W. Soucy, P. Hefti, and A. R. Klempner, 2006, “A metal interposer for isolating MEMS devices from package stresses,” in press, Proc. EFC-16, Alexandoupolis, Greece.

4.

Wei, J., Wong, C. K., and Lee, L. C., 2005, “Wafer-level micro/nanosystems integration and packaging,” Proc. 6th Internat. Symp. on MEMS and Nanotechnology (6th-ISMAN),” pp. 1-12, Portland, OR.

Invited Papers

23

FRACTURE, AGING AND DISEASE IN BONE AND TEETH R. O. Ritchie and R. K. Nalla University of California, Berkeley Department of Materials Science and Engineering, Berkeley, CA 94720, USA [email protected] Biological materials comprising mineralized tissues, such as bone and dentin in teeth, have hierarchical structures with characteristic length scales ranging from nanometers to millimeters. In this presentation, in vitro fracture toughness and fatigue-crack propagation properties of dentin and human cortical bone are examined from a perspective of discerning how these properties depend upon such microstructural hierarchies. The motivation for this is that although there is substantial clinical interest in their fracture resistance, there is relatively little mechanistic information available on how bone and teeth derive their resistance to cracking and how this is affected by cyclic loads. Specifically, in vitro experiments are described that establish that the initiation of fracture is locally strain-controlled (Nalla et al. [1]) and that subsequent crack growth (characterized by resistance-curve behavior) is associated with a variety of extrinsic toughening (crack-tip shielding) mechanisms, most importantly crack bridging (from individual collagen fibrils and especially “uncracked ligaments”), macroscopic crack deflection and to a lesser extent diffuse microcracking (Fig. 1) (Kruzic et al. [2], Nalla et al. [3]).

FIGURE 1. Schematic illustrations of some of the toughening mechanisms possible in cortical bone: (a) crack deflection (by osteons), (b) crack bridging (by collagen fibers), (c) uncrackedligament bridging, and (d) constained microcracking. Quantitative estimates for the relative contributions of these mechanisms to the overall toughness are derived from simple micromechanical models [3]. In a manner not unlike ceramic materials, it is shown that such extrinsic mechanisms act to toughen bone by lessening the magnitude of stresses experienced at the tip of any cracks. Although macroscopic crack deflection along cement lines provides a principal source of toughening in the transverse orientation, crack bridging by intact regions in the crack wake (so-called uncracked ligaments) is the primary toughening mechanism in longitudinal orientations; such bridges act to sustain load that would otherwise be used to propagate the crack. In vitro fatigue experiments that seek to examine time- or cycle-dependent crack-growth behavior, which pertain to stress fractures in bone, are also described [4].

R. O. Ritchie and R. K. Nalla

24

Finally, we show that the role of biological aging, which causes a marked deterioration in the fracture toughness of bone (Fig. 2), can be attributed to an age-related deterioration in the potency of crack bridging [5], a phenomenon that we believe is associated with the role of excessive remodeling in increasing the density of secondary osteon structures. However, the mechanistic aspects of this age-related degradation in bone quality is additionally characterized at multiple dimensions, including molecular (using deep UV Raman spectroscopy), sub-micron (using picoforce atomic force microscopy) and tens of micron scale (using X-ray computed tomography). We attempt to discriminate between possible age-related changes in the constitutive properties of the hard tissue and age-related changes in its microstructure.

FIGURE 2. Resistance curves for stable in vitro crack extension in human cortical bone, showing the deterioration in both the crack-initiation and crack-growth fracture toughness with age from 30 to 99 years.

References 1.

Nalla, R.K., Kinney, J.H. and Ritchie, R.O., Nature Materials, vol. 2, 164-68, 2003.

2.

Kruzic, J.J, Nalla, R.K, Kinney, J.H. and Ritchie, R.O., Biomaterials, vol. 24, 5209-21, 2003.

3.

Nalla, R.K., Stölken, J.S., Kinney, J.H. and Ritchie, R.O., Journal of Biomechanics, vol. 38, 1517-25, 2005.

4.

Nalla, R.K., Kruzic, J.J., Kinney, J.H. and Ritchie, R.O., Biomaterials, vol. 26, 2183-95, 2005.

5.

Nalla, R.K., Kruzic, J.J., Kinney, J.H. and Ritchie, R.O., Bone, vol. 35, 1240-46, 2004.

Invited Papers

25

LABORATORY EARTHQUAKES A. J. Rosakis, K. Xia1 and H. Kanamori2 Graduate Aeronautical Laboratories 1Graduate Aeronautical Laboratories and Seismological Laboratory 2Seismological Laboratory California Institute of Technology, Pasadena, CA [email protected] The goal of the present study is to create model laboratory experiments mimicking the dynamic shear rupture process. We hope to use such experiments to observe new physical phenomena and to create benchmark comparisons with existing analysis and numerics. The experiments use highspeed photography, photoelasticity, and infrared thermography as diagnostics. The fault systems are simulated using two photoelastic plates (Homalite) held together by friction. The far field tectonic loading is simulated by pre-compression and the triggering of dynamic rupture (nucleation) is achieved by an exploding wire technique. The fault forms an acute angle with the compression axis to provide the shear driving force necessary for continued rupturing. Earthquake dynamics and, in particular, the mechanics of dynamic shear rupture are two relatively under-investigated sub-fields of seismology. Most efforts to date have focused on analytical studies (Rice 2001) and on the numerical modeling of dynamic rupture processes using finite element, finite difference, and boundary element methods (e.g., Ben-Zion and Andrews, 1997). As clearly elucidated by Rice (2001), the nature and stability of the predicted process depends very strongly on the choice of frictional laws employed in the modeling and, as a result, validation of the fidelity of such calculations becomes of primary importance.

FIGURE1. A homogeneous system composed of two frictionally held Homalite plates is shown. Purely subRayleigh (D=25°, P=7 MPa) (2A) and purely supershear (D=25°, P=15 MPa) (2B) rupture at the same time (28 Ps) after triggering. Our goals are to investigate the dependence the characteristics of rupturing, such as rupture speed, rupture mode on experimental conditions such as far-field biaxial compression, tilt angle of the fault to the compression axis, as well as on the frictional properties of the fault interface. (Fig. 1.) Results on both homogeneous and bimaterial interfaces are reported. For bimaterial interfaces, various combination of dissimilar materials, including Homalite/polycarbonate pairs, are chosen to

R. O. Ritchie and R. K. Nalla

26

mimic wave speed mismatch conditions that are reported to exist across mature, crustal faults (Xia, Rosakis, Kanamori and Rice 2005). In the present lecture we concentrate on the experimental observation of the phenomenon of, spontaneously unrelated, supershear rupture on the visualization of the mechanics of sub Rayleigh to supershear rupture transition in such frictionally held interfaces. The results suggest that under certain conditions supershear rupture propagation can be facilitated during large earthquakes (e.g. the 2001 central Kunlunshan earthquake in Tibet, (Lin, Fu, Guo, Zeng, Dang, He and Zhao 2002, Bouchon and Vallee 2002); the 2002 Denali earthquake in Alaska, (Ellsworth, Celebi, Evans, Jensen, Nyman and Spudich 2004).

References 1.

Rice, J. R., Lapusta, N., Ranjith, K., J. of the Mech. Phys. Solids, vol. 49 (9) 1865-1898, 2001.

2.

Andrews, D., Ben-Zion, Y. J. of Geophysical Research, vol. 102, 553, 1997.

3.

Xia, K. W., Rosakis, A. J., Kanamori, H., Science vol. 308, 681-684, 2005.

4.

Lin, A. M., Fu, B. H., Guo, J. M., Zeng, Q. L., Dang, G. M., He, W. G., and Zhao,Y., Science, 296 (5575), 2015-2017, 2002.

5.

Bouchon, N and Vallee, M, Science, vol. 301, 824-826, 2002.

6.

Ellsworth, W. L., M. Çelebi, J. R. Evans, E. G. Jensen, D.J. Nyman, P. Spudich, Eleventh Int’l Conference of Soil Dyn. and Earthquake Engineering, Berkeley, CA, 2004.

Invited Papers

27

A HISTORICAL RETROSPECTIVE OF THE BEGINNINGS OF BRITTLE FRACTURE MECHANICS - THE PERIOD 1907-1947 H. P. Rossmanith Institute of Mechanics and Mechatronics, Vienna University of Technology Wiedner Hauptstr. 8-10/325, A-1040 Vienna, Austria [email protected] This contribution presents a historical retrospective of the early years of brittle fracture mechanics. Looking back 99 years, the year 1907 is important for two reasons: 1

the German physicist Karl Wieghardt, a disciple of the famous physicist Arnold Sommerfeld derived the complete stress field around the tip of a crack and gave the correct order of the elastic crack tip singularity, and in solving the so-called Bach-Problem of fracturing of roller bearings, presented the first mixed-mode fracture criterion, and

2

the Father of Engineering Fracture Mechanics, George Rankin Irwin, was born in El Paso, Texas.

In the first part, this paper will highlight and detail the achievements in fracture mechanics by Karl Wieghardt which for a long time – and for various reasons - were completely unknown or disregarded by the fracture mechanics community at large. It will be shown that Wieghardt’s work anticipated later developments by nearly fifty years [Wieghardt 1907; Rossmanith 1995a,b]. The reasons for this neglect will be unveiled. The second part of the paper will shed light on the very beginnings and struggles for recognition of fracture mechanics at the time when the Griffith theory was extended to include small scale plasticity by Irwin and Orowan. The role of research at the Naval Research Laboratory, at North Carolina University at Chapel Hill, at several U.S. West Coast aircraft manufacturing plants, and at Lehigh University in the founding of engineering fracture mechanics will be outlined [Paris, P.C. 1995; Rossmanith 1997]. With the advent of a new generation of fracture mechanics researchers the author feels that the history of fracture mechanics is not a dead branch of a huge tree but should be brought to the attention of the young academics and professionals, and those who are interested [Cotterell B. 2002]. In fact, the future will only be mastered by looking at and understanding the past.

References 1.

Cotterell, B. (2002) The Past, Present, and Future of Fracture Mechanics. Engineering Fracture Mechanics 69:533-553.

2.

Paris, P.C. (1995) Reflections on Progress in Fracture Mechanics Research. ASTM STP 1207:5-17.

3.

Rossmanith, H.-P. (1995) An introduction to K. Wieghardt’s historical paper on splitting and cracking of elastic bodies. Fatigue Fract Engng Mater Struct 12: 1367-69.

4.

Rossmanith, H.-P. (1997) G.R. Irwin – The Father of Fracture Mechanics: A Biographical Sketch. In: Fracture Research in Retrospect. An Anniversary Volume in Honour of G.R.Irwin’s 90th Birthday. 3-36, A.A. Balkem, Rotterdam.

28

H. P. Rossmanith

5.

Rossmanith, H.-P. (1997) The Struggle for Recognition of Engineering Fracture Mechanics. In: Fracture Research in Retrospect. An Anniversary Volume in Honour of G.R.Irwin’s 90th Birthday. 37-94, A.A. Balkem, Rotterdam.

6.

Wieghardt, K. (1907) Ueber das Spalten und Zerreissen elastischer Koerper. Z. Mathematik und Physik 55:60-103; Translation Rossmanith H.P. On splitting and cracking of elastic bodies. Fatigue Fract Engng Mater Struct 1995, 12: 1371-1405.

Invited Papers

29

DYNAMIC CRACK PROPAGATION IN PARTICLE REINFORCED NANOCOMPOSITES AND GRADED MATERIALS A. Shukla Dynamic Photomechanics Lab, Department of Mechanical Engineering University of Rhode Island, Kingston, RI 02881, USA [email protected] An experimental investigation has been conducted to evaluate the mechanical properties of novel materials fabricated using nano and micron sized particles in polymer matrix. Experiments were also conducted to investigate the dynamic crack propagation in theses particle reinforced materials. High-speed digital imaging was employed along with dynamic photoelasticity to obtain real time, full-field quantification of the dynamic fracture process. Birefringent coatings were used to conduct the photoelastic study due to the opaqueness of these materials [1].

Unsaturated polyester resin specimens embedded with small loadings of 36 nm average diameter TiO2 particles were fabricated using a direct ultrasonification method to study the effects of nanosized particles on nanocomposite bulk mechanical properties [2]. The ultrasonification method employed produced nanocomposites with excellent particle dispersion as verified by TEM. The presence of the particles had the greatest effect on fracture toughness. Both static and dynamic fracture toughness showed marked improvements with addition of small volume fractions (up to 1%)of nano particles. Dynamic fracture experiments were conducted with various specimen geometries to study the complete history of dynamic crack propagation from initiation to crack branching. Results from several of these experiments were compiled in order to establish a relationship between dynamic stress intensity factor, KI, and crack tip velocity, a , and the behavior of the nanocomposites is compared with that of the virgin polyester matrix. This relationship is shown in Fig. 1. The specimens used in this study and the nano- particle distribution is also shown in the figure. Crack arrest toughness increased by 64% in the nanocomposite relative to the virgin polyester. Also, Crack propagation velocities in nanocomposites were found to be 50% greater than those in the virgin polyester A detailed analytical and experimental investigation has also been conducted to understand the behavior of a rapidly moving crack-tip in functionally graded materials (FGMs). First, an

A. Shukla

30

elastodynamic solution for a crack propagating at an angle from the direction of property variation in an FGM is developed. Subsequently, the elastic stress, strain and displacement fields around the crack-tip are obtained. This is followed by a comprehensive series of experiments to get more insight into the behavior of propagating cracks in FGMs. The full-field stress data around the propagating crack was analyzed using the stress field expansions developed in the first part of this study. Dynamic fracture experiments were also conducted to study the behavior of a crack moving at an arbitrary angle from the direction of property variation. It was found that when crack propagation is inclined from the direction of property variation, crack-tip experience mixed mode loading even if the far field loading is pure opening mode. Also, dynamic fracture experiments were performed with different specimen geometries (modified compact tension and singe edge notch tension) to develop a dynamic constitutive fracture relationship between the mode I dynamic stress intensity factor (KID) and crack-tip velocity ( a ) for FGMs with crack moving in increasing fracture toughness direction. This relationship is shown in Fig. 2.

The transient nature of crack growth in FGMs has also been investigated both analytically and experimentally. It was concluded that not including the transient higher order terms in the analysis of highly transient crack propagation experiments might give rise to high errors.

References 1.

Der, V. K. and Barker, D. B., Mech. Res. Comm., vol. 5, 313-318, 1978.

2.

Evora, V. F., Jain, N. and Shukla, A., Exp. Mech., vol. 45, 153-159, 2005.

Invited Papers

31

SPATIAL AND TEMPORAL SCALING AFFECTED BY SYSTEM INHOMOGENEITY: ATOMIC, MICROSCOPIC AND MACROSCOPIC. G. C. Sih School of Mechanical Engineering, East China University of Science and Technology, Shanghai 200237, China Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem PA 18015, USA [email protected] Fax: +86 (21) 6425-3500 The impetus of nanotechnology has shed light on the direction of new research for many fields and continuum mechanics is no exception. The current trend is to reach down the scale such that all disciplines would meet and benefit from one another. However, there are overwhelming difficulties associated with the discontinuities of results from the various scales. The prevailing gaps in materials and continuum theories are being referred to “Mesomechanics” [1]. Mesoelectronics has in fact discovered that the heat transfer behavior of small bodies is dinstinctly different and requires fundamental studies of electronics at the subatomic scale. New physical laws may have to be discovered to fill in the gaps. The final answer lies in multiscaling [2,3] where the results at the smaller scales must be translated to the macroscopic level. Modeling of multiscale material damage theories raises several basic issues. To begin with, conditions must be invoked to connect the results observed at the different temporal and spatial scales. Up to now, discussions seem to be confined to a very narrow range of size and time. Furthermore, the models seldom address the effect of the initial or residual state as differentiated from the performance sate. The former becomes increasingly more important as the size of device is reduced to sub-microns. This is the rule rather than the exceptions in microelectronics. It is in this nanoelectronics region that the electron transport behavior does not strictly obey quantum mechanics nor classical physics. It has been referred to as the mesoscopic electronics region, particularly with reference to power dissipation. Micro-chips should be kept sufficiently cool so that they will operate in a stable manner. And yet the density of the transistors must also be high and closely packed. The optimum balance can be achieved only by knowing the limits of how effectively a very small device can dissipate heat. At the mesoscopic scale, the non-equilibrium isoenergy density approach [4] can be applied. It has solved many problems with mesoscopic phenomena [5]. The non-equilibrium theory [4] stresses in particular the power dissipation that is derived directly by considering the mutual interaction of mechanical and thermal effects without invoking artificial dissipation laws and/or constitutive relations. The dissipation has been shown to depend sensitively on the temporal and spatial characters of the local deformation. Under extension, a cooling period has been observed [5] that precedes heating for solid, liquid and gas. This fundamental feature is not considered in classical physics. It can be very important for the design of microchips in electronics. The objective of this work is directed towards the development of physical models that can relate results at different scale ranges with account for change of system homogeneity as the region of interest is reduced in size. A corresponding increase in the time scale follows automatically. In order to preserve the use of equilibrium mechanics in the ranges referred to as atomic, microscopic and macroscopic, attention will be focused in the region where damage is concentrated in the form of a singularity for the stress and energy density fields. The displacement field is required to remain finite and continuous even though its cyclic value may become multi-valued. Cross scale transition is made possible by imposing scale invariant criterion based on the “force” and/or “energy” quantities.

G. C. Sih

32

The singularity representation approach [6] will be applied to illustrate how disorders in the system at the microscopic and atomic scales can interact. The former and latter will be associated, respectively, with micro-cracking and dislocations. Non-linear equation are solved for the coupling of the micro-energy and dislocation-energy designated by Wmicro and W disln in normalized form, respectively. They will be used to derive the length of inhomogeneity for the system.The formulation entails several orders of magnitude extending from 10-11 to 10-1 cm on the lineal scale. Examples will be presented for short time and long time effects where the Lower scale chemical effects can have significant higher scale mechanical effects. They correspond to the problems of solid rocket propellant explosionsand the stress corrosion of low alloy metals in high temperature environment such as the nuclear reactors.

References 1.

Prospects of Mesomechanics in the 21st Century: Current Thinking on Treatment of Multiscale Mechanics Problems, in: G. C. Sih and V. E. Panin, J. of Theoretical and Applied Fracture Mechanics, 37(1-3)(2001) 1-410.

2.

G. C. Sih and X. S. Tang, Dual scaling damage model associated with weak singularity for macroscopic crack possessing a micro/mesoscopic notch tip, J. of Theoretical and Applied Fracture Mechanics, 42(1) (2004) 1-24.

3.

G. C. Sih and X. S. Tang, Simultaneity of multiscaling for macro-meso-micro damage model represented by strong singularities, J. of Theoretical and Applied Fracture Mechanics, 42(3) (2004) 199-225.

4.

G. C. Sih, Thermomechanics of solids: nonequilibrium and irreversibility, J. of Theoretical and Applied Fracture Mechanics, 9(3) (1988) 175-198.

5.

G. C. Sih, Some basic problems in nonequilibrium thermomechanics, in: S. Sienietyez and P. Salamon, (eds.), Flow, Diffusion and Rate Processes, Taylor and Francis, New York, (1992)

218-247. 6.

G. C. Sih and X. S. Tang, Singularity representation of multiscale damage due to inhomogeneity with mesomechanics consideration, G. C. Sih, T. Kermanidis and Sp. Pantelakis, eds., Sarantidis Publications, Patras, Greece (2004) 1-15.

B. TRACKS

B1. Nanomaterials and Nanostructures

1T1. Fracture and fatigue of nanostuctured materials

35

CHANNELING EFFECT IN FRACTURE OF MATERIALS WITH NANOSTRUCTURED SURFACE LAYERS V. E. Panin and A. V. Panin Institute of Strength Physics and Materials Science, SB RAS 2/1, Academichesky pr., Tomsk, 634021, Russia [email protected] 1

The “chessboard” distribution of normal and tangential tensile and compressive stresses on the “nanostructured surface layer – substrate” interface is revealed for metal materials (Fig. 1).

FIGURE 1. The “chessboard” model of the conjugation between nanostructured surface layer and substrate (“+” – compressive stress, “-” – tensile stress) and channeling propagation of localized shear. 2

A stochastic two-level model of the chessboard stress distribution on the interface is worked out. The simulation results correlate well with appropriate experimental data.

3

In tension of metal materials with nanostructured surface layers one can observe the effects of strain channeling in the nanostructured surface layer and fracture of the specimen as a whole. This is related to shear localization and subsequent propagation of the main crack along “chessboard squares” with normal tensile stresses (Fig. 2).

4

On the stage of uniform specimen elongation in the nanostructured surface layer localized deformation bands evolve in the conjugate directions of maximum tangential stresses

W max. On the prefracture stage a localized deformation macroband in the form of an extended neck propagates in the conjugate W max directions zigzagging along the whole specimen length. On the stage of localized neck formation one can see the development of two macrobands self-consistent by the scheme of a dipole or a cross (Fig. 3). 5

We have measured experimentally the evolution of main plastic shear in localized deformation macrobands in the neck and rotational deformation modes associated with localized shears. With non-compensated rotational deformation modes, the main crack is generated in two localized deformation macrobands in the neck and then the specimen fails.

6

Methods of governing the channeling effects of plastic flow and fracture of the material with nanostructured surface layers are proposed.

36

V. E. Panin and A. V. Panin

FIGURE 2. Asymmetrical (a-d) and symmetrical (e-h) necking and fracture pattern of the tensile cold-rolled titanium specimen with the nanostructured surface layer: optical image (a,e); displacement-vector field (b,f); distribution of main plastic shear (c,g); fracture pattern (d,h); H = 17 %. u15.

FIGURE 3. Self-organization pattern of shears in interactions of macroscale localized-shear bands of the dipole (a) and cross configurations (b).

1T1. Fracture and fatigue of nanostuctured materials

37

ATOMISTICS AND CONFIGURATIONAL FORCES IN GRADIENT ELASTICITY P. Steinmann and E. C. Aifantis Chair of Applied Mechanics, University of Kaiserslautern, Dept. of Mechanical and Process Engineering, P.O. Box 3049, D-67653 Kaiserslautern, Germany Laboratory of Mechanics and Materials, Polytechnic School, Aristotle University of Thessaloniki, 54124, Thessaloniki, Greece [email protected] The term Gradient Elasticity was introduced in the early 1990’s by Aifantis and co-workers (e.g. Aifantis [1]) to denote a particular form of higher-order elasticity involving one extra phenomenological coefficient in addition to the usual elastic Lamé constants. It distinguished itself from an excessively large number of generalized elasticity and Cosserat type theories that were advanced in the 1960’s and 1970’s in the sense that the stress remains symmetric and that the extra gradient coefficient or internal length parameter involved may be directly related to the underlying microstructure and determined experimentally. The theory allows for the formulation of conveniently solvable boundary value problems by their reduction to inhomogeneous Helmholtz equation with the source term being the solution of corresponding boundary value problems of classical elasticity (e.g. Ru-Aifantis theorem [2]). It was shown (see also [3-6]) that the special form of gradient elasticity can lead, among other things, to the elimination of singularities from dislocation lines and crack tips. Motivated by this success, a large number of publications on wave propagation, cracks, dislocations and other inhomogeneities (e.g. [7-10] and references quoted therein) have been published recently based, more or less, on the special gradient elastic model introduced in [1]. The aforementioned special linearized gradient elasticity model of [1] was motivated by a simple gradient generalization of hyperelasticity theory elaborated upon by Triantafyllidis and Aifantis [11] in relation to the “loss of ellipticity” in the governing differential equations of nonlinear elasticity and the associated problem of localization of deformation. The gradient hyperelastic model discussed in [11] and its linearized counterpart discussed in [1] are revisited here in view of recent results obtained by Steinmann and co-workers (e.g. [12-14]) in relation to atomistic modeling and configurational forces. In relation to atomistic modeling, the Cauchy-Born rule is first extended to incorporate the second-order deformation gradient. In addition to the Lennard-Jones and Morse interatomic potentials a new interaction potential based on a Gaussian type nonlocal kernel of the form (1 ʌ ʌ m 3 ) e x p [ (  r m b ) 2 ] , where mb is an intrinsic length scale (b denotes as usual the Burger’s vector), will be used. Such nonlocal kernels can be used for the calibration of the gradient coefficient and for obtaining corresponding new expressions for the Peierls stress. The coupling between the molecular dynamics and the finite element method, the so-called hybrid model, will be illustrated by considering the growth of a crack in two dimensions at the nanoscale. The difficulties associated with the correct treatment of the transition between the atomistic and the continuum regions and the role of higher-order gradients to settle the fundamental incompatibility between the nonlocal character of the atomistic description and the local character of the continuum description will be discussed.

Next, expressions are developed for the Peach-Koehler force and the force driving a crack in a gradient elastic solid (J-integral) for the special gradient elasticity model of [1]. The notion of null Lagrangeans and the boundary conditions are of relevance here and both topics will be addressed.

P. Steinmann and E. C. Aifantis

38

The special gradient elasticity model is presented as an example of the use of configurational mechanics to deal with problems of defects within a linearized theory of gradient elasticity and set up the stage for a general nonlinear treatment. Finally, a general framework of the spatial and material settings of geometrically nonlinear gradient hyperelasticity, allowing in particular for the consideration of material defects is presented. Continua which are described within this constitutive class are characterized for the spatial setting by a dependence of the stored energy density per unit volume undeformed configuration on the first and second gradient of the spatial motion. Based on this description the formulation of the corresponding material motion problem or rather of configurational mechanics is developed. The material setting is particularly suited to compute the so-called material motion problem, including the movement of material defects (dislocations, cracks, inclusions, phase boundaries, etc.) relative to the ambient material. We highlight the duality of the spatial and the material setting, in particular, the existence of a stored energy density per unit volume deformed configuration depending on the first and second gradient of the material motion (i.e. the inverse motion, deformation map); provide transition rules between them; and compare the results obtained to those derived for continua without higher-order gradients.

References 1.

Aifantis, E.C., Int. J. Engng. Sci., vol. 30, 1279-1299, 1992.

2.

Ru, C.Q. and Aifantis, E.C., Acta Mechanica, vol. 101, 59-68, 1993.

3.

Altan, B.S. and Aifantis, E.C., J. Mechan. Behav. Mats., vol. 8, 231-282, 1997.

4.

Aifantis, E.C., J. Eng. Mater. Techn., vol. 121, 189-202, 1999.

5.

Gutkin, M.Yu. and Aifantis, E.C., Scripta Mat., vol. 40, 559-566, 1999.

6.

Aifantis, E.C., Mech. Mat., vol. 35, 259-280, 2003.

7.

Georgiadis, H.G. and Vardoulakis, I. and Velgaki, E.G., J. Elasticity, vol. 74, 17-45, 2004.

8.

Georgiadis, H.G., J. Appl. Mech., vol. 70, 517-530, 2003.

9.

Lazar, M., Maugin, G.A. and Aifantis, E.C., Phys. Stat. Sol., vol. 242, 2365-2390, 2005.

10. Zhang, X. and Sharma, P., Int. J. Sol. Struct., vol. 42, 3833-3851, 2005. 11. Triantafyllidis, N. and Aifantis, E.C., J. Elasticity, vol. 16, 225-238,1986. 12. Sunyk, R. and Steinmann, P., Int. J. Sol. Struct., vol. 40, 6877-6896, 2003. 13. Steinmann, P. and Elizondo, A., RTN DEFINO Report No. 3, 2005. 14. Kirchner, N. and Steinmann, P., Phil. Mag., in press, 2006.

1T1. Fracture and fatigue of nanostuctured materials

39

TENSILE BEHAVIOR AND FRACTURE OF CARBON NANOTUBES CONTAINING STONE-WALES DEFECTS K. I. Tserpes and P. Papanikos Laboratory of Structural Mechanics, Department of Rural & Surveying Engineering, National Technical University of Athens Department of Product and Systems Design Engineering, University of the Aegean Zografou Campus, 9 Iroon Polytechniou St., 15780, Athens, Greece Ermoupolis, Syros, 84100, Greece [email protected], [email protected] The effectiveness of carbon nanotubes (CNTs) as reinforcements is designated by their mechanical behavior as stand alone units. One of the most commonly present topological defects, whose effect on the mechanical behavior of CNTs needs to be clarified, is the Stone-Wales (SW) defect. In this paper, the effect of SW defect on the tensile behavior and fracture of armchair, zigzag and chiral single-walled carbon nanotubes (SWCNTs) was investigated using an atomistic-based progressive fracture model (PFM). Following the concept of Li and Chou [1], CNTs are treated as space-frame structures by assuming that the C-C bonds act as load-carrying members and the carbon atoms as joints of the members. The PFM utilizes the FE model developed in Ref.[2] for analyzing the nanotube structure and the Morse interatomic potential, as modified by Belytschko et al. [3], for simulating the non-linear behavior of the C-C bonds. The FE models of the SWCNTs were created using the ANSYS FE code. For the modeling of the C-C bonds, the 3D elastic ANSYS BEAM4 beam element was used. The specific beam element, as all 3D beam elements of the ANSYS FE code, is linear elastic and does not have the ability to model non-linear behavior. This restriction is surpassed by the stepwise procedure of progressive fracture modeling. The nanotube is loaded by an incremental displacement at one of each ends with the other end fixed. At each load step, the stiffness of each beam element is redefined using its axial strain, as evaluated from the FE model, and the force-strain relationship of the modified Morse potential. Ôï optimize the accuracy of computational results, in each analysis, the number of load steps was chosen from convergence tests. Before using the PFM to accomplish the present study, its ability to accurately simulate the tensile behavior of defected SWCNTs was successfully verified through the comparison with the molecular dynamics simulations of Belytschko et al. [3]. The SW defect is the 90o rotation of a bond, which transforms 4 hexagons to 2 pentagons and 2 heptagons. The modeling of the defect is performed during the creation of the FE mesh of the nanotubes. Fig.1 displays the predicted stress-strain curves of the SWCNTs. In all cases, SW defects served as nucleation sites for fracture and their presence reduced the failure stress and failure strain of the nanotubes. The percentage reduction of failure stress and strain depends on the chirality of tubes. On the other hand, the nanotube stiffness was found to be unaffected. Fig.2 shows the evolution of fracture in the (12,12) SWCNT. Fracture initiated from the longitudinal bond connecting the two heptagons of the SW defect and propagated in the r45o direction. The fracture process was completed when all bonds around the circumference failed.

K. I. Tserpes and P. Papanikos

40

FIGURE 1. Predicted stress-strain curves of the SWCNTs.

FIGURE 2. Evolution of fracture in the (12,12) SWCNT containing a SW defect.

References 1.

Li, C. and Chou, T-W., International Journal of Solids & Structures, vol. 40, 2487-2499, 2003.

2.

Tserpes, K.I. and Papanikos, P., Composites Part B: Engineering, vol. 36(5), 468-477, 2005.

3.

Belytschko, T., Xiao, S.P., Schatz, G.C. and Ruoff, R.S., Physical Review B, vol. 65, 235430, 2002.

1T1. Fracture and fatigue of nanostuctured materials

41

ATOMIC-SCALE INVESTIGATION ON FRACTURE TOUGHNESS IN NANOCOMPOSITE SILICON CARBIDE M. Ippolito, A. Mattoni, L. Colombo and F. Cleri1 INFM-SLACS Sardinian LAboratory for Computational materials Science and Department of Physics, University of Cagliari, Cittadella Universitaria, I-09042 Monserrato (Ca), Italy 1 ENEA, Unita` Materiali e Nuove Tecnologie, and INFM Centro Ricerche della Casaccia, CP 2400, I-00100 Roma, Italy [email protected] Ceramic materials are attractive for structural applications because of their low density, chemical inertness, high strenght, high hardness and high-temperature stability. However they have inherently low fracture toughness, so that plastic deformation in ceramics is found to be extremely limited. Ceramic matrix composites (CMC) have been therefore developed to overcome the intrinsic brittleness and lack of reliability of monolithic samples. CMC's consist of a ceramic matrix reinforced with inclusions, such as particles, whiskers or chopped fibers (fiber thoughening). Although the macroscopic toughening is the result of several complex microscopic process, such as the formation of subgrain boundaries and frontal process zone enhancement, the key issue is represented by the interaction between the tip of possible crack front and the fiber. In this work we present an atomistic investigation of the stress states of a crack inclusion pair in nano-composite -SiC. We show that atomistic simulations (AS) are a powerful tool to test the reliability of possible continuum approximations and moreover provide a predictive modelling of stress intensification phenomena in regions where the continuum models fail to offer a unique picture. Our simulations provide a rather general and simple constitutive equation, valid over a range of crack-inclusion elastic mismatch and for a wide range of relative distances. We consider two kind of coherent inclusion: carbon and silicon fibers. Because of the lattice mismatch with respect to the matrix, both the carbon and silicon inclusions induce stress which turns out to be, respectively, tensile or compressive. The interatomic forces are described by the Tersoff potential for Si-C systems [1] and the load is applied by means of the constant traction method[2]. We have compared our AS results [3] with two recent (and conflicting) continuum solutions: a first one by Li and Chen[4], based on Eshelby equivalent inclusion approach, and a second one by Helsing[5], showing that the available continuum models are not able to properly describe the stress intensification phenomena at arbitrary values of distance between the crack tip and the inclusion, and for different matrix-inclusion elastic mismatch. The atomistic results, instead, provide a simple law for the effective variation of the crack toughness, valid in both the silicon and carbon case, i.e. for very different matrix-inclusion mismatch, and provides a simple and robust constitute equation for stress intensification phenomena at any crack-inclusion distance in a ceramic composite.

References 1.

J. Tersoff, Phys. Rev. B, vol. 39, 5566, 1989.

2.

F. Cleri, Phys. Rev. B, vol. 65, 014107, 2002.

42

M. Ippolito et al.

3.

M. Ippolito, A. Mattoni, L. Colombo, F. Cleri, submitted for publication.

4.

Z. Li and Q. Chen, Int. J. Fracture, vol.118, 29, 2002.

5.

J. Helsing, Engng. Fracture Mech., vol.64, 245, 1999

1T1. Fracture and fatigue of nanostuctured materials

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MULTISCALE MODELING AND COMPUTER SIMULATION OF STRESSDEFORMATION RELATIONSHIPS IN NANOPARTICLE-REINFORCED COMPOSITE MATERIALS L. V. Bochkaryova, M. V. Kireitseu, G. R. Tomlinson1, V. Kompis2 and H. Altenbach3 National Academy of Sciences of Belarus, Lesnoe 19 – 62, Minsk 223052 1Rolls-Royce UTC and Dynamics Group, the University of Sheffield, UK 2Department of Mechanics, University of Zilina, Slovakia 3Faculty of Engineering Sciences, Martin-Luther-Universitet Halle-Wittenberg [email protected] A novel concept of nanoparticle vibration damping [1, 2] shows the effect that molecule-level mechanism can have on the damping and that nanoparticles/fibres/tubes-reinforced materials can provide enhanced strength and vibration damping properties. It is particularly worth noting that carbon nanotubes can act as a simple nanoscale spring where rheological modelling can play a significant role while understanding of mechanics of novel systems across the scale length. The mechanisms involved in such materials need to be understood and the relevance to strength/ damping identified. Additionally adequate modelling techniques for the next generation of vibration damping systems are technology gaps that need urgent consideration. The computational models simulating mechanical properties range many scales starting from nano-scale (Molec. Dynam.), investigating the atomic interaction of the nano-particles in a very reinforcing material alone and its interaction with the atoms of matrix [3, 4], up to the description of such composite in large structures with dimension of several meters. The mechanisms involved in such materials need to be understood and the relevance to damping identified. Our aim was to investigate and develop advanced computational FEM-based technique to estimate performance and mechanical/damping properties of nanoparticle/fiber-reinforced engineering materials and then, if successful, assemble them into viable engineering workbench. Carbon nanotube-reinforced structures are principally used at all phases of modeling and simulation. Thus we will form a bridge from the very basic research done by physicists and chemists to the practical applications by engineers. To achieve the objective we performed the development of characterization and modeling technique of the fundamental phenomena that describe relationships between structure and mechanical properties of the materials, formalize the set of structural mechanical approaches to build a bridge between macro and nanoscales. Carbon-nanotube-reinforced composite material was simulated via advanced finite element and meshfree codes, using a hollow shell representation of the individual nanotubes. It’s noted that the recently developed meshfree techniques for shells do not present undesirable membrane and shear locking phenomena, while these locking phenomena are inherent in the more commonly used finite element methods. Our computational approach is fundamentally equal simulation and modelling of materials with combined molecular dynamics (MD) and FEM technique, where an equivalency of each other is shown by mathematical analysis. This conclusion proves a joint application of MD and FEM principles in 2D/3D modeling of materials where stress-deformations are described in angle coordinates of sin and cos found through application of force field methodology and structural mechanic approach [3, 4]. A continuum model for deformation of material reinforced with nanoscale hard fibers/tubes has been developed. A model using the fast multi-pole method (FMM) is presented. The FMM

L. V. Bochkaryova et al.

44

uses the Taylor expansion of the integral equations describing the interaction of rigid inclusion with the closest neighbors and with the flexible matrix. The FMM models reduce drastically both computation time and storage requirements so that models, which were not possible to solve with present computational technique, are investigated. The method enables to solve the continuum containing up to millions of such inclusions in a computer by parallel algorithms. In conclusion, it is worth noting that for a realistic simulation of the stability behavior of the nanoparticle-reinforced material, the nonlinear intramolecular inter-actions between neighboring atoms have to be taken into account. In order to reduce computational costs, it is necessary to develop advanced homogenization technique so as to apply shell elements in the model. Comparing to the FEM, the new technique will introduce further reduction of both computer time and storage requirement. The results will potentially create fundamentals for investigation and development of 3-D reinforced composite structures with high nanoscale structures volume content, using nano-scale reinforcement architecture to reduce component mass and dimension. Although the process of verification and validation is somewhat circular, the entry point into this process is clearly through experiments that help determine the validity of theory and assumptions while also helping to quantify the state variables associated with the problem. It is, therefore, necessary that the Computational Materials approach must use experimental data to establish the range of performance of a material and to validate predicted behaviour. Even at the atomistic level, methods such as molecular dynamics require careful parameterization (fit) to empirical data. Therein, it gives a challenge to Computational Materials: validation of methods across the complete range of length and time scales. To achieve this validation requires advances in measurement sciences as well as advances in theory and models, coupled with integrated, interdisciplinary research. It is imperative that research laboratories maintain a focused effort to develop new programs that provide for the simultaneous growth of all the critical elements that are required for validation of multi-scale methods. Research work of Dr. Kireitseu has been supported by the Royal Society in the UK and WELCH scholarship administered through the Amer. Vac. Soc. / Int.-l Union for Vac. Sc., Tech. and Appl. in the US and Europe. Dr. Bochkareva is continuing her research work under EU INTAS 2005-2007 postdoctoral fellowship Ref. Nr 04-83-3067. It should be noted however that the views expressed here are those of the authors and not necessarily those of any institutions.

References 1.

Rivera J.L., McCabe C., and Cummings P.T. Nanoletters, Vol. 3, No. 8, 2003.

2.

Li J., Ye Q., A. Cassell, H. T. Ng, R. Stevens, J. Han, M. Meyyappan, Appl. Phys. Lett., Vol. 82 (No.15), 2003.

3.

Li C. and Chou T.W. Physical Review B Vol. 68, 2003.

4.

Kireitseu M., Hui D., Bochkareva L., Eremeev S. and Nedavniy I. In Proceedings of the 106th Annual American Ceramic Society Meeting & Exp., Symposium 17 - Innovative Processing and Synthesis of Ceramics, Glasses and Composites. - April 18-21, 2004, edited by G. Geiger. - Indianapolis, IN, USA, 250-264.

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THE MECHANICAL PARAMETERS OF NANOOBJECTS (THEORY AND EXPERIMENT) E. Ivanova, N. Morozov1 and B. Semenov1 Dep. of Teoretical Mechanics, St.-Petersburg State Polytechnical University, Politechnicheskaya str., 29, St.-Petersburg, Russia, 195251 1 Dep. of Elasticity theory, St.-Petersburg State University, Bibliotechnaya sq., 2, Staryi Petergof, St.-Petersburg, Russia, 198904 [email protected] Advances in high technologies, using nanometer-size structures, requires calculation of mechanical properties for the objects of the nanosize scale level. Majority of the theoretical mechanical models for nanoobjects is based on the macroscopic equations of theory of elasticity. However, a lot of researchers have noted inconsistency between the values of the elastic moduli obtained from micro- and macroexperiments. The presented paper is devoted to theoretical and experimental investigation of the influence of the scale effects on the bending stiffness of a nanocrystal, which is extended in one direction and has a limited number of atomic layers in another direction. It is theoretically shown that for small number of atomic layers the bending stiffness of the nano-crystal substantially depends on the number of layers and tends to its elasticity-theory value for large number of layers [1].

FIGURE 1. The problem of the experimental determination of elastic moduli of nanoscale objects is of present interest. The determination of the elastic moduli of thin macroscopic shells is usually based on experiments with plates. It is known that, when grown using certain techniques, nanoobjects are obtained only in the form of shells. Therefore, it is necessary to develop a method for determining the elastic moduli of nanoobjects on the basis of experiments with shells. Experimental determination of the bending stiffness of nanosize shells presents a serious problem, because for such widespread nanoobjects as nanotubes and fullerenes under arbitrary deformation, the material is subjected to both bending and tension. Therefore, all parameters (e.g., natural frequencies) that can be measured directly are complicated functions of both bending and tension stiffness. In recent years, together with nanotubes and fullerenes, nanoobjects of a more intricate configuration have been obtained [2–4]. Nanosize cylindrical helices [2] (see Fig. 1) are of particular interest in connection with the possible experimental determination of bending stiffness. This is due to the fact that in helical shells under arbitrary deformation, the material is mainly bent, so that the material tension effect can be neglected when interpreting experimental data; and the natural oscillation shapes of helical shells are much more easily observed than those of

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46

cylindrical shells associated with pure bending of the material. The latter statement is illustrated in Fig. 2, which presents the first four helical shell oscillation shapes. The analysis of helical shell dynamics may be a theoretical foundation for experimental testing of the applicability of the continuum theory to (a) the calculation of mechanical characteristics of nanoobjects and (b) the experimental determination of the bending stiffness of nanoshells [5].

FIGURE 2. Acoustical and optical methods of measuring of the eigenfrequencies of micro-objects are based on using homodyne laser vibrometers and adaptive photodetectors. Technique for vibration analysis of the laser vibrometer using adaptive photodetectors is based on the effect of non-steadystate photoelectromotive force. The technique enables efficient direct conversion of highfrequency phase modulation of speckle-like optical waves reflected from the vibrating object into output electrical signal with concomitant setting of the optimal operation point of the interferometer and suppression of amplitude laser noise. Methods of measuring of the eigenfrequencies of nano-objects are based on using atomic force microscope. Technique for vibration analysis is based on the effect of mechanical interaction of cantilever needle with nanoobject.

References 1.

Ivanova, E.A., Krivtsov, A.M., Morozov, N.F., Dokl. Phys. 47, 620. 2002.

2.

Golod, S.V., Prinz, V.Ya., Mashanov, V.I., Gutakovsky, A.K., Semicond. Sci. Technol. 16, 181. 2001.

3.

Vorob’ev, A.B., Prinz, V.Ya., Semicond. Sci. Technol. 17, 614. 2002.

4.

Prinz, V. Ya., Microelectron. Eng. 69 (2/4), 466. 2003.

5.

Ivanova, E.A., Morozov, N.F., Dokl. Phys. 50, 83. 2005.

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ADVANCED MANUFACTURING DESIGN CONCEPTS AND MODELLING TOOLS OF THE NEXT GENERATION NANOPARTICLE-REINFORCED DAMPING MATERIALS M. V. Kireitseu, G. R. Tomlinson1, R. A. Williams2 and V. Kompis3 National Academy of Sciences of Belarus, Lesnoe 19 – 62, Minsk 223052

1Rolls-Royce UTC and Dynamics Group, the University of Sheffield, UK 2Institute for Particle Science & Engineering, the University of Leeds, UK 3Department of Mechanics, University of Zilina, Slovakia [email protected] Vibrations and noise exist in almost every aspect of our life and are usually undesirable in engineering structures [1]. Vibrations are of concern in large structures such as aircraft either civil (airbus A 380) or military, as well as small structures such as electronics [2]. It is now accepted that nanotechnology can help solve vibration damping and high noise issues through the utilisation of nanomaterials (or media) that dissipate a substantial fraction of the vibration energy that they receive. The mechanisms involved in such materials need to be understood and the relevance to damping identified via both computational and experimental benchmarks. The main issue is the need to match applications to technologies/materials being developed [35]. Wide-ranging application of damping materials in real-life products is one of the best ways to ensure future development. Commercial utilisation of a damping technology depends from both technical performance and business environment for that. There must be a business support for extensive technology implementation during its life-cycle cost. This has often been seen to be a limiting factor in the utilisation of novel material/technology. In this situation, a broader understanding of the material and its potential application is of great benefit since a “secondary” feature can make the damping system more attractive than its predecessor. Major technical barriers also prevent greater use of damping nanoparticle-reinforced materials. These include sensitivity to temperature (particularly viscoelastic materials based on polymer matrix), ability to manufacture (nanoparticle is expensive to manufacture and disperse in a matrix), increased complexity of both nanoparticle damper and a whole damping system (affecting weight and size) as well as effort required to predict/model performance and to optimize a technology for a specific application. The current drive for increased efficiency and reduced cost of machinery, usually results in a requirement for mass to be minimised. To avoid vibration related problems therefore, considerable effort has to be expended to increase the stiffness or damping of the structure. In terms of development of materials to achieve these goals, damping has probably received the least attention. The focus in this paper is directed toward to the investigation into carbon-based nanoparticle/ fibre/tube-reinforced materials and coating systems and their dynamic/damping characterization. Computational work is concentrated on hierarchical multiscale modelling of damping behaviour as a function of frequency, amplitude and temperature. A computational model is formulated in terms of meso- and nanoscopic ideas of damping behavior and could provide an approach to predict vibration damping properties and optimize some manufacturing design concepts of those material systems so as to enable the efficient synthesis of these novel damping solutions. The novel concept of nanoparticle-based damping technology shows that a molecule-level mechanism can considerably enhance vibration damping and dynamic of aerospace components

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(fan blades) via enhanced energy dissipation because of large surface-to-volume aspects in nanoparticle-reinforced composite material, large damping energy sources for friction and slipstick motion at interfaces of matrix and nanoparticle. Thus carbon nanotube can act as a simple nanoscale damping spring in aerospace materials and is suggested for aerospace damping materials of the next generation. The materials offer the potential to further reduce the mass and dimension, increase performance, and reduce vibrations. As a result the nanoparticle/tube/fibre-reinforced composite material gains advanced damping properties compared with conventional materials reinforced through available technologies as well as other types of commercialized damping solutions. The damping properties of the material can be further enhanced by designing unique aerospace components based on personal manufacturer needs of either civil or military aircrafts. Personalized set of nanoparticles can be introduced into material matrix, for example, through the CVD-based technology combined with conventional particle technologies (thermal spraying, PVD, etc.). The principal conclusions are that by invoking the properties of nano-auxetics/nanostructures it is possible to control the wave/sound/vibration propagation in the material and enhance the energy dissipation that can assist in improving the inherent damping of materials, but an experimental/theoretical environment is required to apply it. Nanoparticles/tubes can be used as a reinforcement of a matrix to provide multi-functionality, and thus we need to create an environment (knowledge) to introduce nanomaterials widely in industry. Developed computational tools and workbench is important part of next generation aerospace design. Topics that could yield particular success for damping in the future include 1) Micro and nanoscaled damping materials where nanoparticle/tube/fibre reinforcement concept might give exceptional, temperature independent damping and negligible added weight; 2) Optimisation methods where structural mechanics/dynamics approaches could be combined with advanced numerical FEM modeling and statistical variation to estimate dispersion of nanoparticles in a matrix; and 3) Low-cost damping systems that is cheaper than current polymer-based coatings. The outcome of the research work is expected to have wide-ranging technical benefits with direct relevance to industry in areas of transportation (aerospace, automotive, rail) and civil infrastructure development, but the goal is aerospace turbine applications.

References 1.

Hollkamp J.J. and R. W. Gordon, Smart Mater. & Struct. Vol. 5(5), 1996.

2.

Chung T.R. Journal of Materials Science. vol. 36, 2001.

3.

Rivera J.L., McCabe C., and Cummings P.T. Nanoletters, Vol. 3, No. 8, 2003.

4.

Li J., Ye Q., A. Cassell, H. T. Ng, R. Stevens, J. Han, M. Meyyappan, Appl. Phys. Lett., Vol. 82 (No.15), 2003.

5.

Siegel R.W., Hu E., and Roco M.C. in Proceedings of WTEC Workshop, May 8-9, 1997 Workshop, Washington, DC, 1998.

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FRACTURE OF NANOSTRUCTURED IONOMER MEMBRANES Yue Zou, X. Huang and K. L. Reifsnider CT Global Fuel Cell Center University of Connecticut, Storrs, CT 06269 [email protected] Thin ionomer membranes showing nanostructure phase separation are widely used in low temperature fuel cells as electrolytes. Examples include perfluorinated sulfonic acid (PFSA) ionomers, better known as NafionTM produced by E. I. du Pont de Nemours and Company. Their electrochemical performance and mechanical strength properties are determined by their molecular morphology, which resembles water-filled hydrophilic micellae (4~5nm in size) dispersed in a hydrophobic matrix. Temperature and humidity are two major parameters in an internal fuel cell working environment, which have significant influence on this nanostructure and consequently influence the material properties. The transport properties of such ionomers have been extensively studied. In this paper, we will discuss fracture and strength of such membranes, as related to humidity and temperature. To understand fracture of the membrane, it is necessary to measure its strength and determine the failure mode(s) under all relevant conditions. Measuring strength at different humidity and temperatures for very thin membranes is difficult. A new method using optical strain measurement (even for submerged specimens) has recently been used in the authors’ laboratory. Some example data and fracture patterns are shown in figure 1.

FIGURE 1. Left, stress-strain response of Nafion 111 membrane under different status of hydration and temperatures; Right, fracture patterns for fully hydrated specimens in 25 ഒ, 65 ഒ and 80 ഒ (in (a), (b) and (c), respectively). The material tested was NafionTM NR111. The specimens were boiled in deionized (DI) H2O for 1 hour to fully hydrate them. With an increase of temperature, there is a significant increase of strain to break, but a decrease of stress to break, as shown in Figure 1. Although this material is ductile, the broken surfaces show a clean severance resembling those formed in brittle fractures. With an increase of water content, the yield behaviour becomes less distinct. It is believed these features are due to the evolution of the nanostructure as a function of temperature and humidity. The micro/nanostructual nature of these phenomena is very complex. We offer some hypotheses that qualitatively explain some of these changes. It is widely accepted that this kind of ionic material contains two immiscible phases, i.e., the hydrophobic fluorocarbon and the hydrophilic ionic phase, and that the ionic groups tend to

Yue Zou et al.

50

aggregate to form tightly packed regions as clusters with a size on the nanoscale [1]. It has been claimed by G. Gebel, that these clusters can vary from spherical structures to a rod-like (phaseinverted) structure [2] with increasing water content in the membrane. For a known hygrothermal history of the membrane, it is possible to determine the water content in a membrane by weight[3]; therefore, the structure can be then determined in principle. With a known structure, we can talk about strength and the failure mechanism of the membrane. For low water content, the membrane behaves like a typical tough thermoplastic material with a very distinct yielding point, which corresponds to the initiation of molecular chain movements over each other as the applied load reaches a critical point that balances out the resistance to chain movement due to entanglement and ionic “cross-linking” through cations. For high water content, we believe that the increase of water reduces the strength of ionic “cross-linking” as the separation distance of the polar groups is increased due to the swelling of the ionic clusters. As a result, chains sliding over each other may occur at relatively low load levels; hence we observe a “spreading out” of the yield point. When the temperature approaches the Tg, the semicrystalline hydrophobic backbone softens; as such we see a reduction of initial modulus and also an increase of failure strain. The large strain observed at high temperature may be due to the drawing out of the chains from the folded semi-crystalline phase. Fracture occurs when the accumulated strain energy propels the complete breaking of the primary bonds and the entanglement points. Models in the literature used to explain the behavior of elastomers attempt to express stressstrain in general and temperature effects in particular, but do not explain the mechanism of fracture. For ionomeric membranes, nanostructure variations caused by changes in material hydration play a major role. This paper will offer some interpretations of the data based on understandings of this behavior and interpretations using multiphysics concepts and representations.

Reference 1.

Gierke, T. D., Munn, G.E. and Wilson, F.G., J. Polym. Sci., Polym. Phys. ED 19, 1687-1704, 1981.

2.

Gebel, G., Polymer, vol. 41, 5829-5838, 2000.

3.

Choi, P. and Datta, R., J. Electrochem. Soc., 150 (12) E601-E607, 2003.

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DEFORMATION AND LIMIT STATES OF CARBON NANOTUBES UNDER COMPLEX LOADING A. V. Chentsov and R. V. Goldstein 117526 Russia, Moscow, Vernadskogo prosp. 101 k.1, RUSSIA [email protected] For real experiments with nanotubes the complex and precision equipment is required. Being an alternative method of research, the computer modelling allows to perform practically any experiments at a level of atoms. These problems are solved by the methods of molecular dynamics. All atoms of such model are in constant thermal motion and their interaction is described by a known potential. At the same time the combination of geometrical scales of the objects like a nanotube (the relation of length to radius is 100-1000, diameter to wall thickness - 15-150) allows to model the nanotube deformation by some models of continuous medium. The regularity of atomic structure of nanotubes enables us to replace the system of atoms with equivalent model of elastic isotropic truss (linear or nonlinear), and the truss system in macroscale by a continuous medium, passing to continuous model of a nanotube. The choice of model of either the continuous cylinder or a cylindrical shell depends on a solved problem. Just as at direct modelling of interatomic interactions in molecular dynamics, within the framework of the deformation description for a nanotube elastic truss model the energetic approach appears to be effective. From the computative point of view the truss model gives the big advantage of a time of calculation. Nanotubes possess an exclusive relationship length / radius. Tubes with such hexagonal cell will be exposed to small deformations of atomic bonds even at significant axial deformations and bends. Such assumption means, that as a potential of interatomic interaction it is sufficient to use harmonic potential. The harmonic potential corresponds to a potential strain energy of the elastic rod (spring) connecting a pair of interacting atoms. Then for any graphene plane it is possible to build the truss system equivalent to the atomic model at equal loading conditions. On the structures of nanometer scale, this approach has been suggested by G.M.Odegard [1]. Covalent interactions of atoms of molecular structure can be quantitatively described by using the methods of molecular dynamics. Forces of attraction and repulsion acting for each pair of atoms depend on relative atomic positions and are presented by the chosen forcefield. These forces give the contribution to full vibrational potential energy of molecular system which is equal to a strain energy of a macroscopic body of equivalent geometry. For nanotube modelling in most cases the only essential degrees of freedom are: tension, change of the angle, nonbonded interactions. Energy of torsion is small enough to be neglected. It only becomes essential in problems with the large bending deformations. Nonbonded interactions were taken into account at interaction of separate nanotubes and graphene planes. To proceed from discrete atomic model to truss, it is necessary to take into account all essential pairwise interactions in structure, and to replace with their equivalent truss. Thus, having covered the entire hexagonal plane by two types of rods, we shall receive model which will be strained just as discrete atoms in model of molecular dynamics.

A. V. Chentsov and R. V. Goldstein

52

For calculation of effective deformation characteristics of a nanotube model a condition is used, that the strain energy at specifically chosen uniaxial loading depends only on one characteristic of elasticity. Thus, to define the model property it is required to calculate only its potential energy in the strained state and its dimensions. By the results of numerical experiments it is possible to make a conclusion, that the Young's modulus of a graphene plane model on chirality has a weak dependence, and is approximately equal to experimental value for graphite. When nanotubes are used as strengthening filler in polymers, the many atoms of nanotubes interact with atoms of a polymeric matrix. These interactions can be covalent and Van-der-Waals [2]. The constructed truss model enables to estimate the influence of external interactions on elastic properties of a nanotube (nanofiber). By the results it is possible to make a conclusion, that at non-covalent interactions with participation of all atoms of a nanotube any significant loading transport onto a matrix does not occur [3]. Only by introduction of covalent interactions significant improvement of elastic properties of filler can be expected. Modelling of the form of loss of stability was performed. The case of an axial compression was investigated. The cases with the following boundary conditions were compared: the finite displacements on the top side of a model, nodal compressive forces. In both cases the bottom row of hexagons was fixed rigidly, the top flange was fixed in a plane, perpendicular to axis of a nanotube. With tubes rather thin and long the form of loss of stability is close to classical for compression of elastic rods. Shorter tubes showed behavior similar to a shell. From comparison of results of calculation of loss of stability on the basis of nanotube truss model with calculations by the theory of shells it follows, that with nanotube elongation the critical loading decreases. However, stability rises with decrease of radius of a tube. It means, that tubes of investigated diameters behave more likely as hollow shells, rather than as continuous rods.

References 1.

Odegard G.M., Gates T.S., Nicholson L.M., NASA Langley Research Center, Technical Memorandum NASA/TM-2002-211454, 2002.

2.

Goldstein R.V., Chentsov A.V., Institute for Problems in Mechanics, Russian Academy of Sciences. Preprint No. 739, 2003.

3.

Goldstein R.V., Chentsov A.V., Mechanics of Solids, N.4, 2004.

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INTERACTION OF DOMAIN WALLS WITH DEFECTS IN FERROELECTRIC MATERIALS D. Schrade, R. Mueller, D. Gross, T. Utschig1, V. Ya. Shur2, D. C. Lupascu1 Institute of Mechanics, TU Darmstadt, Hochschulstr. 1, D-64289 Darmstadt 1Institute of Material Science, TU Darmstadt, Petersenstr. 23, D-64287 Darmstadt 2Institute of Physics and Applied Mathematics, Ural State University, 620083 Ekatarinburg, Russia [email protected] Experimental studies suggest that domain wall movement in ferroelectric materials is strongly influenced by the presence of certain kinds of defects. The intention of this paper is to study this phenomenon using concepts of continuum mechanics to describe ferroelectric material behaviour. Closely following the concept introduced in Mueller et al. [1], a 180° domain wall is modelled as a singular surface across which a jump in the spontaneous polarization occurs. The domain wall can be thought of as an inhomogeneity which allows for the application of configurational or driving forces (cf. Gross et al. [2]), which can also be applied to crack problems. The material behaviour is characterized by linear coupled constitutive equations for the stress and the electric displacement. With the solution of the field equations for the mechanical and electric problem it is possible to calculate the driving force on a domain wall. Motivated by experiments [3], a linear relation between the domain wall velocity and the driving force on the domain wall is postulated. Using 2D finite element simulations, the influence of different kinds of defects on the kinetics of a domain wall in ferroelectric-ferroelastic gadolinium molybdate, Gd2(MoO4)3 (GMO), is studied. Fig. 1 shows a sketch of the model. Three types of defects are considered. The first one is a surface defect, reflecting an imperfect electrode. The second one is a hole in one side of a sample where the electrodes remain intact. The third type involves a polarization defect in one domain. For a single planar domain wall, the following fundamental results were found:

FIGURE 1. Model of a GMO sample containing 2 domains with electrodes attached at top and bottom providing an external field E. •

When approaching an electrode defect, the total driving force on a domain wall decreases significantly resulting in deceleration or even stopping of the domain wall.

•

If the domain wall enters the electrode defect region, it is trapped in the middle of the defect. Considerably higher external fields are necessary to move the domain wall out the

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54

defect region. This and the latter result are in agreement with experimental findings where a domain wall was stopped in front of an electrode defect and trapped inside it. •

A defect in form of a hole in one side at which the electrodes remain intact has little influence on a moving domain wall. Simulations and experiments show that a domain wall cannot be stopped at such a defect. A slight slow-down is predicted by simulation and observed in experiments.

•

For a polarization defect only numerical results are available. It was found that a domain wall can be slowed down and even stopped in front of such a defect. The effect on the domain wall is comparable to that of the electrode defect, however the domain wall is not trapped in the polarization defect.

References 1.

Mueller, R., Gross, D. and Lupascu, D.C., Comp. Mat. Sci., accepted for publication and in print, 2005

2.

Gross, D., Kolling, S., Mueller, R., Schmidt, I., Europ. J. Mechanics A, vol. 22, 669-692, 2003

3.

Flippen, R., J. Appl. Phys., vol. 46, 1068-1071, 1975

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MICROSTRUCTURE AND INTERNAL STRESSES IN CYCLICALLY DEFORMED AL AND CU SINGLE CRYSTALS M. E. Kassner Dept. of Aerospace and Mechanical Engineering, University of California 3650 McClintock OHE 430, Los Angeles, California 90089-1453 [email protected] The concept of "long range internal stresses" (LRIS) is often utilized to explain various aspects of the mechanical behavior of materials, including cyclic deformation and the Bauschinger effect. These internal stresses are usually associated with the heterogeneous dislocation microstructure (Straub et al. [1] and Tippelt et al. [2]). More specifically, it has long been suggested that longrange internal stresses (LRIS) develop with plastic deformation in metals and alloys in association with the development of a subgrain boundaries, cell walls, dipole bundles, etc. The evidence to support the existence of LRIS has included Bauschinger experiments, dislocation radii measurements, stress-dip tests and, especially, and more recently, asymmetry in x-ray diffraction line profiles (XRD LPA) in association with the “composite model.” Convergent beam electron diffraction, weak-beam dislocation dipole separation measurements and in-situ transmission electron microscopy were all performed by the author on cyclically deformed Al and Cu single crystals (Kassner et al. [3-5]). These provide insight into the mechanisms of cyclic plasticity but especially indicate an absence of measurable LRIS. More specifically, the dipole spacing measurements were performed by Kassner et al. [4,5], and indicated that the dipole spacing and statistical distribution of spacings were independent of the location in the heterogeneous substructure of cyclically deformed copper and aluminum single crystals. The dipole spacings were the same in the channel and the veins and the maximum dipole separations in both locations suggested that the stress to separate the dipoles was within a factor of about one or two of the applied stress in both channels and veins. Independent work by Tippelt et al. [6] on nickel also found dipole spacings that were independent of location. These experiments suggest an absence of LRIS. The extensive convergent beam electron diffraction measurements that were made on creep deformed aluminum and copper, and cyclically deformed copper, by Kassner and co-workers, showed that the lattice parameter was unchanged, at the equilibrium or stress-free value, within the interior of the subgrains/dipole-bundles and along (within a one-beam diameter) the subgrainboundaries/dipole-bundles. If LRIS were present, a measurable variation in lattice parameter between the interior of the subgrain, and near the subgrain boundary would be expected. It must be considered possible that residual stresses were once present, but relaxed to an undetectable level with sample thinning. In-situ, reversed deformation of pre-cyclically deformed aluminum single crystals was performed in the HVEM. These experiments allowed the imaging of dislocation motion during “forward” and “reversed” deformation. Screws were imaged shuttling back and forth in the channels, and their relaxation upon unloading was observed. However, no reversed motion or bowing of dislocations was evident with unloading. If long-range internal stresses were present, reversed motion of screws in the channels or reversed bowing of dipole bundle loops upon unloading would be expected. X-ray diffraction line profile analysis (XRD, LPA), specifically, the interpretation of asymmetry in strain broadened Bragg diffraction peaks, has been extensively used to support LRIS. A popular interpretation of asymmetry involves deconvoluting the asymmetric profile into

M. E. Kassner

56

two symmetric sub-profiles; one peak associated with elevated LRIS. This method follows from the composite model and is used as evidence for the existence of LRIS (e.g. Straub et al. [1]). However the author suggests that there is more than one reasonable explanation for x-ray line asymmetry, and that LRIS is not required for asymmetry to be present. Computer simulation of xray line profiles was undertaken by the author and co-workers in an attempt to determine what arrangements may lead to asymmetry. The technique calculates atomic positions based on elastic theory, then uses a kinematic scattering approximation in which reciprocal space intensities are calculated using the squared Fourier transform (structure factor) of the real space atomic arrangement. This technique was previously used successfully by Levine and Thomson [6]. In this study, diffraction from screw dislocation dipoles was simulated, in an attempt to test the analytical asymmetry predictions of Gaal [7]. These simulations were successful in replicating the behavior predicted by Gaal, as the x-ray line profile from the polarized dipole ensemble was asymmetric, and had a peak offset relative to the randomly polarized dipole ensemble. Other computer modelling of x-ray diffraction from dislocated crystals is being performed using standard and novel approaches, and these will be discussed.

References 1.

Straub, S., Blum, W., Maier, H.J., Ungar, T., Borbely, A. and Renner, H., Acta Mater., vol. 44, 4337-4350, 1996.

2.

Tippelt, B., Bretschneider, J. and Hahner, P., Phys. Stat. Sol. A, vol. 163, 11-26, 1997.

3.

Kassner, M.E., Wall, M.A., and Delos-Reyes, M.A., Metall. Mater. Trans. A, vol. 28, 595609, 1997.

4.

Kassner, M.E. and Wall, M.A., Metall. Mater. Trans. A, vol. 30, 777-779, 1999.

5.

Kassner, M.E., Perez-Prado, M.-T. and Vecchio, K.S., Mater. Sci. Eng. A, vols. 319-321, 730734, 2001.

6.

Levine, L. E. and Thomson, R., Acta Cryst. A, vol. 53, 590-602, 1997.

7.

Gaal, I., In Proceedings of the 5th International Riso Symposium on Metallurgy and Material Science, edited by N.H. Anderson et al., Roskilde, Denmark, 1984, 249-254.

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DETERMINATION OF EQUILIBRIUM CONFIGURATIONS OF ATOMIC LATTICES AT QUASISTATIC DEFORMATION S. N. Korobeynikov Lavrentyev Institute of Hydrodynamics, 630090, Novosibirsk, Russia [email protected] Currently many researches simulate both initiation and propagation of cracks in a solid at the atomic level making use of nanomechanics equations. There exist two commonly used approaches to mathematical simulation. The first approach uses equations of molecular dynamics for immediate simulation of initiation and propagation of cracks; the second one is based on solution of problems of atomic lattice quasi-static deformation under the assumption that atomic lattice buckling is a starter for initiation and growth of a crack. The present work is aimed at developing the second approach to simulation of fracture of atomic lattices. First solutions of problems of atomic lattice buckling were found by Novozhilov [1], Thompson and Shorrock [2], Kornev and Tikhomirov [3]. However, the analytical methods for solving the problems suggested by these authors cannot be applied for solving problems of deformation and buckling of atomic lattices in the general case. Numerical methods for solving general 2/D and 3/D problems of quasistatic deformation of atomic lattices have been developed in Korobeynikov [4], Dluzewski and Traczykowski [5], Korobeynikov [6]. In the typical case, the Cauchy problem is solved in the form K ( U ) U

R ,

U (0)

U 0,

(1)

where U is the displacement vector of atoms in a lattice, R is the vector of internal forces acting on lattice atoms, K is the symmetric tangential stiffness matrix of a lattice, a superimposed dot denotes derivative of the magnitude with respect to the monotonically increasing deformation parameter t . The matrix K is determined by summing tangential stiffness matrices of all atomic pairs in the lattice. System (1) is solved by step-by-step integration with iteration refinement of solution for each discrete value of the parameter t . Atomic lattice buckling takes place when singular points on the integral curve are attained, i.e., at the points of the matrix K degeneracy:

det K

0.

(2)

Singular points can be turning points or bifurcation points as well as turning and bifurcation points simultaneously. At the bifurcation points there exist several continuations (branches) of solutions. In the vicinity of singular points, the arc-length method of step-by-step integration of equations (1) is most appropriate. In this case, the solution process continues through the turning points without any difficulties. However when bifurcation of solution of problem (1) occurs, it is desirable that all branches of the solution be determined. To do this, we solve the auxiliary problem on determination of eigenvectors W :

KW

0

(3)

To determine equilibrium configurations, we propose to introduce small perturbations into potential parameters of atom pairwise interaction in conformity with the form of eigenvector W .

S. N. Korobeynikov

58

This method of continuation of solutions by the side branch is proposed as alternative to more exact but, at the same time, more complicated method presented by Sokol and Witkowski [7]. Presented procedures of solution continuation through singular points of integral curves require as exact definition of a matrix K as possible in order to improve a convergence as well as for prevent a divergence of iteration processes applied for the solution refinement. The expressions refined in comparison with expressions given in [4,6], which account for both tension/compression of segments connecting atomic pairs and their rotations have been proposed by Korobeynikov [8]. The approaches to solution of problems of atomic lattices deformation in the presence of singular points on integral curves are realized in the PIONER code (cf., Korobeynikov et al. [9]). Using this code, solutions of some problems of atomic lattice buckling are obtained, which show the efficiency of algorithms mentioned above. The supports from Russian Foundation for Basic Research (04-01-00191) and Integration Project of Russian Academy of Science No. 3.11.1 are gratefully acknowledged.

References 1.

Novozhilov, V.V., Prikladnaja Matematika i Mekhanika, vol. 33, 797-812, 1969 [in Russian].

2.

Thompson, J.M.T. and Shorrock, P.A., J. Mech. Phys. Solids, vol. 23, 21-37, 1975.

3.

Kornev, V.M and Tikhomirov, Yu.V., J. Appl. Mech. Techn. Phys., vol. 34, No. 3, 439-448, 1993.

4.

Korobeynikov, S.N., Application of the FEM to solving nonlinear problems of deformation and buckling of atomic lattices, Preprint No 1-97, Inst. Hydrodynamics, Sib. Div., Russ. Acad.of Sci., Novosibirsk, Russia, 1997 [in Russian].

5.

Dluzewski, P. and Traczykowski, P., Arch. Mech., vol. 55, 393-406, 2003.

6.

Korobeynikov, S.N., Int. J. of Fracture, vol. 128, 315-323, 2004.

7.

Sokol, T. and Witkowski, M., In Proceedings of the Second International Conference on Computational Structures Technology: Advances in Non-linear Finite Element Methods, edited by M. Papadrakakis and B.H.V. Topping, Civil-Comp Press, Edinburgh, 1994, 35-45.

8.

Korobeynikov, S.N., Arch. Mech. (to be published).

9.

Korobeynikov, S.N., Agapov, V.P., Bondarenko, M.I. and Soldatkin, A.N., In Proceedings of the International Conference on Numerical Methods and Applications, edited by B. Sendov et al., Publ. House of the Bulgarian Acad. of Sci., Sofia, 1989, 228–233.

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MULTISCALE MECHANICS OF CARBON NANOTUBES AND THEIR COMPOSITES X.-Q. Feng Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China [email protected] Since the discovery of carbon nanotubes (CNTs) by Iijima in 1991, interest in carbon nanotechnology has grown very rapidly because of the unique, often enhanced, properties of nanoscale materials. Owing to their superior mechanical and physical properties, carbon nanotubes seem to hold a great promise as an ideal reinforcing material for advanced composites of high-strength and low-density. However, in most of the experimental results, only modest improvements in the strength and stiffness have been achieved by incorporating carbon nanotubes in polymers. In this talk, the mechanical properties of carbon nanotubes and their composites will be investigated by multiscale mechanics methods. There are many factors that influence the overall mechanical property of CNT-reinforced composites, e.g., the weak bonding between CNTs and matrix, the curviness and agglomeration of CNTs. Even though the adhesion strength between the CNTs and the matrix may significantly affect the failure behavior of composites (e.g., the ultimate tensile strength and fracture toughness), its influence on the effective elastic modulus of composites can be negligible. Therefore, it is thought that two most significant reasons that limit the effective elastic property of CNT composites are the curve shape and agglomeration of CNTs due to their nanometer diameters and large aspect ratios. In the present paper, the effects of the widely observed waviness and agglomeration of carbon nanotubes are examined theoretically. The Mori-Tanaka effective-field method is first employed to calculate the effective elastic moduli of composites with aligned or randomly oriented straight CNTs. A novel micromechanics model is then developed to consider the waviness or curviness effect of CNTs which is assumed to have a helical shape. Finally, the influence of agglomeration of CNTs on the effective stiffness is analyzed, and analytical expressions are derived for effective elastic stiffness of CNT-reinforced composites accounting for the effects of waviness and agglomeration. It is established that these two mechanisms may significantly reduce the stiffening effect of CNTs. The present study not only provides the important relationship between the effective properties and the morphology of CNT-reinforced composites, but also may be useful for improving and tailoring their mechanical properties. It is of great interest to gain a deep understanding of fracture behaviors of CNTs. We use here a hybrid atomistic/continuum mechanics method to simulation defect nucleation and facture of CNTs under tension or torsion. Under a lower tensile strain, a CNT undergoes uniform deformation, with the positions of atoms being determined by using the modified Cauchy-Born rule and the Tersoff-Brenner potential. When the tensile strain reaches a critical value, defects may nucleate as a result of the so-called Stone-Wales transformation. We use the atomistic-based continuum mechanics theory to determine the displacements of atoms far from the defect, and an atomistic mechanics method to calculate the positions of atoms in a local subregion around the defect. It is found that the critical strain of defect nucleation and the subsequent fracture modes of CNTs are sensitive to the chiral angle, and that the critical strain of a zig-zag CNT is about two times of that of an armchair one. At low temperature, both armchair and zigzag CNTs fracture in a brittle manner. Our numerical results on the fracture strains and tensile curves compare well with experimental results.

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The exceptional mechanical properties of CNTs make this new form of carbon an excellent candidate for composite reinforcement. However, studies on deformation and fracture of CNTs in composites are difficult both in experimental observation and in theoretical modeling. The above method is also extended to analyze the fracture problem of CNTs embedded in a composite matrix. In our hybrid atomistic/continuum method, the unit cell is divided into three zones, A, B and C, which are dealt with in different manners according to their deformation features and the numbers of atoms in them. The deformation of CNTs is constrained partly by the surrounding matrix. Interaction among CNTs is considered by the Mori-Tanaka method. The calculation results of the critical strains of defect nucleation of CNTs are given in Fig. 1. Our results show that both armchair and zigzag CNTs in a composite are easier to fracture due to the effect of CNT-matrix interaction.

FIGURE 1. Critical strains of defect nucleation upon the chiral angles and diameters of CNTs.

References 1.

Shi, D.L., Feng, X.Q., Huang, Y., Hwang, K.C. and Gao, H., Trans. ASME, J. Eng. Mater. Tech., vol. 126, 250-257, 2004.

2.

Shi, D.L., Feng, X.Q., Jiang, H.Q., Huang, Y. and Hwang, K.C.., Int J. Fracture, (in press).

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IN-SITU SCANNING ELECTRON MICROSCOPE INDENTATION OF GALLIUM ARSENIDE Pouvreau C., Wasmer K., Giovanola J.1, Michler J., Breguet J. M.1 and Karimi A.1 Swiss Federal Laboratories for Materials Testing and Research (EMPA) Feuerwerkerstrasse 39, 3602 Thun, Switzerland 1 Ecole Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland [email protected] Indentation is a commonly used method to evaluate the fracture toughness of brittle materials through crack length measurements. Many models for toughness estimations are available and rely on the assumption that surface traces of the cracks are either of the Half Penny type, Lawn and Evans, [1], Lawn, et al., [2], or of the radial type, Niihara, et al., [3], Niihara, [4]. However, it has been shown that, especially at low loads, the crack morphology depends strongly on material and thus this dependence affects calculated toughness values, Cook and Pharr, [5].

Figure 1: SEM micrographs taken during an in-situ indentation experiment showing the cracking sequence : a) Half-load (250 mN); b) Maximum load (500 mN); c) Half unload (250 mN); d) Full unload. This paper reports on the results of indentation experiments on Gallium Arsenide (GaAs) with two types of indenters (conical with 60° or 120° apex angles and cube corner) using two novel experimental techniques, (1) in-situ indentation in the Scanning Electron Microscope (SEM) while recording indentation load and displacement and (2) sectioning of indent zones by cleavage to reveal the subsurface crack morphology. The first technique, described by Rabe, et al., [6] serves to establish the cracking kinetics by correlating surface cracking observations with loaddisplacement histories. The second technique is used to establish accurately crack shapes, orientations and sizes. In this cleavage technique, a starter crack is generated by scratching the sample along the [110] direction with an indenter. Then, five series of five indents each are made with a Nanoindenter XP at a given load level, each series shifted by 10 µm with respect to the preceding one, perpendicularly to the scratch direction in the indentation plane. Finally, the starter crack is propagated through the whole set of indents with a home made cleaving device. The indenter geometries were chosen to study the influence on crack generation of axisymmetric and singular stress fields, respectively. Moreover, for the wedge and conical indenters, 60° and 120° apex angles have been used to evaluate the indentation fracture dependence on indenter geometry. One edge of the cube corner indenter was aligned with the [10] direction. The following observations were made combining the two novel techniques.

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The cracking sequence of an in-situ indentation with the 60° conical indenter is presented on Figure 1a) to d). For conical indentations, radial cracks are initiated at loads lower than 50 mN. Manufacturing imperfections on the conical indenter strongly influence the crack initiation site and conditions. At 500 mN, chipping out occurs at the end of the loading cycle when at loads lower than 250 mN it generally occurs at the final stage of the unloading. Generally, this chipped region has the shape of a Maltese cross. This pattern is commonly observed in glasses and is generally associated with the residual stress field. During indentations with the cube corner, important cracks emanate from the indenter corner during the loading part of the cycle, followed by secondary cracks from the indenter faces. These cracks have an angle of 45° with the [110] direction and could be the traces of cracks propagating in a {110} plane. Additionally, traces of slip bands are easily visible at the surface of the indented material as previously observed (Fujita, et al., [7]). These results demonstrate that the combination of in-situ SEM indentation and transverse cleaving through indents opens new perspective for crack investigation in brittle single crystals since crack morphologies, cracking sequence and cracking conditions can all be accurately determined and correlated, for a broad range of indentation parameters.

References 1.

Lawn, B. R. and Evans, A. G., J Mater Sci, 12,2195-2199, 1977

2.

Lawn, B. R., et al., J Am Ceram Soc, 63,574-581, 1980

3.

Niihara, K., et al., Journal of Materials Science Letters, 1,13, 1982

4.

Niihara, K., Journal of Materials Science Letters, 2,221, 1983

5.

Cook, R. F. and Pharr, G. M., J Am Ceram Soc, 73,787-817, 1990

6.

Rabe, R., et al., Thin Solid Films, 469-70,206-213, 2004

7.

Fujita, S., et al., Philos Mag A, 65,131-147, 1992

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FRACTURE OF NANOSTRUCTURED LITHIUM BATTERIES K. E. Aifantis, J. P. Dempsey1 and S. A. Hackney2 Univ. of Cambridge & Univ. of St Petersburg Wilberforce Road, Cambridge CB3 0AL, UK 1 Clarkson Univ., 8 Clarkson Avenue, Potsdam, NY 13699-5710, USA, [email protected] 2 Michigan Technological Univ., 1400 Townsend Dr., Houghton, MI 49931, USA, [email protected] [email protected], [email protected] Lithium-ion batteries have gained considerable attention during the past twenty years due to their favourable properties over nickel-cadmium and nickel-metal-hydride batteries. Unlike the aforementioned material systems Li is non-toxic and it is the third lightest element. Moreover, the high energy density of Li batteries reduces their weight by half and their volume by 20% to 50% compared to the same capacity of nickel-cadmium and nickel-metal-hydride batteries. However, the use of pure Li as a negative electrode is not feasable due to safety and reliability concerns. Therefore, extensive research is being performed to find suitable material canditates that form alloys with Li. Unfortunately, many materials that form Li alloys with the required high volumetric density of Li also show over 100% volume change during the discharge and charge of the battery, leading to fracture of the electrode material and associated loss of capacity. Thus, materials designs are being explored which can stabilize the mechnical integrity of the electrode material while still providing large volumetric Li density. In particular, battery developers have suggested that composite materials which contain domains of electrochemically active and inactive materials may provide resistance to mechanical degradation while still providing capacities between 900 and 4000 mAh g-1, Beaulieu et al. [1]. Graphitic carbon, which is the material that is presently being used for the anode by Li ion battery manufacturers, gives a much lower Li capacity of 372 mAh g-1, Graetz et al. [2]. These active/ inactive composites typically comprise of a metal inclusion (such as Si, Sn, Al, Bi) that forms rich Li compounds and is surrounded by an inert ceramic or glass, as shown in Fig. 1.

FIGURE 1. Idealized geometry of the electrode: Li-insertion particles (shaded) embedded in a glass (blank) matrix. A unit cell is defined by a circle of radius b surrounding a circular particle of radius a. However, these composite materials designs have not been optimized for fracture resistance and Li capacity. We consider an idealized analytical model to consider some major design parameters for this problem. In particular, to model fracture of the anodes, the unit cell of Fig. 1 is divided in three zones: the active site, the damage zone that develops at the active site/matrix interface, and the undamaged matrix (see Fig. 2). It should be noted here that experimental studies suggest that if the active sites are of nanometre size and are surrounded by a ceramic, the surface of

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the active site does not fracture, and hence the damage zone consists only of ceramic nanoparticles.

FIGURE 2. Damage in unit cell of anode: a and b denote the radii of the active site and matrix, respectively, ' denotes the free expansion the active site would undergo during charging, and U-a denotes the crack length. The present authors have modelled the internal stresses that develop during the charge and discharge of the battery, Aifantis and Hackney [3], and they have also predicted the stability of these systems, Aifantis and Dempsey [4]. The purpose of this study is to determine the critical crack length at which the electrode will fracture. Furthermore, the effect that the size of the active site has to overall capacity of the battery will explored and finally, predictions will be made for the values of a and b that will result in no cracking.

References 1.

Beaulieu, L. Y., Eberman, K. W., Turner, R. L., Krause, L. J., Dahn, J. R., Electrochem. Solid-State Lett., vol. 4 (9), A137, 2001

2.

Graetz, J., Ahn, C.C., Yazami, R., Fultz, B., Electrochem. Solid-State Lett., 6(9), A194, 2003

3.

Aifantis, K.E., Hackney, S.A., J. Mech. Behav. Matls, 14, 413, 2003

4.

Aifantis, K.E., Dempsey, J.P, J. Power Sources, 143, 203-211, 2005

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ANALYTICAL AND EXPERIMENTAL CHARACTERIZATION OF A MICROMIRROR SYSTEM E. J. Pryputniewicz, C. Furlong1, and R. J. Pryputniewicz1 Current address: Department of Homeland Security, Science and Technology, Alexandria, VA 1Worcester Polytechnic Institute, Mechanical Engineering Department / CHSLT-NEST [email protected] Continued demands for miniaturization and increased functionality of microelectromechanical systems (MEMS) require construction of complex three-dimensional structures. Recent developments at Sandia National Laboratories allow construction of such structures from parts fabricated in a plane of a wafer, by actuating them to extend hundreds of microns in the direction normal to the fabrication plane. One such structure is a hinged positionable micromirror system actuated by an electrostatic microengine, Fig. 1. It should be emphasized that this structure is batch fabricated with no piece part assembly required and that it is actuated using only the on-chip microengine; the torque delivered by the microengine is amplified by the transmission, which, in turn, pushes a linear rack that positions the hinged micromirror, Fig. 2. In the configuration shown, the micromirror can be used to reflect light beam capable of triggering, or activating, sensors and other circuitry when it is in its elevated position. Therefore, repeatability of a reflected beam impinging on a target, changes in performance of the micromirror over time, and distortion of its surface during activation are just some of the characteristics that must be determined with high accuracy and precision. Until recently, this characterization was hindered by lack of suitable methodologies. However, building on advances in photonics, electronics, and computational analyses, we have developed a new methodology Pryputniewicz et al. [1], using fiber-based laser optoelectronic holography system, Fig. 3, to quantitatively characterize micromirror systems in motion, Figs 4 and 5. In addition, in order to determine forces acting on various components of the system, we have also developed analytical models to study kinematics and kinetics of these components, based on vector calculus Pryputniewicz [2], Pryputniewicz [3]. According to this model, magnitudes of forces, acting on the smallest gear (60 Pm diameter) in the system, range from 4 nN to 27 Pm, as a function of rotational speed. The corresponding displacements of the micromirror are 113 Pm. In this paper, the methodology for analytical and experimental characterization of a micromirror system is described and its use is illustrated with a representative case study. By characterizing performance of the micromirror system, we can make specific suggestions for their future improvements and we can verify the effect of these improvements. The micromirror systems used in this study were fabricated at and provided by Sandia National Laboratories. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Company, for the United States Department of Energy under Contract DE-AC04-94AL85000.

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A METAL INTERPOSER FOR ISOLATING MEMS DEVICES FROM PACKAGE STRESSES R. J. Pryputniewicz, T. F. Marinis1, J. W. Soucy1, P. Hefti, and A. R. Klempner Worcester Polytechnic Institute, Mechanical Engineering Department / CHSLT-NEST 1Draper Laboratory, Electronic Packaging Department, Cambridge, MA [email protected] Many classes of MEMS devices, such as those with resonant structures, capacitive readouts, and diaphragm elements, are sensitive to stresses that are exerted by their surrounding package structure. Such stresses can arise as a result of changes in temperature, ambient pressure, or relative humidity. We have demonstrated a dramatic reduction in scale factor bias over temperature for a tuning fork gyroscope by mounting it on an interposer structure within a conventional chip carrier, Fig. 1. Optimization of a MEMS sensor package for high performance subject to various constraints cannot be accomplished by analysis alone Hanson et al. [1]. There are too many unknown parameters, e.g., material properties, process conditions, and components/ package interface conditions, to make this feasible. Extensive performance evaluation of packaged sensors is also prohibitively expensive and time consuming. However, recent advances in optoelectronic laser interferometric microscope (OELIM) methodology Furlong and Pryputniewicz [2] offer a considerable promise for effective optimization of the design of advanced MEMS components and MEMS packages. Using OELIM, sub-micron deformations of MEMS structures are readily measured with nanometer accuracy and very high spatial resolution over a range of environmental and functional conditions. This greatly facilitates characterization of dynamic and thermomechanical behavior of MEMS components, packages for MEMS, and other complex material structures. In this paper, the OELIM methodology, which allows noninvasive, remote, full-field-of-view measurements of deformations in near real-time, is presented and its viability for development of MEMS is discussed. Using OELIM methodology, sub-micron displacements of sensors can be readily observed and recorded over a range of operating conditions, Fig. 2. In addition, detailed mapping of deformation fields due to process conditions can also be made, Fig. 3. In this case, the OELIM results clearly show that the proof masses are not flat, but rather exhibit curvature, with the maximum deviation from planarity of 1.05 Pm. This curvature, which affects performance of the sensor, is due to residual stresses generated during fabrication of the device. Where applicable, the OELIM measurements are coupled with the corresponding analytical and computational modeling results, in order to validate and refine quantitative models of packages and complex material structures Przekwas et al. [3] and Pryputniewicz et al. [4] as well as to develop operational relationships for MEMS structures, which offer considerable promise for effective optimization of design of advanced sensor packages and their fabrication processes.

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References 1.

Hanson, D. S., T. F. Marinis, C. Furlong and R. J. Pryputniewicz, “Advances in optimization of MEMS inertial sensor packaging,” Proc. Internal Congress on Applied Mechanics for Emerging Technologies, Portland, OR, pp. 821-825, 2001.

2.

Furlong, C., and R. J. Pryputniewicz, “Absolute shape measurements using high-resolution optoelectronic holography methods,” Opt. Eng., 39:216-223, 2000.

3.

Przekwas, A. J., M. Turowski, M. Furmanczyk, A. Hieke, and R. J. Pryputniewicz “Multiphysics design and simulation environment for microelectromechanical systems,” Proc. Internat. Symp. on MEMS: Mechanics and Measurements, Portland, OR, pp. 84-89, 2001.

4.

Pryputniewicz, R. J., P. Galambos, G. C. Brown, C. Furlong, and E. J. Pryputniewicz, “ACES characterization of surface micromachined microfluidic devices,” Internat. J. Microelectronics and Electronic Packaging (IJMEP), 24:30-36, 2001.

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COMPUTATIONAL MODELING OF NANOPARTICLES IN BIOMICROFLUIDIC DEVICES R. J. Pryputniewicz, Z. Sikorski1, M. Athavale1, Z. J. Chen1 and A. J. Przekwas1 Worcester Polytechnic Institute, ME/CHSLT-NEST, Worcester, MA USA 1CFD Research Corporation, Huntsville, AL, USA [email protected] Focused laser beam can be used to trap and manipulate small particles without mechanical contact. Particles trapped by laser tweezer can be used as local force probes in biomicrofluidic environment. Optical tweezer forces are in the pico-Newton range, which makes them suitable for study of physics of biological objects like cells, viruses, bacteria, and research in genetics. Theoretical models of optical forces acting on particles much smaller than wavelength of light (Rayleigh regime) are based on dipole model of interaction of light with a dielectric particle. Total optical force can be split into gradient force, which drags particle toward maximum of laser beam intensity in the focal region, and scattering force, which pushes particle in the direction of Poynting vector of laser light. Ratio of scattering force to gradient force increases with a particle radius. Stable trap requires gradient force to be larger than scattering force. If potential well produced by optical force field is higher than other forces acting on particle (e.g., viscous, Brownian, biological interactions) it remains in the trap. Optical manipulation of nano-beads attached to a complex biomolecule allows to rotate, stretch, and cut it, measure kinetic constants of binding, and study behavior of molecular motors. This paper presents a model of optical manipulation of nanoparticles in a scanning laser beam Sikorski et al. [1] Laser beam is fast scanned in one direction and slow scanned in the other. Optical field time averaged over the fast scan builds an optical trap. Slow scan in the second direction allows dragging particles by this elongated optical trap. Formulas for optical forces are derived for this case. CFDRC multiphysics solver ACE+ has been used for transient simulation of particle manipulation in biomicrofluidic devices. Figure 1 shows an H-filter which is 1 mm high. In this filter, the channel width is 20 Pm and beads of 70 nm radius, made of material with index of refraction of 1.56, are used. The slow scan velocity, transverse to the channel, is 10-5 m/s. Observed is particle rotation and sweeping for different shapes of particles. Device heating and influence of temperature distribution on particle and fluid movement are presented. Figure 2 shows an enlarged snapshot of the H-filter separation region, after 1500 time steps of 50 ms each. Although the laser beam is not shown in Fig. 2, its effects are visible: beads change from RHS stream to the LHS stream. If the laser were not present, the beads would continue in the RHS stream. Since this effect depends on the size and properties of the beads (i.e., particles, molecules, etc.) it can be used to separate them. Continued work will result in additional examples.

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References 1.

Sikorski, Z., M. Athavale, Z. J. Chen, A. J. Przekwas, and R. J. Pryputniewicz, “Modeling of optical trapping and manipulation of nanoparticles in biomicrofluidic devices,”, Proc. 4th Internat. Symp. on MEMS and Nanotechnology (4th-ISMAN), Charlotte, NC, pp. 350-357, 2003.

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CHARACTERIZATION OF A MEMS PRESSURE SENSOR BY A HYBRID METHODOLOGY R. J. Pryputniewicz and C. Furlong Worcester Polytechnic Institute, Mechanical Engineering Department / CHSLT-NEST [email protected] Recent advances in surface micromachining and microelectromechanical systems (MEMS) technology have led to development of a MEMS pressure sensor, Fig. 1a. In this sensor, pressure changes are detected by deformations of a diaphragm, Fig. 1b. This diaphragm is about 400 Pm long, 100 Pm wide, and about 2 Pm thick, made of several different materials, each having different properties, especially different coefficients of thermal expansion (CTE). As a result, as the sensor is exposed to the environment, where in addition to pressure changes temperature changes also, its measurements will be affected by thermomechanical response. The objective of this paper is to develop a hybrid, computational and experimental, methodology for characterization of thermomechanical behavior of MEMS pressure sensors. The computational development is based on a finite element method (FEM). The experimental development is based on the state-of-the-art optoelectronic laser interferometric microscope (OELIM) method Pryputniewicz et al. [1]. Accurate and precise pressure measurements by MEMS sensors are limited by the effects that environmental temperature variation has on their performance. As the sensor is exposed to a changing pressure, the diaphragm deforms. Deformations of the diaphragm cause changes in resistance of the bridge circuit, which is an integral part of the MEMS sensor. In this study the sensors were subjected to a differential pressure of 0.2 MPa and a temperature ranging from 10qC to 50q C. The analyses were performed for the combined pressure and thermal loads. Representative results are shown in Figs 2 and 3. Figure 2 shows typical fringe patterns due to changes in the differential pressure. Ideally, there should be no fringes when the sensor is at rest, i.e., at atmospheric pressure. However, because of residual stresses due to fabrication, the diaphragm is deformed by about 40 nm. Also, deformation nonlinearity, due to loadings by a positive and a negative pressure differences of the same magnitude, is vividly displayed by the corresponding fringe patterns; the negative pressure difference yields the maximum deformation of 792 nm, while the positive one yields the magnitude of 813 nm, resulting in a difference of 21 nm, which is significant while interpreting the results. Computationally determined deformations and stresses due to the positive pressure difference are shown in Fig. 3. Comparison of computational and experimental results indicates good correlation and shows that the hybrid methodology is very effective for characterization of MEMS pressure sensors.

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NEW APPROACH TO SYNTHESIS OF LASER MICROWELDING PROCESSES FOR PACKAGING R. J. Pryputniewicz, W. Han and K. A. Nowakowski Worcester Polytechnic Institute, Mechanical Engineering Department / CHSLT-NEST [email protected] Microelectronics and packaging industry has ever-increasing requirements for miniaturized features with high edge acuity and negligible thermal damage zone. Laser micromachining is a unique way of processing materials with less thermal distortion and minimum metallurgical damage to the workpiece, therefore it is a good alternative to conventional micromachining processes. Typical applications of laser micromachining include laser bonding of a wafer, or of a microsystem chip, to one or two parts Mescheder et al. [1], and laser micromachining of 3D microchannel systems in chemical, biomedical, DNA, and environmental science analyses Qin and Li [2]. In laser micromachining processes, such as laser welding, drilling, and cutting, the materials experience heating, melting, evaporating, and re-solidifying stages. As a result, the laser micromachined components can be affected by a number of factors such as laser beam properties, system-cooling conditions, and surface roughness/reflectivity of the areas exposed to laser light. This paper presents synthesis of the laser microwelding processes for packaging. More specifically, various parameters are evaluated individually and then together to determine their influence on the finished product. This evaluation is done analytically, computationally, and experimentally Han and Pryputniewicz [3]. Analytical and computational results yield temperatures in the heat affected zones (HAZs), Fig. 1. In order to make these results valid, they are correlated with time dependent temperature measurements, Fig. 2; to facilitate this correlation, the results shown were normalized. Thermal gradients developed during laser microwelding cause deformations of surfaces exposed to laser beam. Successful development of advanced packaging depends on accurate knowledge of these deformations. In order to quantify surface deformations due to laser microwelding, we have developed an optoelectronic methodology based on the use of CCD cameras for high-resolution imaging of the affected areas. Figure 3 shows a representative fringe pattern recorded for one of the HAZs. Interpretation of this fringe pattern produces detailed spatial distribution of deformations, Fig. 4; the maximum deformations shown are 2.5 Pm, which may lead to fractures. In fact, in order to understand the influence that a laser beam has on the materials, we make these measurements before, during, and after the laser microwelding, based on which we will optimize the processes to obtain minimal deformations. Comparison of preliminary analytical, computational, and experimental results shows good correlation and indicates viability of the approach we have developed for synthesis of laser microwelding processes for packaging.

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THERMAL MANAGEMENT OF RF MEMS RELAY SWITCH R. J. Pryputniewicz Worcester Polytechnic Institute, Mechanical Engineering Department / CHSLT-NEST [email protected] Radio frequency (RF) switches are one of many MEMS devices that make it possible to communicate, sense, and measure while using minimal amount of space and very low power. The RF microswitches have either capacitive or resistive configuration. The capacitive switches use a flexible membrane design, in which capacitance between two electrodes is induced via electrical voltage; reaching threshold capacitance activates the switch, which enables transmission of a signal. The resistive switches, on the other hand, make direct metal to metal contact. Such design usually uses a cantilever beam that bends as voltage is applied to the two electrodes. In the RF MEMS contact switch configuration, a moving component is a cantilever beam with a shorting bar at its free end, Fig. 1. The shorting bar comes into contact with the traces on the substrate as the beam deflects under the electrostatic force loading. As the shorting bar makes contact with the traces, i.e., as it closes the path, electric signals pass from one trace to the other. Because of finite internal resitances of the components as well as resistance of the contact interfaces, Joule heat is generated, affecting performance of the switch. In this paper, we investigate the Joule heating effects computationally using thermal analysis system (TAS) software. TAS models the structure to be analyzed by geometrically simple finite elements, Fig. 2, convert these elements into resistors representing all three modes of heat transfer: conduction, convection and radiation, and then solves the resistor network using the finite difference solver, which performs heat balance at each node of the model Pryputniewicz et al. [1]. This entails calculating a node temperature based on the resistances and the temperatures of all nodes attached to the node in question. During TAS model execution, temperature, or time dependencies are interpolated for each computation time step. Representative results obtained for 300 mA current are displayed in Figs 3 and 4. Figure 3 shows that the shorting bar reaches temperatures from 680qC to 717qC, for the geometry, dimensions, and the material properties considered in this case; for other set of parameters the results would be different. Figure 4 shows that temperatures in the traces range from 25qC to 45qC. It should be observed that the 665qC temperature difference between the components shown in Figs 3 and 4 is due to effective heat transfer between the individual components of the switch as well as with its environment. Results generated in this study show that TAS provides an effective approach for thermal management of RF MEMS switch designs.

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BUCKLING AND DELAMINATION OF THIN LAYERS ON A POLYMER SUBSTRATE A. A. Abdallah, D. Kozodaev1, P. C. P. Bouten2, J. M. J. den Toonder2 and G. de With Laboratory of Materials and Interface Chemistry, Eindhoven University of Technology Den Dolech 2, 5600 MB Eindhoven, The Netherlands 1 NT-MTD Co./NTI-Europe. Arnhemseweg 34 d, 7331 BL Apeldoorn, The Netherlands 2 Philips Research Laboratories, Prof. Holstlaan 4, 5656 AA Eindhoven, The Netherlands [email protected] Flexible displays are multi-layered structures consisting of a polymer-based substrate sandwiched between a numbers of functional layers that act as a gas barrier layer, e.g. inorganic thin silicon nitride layer (Si3N4), and a transparent conducting oxide layer, e.g. indium tin oxide layer (ITO). For the realization of flexible displays, a study of the mechanical integrity of multi-layered structures and their reliability is required. High compressive stresses in the thin layer in combination with insufficient adhesion at the interface can cause the layer to buckle and to delaminate from the substrate (see Fig.1). These buckling phenomena are undesirable from a functional and reliability point of view and therefore should be avoided.

FIGURE 1: Atomic force microscope image obtained for buckling and delamination of a 400 nm thin Si3N4 layer on a polymer substrate. Circular buckles with layer cracking due to uniaxialcompressive external stress. In the framework of buckling theory for a beam clamped on both edges, numerous buckle morphologies have been studied for various thin layer structures on substrates, often neglecting the effect of the substrate’s deformation. Recently, attention is paid to buckling on compliant substrates [1, 2, 4]. When the substrate deformation is taken into account, significant effects of the energy release rate on buckles are described, leading to lower critical strains for buckling onset. Bouten and Van Gils [4] present buckling maps for compliant substrates; buckle sizes (height and width) are related to adhesion energy and internal strain (prior to buckling). Yu and Hutchinson [2] define a characteristic length l, adjacent to the buckle, contributing to the energy release upon buckling. This length is given as

l=

2 hf 1D

(1)

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where hf is the layer thickness, D is the elastic mismatch (Dundurs’ parameter [3]). Assuming that only the elastic energy release of the buckling layer contributes to the buckling process, the energy balance for buckling can be written as [4]

2bGss=2(b  l )(Go  Gc)

(2)

where Go is the elastic energy stored in a thin layer per unit width, Gc is the remaining energy in the buckled portion of the layer and b is characteristic buckle size. The right hand term describes the energy release in the thin layer upon buckling as a function of the effective buckle length (b + l), which depends on the layer thickness and the elastic mismatch. As a consequence significantly more elastic energy is available for buckling formation. The steady-state energy release rate of the advancing buckle Gss is an important parameter to describe layer buckling and delamination. The left hand term represents the energy required for delamination. In this paper attention is paid to the influence of loading mechanism, layer thickness, and level of adhesion on buckle initiation and propagation. Based on the results of the experimental work, a numerical model has been formulated to describe buckling and delamination phenomena in these structures using the J-integral and cohesive zone elements. Different types of buckle profiles are presented and the buckle evolution mechanism associated with the applied stress is discussed. The results showed that the buckle onset strain defined at a given quality of adhesion for a compliant substrate is lower than the one predicted by the model for a rigid substrate [5]. Apart from that, the critical buckling strain Hc is found to be reduced for a stiff layer on a compliant substrate due to the rotation and the displacement at the buckle edges. The buckle size is found to increase with the layer thickness and the uniaxial-compressive strain.

References 1.

B. Cotterell and Z. Chen, Int. J. Fracture 104, 169-179, 2000.

2.

H.H. Yu and J.W. Hutchinson, Int. J. Fracture 113, 39-55, 2002.

3.

J. Dundurs, J. App. Mech. 36, 650-652, 1969.

4.

P.C.P. Bouten and M.A.J van Gils, In Proceedings of MRS, Boston, 2004. T4.9

5.

J.W. Hutchinson and Z. Suo, Adv. Appl. Mech. 29, 63-191, 1992.

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CARBIDE COATED CUTTING TOOL PROPERTIES INVESTIGATION BY NANO-MECHANICAL MEASUREMENTS UNDER 250-500°C. B. Vasques, D. Joly, R. Leroy, N. Ranganathan and P. Donnadieu1,2 LMR, Productique Department, University François Rabelais de Tours, 7 rue Marcel Dassault, 37204 Tours, France 1 SAFETY Production SA, rue Henri Garih, 37230 Fondettes, France 2 CEROC Cutting Tool Research Centre, rue Henri Garih, 37230 Fondettes, France [email protected], [email protected], [email protected] Since most mechanical properties are temperature dependent. This one of the reasons that usual mechanical tests at room temperature are insufficient to characterize advanced PVD coatings designs. Many of these coating inserts are exposed to high temperatures in either processing or working environments such as high speed machining or dry cutting operations [1, 2, 3, 4]. Wear reaction between tool and work piece takes place at high temperature [5]. We need to study these materials under such environment to really understand and predict there behavior. That’s why wear resistance of PVD hard coatings are investigated with a particular attention to their critical mechanical properties at higher temperature. These properties are measured by a Nano Test pendulum set up specially equipped for high temperature measurements. The hot stage consists of a thermally insulating ceramic block that is attached to the specimen holder. A thermal shield is placed between the pendulum and the stage to prevent thermal instability of the probe (Fig. 1).

Figure 1: Nano Test pendulum modified for high temperature measurements. Indentations are performed at room temperature, 250 and 500°C using a Berkovich indenter. The following parameters are used for the measurements: maximum load (50-250mN), loading rate (2-5 mN/s, dwell time at maximal load (10-30 s). Scratch and impact experiments are employed at the same room temperature to analyze critical load to adhesion failure and fatigue properties allowing identification of operating limits. Microstructure analysis of film is done by Scanning Electronic Microscopy (Jeol JSM6480). Investigation of thin films and surface mechanical properties at high temperature will allow optimizing the “Couple Tool Material “projects in metal cutting. Keywords: Berkovich indenter, coated inserts, PVD films, High Temperature, Nano Test techniques

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References 1.

Beake D., Garcia M. and Smith F., Thin Solid Films, 398-399 (2001) 438-443.

2.

Beake D. and Ranganathan, ICMAT, Singapore, 3-8 July 2005.

3.

Karimi A., Wang Y., Morstein M., Thin Solid Films, 420-421 (2002) 275-280.

4.

Gong J., Miao H., Peng, Acta Materialia, vol. 52, 785-793, 2004.

5.

Morant C., Prieto, Forn A., Surface and Coated Technology, 180-181 (2004) 512-518.

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DIAMOND COATING DEBOUNDING IN TOOL APPLICATION David Moulin, Pierre Chevrier, Paul Lipinski and Thierry Barré1 Laboratoire de Physique et Mécanique des Matériaux (LPMM) / Ecole Nationale d’Ingénieurs de Metz (ENIM) ENIM, ile du Saulcy, 57045 Metz, France 1Balzers Luxembourg, ZI Hanoesbesh, Luxembourg [email protected], [email protected], [email protected], [email protected] Machining of recent engineered complex materials such as aeronautical ones always require new tools to lower production cost and in the same time increase quality. One promising solution is the use of Chemical Vapour Deposition (CVD) diamond coatings on carbide tools, which is studied here. Diamond is used because of its extreme hardness, which made it a perfect candidate to reduce wear of the cutting edge. It is synthesized in a batch at low pressure and medium temperature directly on the tools. Deposition process on tungsten carbide tool bound with cobalt, which is the main industrial material for tool manufacture, and especially the adhesion of the diamond layer to the substrate has to be improved, and many research are focused on this point [1]. The whole process of deposition is described elsewhere [2]. This paper proposes an approach to study the decohesion of the diamond layer via a combination of experiments and simulation. Many techniques to study adhesion of the diamond layer were developed, such as indentation [3], sand blasting [4]. However, these techniques have a high limitation: they are only qualitative, and don’t take into account the physic of adhesion. Results obtained with these techniques depend of the test procedure and of the machine used to apply the load. Results of a series of tests cannot be compared to others. A better comprehension of the physic involved can lead to a quantitative test, with a good repeatability and a measured value, which do not depend of the test process. Experimentally, it can be observed that diamond delamination occurs because of a stress along the interface between carbide and diamond (Fig. 1).

Figure 1 : Diamond fracture on rake face of a turning insert This stress is of different natures. When coating flaked during machining, pressure and temperature induced by the machining process, which are external loads, are responsible of the degradation of the interface. However, debounding can occurs into the batch, without any external loading, because high thermal stresses during cooling (see Fig. 2). These high thermal stresses are due to by the difference of thermal dilatation coefficients and can be calculated with a finite element model. This stress has to be taken into account together with that due to the external loading. Observation of the insert after decohesion (fig 1) confirms that fracture occurs at the interface of the two materials.

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Figure 2 : Normal stresses induced by thermal cooling along the interface Carbide – diamond depending on thickness and edge radius (centred on the edge)- Results on FEM calculation In this work, adhesion is studied by completing experimental loading of the system by simulations with a Finite Element Model (FEM) in order to obtain the stress state responsible for the de-bounding of the diamond layer. A criteria is then written to characterize the behavior of the system based on a combination of the normal and shearing stress responsible for de-cohesion. Different loading configurations are imagined to obtain the form of the criteria: 3 or 4 points flexion tests, impact tests, and variation of the radius edge. Flexion tests induce pure tractioncompression stress in both the coating and the substrate but with two different levels, leading to shearing of the interface and to debounding of the coating. Indentation and impacts tests are more complex loads, respectively quasi-static and dynamic in nature. Deposition on different edge radii leads to different thermal residual stresses, which play the role of the load. A critical radius can be found, which is the smallest radius before debonding. Stress state can be calculated according to this radius. These different techniques, combined with the simulation, give a better understanding of the phenomenon that control the adhesion. They lead to a debounding criteria useful to characterize adhesion.

References 1.

S. Kamiya, U.H. Takahashi, R. Polini and E. Traversa, Diamond Relat. Mater. , vol 9, 191194, 2000

2.

H.G. Prengel, W.R.Pfouts, and A.T. Santhanam, Surf. Coat. Technol. , Vol. 102, 183 – 190, 1998

3.

G.Jörgensen, M.Lahres, and J.Karner, Surf. Coat. Technol. , vol 97, 238-243, 1997

4.

Friedrike Deuerler, Heiko Gruner, Michael Pohl and Ladji Tikana, J. Mater. Process. Technol. , Vol. 99, 266 – 274, 2000

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INTERFACIAL STRENGTH OF CERAMIC THIN FILM ON POLYMER SUBSTRATE M. Omiya and K. Kishimoto Department of Mechanical and Control Engineering, Tokyo Institute of Technology, 2-12-1, O-okayama, Meguro-ku, Tokyo, 152-8552, Japan [email protected] In this paper, we aim to evaluate the interfacial adhesion strength between ITO (Indium Tin Oxide) coating layer and PET (Poly-Ethylene Terephthalate) substrate. To evaluate the interfacial adhesion strength, we focused on the buckling phenomena of the coating layer during simple tensile tests. During the tensile tests of PET/ITO specimen, the buckling induced delamination occurred on the coating layer. These phenomena are related to the interfacial adhesion strength and we evaluated the interfacial adhesion strength by considering the energy balance during the buckling induced delamination and cracking. During tensile tests, two types of cracks are formed on the coating layer: vertical cracks and parallel cracks. Parallel cracks are induced by the buckling of thin coating film on the polymer substrates and these phenomena are strongly related to the interfacial adhesion strength. Therefore, we estimate the strain energy stored in the coating film by modified shear-lag model[1] and considering the energy balance to evaluate the interfacial adhesion strength between thin film and substrate. Due to the tensile loading, the coating layer is assumed to be segmented as shown in Fig.1. In the coating layer, the compressive loads are induced by the interfacial shear force. From modified shear-lag model, when the compressive stress in the substrate is

V c , the compressive stress in the

coating layer is,

(1) where,

E f , Es

are Young’s modulus for coating layer and substrate, respectively.

h, H

are the

thickness of the coating layer and the substrate. L is the segment length of the coating layer andăis the load transfer length. The energy balance before and after buckling induced delamination and cracking is,

We

Wd  Wec  W f

(3)

where the strain energy before buckling crack is energy of undelaminate coating layer is W

ec

W e , the delamination energy W d , the strain

and the energy for crack formation is W f . Note that

the change of the strain energy in the substrate is small because the compressive stress is continuously acting on the substrate from the applied load and it constrains the elastic recover of the substrate due to the delamination and cracking. Then, the interfacial strength, described as,

* d , can be

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(4) where

is the fracture toughness of the coating layer,

l d is the delamination length and b is the

width of the segmented film. In this study, the dimensions needed to evaluate the interfacial strength from by Eq.(4) are measured by atomic force microscope. From this observation, we obtained the delamination length,

l

d , and evaluate the interfacial adhesion strength,

* d . The

2

average value of the interfacial strength for PET/ITO specimen is 19.6 J/m and PET/ITO(UV) specimen is 9.6J/m2. The obtained results agree well with the peel test results[2] as shown in Fig.2. During the buckling and delamination process of the coating layer, the phase angle continuously changes. Therefore, the obtained results are considered to be the averaged interfacial strength for several phase angles. However, this simple approach is useful for the first estimation of the interfacial strength and it is valuable for quick interfacial evaluation at manufacturing premises.

FIGURE 1. Buckling induced delamination and cracking.

FIGURE 2. Comparison with the results measured by Multi-stages Peel Test.

References 1.

Yanaka, M., Kato, Y., Tsukahara, Y. and Takeda, N., Thin Solid Films, Vol.355-356, 337342, 1999.

2.

Omiya M., Inoue H., Kishimoto, K., Yanaka, M. and Ihashi, N., Journal of the Society of Materials Science, Japan, Vol.52, 856-861, 2004.

3.

Omiya M., Inoue H., Kishimoto, K., Yanaka, M. and Ihashi, N., Key Engineering Materials, Vol.297-300, 2284-2289, 2005.

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DELAMINATE BEHAVIOR OF PVD/CPVD THIN FILM S. Doi and M. Yasuoka 700 Dannoharu Oita-shi,JAPAN [email protected] Accompanied with sophistication of the technology of creating surface, multi-layered structures of film tend to increase for improving the accuracy with a large degree of the freedom playing an important role. In particular, various kinds of methods for producing film have been proposed and the application range of film has become wider. In this research, focusing on coating film materials fabricated using PVD, CVD and a combined method of PVD+CVD, grasping their surface morphology is aimed. On the other hand, the reliability of such a new material with a different property between the surface function and the interface function is required. Accordingly, different techniques from conventional methods of evaluating functions of laminated material are needed. Therefore, in this research, so-called textured materials with new structure coated by a series of carbon film or titanium nitride film as described in the following, were selected. The effect of applied impact loading on the adhesion and the interface quality of their films was investigated by observation using laser confocal microscope and fractal dimensional analysis of cracks or exfoliation surfaces. The molecular structure of DLC attracting attention recently differs from one of diamond and graphite and constitutes a crystal structure with no aligning. This structure is said to be a kind of amorphous structure with a similar characteristic to one of diamond showing high hardness and a partially similar to one of graphite. The basic arrangement of the carbon includes the atomic arrangement of SP‚R and this causes a different property of hardness of DLC. Also, TiN has a structure with substrate of M35, that is to say, a two-layered structure and this leads to a crystalline textured structure constituting the interface and the surface, respectively. As a method of examining surface characteristics in fractal dimensional analysis, the box count method was adopted because this is an adequate method for observing the local change.

86

S. Doi and M. Yasuoka

Fig.2 Relationship fractal dimension and cyclic impact numbers

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EXPERIMENTAL STUDY OF MICROHARDNESS AND FRACTURE OF IMPLANTED GÁLLIUM NITRIDE FILMS P. Kavouras, M. Katsikini, E. Wendler1, W. Wesch1, H. M. Polatoglou, E. C. Paloura, Ph. Komninou and Th. Karakostas Physics Department, Aristotle University of Thessaloniki 541 24 Thessaloniki, Greece 1Institut für Festkörperphysik, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, Jena D07743, Germany [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected] The investigation of radiation effects in III-V semiconductors is of current interest because of the potential application of ion implantation in the production of electronic and photonic devices. Of the plethora of III-V semiconductors, gallium nitride (GaN) has attracted keen interest, during past decade, as wide gap semiconductor for numerous applications, including high-power or high frequency devices and high-power switches. Although there is considerable interest in determining the influence of ion implantation on the mechanical properties of GaN films, the matter has received only scant attention, see for example Kavouras et al. [1]. Indeed, studies of the processes controlling hardness, contact damage and cracking of epitaxially grown GaN films have significant technological importance. In this work, we present the results of the application of the Static Indentation (SI) technique, using Vickers and Knoop indenter geometries, in the investigation of implantation induced effects on the mechanical properties and fracture of epitaxially grown GaN films. More specifically, we compare a number of physical characteristics that govern the elasto-plastic behavior before and after implantation. The implanted species used to produce implantation induced damage were Au, Xe, Ar and O ions. TABLE 1. Structure and microhardness of as-grown and implanted GaN films. The errors represent the standard deviations. Material As-grown GaN Au-implanted Xe-implanted Ar-implanted O-implanted

Name GaN GaN:Au GaN:Xe GaN:Ar GaN:O

Structure Amorphous Amorphous Amorphous Heavily damaged

Microhardness / GPa 13.73r0.12 12.28r0.16 10.19r0.10 9.41r0.14 14.53r0.26

A Knoop indenter was utilized to obtain the microhardness values (Table 1). The structure of GaN implanted epilayers was obtained by X-ray Absorption Fine Structure (XAFS) technique. It was found that in the case where implantation produces heavily damaged structure microhardness is increased, while implantation induced amorphisation lowers microhardness value. Additionally, the influence of the indentation load on the microhardness value was studied, i.e. the Indentation Size Effect (ISE) curves were obtained in all cases. It was observed that GaN and GaN:O showed a normal ISE behavior, i.e. microhardness value increases with decreasing indentation load, while GaN:Au, GaN:Xe and GaN:Ar showed a Reverse ISE (RISE), i.e. microhardness value decreases with decreasing indentation load. The magnitude of the post-indentation healing of indentation

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prints was evaluated by measuring (a) the relative length of the two normal diagonals of Knoop indentation prints and (b) the depth of residual indentation prints by means of Atomic Force Microscopy (AFM). The above information can give an estimation of the elastic behavior and elastic modulus, as it was firstly recognized by Marshall et al. [2].

FIGURE 1. Optical micrographs, under transmitted illumination, of fracture formation sequences for GaN (a, b and c) and GaN:O (d, e and f) films. Fracture sequence was also observed in all cases, utilizing Vickers indenter geometry according to the formalism elaborated by Cook and Pharr [3]. GaN did not show initiation of a specific microcrack type. Only cumulative fracture events and/or film detachment were observed for indentation loads higher that #1.5 N. In all other cases, fracture occurred in lower loads, indicating that implantation has an effect analogous to embrittlement. Fig. 1 shows characteristic sequences of fracture formation in the cases of GaN and GaN:O.

References 1.

Kavouras, P., Katsikini, M., Kehagias, Th., Paloura, E.C., Komninou, Ph., Antonopoulos, J., Karakostas, Th., J. Phys. Cond. Mat., vol. 14, 12953-12959, 2002.

2.

Marshall, D.B., Noma, T., Evans, A.G., J. Amer. Cer. Soc., vol 65, C175-C176, 1982.

3.

Cook, R.F. and Pharr, G.M., J. Amer. Cer. Soc., vol 73, 787-817, 1990.

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CRACK TIP STRAIN FIELD AND ITS PROPAGATION CHARACTERISTICS IN A POLYMER FOAM Fu-pen Chiang, Sheng Chang and Yi Ding Department Of Mechanical Engineering, Stony Brook University [email protected], [email protected] In recent years there has been an increasing interest in using foam composites as shipbuilding materials. A sandwich panel built of fiberglass face sheets and a foam core has strong rigidity and bending strength. It’s advantage for ship construction is obvious. Furthermore when a small amount of nanoparticles are added to the material, it tends to increase its stiffness and retards fire as well. In this paper we employ a unique micro/nano speckle technique to investigate the crack tip deformation field of two different polymer foams at a length scale that has never been studied before. The principle of the technique is described in [1]. Figure 1 shows the micrograph recorded by a scanning electron microscope of a crack propagating through a NEAT foam specimen under uniaxial tension. The void in front of the crack tip was kind of spontaneously generated as a result of the load. The main crack then tends to link itself towards the void as demonstrated in the sequence of pictures shown.

Fig 1. Crack propagation in a NEAT foam specimen under uniaxial tension While in the macro scale the crack will largely show propagation in the mode I characteristics at a micro/nanoscale the crack path is far from being a straight line. It tends to circle around a foam cell and then advance. But under the right circumstance it will break across the cell-to-cell interface. The nature of the propagation characteristics is revealed in the next example. Figure 2 shows the two micrographs (again recorded by an scanning electron microscope) at 50X and 100X magnifications, respectively, of a nano-phased foam beam specimen under 3-point bending with a single edge crack. The crack is perpendicular to the longitudinal axis of the beam and the tip of the crack is visible in the SEM micrograph at 50X. Figure 3 shows the displacement contours surrounding the crack tip at 50X magnification. The deformation field is rather complicated and it bears almost no relationship to the classical displacement field in the region around a crack tip. At a higher magnification, the deformation field is even more complicated, as shown in Figure 4.

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Fig 2. SEM micrograph of a nano-phased PVC foam beam under 3 point bending with a single edge crack

Fig 3. u and v displacement fields at 50x. Contour constant = 0.002Pm

Fig 4. u and v displacement fields at 100x. Contour constant 0.001Pm, Nano-phased PVC foam specimen with an edge crack under 3 point bending. As can be seen this is not a classical crack tip deformation field (for an isotropic and homogeneous material) at all. Of particular interest is the dense contour lines (at 1 nm/contour) surrounding a foam cell in front of the crack tip, indicating a stress concentration region. This implies that the cell-to-cell interface is strong and the crack tends to propagate around the foam cell as observed.

Acknowledgement The author would like to thank Dr. Yapa D.S. Rajapakse, Manager of the Solid Mechanics Program, US Office of Naval Research for supporting this work through grant #N000140410357 and Professor Hazzan Mahfuz of Tuskepee University for providing the foam materials.

Reference 1.

Chiang F.P., 2003a, “Evolution of white light speckle method and its application to micro nanotechnology and heart mechanics”, Optical Engineering Vol. 42 no.5, 1288-1292.

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HOW TO TOUGHEN CERAMICS – NANOCOMPOSITES H. Awaji and S.-M. Choi Nagoya Institute of Technology Gokiso-cho, Showa-ku, Nagoya, 466-8555 Japan [email protected] Ceramic-based nanocomposites with intra-type nano-structure have high strength with moderate fracture toughness. In this research, the toughening and strengthening mechanisms of the ceramicbased nanocomposites will be explained by dislocation activities even in brittle materials. Based on these mechanisms, we fabricated toughened and strengthened alumina-nickel nanocomposites. Fracture toughness of the annealed nanocomposites was 7.6 MPam1/2, which was two times higher than that of monolithic alumina.

Dislocation activities In intra-type nano-structure, nano-sized second-phase particles are embedded within the matrix grains. The highest strength or fracture toughness is mostly achieved when only a few volume percent of the second-phase particles are dispersed in ceramic materials. The structural characteristic of these nanocomposites results in the generation of thermally induced residual stresses around the dispersed particles in matrix grains [1]. We analyzed residual stresses using a simplified model consisting of a spherical particle within a concentric matrix sphere with axial symmetry [2]. Residual stresses numerically calculated on the particle-matrix boundary for alumina/nickel nanocomposites are shown in Table 1, where the symbols with suffix p indicate the properties of the particle (nickel) and the symbols with suffix m are the properties of the matrix (alumina). It is noted that there is a large maximum shear stress on the boundary. Figure 1 shows the temperature dependence of the residual shear stress on the boundary of alumina/nickel, and critical resolved shear stresses for basal and prism plane slips in a single áalumina crystal measured by Lagerlöf et al. [3] This figure indicates that dislocation movements are possible in the alumina grains at temperatures ranging from 600 to 1400 ºC, suggesting that this temperature range is quite important in creating dislocations in the alumina matrix during the cooling process.

Strengthening mechanism The grains of sintered alumina contain tensile residual stresses resulting from anisotropic thermal expansion, etc. Therefore, it is conceivable that the large crack along a grain boundary created by the synergetic effect of both residual stresses and processing defects, will be equivalent to the grain size of the materials and that the weakest crack generated along a boundary in the specimen will dominate the strength of the specimen. Nanocomposites, however, will yield dislocations around the particles, and the dislocations release residual stresses in the matrix. Consequently, the defect size along the grain boundaries is reduced in nanocomposites. TABLE 1. Residual stress along the particle-matrix boundary in alumina-nickel nanocomposites.

System Al 2 O 3 -Ni

Į m /Į p ×10 -6 (K -1 ) 8.8/13.3

E m /E p (GPa) 380/207

IJ m ax (GPa) 1.0

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Also, the dislocations are difficult to move in ceramics at room temperature, serve as origins of small stress concentrations, and create nano-cracks around the propagating crack tip. These nanocracks reduce the strength of the alumina matrix slightly and change the fracture mode from intergranular fracture in monolithic alumina to transgranular fracture in nanocomposites.

Toughening mechanism To improve the intrinsic fracture toughness of ceramics, the fracture energy consumed in the frontal process zone (FPZ) must be increased [4], which is called the FPZ toughening mechanism. Because ceramics are brittle, the FPZ of ceramics is considered to be constructed by many nanocracks rather than dislocations in metals. Therefore, we must consider how to create many nanocracks in the FPZ. Assuming that we obtained the nano-structure with dispersed dislocations within the matrix grains after annealing, these dislocations become sessile dislocations at room temperature. In this situation, when the tip of a propagating large crack reaches this area, these sessile dislocations will operate as nano-crack nuclei in the vicinity of the propagating crack tip. The highly stressed state in the FPZ is then released by nano-crack nucleation, and the nano-cracks expand the FPZ size, enhancing the intrinsic fracture toughness of the materials.

References 1.

T. Matsunaga, et al., J. Ceram.Soc., Japan, vol. 113, 123-125, 2005

2.

H. Awaji, et al., Mechanics of Materials, vol. 34, 411-422, 2002.

3.

K. P. D. Lagerlöf, et al., J. Am. Ceram. Soc., vol. 77, 385-397, 1994.

4.

S-M. Choi and H. Awaji, Science & Tech. of Advanced Mater., vol. 6, 2-10, 2005.

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DEFORMATION AND FRACTURE BEHAVIOUR OF NANOCOMPOSITES S. Dunger, J. K. W. Sandler, K. Hedicke and V. Altsadt University of Bayreuth, Department of Polymer Engineering, FAN A - Universitatsstrase 30 95448 Bayreuth, Germany [email protected] Polymer nanocomposites are of great scientific interest due to the potential of improving the resulting physical and mechanical properties of components, which cannot be modified using conventional reinforcements. However, the successful development and industrial implementation of such novel materials, especially of structural components, pose unique challenges. Nanocomposites with oriented nanoparticles and good adhesion between both phases can offer a stiffness and strength increase comparable to conventional fibre-reinforced composites [1 - 3]; however, only moderate filler weight fractions are possible due to the large specific surface area of the particles [4]. Nevertheless, at the same time, nanoscale fillers can maintain or even increase the composite thoughness [5-7]. For certain applications such as delicate structures the use of nanoscale reinforcements therefore offers a unique potential [8]. For a given matrix and nanoscale reinforcement system, processing leading to a good dispersion and distribution as well as orientation of the nanophase is crucial. The dispersion of nanoparticles especially depends on a magnitude of processing parameters, e.g. shear rate and processing temperature, as well as on the selection of appropriate materials. In addition, interactions between the nanoscale reinforcement and the polymer matrix during processing significantly influence the orientation of individual particles and the molecular morphology in the vicinity of the particles. The presentation will highlight the resulting deformation and fracture behaviour of different polymer nanocomposites, taking into account variations in the matrix morphology as a function of nanofiller type, geometry, surface chemistry and processing. Given that nanofillers have been shown to lead to distinct variations in the resulting interphase, an investigation of the fracture mechanics is especially important in order to understand the commonly occurring transition from a ductile to a brittle behaviour of such nanocomposites. In order to analyse the influence of the matrix ductility on the resulting nanocomposite fracture behaviour, polystyrene, polyamide 6, and polystyrene-polybutadiene-polystyrene block copolymer were chosen as matrix materials. The influence of the nanofiller geometry is investigated by using silicate clays, silicium dioxide nanoparticles and tubular clay nanostructures. Moreover, the resulting interphase properties are modified by different silicate surface treatments. The mechanical properties of the nanocomposites as well as of comparative glass fibre-reinforced composites were characterised by tensile tests, KIc tests and crack propagation tests. The fractured surfaces of the specimens were extensively analysed by SEM. In order to investigate the fracture behaviour during deformation, TEM analyses help to observe and explain the crack propagation of the nanocomposites as presented in fig 1. Finally, a comparison between traditional fibre-reinforced systems and the novel nanocomposites is made.

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Fig. 1: Crack propagation and deflection in polyamide 6 nanocomposites

References 1.

Fornes, T. D., Paul, D. R.; Polymer 44, (2003), 4993-5013

2.

Galgali, G., Agarwal, S., Lele, A.; Polymer 45, (2004), 6059-6069

3.

Fisher, F. T., Bradshaw, R. D., Brinson, L. C.; Composite Science and Technology 63, (2003), 1689-1703

4.

Luo, J.-J., Daniel, I. M.; Composite Science and Technology 64, (2003), 1607-1616

5.

Zerda, A. S., Lesser, A. J.; Journal of Polymer Science: Part B 39, (2001), 1137-1146

6.

Chen, L., Wong, S.-C., Liu, T., Lu, X., He, C.; Journal of Polymer Science: Part B 42, (2004), 2759-2768

7.

Gojny, F. H., Wichmann, M. H. G., Kˆpke, U., Fiedler, B., Schulte, K.; Composite

8.

Science and Technology 64, (2004), 2363-2371

9.

Nam, P. H., Maiti, P., Okamoto, M., Kotaka, T.; Polymer Engineering and Science 42, (2002), 1907-1918

1T9. Failure of nanocomposites

95

FRACTURE MECHANISMS IN CARBON NANOTUBE-REINFORCED COMPOSITES E. T. Thostenson and T.-W. Chou Department of Mechanical Engineering and Center for Composite Materials University of Delaware Newark DE 19716 USA [email protected] Carbon nanotubes have been targeted for potential applications ranging from the next generation of computers and flat-panel displays to structural and functional materials. In addition to their wellknown stiffness (> 1 TPa) and strength (~30 GPa) properties, carbon nanotubes also possess exceptionally high electrical and thermal conductivities, with the axial thermal conductivity near that of crystalline diamond. The unique mechanical and physical properties of nanotubes offer tremendous opportunity for the development of multi-functional composites [1, 2]. Full understanding of the thermo-mechanical behavior of nanotube-based composites, requires knowledge of the elastic and fracture properties of carbon nanotubes as well as interactions at the nanotube/matrix interface. Although this requirement is no different from that in conventional fiber composites [2], the scale of the reinforcement phase diameter has changed from micrometer (e.g. glass and carbon fibers) to nano-meter. The change in reinforcement scale poses new challenges in the development of processing techniques for these composites as well as characterization techniques and methodologies to measure their elastic and fracture behavior. A fundamental knowledge of the process/structure/property relationships is required to enable the design of multi-functional materials by structuring at the nanoscale. A novel technique to produce continuous nanocomposite ribbons of aligned multi-walled carbon nanotubes has been developed [3]. This model nanocomposite system serves as a basis for the investigation of structure/property relationships through characterization of their elastic and fracture behavior. The elastic and fracture behavior of the model nanotube composites indicate the anisotropy in the load transfer and confirm that nanotubes are able to carry load that is transferred via shear stresses at the nanotube/matrix interface and through characterization of this model system a fundamental knowledge of their structure/property relations has evolved [4]. The tensile fracture behavior of carbon nanotube composites show similar mechanisms as in traditional fiber composites including nanotube fracture, pullout, and crack bridging [3]. For compressive deformation, critical nanoscale buckling behavior of carbon nanotubes was observed where small diameter nanotubes deform through global bending analogous to Euler-type buckling and large diameter nanotubes show locally sharp kinking [5]. These deformation behaviors suggest a critical diameter may exist for the change in buckling modes and could have significant implications on the nanoscale design of composite compressive properties. Recent research by Gojny et al. [6] has shown that very low concentration of double-walled carbon nanotubes (0.1 wt%) can result in substantial improvements in fracture toughness. In order to evaluate the influence of multi-walled carbon nanotubes on the fracture toughness of epoxy nanocomposites we fabricated composites with nanotube contents ranging between 0.1 wt% and 1 wt% in an EPON 862 epoxy matrix. The nanotubes were first dispersed in the epoxy resin and the curing agent (Epi-Cure W) was added. The nanocomposites were then placed in a mold and cured for 6 hours at 130oC. Fracture toughness measurements were conducted using the single-edgenotch bending (SENB) method. Specimens were notched with a tapered diamond blade and a precrack was introduced by tapping with an ultra-sharp carbon steel razor blade.

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The fracture toughness of the epoxy nanocomposites was significantly improved as compared to the unreinforced resin. This indicates that nanotubes provide a reinforcing effect in improving the fracture toughness through crack deflection or nanotube fracture and pullout. SEM micrographs of the composite fracture surface show a change in the micron-scale surface roughness and also the presence of nanotube pullout.

References 1.

Thostenson, E.T., Li C.Y. and Chou T.W. Compos. Sci. Technol., vol. 65, 491-516, 2005

2.

Thostenson, E.T., Ren Z.F. and Chou T.W. Compos. Sci. Technol., vol. 61, 1899-1912, 2001

3.

Thostenson, E.T. and Chou T.W. J Phys D: Appl. Phys. vol. 35, L77-L80, 2002

4.

Thostenson, E.T. and Chou T.W. J Phys D: Appl. Phys. vol. 36, 573-582, 2003

5.

Thostenson, E.T. and Chou T.W. Carbon vol. 42, 3015-3018, 2004

6.

Gojny F., Wichmann M and Kopke U, et al. Compos. Sci. Technol., vol. 64, 2363-2371, 2004

B. TRACKS

B2. Engineering Materials and Structures

2T1. Physical aspects of fracture

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FRACTAL APPROACH TO CRACK PROBLEMS WITH NON-ROOT SINGULARITY A. Kashtanov St.-Petersburg State University Universitetsky pr. 28, 198504 St.-Petersburg, Russia [email protected] Fractal approach to the problems of fracture mechanics with non square root singularity of the stress field is discussed. Fractal generalization of Griffith energy balance equation is proposed and analysis of the fracture process at the sharp angular notch in a plate is performed. Good correspondence between suggested approach and experiments is observed. It is obvious that propagation of fracture surface is much more complex process than a simple spreading of rectilinear crack with smooth faces and usually the crack surface has a lot of irregularities of different sizes. The roughness of fracture surface can be accounted with the help of fractal correction for the calculation of specific properties suggested by Mandelbrot [1]. It allows us to receive more precise model of fracture process and to solve the problems of crack mechanics, which do not have an adequate solution within the frameworks of traditional theory. One way is the simulation of the crack by fractal with dimension determined from some theoretical reasons at the fixed scale level. Then, solving a specific problem for simulated “fractal” crack it is possible to determine some physical magnitudes, which values can be easily checked experimentally, for example, the value of critical loading. In particular it is suggested to evaluate the fractal dimension by sufficing to the energy balance equation. In order to construct this equation for the case of “fractal” cracks the following generalized energy balance concept was proposed by Kashtanov and Petrov [2]: •

The work of crack opening ' W is the integral parameter of stated problem and is determined at the macroscopic scale level.

•

The surface energy of crack '3 is calculated using the crack fractal length L to take into account the microstructure of crack surface.

•

The fractal dimension D of simulated crack is defined from the validity of energy balance equation ' W '3 at the macroscale.

•

At the macroscopic scale level the fracture process is characterized by the size of an elementary fracturing cell

d

2 K 12c

S V c2

(1)

where V c is the ultimate strength of defectless material and K 1c is the static fracture toughness. Therefore it is convenient to use the fractal low at the macroscale in the form

L where

l

l d D d

is the crack length at the macroscale.

(2)

A. Kashtanov

100

As an example of such approach the plane problem about an angular notch can be considered. This problem is characterized by the non square root singularity of the stress field and it has no solution in Griffith–Irwin theory of fracture. Nevertheless, if we suppose that the crack formed in the notch vertex is a fractal then the connection between the value of fractal dimension of modeled crack and actual structural parameters of fracture process can be constructed analytically from the generalized energy balance equation. Then the critical load required for fracture at the crack tip can be found and good coincidence with experiments is observed (Fig. 1).

FIGURE 1. The dependence between the critical loading and the hole length. At the Fig. 1 the dependence between fracturing loading and the notch angular is displayed. The solid line corresponds to the solution of generalized energy balance equation; the dotted line displays the same dependence calculated from Neuber – Novozhilov fracture criterion; and experimental data are pointed by circles. All the experiments have been conducted in St.-Petersburg University by I. Bugakov and I. Demidova.

References 1.

Mandelbrot, B. B., The Fractal Geometry of Nature, Freeman, Berlin, New York, 1983.

2.

Kashtanov, A.V., Petrov, Y.V., Int. J. of Fracture, vol. 128, N 1, 271-276, 2004

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NEW METHOD FOR ANALYSING THE MAGNETIC EMISSION SIGNALS DURING FRACTURE Gy. B. Lenkey, N. Takacs1, F. Kun2 and D. L. Beke3 Bay Zoltán Foundation for Aplied Research, Institute for Logistics and Prod. Systems, Miskolc, Hungary 1 Metalelektro Co. Budapest, Hungary 2 Department of Theoretical Physics, University of Debrecen, Debrecen, Hungary 3 Department of Solid State Physics, University of Debrecen, Debrecen Hungary [email protected], [email protected], [email protected], [email protected] In dynamic fracture testing the precise determination of the onset of crack initiation is crucial in order to obtain characteristic quantities of the material. This task can be solved easier in case of brittle fracture since brittle fracture is usually accompanied by a sudden drop in the force signal. But in case of ductile fracture or if stable crack propagation occurs before unstable one, the instant of crack initiation cannot be determined directly from the force signal. In these cases additional measurement techniques should be applied. The magnetic emission technique has been proved for detecting brittle crack initiation of ferromagnetic materials [1-3]. Two physical phenomena contribute to the magnetic emission signal [1]: (a) mechanically induced Barkhausen signals appear when the internal magnetic structure changes during loading, and (b) a propagating crack causes the internal magnetic field to emerge from the solid into the gap between the two crack surfaces, thereby changing the external magnetic field. These field variations can be observed locally by a magnetic transducer which basically consists of a coil. The transducer's output voltage is the magnetic emission (ME) signal which is proportional to the derivative of the magnetic field (MF). The aim of the present work was to apply new statistical methods [4-9] to analyze the magnetic emission signal to extract more information about the fracture process. Magnetic emission spectra recorded in dynamic fracture experiments on ferromagnetic materials are composed of more or less well-separated voltage peaks which provide direct information about the microscopic processes involved in fracture. It will be illustrated, that before crack initiation sudden movements of domain walls under external mechanical loading results in low peaks. After crack initiation the opening of the growing crack provides the dominating contribution for the voltage signals and is responsible for the higher peaks of the spectrum. After removing a background voltage level the ME spectrum is characterised by the distribution of the height, area, and width of peaks, furthermore, correlations among these quantities. One example for the evaluated peak parameters is shown in Fig. 1. While for the “low peaks” part (before crack initiation) no typical functional form can be extracted, for the height distribution of peaks in the crack propagation regime the distributions show power law behavior over a range of one order of magnitude. The analyses of magnetic emission signals recorded during brittle and ductile failure showed that the value of the exponent of the power law regime is characteristic for the failure mode: an exponent significantly higher than for brittle failure characterizes ductile failure. The distribution of the peak areas has a similar overall character, however, the power law regime spans practically two orders of magnitude and the area distribution is universal in the sense that it does not change with the impact velocity: it depends solely on the failure mode.

Gy. B. Lenkey et al.

102

FIGURE 1. Area distribution of peaks p(A) for different impact velocities and failure modes.

References 1.

Gy. B. Lenkey, S. Winkler.: Fatigue and Fracture of Engineering Materials and Structures, Vol. 20., No. 2., pp. 143-150., 1997

2.

Equation Section 1 Gy. B. Lenkey, L. Tóth: Mat.wiss. und Werkstoffmech., 32, 1-6, pp. 1-6., 2001

3.

Gy. B. Lenkey: ASTM STP 1380, T. Siewert and M. P. Manahan, Sr., Eds., American Society for Testing and Materials, West Conshohocken, PA, pp. 366-381., 1999

4.

M. C. Miguel, A. Vespignaid, S. Zapperi, J. Weiss and.J. Grasso, Nature 410, 667, 2001

5.

A. Maes, C. Van Moffaert, H. Frederix, and H. Strauven, Phys. Rev. B 57, 4987, 1998.

6.

A. Guarino, S. Ciliberto, A. Garcimartin, M. Zei, and R. Scorretti, Eur. Phys. Jour. B 26, 141, 2002

7.

R. A. White and K. A. Dahmen, Phys. Rev. Lett. 91, 085702, 2003

8.

L. I. Salxninen, A. I. Tolvanen, and M. J. Alava, Phys. Rev. Lett. 89, 185503, 2002

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ELECTROMAGNETIC RADIATION METHOD FOR IDENTIFICATION OF MULTI-SCALE FRACTURE Yu. K. Bivin, A. S. Chursin, E. A. Deviatkin and I. V. Simonov Institute for Problems in Mechanics of RAS Vernadskogo av. 101-1, 119526 Moscow, Russia [email protected] The electromagnetic radiation (EMR) as well as acoustic emission (AE) is the statistical phenomenon in fracture. Measurements of EMR can serve the purpose of identification. The experimental data on this point are known for ion crystals, metals, rocks. The explanation of physical mechanism has been given ideally, for example, in the case of shock wave in an “ideal” metal. Aim of the present work is to develop this promising method of EMR and to show its possibilities for registration of multi-scale fracture mainly within non-conductors, structural materials. A review of experimental results includes the following events: the fast micro-fracture in ice, the single crack propagation in glass, the velocity decay during ball penetration in a ground medium, the single free fiber break. The EMR signals were recorded by an antenna over radio range of frequency spectrum. It is noteworthy that they reflect adequately the mentioned dynamic fracture processes. So, when a single crack propagates with a constant or varying velocity, the EMR signal behaves in like manner. Moreover, the high frequencies appear also due to microcracking on the crack surfaces, and even their vibrations with low frequencies after the crack stop is designed clearly on the oscillogram. Series of tests on edge splitting of plates has been also conducted. Sizes of specimens from polymetilmetacrilate (PMMC), glass-epoxy (GE) and carbon-carbon composite (CCC) (the last two are the unidirectional fiber-reinforced composites) were approximately uu mm³. The artificial initial 10-15 mm length cut along the central plane was sharpened. Each specimen was loaded step by step with the incremental normal force on the split plate edge. The determination of fracture parameters was performed by a compliance calibration technique, in particular, for the purpose of validation of the tests. The theoretical predictions base on the principles of linear fracture mechanics and the two conventional methods are demonstrated in the tests. To determine the fracture toughness and Young’s module, the limit load and edge displacement were measured at the crack start. These values are in agreement with the tabular ones. Another concerns the calculation of new crack surface and the loss of work per the "loadingunloading" cycle on the "force-displacement" quarter-plane during a crack jump. Then the energy release rate can be determined. The acoustic emission and the outward electric field near to crack tip were simultaneously recorded. The load and displacement as a mechanical field, along with the AE and EMR, say, the physical fields, exhibit different feature before the crack start and during its galloping motion. The AE and EMR appear at the sharp increasing the load when a damage (micro-cracking, fiber break) apparently occurs nearby the stationary crack front. The downward load jump corresponds to the crack start and a maximum of the physical fields activity. The analysis of correlation of these fields and comparison their amplitude and frequencies for different structures with each other are the new elements in the failure/fracture. It was revealed that the GEC gives maximum the AE and EMR activity among the materials tested. This reflects the intense micro-cracking of GEC which has been proved by visual inspection. The minimum accounts for the CCC that is rather more “perfect” structure than GEC. The EMR pulses turn out to possess the good sensitiveness and

104

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correlate with AE data in the main. But the electric activity minimum in the case of CCC is also explained by good carbon conductivity. It can be concluded that the EMR record is the very simple, non-destructive, temperature independent, and cheaper method for detection of different dynamic fracture stages into structural materials and determination of limit loads. To use this method in combination with the AE technique will lead to essential increasing reliability for the event identified, especially, in the cases when the noise influence is expected. The future experimental data will also be presented. This work was partly supported by the Program N13 of the Russian Academy of Sciences and the Russian Foundation of Basic Researches, N 05-01-00628.

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MICROMECHANICAL MODELING OF GRAIN BOUNDARY RESISTANCE TO CLEAVAGE FRACTURE PROPAGATION M. Stec and J. Faleskog KTH Solid Mechanics, Royal Institute of Technology Osquars Backe 1, SE-100 44 Stockholm, SWEDEN [email protected], [email protected] Failure of polycrystalline structures due to cleavage fracture can be summarized in three critical steps: (i) fracture of a brittle particle, e.g. a carbide, cause rapid growth of a micro-crack, (ii) which must generate sufficient energy release to propagate into the much tougher surrounding matrix material. In order to become critical, (iii) the micro-crack must propagate over grain boundaries into neighbouring grains. An initiated microcrack may arrest at several instances. In a micromechanical analysis by Kroon and Faleskog [1] step (ii) was examined and they found that a micro-crack can arrest before the first grain boundary is reached. Based on a weakest link concept Anderson et al. [2] studied cleavage crack growth across hexagonal grains and showed that grain boundary resistance have a direct influence on the fracture toughness threshold. Moreover, they also showed that if the microcrack arrests, it will most likely arrest at the first grain boundary encountered. In this study the conditions for a microcrack to arrest at the first encounter with a grain boundary is investigated using micromechanical analysis. The cleavage planes in ferritic steels is one of the three {100} planes (Miller index notation). At a grain boundary, the orientation of cleavage planes typically changes, as illustrated in Figure 1(a), where the cleavage crack has propagated from grain A into grain B. The relative difference in orientation between adjacent cleavage planes can be characterized by two angles: a tilt-angle and a twist-angle , see Figure 1(a). A grain usually has about 5-6 neighboring grains. The distance along the grain boundary, where grain A meets primary cleavage planes of grain B, is here on the average taken as w, see Figure 1(c). Experimental estimations of w can be found in a series of fracture tests carried out by Qiao and Argon [3]. The micromechanical analysis is in the present study inspired by the experimental observations made by Qiao and Argon [3] and based on an idealized model of two grains, where grain A is modeled as a circular cylinder entirely surrounded by grain B, see Figure 1(b). Furthermore, the primary cleavage planes in grain A and grain B are assumed to intersect each other with a periodicity of w, as is illustrated in Figure 1(c). In order to understand to what extent the grain boundary can act as a barrier and obstacle, an effective energy release rate for a microcrack that has propagated to radius R ( t R G B ) an be formulated as *e

K 2 * A  (1  K 2 ) * B f B (\ , M )  K 2 * GB

w R GB

f GB (\ , M )

.

(1)

Here, *A , *B and *GB are critical energy release rates associated with grain A, grain B, and the grain boundary, K

RGB R (see Figure 1(a)), and f

B

and f GB are functions of the

misalignment angles ( ȥ , ij ) and is of order unity. Both grain A and grain B are modeled as elastic viscoplastic materials. The crack growth is modeled using cohesive surfaces, where the tractions are governed by a modified exponential cohesive law in order to control the initial slope. The micromechanical model was numerically analyzed by use of finite element modeling. The analysis consisted of two phases. In the first one, true (Cauchy) tractions were applied quasi-statically on the remote boundary (see Fig. 1(b))

M. Stec and J. Faleskog

106

corresponding to the axial and radial stresses Ȉ Z and Ȉ R , respectively. In the following dynamic phase both Ȉ Z and Ȉ R were held constant. The cleavage crack was then initiated in grain A and started to grow in the radial direction until it encountered the grain boundary. The crack plane either penetrated the grain boundary and continued into grain B or arrested. The main question in the analysis was: given the overall stress state—how large can grain A be in order for the cleavage crack not to penetrate grain B and possible cause catastrophic failure. The critical stress state required to propagate the cleavage microcrack across grain boundary into grain B and further depends

primarily

on:

stress

ratio

[6R 6Z ]

and

grain

boundary

features

[ ȥ , ij , w * G B ( R G B * B )].It should also be pointed out that the characteristics of the cohesive surfaces and the elastic viscoplastic behavior affects the results.

Figure 1. Grain boundary model characterization: (a) orientation of cleavage planes, (b) idealized micromechanical model and (c) crack plane definition at grain boundary.

References 1.

Kroon M., Faleskog J., J. Mech. Phys. Solids, vol. 53, 171-196, 2005

2.

Anderson T., Stienstra, D. and Dodds, Jr. R. H., In Fracture Mechanics: 24th volume, ASTM STP 1207, edited by J.D. Landes, et al. ASTM, Philadelphia, 1994, 186-214.

3.

Qiao Y., Argon A.S., Mech. Mat., vol. 35, 313-331, 2003.

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MICROSTRUCTURE OF REACTOR PRESSURE VESSEL STEEL CLOSE TO THE FRACTURE SURFACE M. Karlik, P. Hausild and C. Prioul1 Czech Technical University, Faculty of Nuclear Sciences and Physical Engineering, Department of Materials, Trojanova 13, 120 00 Praha 2, Czech Republic 1 Ecole Centrale Paris, LMSS-Mat,Grande Voie des Vignes, 92295 Châtenay–Malabry, France [email protected], [email protected], [email protected] A transmission electron microscopy study of microstructure in the vicinity of fracture surface was carried out in French tempered bainitic nuclear reactor pressure vessel steel 16MND5 (equivalent to the American standard A508 Class 3). Cross-section thin foils from nickel electroplated Charpy V-notch specimens fractured in impact and quasi static loading at -30°C (ductile to brittle transition temperature region) were prepared in the ductile tearing and cleavage regions of the fracture surface (Fig. 1).

FIGURE 1. Slice cutting in the central part of a Charpy V-notch sample and the TEM disc positions in cleavage – C and ductile – D fracture zones. In the ductile tearing zone, the microstructure was very heterogeneous. Dislocation cells, shear bands, and fine heavily deformed subgrains were found. The deformation in the impact specimen was often localized only in the vicinity of the fracture surface, where long thin cells formed due to dynamic recovery (Fig. 2). In the quasi static three-point bend specimen, the localization was found also in deeper areas under the fracture surface. There were shear bands (bundles of long thin cells) mostly aligned in parallel to the fracture surface. Numerous areas of the shear band intersections (at ~45° to the main shear band direction) were also observed. Comparing the microstructure in the ductile tearing zone of the Charpy impact specimens with the corresponding part of the fracture of the CT25 fractured in quasi-static loading in previous research [1], there are two similar features. The deformation is very heterogeneous - heavily deformed material with very small and dislocation arranged in cells. On the other hand, there were no twins, neither shear bands found in Charpy specimens. The shear bands were transformed by dynamic recovery into long thin subgrains.

M. Karlík et al.

108

FIGURE 2. Microstructure of the steel in the ductile tearing region - very thin subgrains (50 to 100 nm) formed due to the local increase in temperature leading to dynamic recovery of dislocations during rupture of impact specimen. In the cleavage zones of both types of specimens, only an increased dislocation density was found, no twins were observed. The reason for the absence of twins could be that the material of the much smaller Charpy specimen was plastically deformed (bending of the test specimen) before the cleavage crack propagation and the twins could not form due to an increased density of dislocations.

References 1.

Karlík, M., Nedbal, I., Siegl, J., Mater. Sci. Eng. A 357, 2003, 423-428.

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BRITTLE FRACTURE IN HEAT-AFFECTED ZONES OF GIRTH WELDS OF MODERN LINE PIPE STEEL (X100) A. S. Bilat, A. F. Gourgues-Lorenzon, J. Besson and A. Pineau Centre des Matériaux, Ecole des Mines de Paris, UMR CNRS 7633, B.P.87, F-91003 Evry cedex [email protected], [email protected] Gas field development requires a cost reduction of gas transport. For that purpose, one solution is to increase gas pressure inside pipes. High strength steels of API grade X100 (yield stress above 690 MPa) are potentially good candidates for these new applications [1], but the toughness of X100 welded joints involves characterization. The aim of this project is to improve the accuracy of prediction tools of the toughness and defect acceptability in such a GMAW welded joint, by building a quantitative prediction tool of the risk of brittle fracture, adapted to the girth welds of new X100 steels, and by determining and validating a crack initiation criterion in the most critical zones of this welded joint. This study is conducted according to the local approach to fracture procedure [2]: first, metallurgical and mechanical characterization of the girth weld, then, thermal welding cycle simulation of the most critical zones and characterization of their fracture properties and, finally, finite element modelling of brittle fracture initiated at these critical zones. Hardness and microstructures were thoroughly characterized in each zone (Fig. 1). The weld consists of three main zones: the base metal (BM), the weld metal (WM) and the Heat-Affected Zone (HAZ). The BM microstructure is a textured bainitic matrix with ferrite and some secondary phases; the WM is acicular ferrite and the Heat-Affected Zone is upper bainite. The HAZ is itself divided in three zones: the coarse-grained (CG)HAZ (austenite grain size around 30 µm, spread over 100 µm) near from the WM, the fine-grained (FG)HAZ (austenite grain size around 10 µm, spread over 100 µm), and the intercritical (IC)HAZ (MB tempered between Ac1 and Ac3 spread over 1 to 2 mm). The mechanical strength of the joint was characterized by using tensile and impact tests (Fig. 2). Specimens were cut from the BM, and the WM, but the HAZ is too small to machine homogeneous specimens, so that it is necessary to reproduce some HAZ microstructures. Two microstructures (CG and FG) are reproduced by applying a simulated weld thermal cycle on base metal blanks with a thermal-mechanical simulator (Gleeble). The welding thermal cycles are determined experimentally by inserting a thermocouple in the heat affected zone of the joint during a real welding operation and the Rykaline model [3]. All these specimen are then machined and mechanically tested in tension at various temperatures. The weld is matched in yield stress (YSWM=YSBM), and overmatched in tensile strength (TSWM>TSBM), because the base metal of the pipe exhibits little work-hardening. The impact tests show low fracture energy at –20 °C, when the specimen is taken from the inner subsurface part of the pipe wall and the notch is located on the fusion line (FL i). The brittle fracture of these specimens is systematically localized in the CG zone, which consists of upper bainite with Martensite-Austenite constituents. The mechanical properties of the various zones of the weld will be used in a numerical finite element model together with a statistical brittle fracture criterion to describe the behaviour of this “multi-material” assembly.

A. S. Bilat et al.

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Acknowledgments: Technical support and constant interest from Serimer-Dasa, Gaz de France and Europipe as well as financial support from CEPM are gratefully acknowledged.

References 1.

Glover, A., In Proceedings of the international Pipe Dreamer’s Conference, co-organized by M.Toyoda and R. Denys, Yokohama, Japan, 2002, 33-52.

2.

Besson, J., Local approach to fracture, Presses de l’Ecole des Mines, Paris, France, 2004.

3.

Rykaline, N. N., Calcul des processus thermiques de soudage, Soudage et Techniques connexes, 1961 (in French)

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CLEAVAGE FRACTURE OF STEELS AT VERY LOW TEMPERATURES R. Rodriguez-Martin, I. Ocana and A. Martin-Meizoso CEIT, Centro de Estudios e Investigaciones Técnicas de Guipúzcoa and TECNUN, Escuela Superior de Ingenieros, University of Navarra Paseo Manuel de Lardizábal, 15, 20018 San Sebastián, Spain [email protected], [email protected], [email protected] The mechanical strength of polycrystalline metals is frequently associated with the propagation of defects present in their structure as cracks or dislocations. Nevertheless, when these defects are absent, the crystal lattice becomes decisive and the strength is determined by the stress at which the lattice losses its stability. This stress is known as the ideal strength, Clatterbuck et al. [1], Krenn et al. [2], and it is especially relevant in experimental situations where there are few mobile defects. This paper proposes that, in bcc metals, brittle fracture at very low temperatures is caused when an ideal cleavage strength is reached in their structure. At such low temperatures, the movement of the defects is frozen and the material will behave as if it were free from defects. Under these conditions, a common bcc metal would cleavage on (100) planes under an uniaxial tensile stress. The mechanism proposed lies in the initial breakage of the grain having the best oriented (100) plane with respect to the applied load. Subsequently, other grains with a favourable orientation take its load and may break, causing the macroscopic failure of the test-piece or component. Figure 1 shows an example of a random grain distribution with their respective orientation for their (100) planes.

FIGURE 1. Schematic of a fatigue pre-cracked body with a random grain distribution at the fatigue crack front. The orientation of a (100) plane is showed for some grains. The value of the ideal cleavage strength on (100) has been investigated for many bcc metals on the basis of ab-initio electronic structure calculations, [1-2], Friak et al. [3]. From these calculations, cleavage fracture of the high strength steels of which chemical compositions are listed in Table 1, has been analysed.

R. Rodriguez-Martin et al.

112

TABLE 1. Chemical composition of steels (%).

Previously precracked compact tensile specimens extracted from these materials have been used in fracture tests. These tests were conducted at very low temperatures (liquid nitrogen). Subsequent fractographic analyses showed the presence of multiple initiation sites situated close to the fatigue crack in the fractured specimens of all the materials. Also a low-scatter in the obtained results suggested that a similar mechanism causes the brittle failure for the three materials studied. Taking into account all these experimental observations, the possibility of ideal cleavage strength to control the brittle fracture makes sense. In order to predict this fracture behaviour at low temperatures, a simulation program has been developed in Matlab£ code. The program generates a random grain distribution for a precracked body. The crack is assumed to blunt under load, following the behaviour proposed by McMeeking [4]. From this point forward, the program calculates the applied load required for the failure of the random grain distribution by cleavage. This is achieved by taking into account that the ideal cleavage strength is reached in the grain with the best oriented (100) plane and subsequently transmitted to other grains with a favourable orientation.

References 1.

Clatterbuck, D.M., Chrzan, D.C. and Morris, J.X., Acta Mater., vol. 51, 2271-2283, 2003.

2.

Krenn, C.R., Roundy, D., Morris, J.W., Cohen, Marvin L., Mat. Sci. Eng. A319-321, 111-114, 2001.

3.

Friak, M., Sob, M. and Vitek, V., Phil. Mag., vol. 83, 3529-3537, 2003.

4.

McMeeking, R.M., J.Mech.Phys.Solids., vol. 25, 357-381, 1977.

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NEW FORMULATION OF THE RITCHIE, KNOT AND RICE HYPOTHESIS A. Neimitz, M. Graba and J. Galkiewicz Kielce University of Technology Al. 1000 lecia P.. 7, 25-314 Kielce, Poland [email protected] Several authors adopted a local fracture criterion to assess the constraint influence on fracture toughness. They assumed that the cleavage fracture to happen requires that the opening stress reaches critical value, Vc at certain distance from the crack tip, rc or within the certain volume in front of the crack tip. O’Dowd at al [1] adopted modified small strain HRR solution, henceforth called the OS model, to derive simple, approximate formula in order to predict the influence of in-plane constraint on fracture toughness of structural element. According to O’Dowd’s model the critical conditions must be satisfied independently the level of constraint, which was quantified by the actual value of the Q-stress, utilizing the OS theory. O’Dowd’s final formula to compute the actual value of fracture toughness is as follows:

JC

§ Q J IC ¨¨ 1  V c /V 0 ©

· ¸¸ ¹

n 1

(1)

where J is the J-integral, Vo is a yield stress, subscript c or Ic denotes critical state, Q is a parameter “measuring stress level in the modified OS model [1] Eq. 1 follows from the Ritchie, Knot, Rice (RKR) hypothesis provided one assumes that the stress field in front of the crack is singular (small strain assumption). In such a case the opening stress is greater than critical one over the distance rc from the crack front. However, the critical stress Vc is simply the parameter which adjusts theoretical prediction to experimental results. Almost all other theories concerning the local approach to fracture use the stress distribution in front of the crack characteristic for the finite strain. In real elastic-plastic materials the crack tip, originally sharp, is blunted by plastic deformation. This process modifies the small-strain HRR solution in front of the crack. Instead of singular stress field at the crack tip the opening stress decreases towards the blunted crack tip after reaching a maximum at the normalized distance r=MJ/V0 from the crack tip. Here, M is a function of constraint level, and the Ramberg-Osgood power exponent n at given external loading. In such a case the RKR hypothesis should be based on another assumption. Hypothesis: It is assumed that the cleavage fracture may happen if the opening stress in front max

of the crack exceeds the critical level over the distance l greater than lcrit ( V 22

>Vc and ltlc ).

max

If V 22 >Vc but l

@

fracture from the O, takes place along the direction OL, (OL)= c , when the dW / dV max min L reaches the critical value (dW/dV)c. The predicted crack path during propagation is the curve that starts from point L passes the points with the maximum gradient of (dW/dV) and ends up at point G, where the global minimum value of (dW/dV) develops. On the map, the crack path is indicated by V shaped contours of the strain energy density. If the apicals of the Vs points are joined by a line, then the resulted plot curve, starts from the peak O and arrives in the vicinity of the point G. In the geographic map the curve OG, represents a gorge or a riverbed, which starts from the hilltop O. The drawing of this gorge can give additional information for the estimation of the crack path’s stability according to following hypothesis: The stability of the crack path can be deduced from the degree of the sharpness with which the curve of the "gorge" is drawn. By collecting the results for different geometric characteristics of the specimens, we create a classification diagram of crack path stability. Our experiments were performed on double cantilevering beam (DCB) specimens made from PMMA material. The tests were performed by using a testing machine with controlled displacement at a rate of 0.5mm/min or less. These slow rates were chosen to reveal the specimens behavior while transiting across regions with different crack path stability of the classification diagram.

References 1.

Zacharopoulos, D.A., “Stability Analysis of Crack Path Using the Strain Energy Density Theory”, Theoretical and Applied Fracture Mechanics, vol. 41, 327-337, 2004.

2.

Sih G.C., “Introductory chapters in Mechanics of Fracture”, Vols. I to VII, ed. G.C. Sih, Martinus Nijhoff: The Netherlands, (1972-1982).

3.

Gdoutos, E.E., “Fracture mechanics”, Kluver Academic Publishers, 1993.

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SCRATCHING AND BRITTLE FRACTURE OF SEMICONDUCTOR IN-SITU SCANNING ELECTRON MICROSCOPE K. Wasmer, C. Pouvreau1, J. Giovanola1 and J. Michler Swiss Federal Laboratories for Materials Testing and Research (EMPA) Feuerwerkerstrasse 39, 3602 Thun, Switzerland 1 Swiss Federal Institute of Technology Lausanne (EPFL), ME A1 400, Station 9, 1015 Lausanne, Switzerland [email protected] Mastering the brittle facture (also called cleavage) of semiconductors is important when separating complex devices produced on epitaxially grown multi-layers or when processing III-V optical devices. Cleavage is usually performed in two stages. The surface is first micro-scratched with a sharp diamond tip, which induces structural defects. Secondly, by applying a load to the sample, fracture propagation is initiated, starting from the defect area. However, the mechanisms leading to the preparation of high quality cleavage surface are often not fully understood. The main objective of this paper is to present the fundamental phenomena occurring during the scribing and subsequent fracturing process of brittle semiconductors via in-situ Scanning Electron Microscope (SEM). In the literature, nano-indentation has been largely investigated also for semiconductors, Bradby et al. and Grillo et al. [1-2], but very little information is available in comparison in the field of scratching, Ballif et al. and Gassilloud et al. [3-4]. In this paper, the complete sequence of scratching is dissected via in-situ SEM observations. In order to perform these observations, a miniaturized microscratch device has been built for use inside a scanning electron microscope, Rabe et al. [5]. Also performed are Transmission Electron Microscope (TEM) investigations to visualise the network of dislocations. It has been found that the scratching operation can be divided into 5 distinct regions which are dependent of several parameters such as the shape of the diamond tip, the scratching direction and the applied loads. The first one is the elastic regime which cannot be observed in normal condition due to the total recovery after the withdrawal of the load. The second is the plastic regime where dislocation nucleation and / or slip bands are generated. This is followed by the subsurface cracking regime where median cracks (MC) along crystallographic planes are created. Then, cracks such as radial and lateral appear at the surface. The last regime takes place when the radial and lateral cracks join together since at this point a large amount of chipping out occurs. In order to obtain atomically flat cleavage surfaces, only the median crack, which depth will influence significantly the crack initiation and propagation, is required. Based on our experiments, it has been also seen that the depth of the MC can be assumed to be either linear or to the power 3/2 to the applied load as described by Eq. (1). This latter expression has already been reported to be valid for the nano-indentation Lawn [6]. Furthermore, the influence of the different epilayer on GaAs wafer is perceived to influence the onset of the crack median as well as its depth for loads ranging between 10mN and 50 mN.

(a) P v c ˜ d and (b) P v c ˜ d 3 / 2

(1)

The second part of the paper scrutinise the fracture process in brittle semiconductors such as GaAs. This includes the crack initiation of a defect in GaAs wafer, GaAs + epilayer wafer and laser diode processed on GaAs wafer with a thickness of around 150 m. The defect is assumed to be semielliptic with a length of 400 m and a depth in ranging from 5 to 20 m depending on the applied load. The wafer is then subjected to bending stress through two apparatus allowing in-situ cleavage

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118

of devices. The first one, integrated into the SEM chamber, has a stroke of several hundred of micrometers and is "displacement-controlled". Its displacement control is better than 100 nm and the force applied by the cleaving rod is acquired simultaneously. The second apparatus is very similar to the first one with a major advantage which is to be able to follow the crack during its propagation. With these tools, it has been demonstrated that although, semiconductors such as GaAs are considered as very brittle, it is possible to control the crack propagation when a big enough starter crack is present. For uncontrolled crack growth, features are visible on the cleaved surface which is consistent with the dynamic fracture mechanics principle Sauthoff et al. [7]. Finally, the effects due to the different epitaxial layers are in line with those observed on the depth of the median crack.

FIGURE 1: SEM pictures of a (a) scratch with a Cube Corner diamond tip; b) cleave showing crack deviation

References 1.

Bradby, J. E., Williams, J. S., Wong-Leung, J., Swain, M.W., MV, and P. Munroe, J. Mater. Res. Vol. 16, pp: 1500-, 2001.

2.

Grillo, S. E., Ducarroir, M., Nadal, M., Tourni, E. and Faurie, J.-P., J. Phys. D: Appl. Phys. Vol. 36, pp: 5-, 2003.

3.

Ballif, C., Wasmer, K., Gassilloud, R., Pouvreau, C., Rabe, R., Michler, J., Breguet, J.-M., Solletti, J.-M., Karimi, A. and Schulz, D. Advanced Engineering Materials, June 2005.

4.

Gassilloud, R., Ballif, C., Michler, J. and Schmuki, P., Submitted at Journal of Material Research.

5.

Rabe, R., Breguet, J.-M., Schwaller, P., Stauss, S., Patscheider J. and J. Michler, Thin Solid Films, Vol. 469-470, pp: 206-213, 2004.

6.

Lawn, B., "Fracture of Brittle Solids", 2nd Ed., Cambridge University Press, 1997.

7.

Sauthoff, K., Wenderoth, M., Heinrich, A. J., Engel, K. J., Reusch, T. C. G. and Ulbrich, R. G., Phys. Rev. B, Vol. 60, pp: 4789-95, 1999.

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CRACKS IN THIN SHEETS: WHEN GEOMETRY RULES THE FRACTURE PATH Pedro M. Reis, Basile Audoly1 and Benoit Roman2 Levich Inst., City College of New York, 140th St. & Convent Av., New York, NY 10027, USA 1 LMM, UMR 7607 CNRS/UPMC, 4 place Jussieu, case 162, 75252 Paris cedex 05, France 2 PMMH, UMR 7636 CNRS/ESPCI, 1O rue Vauquelin 75231 CEDEX 5 Paris, France [email protected] We study both experimentally and theoretically the propagation of brittle fracture coupled to large out-of-plane bending, as when a brittle elastic thin sheet is torn by a rigid moving object [1-3]. Taking into account the separation of the film’s bending and stretching energies and using classical fracture theory we have shown that such cracks can propagate according to a simple set of 2D geometrical rules in the limit of vanishing thickness, h [3]. Numerical integration of our geometrical model accurately reproduces both the shape of the fracture pattern and the detailed time evolution of the propagation of the crack tip. In our experiments, a rigid object, the cutting tool, is forced through a thin polymer film and tears through the material as it advances. A schematic diagram of the process is presented in Fig. 1(a,b). The film is clamped at its lateral boundaries imposing no initial tension. The cutting tool is oriented perpendicularly to the horizontal film and is driven through the material at constant velocity, v, in a direction parallel to the film’s major length. We have used biaxially-oriented polypropylene (BOPP) and acetate films (25* /(EL)@ and EaSwhere * is an effective toughness of the film (dimensions of surface tension), E is the Young’s Modulus and L is a typical length scale near the crack tip. We have numerically integrated our geometrical model and have found excellent agreement with experiments, as shown in Fig. 2. Both the kinks and the subsequent bursts of dynamic propagation arise from a simple set of rules and are therefore intrinsic feature of the tearing process. To our knowledge this is the first example where a complex crack motion is entirely ruled by geometry.

References: 1.

Roman B., Reis P.M., Audoly B., De Villiers S., Viguié V., Vallet D., C.R. Mecanique 331 811 (2003).

2.

Ghatak A. and Mahadevan L., Phys. Rev. Let. 91, 215507 (2003).

3.

Audoly B., Reis P.M. and Roman B., Phys. Rev. Lett., accepted, in press (2005);

4.

Audoly B., Reis P.M., Roman B., http://www.lmm.jussieu.fr/platefracture/

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CLEAVAGE MECHANISMS IN A SHIP PLATE STEEL R. Cuamatzi, I. C. Howard and J. Yates Mechanical Engineering Department, Sheffield University, Mappin Street, Sheffield, S1 3JD, UK [email protected] The proportion of Grade A ship plate steel for the construction of merchant ships is huge, however there is an increasing concern about the susceptibility of Grade A steel plate to brittle fracture. A recent ship failure [1] illustrate the importance of the concern. At low enough temperature, the fracture of structural steels is often dominated by cleavage. McMahon and Cohen [2] demonstrated that the cracking of carbide particles located at ferrite grain boundaries represents a primary initiation mechanism in mild steels. Further investigation led to the Smith model [3] which assumed that a cleavage crack could initiate when a grain boundary carbide is fractured by impingement of a dislocation pile-up, and the final fracture is controlled by the carbide-sized crack propagation into the neighbouring ferrite grain. A number of studies [4-8] have used notched specimens to investigate the mechanism controlling cleavage fracture and the fracture criterion. In the present work, an investigation into the micro-mechanisms for cleavage fracture has been undertaken using notched specimens. The material used for the investigation of cleavage fracture is a Grade A ship plate steel. The chemical composition is given in table 1. The microstructure reveals the ferrite matrix and bands of pearlite. Table 1. Chemical composition of Grade A ship plate steel, 20 mm plate (in wt %)

A set of three blunt-notch four-point bend laboratory specimens were tested at test temperature of -60oC, which is in the lower transition region close to the lower shelf, on a servo-hydraulic Instron 8501 test machine under displacement control of 0.01mm/s to analyze the consistency of the observations in each test. It is well known that in double-notched 4PB specimens, when cleavage initiates from one notch, fracture will certainly propagate in that notch and the surviving notch must be very close to the critical state due to the same stress condition developed in that notch. The surviving notches were sectioned for subsequent examination using scanning electron microscopy for the identification of microcracks and possible particles that induce those microcracks. Metallographic samples were prepared and etched with 5% nital and numbered.

Figure 1 – Typical microcracks found about 50 m ahead of the notch root. Observations were made of microcracks developed in front of the notch root of each slice. Typical micrographs of microcracks are shown in Figure 1. Numbers were used to identify

R. Cuamatzi et al.

122

microcracks nucleated in lamellar pearlite microstructure and capital letters were used to identify microcracks nucleated in the pearlite boundary. Figure 1 was taken from slice two 50m ahead of the notch root; this figure shows microcracks nucleated in both, the pearlite lamellar microstructure and the pearlite boundary microstructure. Microcrack 1 initiated in the lamellar pearlite microstructure, grew and crossed the pearlite microstructure and finally stopped in the boundary of the ferrite matrix. Microcrack 2 was nucleated in the centre of the pearlite microstructure and grew about 5m. Microcrack A originated from pearlite microstructure and stopped in the ferrite boundary. These two mechanisms of cleavage nucleation also appeared in slices 3, 4 and 5. For most microcracks, cracked carbides are clearly visible. A microcrack of about 210m size was found in a pearlite colony, the distance of the tip of this microcrack to the notch root is 184m, that crack was nucleated in the pearlite lamellar microstructure and grew along a pearlite boundary. Once the tip reached the ferrite grain, it stopped. More microcracks closer to the notch root were developed. For all these microcracks, cracked carbides are identified as the cleavage nucleation site. A JEOL Scanning Electron Microscope was used to obtain more detailed resolution to provide evidence of cracked carbides as the controlling mechanism for cleavage initiation. Carbides with a diameter of approximately 0.4m were found. In order to identify which of either mechanism is the dominant one for nucleating microcracks, the microcracks were counted and it was found that the domain mechanism for cleavage nucleation is that of microcracks nucleated in the lamellar pearlite microstructure and that cracked carbides are the controlling mechanism for cleavage initiation which are probably the critical event of cleavage for this steel. The critical length of the microcracks for cleavage extension is related to the size of pearlite colonies, suggesting that the weakest link for cleavage to take place is the pearlite microstructure. Cracks adjoining the initial microcracks determine the catastrophic event.

References 1.

Transportation Safety Board of Canada, Marine Investigation Report, Report Number M02L0021, Hull Fracture Bulk Carrier Lake Carling Gulf of St. Lawrence, Quebec. March 2002.

2.

C. J. McMahon and M. Cohen, Initiation of cleavage in Polycrystalline Iron, Acta Metall., 1965. 13: p. 591-604.

3.

E. Smith, The nucleation and growth of cleavage microcracks in mild steels, Proceedings of the conference on physical basis of yield and fracture, Institute of Physics and Physical Society, London, 1966: p. 36.

4.

Hendrickson J.A., Wood D. S. and Clarke, D. S., The cleavage fracture of mild steel, Transaction ASM, 1958(50): p. 656-676.

5.

J. F. Knott, Some effects of hydrostatic tension on the fracture behavior of mild steel, Trans. Iron steel institute, 1966(204): p. 104-111.

6.

Eric M. Taleff, John J. Lewandowski, and Bamdad Pourladian, Microstructure-property relationships in pearlitic eutectoid and hypereutectoid carbon steel, Metallurg. Trans. 2002.(6): p. 25-30.

7.

G. Z Wang and J. H. Chen, A statistical model for cleavage fracture in notched specimens of C-Mn steel, Fatigue Fract. Engng. Mater. Struc, 2001(24): p. 451-459.

8.

S. R. Bordet, A. D. Karstensen, D. M. Knowles, C.S. Weisner, A new statistical local criterion for cleavage fracture in steel. Part II: application to an offshore structural steel, Engineering fracture mechanics, 2005(72): p. 453-474.

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FAILURE BEHAVIOR OF HYBRID-LASER WELDS A. Bajric and W. Dahl Department of Ferrous Metallurgy, Aachen University, Intzestr. 1, 52072 Aachen, Germany [email protected] In recent years the failure behavior of power beam welds have been investigated by means of Finite Element Analysis. In order to determine the local stress state around a crack tip before the crack initiation occurs, the J-Q-M concept has been applied [1]. A Q-factor is added to the crack driving force, expressed as a J integral and account is taken of the effect of strength mismatch by the M factor. As a results the recommendations for the application of constraint corrections have been derived. Additionally the stable crack growth and crack path deviation have been simulated by using the GTN damage model. Based on these results the further numerical and experimental investigations have been carried out on the hybrid laser welds. The objective is to analyze the failure behavior of these welds, with different geometry and mismatch, which lie between the conventional and pure laser weldments. First the local stress state in front of the crack tip are quantified by stress triaxiality and Q+M in dependence of material properties, thickness, mismatch, weld seam geometry and type of loading. Hence the conclusions are drawn, which can be used for safety assessment of the component with hybrid laser welds. For simulation of the stable crack growth the damage models are applied The GTN damage model and cohesive zone model are compared with regard to prediction of the crack resistance curves and crack path. The identified parameter sets are verified on fracture mechanics and component like specimens with different in-plane and out-of-plane constraints. The transferability of GTN damage parameters have already been demonstrated in [2]. The FIGURE 1 shows measured (Exp.) and calculated (GTN) load versus diameter reduction curves for round bar specimens with different notch radii U and net diameter DN. The damage parameters are determined both for base and weld metal. As regards the crack growth and load-deformation behavior of CT specimen, the well agreement is achieved between experiments (Exp.) and calculations (GTN_Model A) (see FIGURE 2). The model A represents due to symmetry one fourth of the specimen. For the opening displacement greater then 3 mm the crack growth is underestimated due to the advanced distortion of the elements. This problem can be avoided, when one half of the specimen is modelled (GTN_Model B). Since the course of crack path depends besides on the mismatch also on the weld seam geometry, the variation of the weld seam width across the specimen thickness will be taken in account.

A. Bajric and W. Dahl

124

FIGURE 1. Load versus diameter reduction curves for the notched round bar specimens of homogenous base metal

FIGURE 2. Load and crack growth versus opening displacement curves for 0.4CT specimens with hybrid laser welds

References 1.

Heyer, J., Lokale Beanspruchung in angerissenen strahlgeschweißten Stahlbauteilen, Berichte aus dem Institut für Eisenhüttenkunde, vol. 9/2004, Shaker Verlag, August 2004.

2.

Nègre, P., Steglich, D., Brocks, W., Crack extension in aluminium welds: a numerical approach using the Gurson-Tvergaard-Needleman model, Engineering Fracture Mechanics, Nr.7, S. 2365-2383, 2004.

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FRACTURE OF PLASTIC BODIES. DEFORMATIONS CONCENTRATORS A. I. Khromov, A. A. Bukhanko, S. L. Stepanov and E. P. Kocherov Institute of Machining and Metallurgy Far Eastern Branch of the Russian Academy of Sciences 1, Metallurgov Str., Komsomolsk-on-Amur, 681005, Russia [email protected], [email protected] On the basis of the theory of ideal rigid-plastic body the approach to definition of invariant tensorial characteristics of fracture is formulated on the basis of standard mechanical tests on uniaxial tensile of flat and cylindrical samples. Instead of experimentally determined characteristics of materials fracture (relative extension and narrowing of a sample at fracture), two are entered invariant tensorial characteristics of a degree of sample deformation. They correspond to the moment of macrocrack initiation and critical deformation in the crack vertex determining process of crack propagation. One of problems of the theory of ideal rigid-plastic bodies is nonuniqueness of position, mode of plastic area and together with it nonuniqueness of a field of displacement velocities which define change of a body geometry. For practical use of theoretical solutions it is offered: criterion of a choice of a preferable instant field of displacement velocities and the criteria determining change of a velocities field in time (change of plastic area). Suggested criteria are based on extreme principles of nonequilibrium thermodynamics. Within the framework of the theory of ideal rigid-plastic body the approach to investigation of areas of abrupt change of the form as strains concentrators is offered. Definition of strains fields in the neighbourhood of the concentrator is reduced to integration of the ordinary differential equations. The number of analytical solutions for concentrators as V-notched bar is received. Dependence of strains fields on form change and plastic area position is investigated during plastic current. The number of solutions of a problem about fracture of V-notched rigid-plastic bar is offered. The approach to investigation of fracture processes for more complex bodies models is formulated on the basis of the obtained solutions: elasto-plastic, strengthened plastic bodies, etc. It is offered to consider the material in the neighbourhood of vertex crack as rigid-plastic material. It allows to carry out the analytical description of strains fields in the neighbourhood of vertex crack and to apply new deformation and power fracture criteria.

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3D DUCTILE TEARING ANALYSES OF BI-AXIALLY LOADED PIPES WITH SURFACE CRACKS Andreas Sandvik, Erling Ostby1 and Christian Thaulow Department of Engineering Design and Materials, The Norwegian University of Science and technology, N-7491 Trondheim, Norway 1Department

of Applied Mechanics and Corrosion, SINTEF Materials and Chemistry, N-7465 Trondheim, Norway [email protected], [email protected], [email protected]

This paper concerns 3D ductile tearing analyses of outer surface cracked pipes subjected to tension loading and internal pressure. Many new offshore development projects are in ultra-deep water depths with high pressure and temperature reservoirs. Consequently, the pipelines may be exposed to extreme loadings under service conditions and/or laying. Today, the tensile side often limits the allowable strain, and therefore might limit the material utilization. It is believed that existing procedures/standards are rather conservative with regard to fracture assessment for scenarios with global plastic strain occurring. As a consequence, more knowledge is needed about the governing fracture response parameters. In this work we present FEM analyses of 3D outer surface cracked pipes loaded in tension with and without internal pressure. The outer diameter, D, is 400[mm] and thickness, t, 20[mm]. Three different crack depths and crack lengths are chosen. All the dimensions of the cracks are chosen such that they are representative examples for possible girth weld defects. The canoe type defect geometry assumed is illustrated in Fig.1. The analyses are performed with a material isotropic power law hardening on the form:

Vi where V

i

§ H V 0 ¨¨1  p © H0

· ¸¸ ¹

n

is the flow stress, V

(1) 0

is the stress at the proportional limit, H

p

is the plastic strain,

and n is the hardening exponent. H 0 = V 0 e E , is the strain at the proportional limit, and E is the Young’s modulus. If V  V 0 the material behaviour is linear elastic. Further, n

V0

7 and

460 [MPa] are assumed in the current analyses.

Ductile tearing is taken into account using the so-called Gurson-Tvergaard-Needleman model, [1,2]. This model accounts for void growth and void coalescence. The void coalescence is modelled with the Tvergaard and Needleman’s [3] “effective void volume fraction”. The value for the initial void volume fraction parameter was fitted to represents a realistic material resistance found from X65 pipeline-steel.

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FIGURE 1. (a) The pipe geometry with an external circumferential constant-depth surface flaw. (b) Details of the canoe type defect with arc length, 2c, depth, a, and end radius, r, equal to the crack depth, a. The FEM model was solved using Abaqus Explicit [4], which originally was developed to solve dynamic events. However, it is possible to retrieve quasi-static solutions with this solver, as long as you prevent significant mass effects. The results show how variations in crack lengths and crack depths, in addition to the effect of internal pressure, influences the crack driving force and the strain capacity of the pipe.

References 1.

Gurson, A.L., Continuum theory of ductile rupture by void nucleation and growth: Part I – Yield criteria and flow rules for porous ductile materials J. of Eng. Materials, vol. 99, 2-15, 1977.

2.

Tvergaard V., Influence of voids on shear band instabilities under plane strain conditions, Int. Journal of Fracture, vol. 17, 389-407, 1981.

3.

Tvergaard, V, Needleman, A., Analyses of the cup-cone fracture in a round tensile bar”, Acta Metallurgica, vol. 32, 157-169, 1984.

4.

Abaqus User’s manual, Version 6.5, Abaqus Inc., 2004.

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NEW MODEL MATERIALS FOR DUCTILE FRACTURE STUDIES A. Weck and D. S. Wilkinson Department of Materials Science and Engineering, McMaster University 1280 Main St. West, Hamilton, ON, L8S 4L7, Canada [email protected] Ductile fracture of metals involves a sequence of overlapping processes that include the nucleation, growth and coalescence of voids. Of these, the last is the most important because it dictates the ductility of metals but is however the less understood. As the coalescence is a stochastic event occurring over very short strains, it is really difficult to capture experimentally. Attempts to fabricate model materials that would simplify the analysis of the ductile fracture process have already been made by Babout et al.[1], Gammage et al.[2], Magnusen et al.[3], Jia and Povirk [4] and Nagaki et al.[5]. However, they are of limited help when one wants to study the coalescence event in detail because of their complicated microstructures, of there limited ductility, of the controlling effect of the nucleation event, of the lack of constraint (2D approaches instead of 3D) or simply because they do not reproduce the key features of the microstructure (like the void size for instance). The present work describes the fabrication and characterization of two new model materials for ductile fracture studies that overcome the previously described limitations. The first consists of a controlled two dimensional array of laser drilled holes in metallic sheets (2D approach) and the second consists of a controlled three dimensional array of laser drilled holes in the bulk of metallic samples (3D approach). To drill the holes, a femtosecond laser is chosen for the small heat affected zone that is created around the hole and the small hole size (10microns) that can be produced. The first model material consists of an array of laser drilled holes in 100microns thick metallic sheets (Fig.1).

The samples are then tested in-situ in a Scanning Electron Microscope to capture the coalescence event (Fig.2). Different arrays of holes can be used and the preliminary results are that different modes of coalescence are obtained depending on the array of holes. For the second model material, the laser holes are drilled in thin (typically 15 microns in thickness) metallic sheets and the sheets are then diffusion bonded to obtain the 3D structure (Fig.3). These samples are then tested in situ in the X-Ray Computed Tomography set-up at the synchrotrons in France (ESRF) and in Japan (SPring-8).

A. Weck and D. S. Wilkinson

130

The results from the tomography experiments (Fig.4) confirm the successful fabrication of the model material. Furthermore, the holes growth and coalescence can be easily followed allowing valuable experimental data to be collected to support subsequent modeling efforts.

References 1.

L. Babout, E. M., J.Y. Buffière and R. Fougères, Acta Mater., 49, 2055-2063, 2001.

2.

J. Gammage, D. S. Wilkinson, J. D. Embury and Y. Brechet, Acta Mater., 52, 5255-5263, 2004.

3.

Magnusen, P. E., E. M. Dubensky, et al., Acta Metallurgica, 36, 1503-1509, 1988.

4.

S. Jia, G. F. R., G.L. Povirk, International Journal of Solids and Structures, 39, 2517–2532, 2002.

5.

Nagaki, S., Y. Nakayama, et al., International Journal of Mechanical Sciences, 40, 215-226, 1998.

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FATIGUE THRESHOLD COMPUTATION MODEL BASED ON THE SHAKEDOWN ANALYSIS M. A. Belouchrani, D. Weichert1 and A. Hachemi2 Laboratoire Génie des Matériaux, E.M.P. BP 17C Bordj El Bahri Alger Algérie 1Insa de Rouen, Place Emile Blondel, BP 8 76131, Mont-Saint-Aigan France 2Institut für Allgemeine Mechanik, RWTH-Aachen, D-52056, Aachen Germany [email protected] The fatigue thresholds remain very significant parameters, helping the designer and the manufacturer in their decision to reform a mechanical structure or its dimensioning. These last years, several models were advanced in order to propose a method of their determination or the study of their influence factors such as the microstructure or the load ratio. The established fatigue threshold models can be classified in two groups, the theoretical models and the models based on the experimentation. The majority, not to say all the models, agree on the fact that the fatigue threshold increases with the size of the grain and depends strongly on the yield stress of the material. The fatigue threshold is interpreted physically as the sum of two components, one i c microstructural 'Kth and the other physics 'K th caused by the crack closing effect. So that:

' K th

' K thi  ' K thc

(1)

For a structure with a regular distribution of the grains and with various orientations, the relation allowing to connect the values of the microstructural threshold with the microstructure dimension [ (grain size) combined with the definition of the crack propagation force related to the deformation energy located at the crack tip, provided the expression of the fatigue threshold depending on R (load ratio) [1, 2]:

' K th

i c ' K th  ' K th

( C 1 (1  R ) 

1 2

)V FL max

S[ (2)

For materials verifying the law of Petch, the fatigue threshold can be written like:

' K th

C 2  C 3[ 0 . 5

(3)

Expression formulated in experiments by the majority of the researchers, who consider nevertheless the values thresholds for propagation velocities of about 10 -8 mm/cycle [3]. In this work, we will present a synthesis of these models which will be compared with our model based on the shakedown analysis [4]. This analysis consider an elastic-plastic structure, subjected to variable mode I loading P(t) and occupying a volume : with a surface * consisting of disjoint parts *V and *u, where statical and kinematical conditions are prescribed, respectively. The values of P(t) vary arbitrarily with time t, but remains between a prescribed loads Pmin and Pmax. One then looks for the maximum value of the load factor D, such that the structure shake down under the loads DP(t). This load factor called shakedown load factor DSD is determined as solution of the following optimisation problem:

M. A. Belouchrani et al.

132

D SD

U ij$ , j

n j U ij$

max$ D D ,U

(4) in :

0

0

on *V

F (DV c ( P )  U $ , V s )  0

a lim

(5) (6)

in :

 P  >P min , Pmax

1 ªm 1 1 D º a0  « U ij$ L ijkl U kl$ d : » ³ : 2 ¬ m K D 1 ¼





m

@

(7)

( m 1)

 ac (8)

Here, F is a convex yield surface, V s the yield stress, a0 and ac are, respectively, the initial crack length and the critical one for which unstable crack propagation occurs, when alim is the limit crack length which can be attained when the shakedown state is reached V c (t ) is the timedependent stress state for a purely elastic comparison problem, differing from the original problem only by the fact that the material reacts purely elastically with the same elastic moduli as for the elastic part of the material law in the original problem and U $ time-independent state of residual stress. With the shakedown load factor D SD computed for a cracked structures loaded in mode I. We can compute the fatigue threshold corresponding to the shakedown state 'K th , given by : 'K th

D SD .P. Sa

(9)

The computation of 'Kth with different grain size shows that for materials verifying the law of Petch, the fatigue threshold can be written like [5]: 'K th

(C4  C5[ 0.5 )V s

(10)

Where C1, C2, C3, C4, C5, m and K are material constants. The comparison of all these models shows that the shakedown analysis constitutes an effective tool in the determination of the fatigue thresholds. It has the advantage of determining them at the initiation of the crack propagation and correctly translated the effect of the yield stress of the material by the influence of the residual stresses and the grain size.

References 1.

Wasen J., Hamberg K. and Karlsson B., Mater. Sci. Engng. A, 102, 217-226, 1988

2.

Ravichandran K. S. and Dwarakadasa E. S., Acta Metall. Mater., vol. 39, N° 6, pp. 1343-1357, 1991

3.

Nakai Y., Tanaka K. and Nakanishi T., Engng. Fract. Mech., vol. 15, N° 3-4, pp. 291-302, 1981.

4.

Belouchrani M. A., Weichert D., Int. J. Mech. Sci., vol. 41, N° 2, pp. 163-177, 1998.

5.

Belouchrani M. A., Weichert D. and Hachemi A., Mechanics. Resea. Comm., vol. 27, N° 3, pp. 287-293, 2000

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VOID COALESCENCE IN METALS INVOLVING TWO POPULATIONS OF CAVITIES D. Fabregue and T. Pardoen Unité de Matériaux et des Procédés (IMAP), Université Catholique de Louvain (UCL) Place Sainte Barbe 2, B-1348 Louvain-la-Neuve, Belgium [email protected], [email protected] Void coalescence is the final stage in the failure of ductile materials. It consists in the localization of the plastic deformation in the intervoid ligament between neighbouring voids. Several experimental evidences obtained from fractographic analyses of broken samples or metallographic analyses of polished samples strained near fracture have shown that a second population of cavities nucleated on small particles significantly affect the damage process controlled by the first population of cavities nucleated on larger particles. Although a second population of voids is considered for a while in the literature as very detrimental for the ductility (e.g. Marini et al. [1]), only a limited number of studies have been devoted to the modelling of this phenomenon (Tvergaard [2], Brocks et al. [3], Faleskog and Shih [4], Perrin and Leblond [5], Enakousta et al. [6]). The aim of this work is to develop a constitutive model for the nucleation, growth and coalescence of voids that incorporate the effect of this second population on the onset of coalescence. Firstly, FE unit cell simulations have been performed with a first population of cavities explicitly modelled in the mesh while the second population is introduced through the use of the Gurson response for the matrix surrounding the first population (Gurson [7]) such as in Brocks et al. [3]. The underlying assumption of this approach is thus that the second population is made of much smaller voids than the first population, with a volume fraction sufficient to smear out their effect within the ligament between the big voids. Calculations have been carried out for different volume fractions of the first population, different stress triaxialities, different volume fractions of the second population and different nucleation conditions for the second population. Fig. 1 shows that the onset of coalescence is about 0.76 for a first population of 1.5% without second population whereas the coalescence occurs for a macroscopic strain of 0.46 if a second population is present for the same overall amount of initial porosity. Cell calculations show that the presence of the second population significantly cut down the strain at the onset of coalescence. The effect of the nucleation strain is also exhibited in Fig. 1. The cell calculations show that the presence of a second population essentially affects the onset of coalescence and not the evolution of the first population before coalescence. The void coalescence model of Thomason (Thomason [8]) has been modified to take into account the presence of the second population of voids through its softening effect on the strength of the matrix material. Cell calculations show that the onset of coalescence is dictated by the local softening caused by the second population inside the ligament very close to the large void. This model provides very accurate predictions of the onset coalescence when all the evolutions of the variables (relative void spacing, void aspect ratio of first population and current yield stress near the large void) are extracted from the FE cell calculations. As a second step, the coalescence model is coupled to an enhanced Gurson model for the description of the first population (Pardoen and Hutchinson [9]). The difficulty relies on approximating the local strains near the large voids to solve the Gurson model locally in order to calculate the evolution of the second population of voids introduced into the void coalescence conditions. This approach which assumes that the second population mostly affect the void coalescence conditions must be contrasted with another

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134

assumption which treat the second population as an extra contribution to growth rate of first population by repetitive coalescence between the big and small cavities (Enakousta et al. [6]).

FIGURE 1. Influence of the presence of the second population in cell calculations (f1=fraction of 1st population, f2=fraction of 2nd population, ånucl=strain at nucleation of the 2nd population)

References 1.

Marini, B., Mudry, F, Pineau, A., Engng. Fracture Mech., vol.22, 989-996, 1985

2.

Tveergard V., Int. J. Solids Structures, vol.35, 3989-4000, 1998.

3.

Brocks, W., Sun, D.Z., Hönig, A., International Journal of Plasticity, vol.11, 971-989, 1995.

4.

Faleskog, J., Shih, F.C., Journal of the Mechanics and Physics of Solids, vol.45, 21-50, 1997.

5.

Perrin, G., Leblond, J.B., International Journal of Plasticity, vol.6, 677-699, 1990.

6.

Enakousta, K., Leblond, J.B., Audoly, B., In Proceedings of the 11th International Conference on Fracture, CD-Rom, 2005.

7.

Gurson, A.L., Journal of Engineering Materials and Technology, vol.99, 2-15, 1977.

8.

Thomason, P., Ductile Fracture of Metals, Pergamon Press, Oxford, 1990.

9.

Pardoen, T., Hutchinson, J.W., Journal of the Mechanics and Physics of Solids, vol.48, 24672512, 2000.

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EFFECTS OF CHARACTERISTIC MATERIAL LENGTHS ON DUCTILE CRACK PROPAGATION E. Radi Dipartimento di Scienze e Metodi dell’Ingegneria, Università di Modena e Reggio Emilia Viale Allegri, 13. I-42100 Reggio Emilia, Italy [email protected] Classical plasticity theories fail in characterizing the constitutive behavior of ductile materials at the micron scale, which is necessary to define in order to investigate the stress and strain fields near a propagating crack tip. Experimental observation on the macroscopic fracture toughness and atomic work of separation of an interface between a ductile crystal of niobium and a sapphire single crystal performed by Elssner et al. [1] found that the interface between the two materials remained sharp and not blunted up to the atomic scale. Moreover, the stress level required to produce atomic decohesion of the lattice turns out to be about 10 times the tensile yield stress, whereas fracture mechanics analyses based on classical plasticity theories (Drugan et al., [2]) provide a maximum stress level near a crack tip not larger than 4–5 times the tensile yield stress. Classical continuum theories are also unable to predict the size effect arising at small scales, due to the lack of a length scale. Therefore, in order to describe the stress and deformation fields very near the crack-tip during its propagation, it become necessary to adopt enhanced incremental constitutive models, which account for the non linear behaviour of the material as well as for the microstructure and the presence of dislocations, by incorporating one or more characteristic lengths, typically of the order of few microns for ductile metals. The couple stress (CS) flow theory of strain gradient plasticity has been introduced, in a first attempt, by Fleck and Hutchinson [3]. Their model involves an intrinsic material length " and an elastic length scale "e arbitrarily introduced in order to partition the deformation curvature rate tensor into its elastic and plastic parts. The incremental model of CS plasticity developed by Ristinmaa and Vecchi [4] and Ottosen et al. [5] is based on the Koiter [6] theory of couple stress elasticity and introduces two distinct intrinsic material length, namely " and "c, whose effect on the propagating crack tip field is almost unexplored. Several analyses, carried out to investigate the effects of microstructure in fracture mechanics, showed that the incorporation of couple stress and rotation gradients in the constitutive description of ductile materials improves considerably the estimation of the stress traction level ahead of the crack-tip. In particular, for the problem of mode I steady-state crack propagation, Wei and Hutchinson [7], analysed the effects of stretch gradients (SG plasticity) in a numerical simulation and found a sensible amplification of the traction level ahead of the crack-tip. It must be observed that former investigation of crack propagation in linear hardening ductile materials described by classical plasticity theories (Ponte Castañeda, [8]; Bigoni and Radi, [9, 10]) predicted an extremely weak stress singularity for the typically small values of the strain hardening coefficient. Recently, Radi [11] performed an asymptotic analysis of the same problem adopting the CS flow theory of plasticity developed in [3] and found that the couple stress field is dominant near to the crack-tip and produces a remarkable increase of the stress singularity, even for low hardening. However, these analyses showed that the contribution of the elastic strain gradients strongly affects the asymptotic crack-tip fields, through the elastic length scale "e. The further analysis performed by Radi and Gei [12] indicated that the stress singularity increase at the crack-tip also for the Mode III crack problem, due to the sole effects of rotation gradients provided by the CS theory of plasticity, with no need to take stretch gradients into consideration.

E. Radi

136

In the proposed paper, the effects of strain rotation gradients on steady-state crack propagation are investigated by performing an asymptotic analysis of the crack-tip fields derived from the flow theory of CS plasticity with two characteristic material lengths. Rotation gradients are expected to become significant at a distance from a crack-tip smaller with respect to these characteristic lengths, and negligible at larger distances, with a gradual transition in the intermediate region. According to the results obtained for a single characteristic material length " in [11, 12], the couple stress and the skew-symmetric stress field are expected to dominate the asymptotic field under Mode I and Mode III loadings conditions, respectively, and to produce an increase of the stress singularity at the crack tip, also for a small hardening coefficient. The role of both characteristic lengths " and "c will be examined in detail and their influence on the stress singularity will be explored by numerical investigations of the asymptotic crack tip fields. The performed asymptotic analysis will provide predictions on the level of traction ahead of the propagating crack-tip more realistic then the classical solution obtained for the J2-flow theory or for a single characteristic length, allowing the detailed mechanisms by which fracture may grow and propagate in ductile metals to be understood in more depth, up to the micron scale.

References 1.

Elssner, G., Korn, D. and Ruehle, M., Scripta Metall. Mater. vol. 31, 1037-1042, 1994.

2.

Drugan, W.J., Rice, J.R. and Sham, T.L., J. Mech. Phys. Solids, vol. 30, 447-473, 1982.

3.

Fleck, N.A. and Hutchinson, J.W., J. Mech. Phys. Solids, vol. 41, 1825-1857, 1993.

4.

Ristinmaa, M., and Vecchi, M., Comp. Meth. Applied Mech. Engnrg., vol. 136, 205-224, 1996.

5.

Ottosen, N.S., Ristinmaa, M. and Ljung, C., European J. Mech. - A/Solids, vol. 19, 929-947, 2000.

6.

Koiter, W.T., Proc. Roy. Netherlands Acad. Sci. vol. B67, 17-44, 1964.

7.

Wei, Y. and Hutchinson, J.W., J. Mech. Phys. Solids, vol. 45, 1253¯1273, 1997.

8.

Ponte Castañeda, P., J. Mech. Phys. Solids, vol. 35, 227-268, 1987.

9.

Bigoni, D. and Radi, E., Int. J. Solids Struct., vol. 30, 899-919, 1993.

10. Bigoni, D. and Radi, E., Int. J. Fracture, vol. 77, 77-93, 1996. 11. Radi, E., J. Mech. Phys. Solids, vol. 51, 543-573, 2003. 12. Radi, E., Gei, M., Int. J. Fracture, vol. 130, 765-785, 2004.

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DUCTILE FRACTURE BY VOID NUCLEATION AT CARBIDES J. Giovanola, D. Cannizzaro, R. Doglione1 and A. Rossoll Ecole Polytechnique Fédérale de Lausanne LCSM-IPR-STI, EPFL, Station 9, 1025 Lausanne, Switzerland 1Politecnico Torino [email protected] Predicting ductile fracture of initially undamaged structures still represents a challenge in most applications such as for instance crashworthiness evaluations. This paper focuses on ductile fracture by the process of void nucleation at tightly bonded and closely spaced inclusions in an otherwise homogeneous ductile matrix. Particular attention is given to loading conditions involving only low stress triaxialities (0 to 0.5). As model material for the investigation, we selected a Vacuum Arc Remelted (VAR) steel: DIN Standard 39NiCrMo4, AMS 6414, austenitized at 860 °C for 1 h, oil quenched, tempered at 704 °C for 1h. and air cooled. This heat treatment resulted in a material with a ferritic matrix (yield strength of 700 MPa, ultimate strength 800 MPa, reduction of area 37.5%) and a dense distribution of fine carbides (volume fraction of about 6% with a size distribution ranging from 0.1 to 1 Pm, with an average size of 0.23 Pm). We developed a simple torsion-tension test using a thin-walled tubular specimen (Fig. 1) that allowed us to investigate void nucleation at carbides under low triaxiality loading (0 – 0.5, axial load of 0, 1/3 and 2/3 of the limit load Plim). We were able to measure local strains and to interrupt the test during the softening stage of deformation and thus gain access to the damage history in the specimen.

FIGURE 1. (a) Thin-walled cylindrical specimen for low triaxiality tension-torsion tests. (b) Torque and axial displacement versus twist angle curves. By means of grid deformation and high speed photography techniques, we demonstrated that in the investigated quenched and tempered VAR steel, two competing failure mechanisms lead to fracture: shear localization, which dominates at very low triaxialities and micro-void nucleation and coalescence, as soon as some significant tensile load is superimposed on shear deformation. We modeled the observed void nucleation process by means of a critical interfacial stress condition. We used a published interfacial stress model based on dislocation theory, the Brown Stobbs [1] Kwon Asaro [2] model (BSKA) to calculate an average interfacial stress acting in a

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138

representative volume element from the continuum stress and strain fields applied to this element. Using the BSKA model to estimate the critical interfacial stress from experimental data obtained in low-triaxiality tension-torsion tests, as well as in notched tension tests with higher triaxialities, we estimated a critical interfacial stress of 3000 MPa and were able to fit a single void nucleation threshold curve over a range of triaxialities from 0 to 1.5 (Fig. 2)

FIGURE 2. Void nucleation threshold curve: fit of BSKA model to experimental data for a critical interfacial stress value of 3000 MPa. We provided a first qualitative validation of the predictive capabilities of the model by combining stress and strain results of finite elements calculations with the BSKA model to determine the location in various torsion and torsion-tension specimens, where voids nucleate first i.e the location of the maximum interfacial stress, The results of these simulations indicate that, as axial loading is increased, the site of first void nucleation moves from the outside edge toward the center of the specimen section. These predictions were confirmed by detailed fractographic observations of tested thin-walled cylindrical specimens.

References 1.

Brown, L. M. and Stobbs, W. M. , Phil. Mag., 34, 351-372, 1976.

2.

Kwon, D. and Asaro, R.J., Metallurgical Transaction A, 21A, 117-134, 1990.

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THE SIGNIFICANCE OF MAXIMUM LOAD ON A LOAD-DISPLACEMENT CURVE WITH STABLE CRACK EXTENSION J. R. Donoso and J. D. Landes Universidad Técnica Federico Santa María, Valparaíso, CHILE University of Tennessee, Knoxville, TN, USA [email protected], [email protected] The ASTM standard method for the measurement of fracture toughness, E 1820 [1], covers procedures and guidelines for the determination of this material property in metallic materials using the parameters K, J or CTOD. The fracture toughness may be measured as a point value, or as a complete fracture toughness resistance curve. In the latter option a J- or CTOD-based resistance curve may be obtained from a single specimen fracture test, in which the crack length is measured from compliance changes, and later verified by optical measurements. The single specimen J-R curve construction procedure defined in E1820 involves several steps, which go from obtaining and plotting the raw J-'a data, to calculating an interim value of J, termed JQ, to finally qualifying JQ as JIc, a size-independent value of fracture toughness. Recently, Donoso, Zahr and Landes proposed an alternative way of obtaining the specimen J-R curve using the Concise and Common (C&C) Formats [2]. The Concise Format [3] and the Common Format [4] developed by Donoso and Landes are calibration functions that relate the load, P, to the displacement, v, and the crack length, a, of a fracture toughness specimen. The Concise Format stands for the elastic regime, in which v = vel [3], whereas the Common Format deals with the plastic component of the displacement, vpl [4]. The Common Format Equation, CFE, was originally proposed by Donoso and Landes [4] as an extension of the load separation concept [5] to describe the load-plastic displacement relationship for a blunt-notch fracture specimen. As such, it relates the load P with two variables representing the non-linear deformation of a fracture specimen with a stationary crack: vpl/W, the plastic component of the load-line displacement, normalized by the specimen width W, and b/W, the normalized ligament size (ligament b in lieu of the crack length a). The CFE also includes a term that denotes the out-of-plane constraint, :*, and is written as: P = :*˜B˜C˜W˜(b/W)m ˜V*˜(vpl/W) 1/n

(1)

where B is the specimen thickness; C and m are the geometry function parameters, and V* and n are material properties, obtained from a stress-strain curve. In order to obtain the specimen J-R curve using the Concise and Common (C&C) Formats, Donoso, Zahr and Landes [2] proposed a “crack growth law” to account for the relation between stable crack extension, 'a, and vpl. The assumed crack growth law is a two-parameter power law equation relating the change in crack length, 'a, with normalized plastic displacement, vpl/W, that has the form 'a W

§ v pl l 0 ¨¨ © W

· ¸ ¸ ¹

l1

(2)

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The crack extension, 'a, may also be written in terms of the change in ligament size, that is, 'a = bo – b, where bo is the initial ligament size (equal to W minus the initial crack length, ao). Thus, Eq. (2) gives the following expression for the current ligament size, b: b W

b W

o

§ v pl · ¸ ©W ¹

l1

 lo¨

(3)

Substitution of Eqs. (2) and (3) into Eq (1) yield the following expression in terms of only the plastic displacement when there is stable crack growth, with D being the product of the parameters V* and :*:

P

DBCW

§ § v pl ¨ bo  lo ¨ ¨ ¨ W ¨W © ©

·l 1 ·¸ ¸ ¸ ¸ ¸ ¹ ¹

m

§ v pl ¨ ¨W ©

1/ n

· ¸ ¸ ¹

(4)

The use of Eq. (4) not only has made it possible to generate Jpl as a first step to obtaining the complete J-R curve [2], but also to predict maximum load on a load vs. displacement (P-v) curve for a specimen that undergoes stable crack growth [6]. The purpose of this paper is to show how the maximum load on a P-v curve obtained with a 1T-C(T) fracture specimen showing crack extension relates to the value of J at initiation of ductile cracking, as defined by JQ following the construction procedure of E1820. Following this, the potential use of the maximum load on a P-v curve to determine directly a value of JQ will be explored and discussed.

References 1.

E1820-99, Standard Test Method for the Measurement of Fracture Toughness, Annual Book of Standards, Vol. 03.01.

2.

Donoso, J.R., Zahr, J., and Landes, J.D., Second International ASTM/ESIS Symposium on Fatigue and Fracture Mechanics, Tampa, FL, USA, November 2003.

3.

Donoso, J.R. and Landes, Fatigue and Fracture Mechanics: 32nd Volume, ASTM 1406, R. Chona. Ed., American Society for Testing and Materials, West Conshohocken, PA, 2001, 261-278.

4.

Donoso, J.R. and Landes, J.D., Engineering Fracture Mechanics, vol. 47, No. 5, 619-628, 1994.

5.

Ernst, H.A, Paris, P.C., and Landes, J.D., Fracture Mechanics; Thirteenth Conference, ASTM STP 743, Richard Roberts, Ed., American Society for Testing and Materials, 1981, 476-502.

6.

Donoso, J.R. and Landes, J.D., An Instability Analysis for a Crack Growth Situation Based on the Common Format, ECF-15, Stockholm, 2004.

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3D VISUALIZATION OF DUCTILE FRACTURE USING SYNCHROTRON XRAY COMPUTER TOMOGRAPHY L. Qian, H. Toda, T. Ohgaki, K. Uesugi1, M. Kobayashi and T. Kobayashi Department of Production Systems, Toyohashi University of Technology, Toyohashi, Aichi, 441-8580, Japan 1Japan Synchrotron Radiation Research Institute, Sayo, Hyogo, 679-5198, Japan [email protected] (L. Qian) The initiation, growth and coalescence of voids during ductile fracture can be evidenced by means of traditional methods such as optical microscope or SEM. However, the obtained information is limited by the surface observations in that the surface stress-strain state differs from that of the interior material. In addition, false images may arise from sample surface preparation. Recently, synchrotron X-ray CT has been applied to investigate fatigue crack problems [1,2]. The purpose of the present work is to use this advanced technique to visualize three-dimensionally the fracture process in a practical ductile material, hence gaining a new insight into the ductile fracture. Uni-axial tensile tests were conducted on a notched specimen made of Al-Si alloy using a test rig specially designed for the X-ray tomography. The in-situ observations were performed during tensile loading using a high resolution X-ray tomography at the X-ray imaging beamline BL47XU of SPring-8. The reconstructed 3D images, with a resolution of 0.474Pm, of the damaged material were quantitatively visualized. It is found that at a smaller load, voids are nucleated in front of the notch. The voids occur mainly within the eutectic region and are closely related to the eutectic particles. With increasing load, the size and number of voids are increased, and some adjacent voids coalesce with each other. Sectional images indicate that the number, size and shape of the voids differ so much from slice to slice. Some slices demonstrate crack length longer than 60 Pm while other slices show only a few small voids. Fig. 1(a) and (b) presents the reconstructed 3D images after two loading stages, showing the void distributions by removing other material components. On the whole, the high density of voids is mainly concentrated near the notch, and increasing load leads to an increase in number and size of the voids. Quantitative analyses indicate that the generated voids almost lie within a region of about 150 Pm near the notch tip. Both the number and size become even larger with further increasing the load. It is also indicated that more and larger voids are generated in the internal region than on the side surfaces.

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FIGURE 1. Void distribution in front of notch after loading to (a) 51.6 N and (b) 55.0 N. Arrows indicate crack growth direction. In conclusion, the high resolution X-ray CT has been proved to be a feasible way to visualize and quantify the ductile fracture, and provide much more information than traditional methods. Voids are nucleated more easily in notch front than in remote regions. The distribution of voids is not uniform in a real material, and the initiation, growth and coalescence of voids are not simultaneous along the notch front. In addition, three-dimensional architecture of particles packing in the eutectic region, and the 3D morphology of D-phases are also visible, which can be applied as input data for numerical simulations of fracture behavior. Finally, the synchrotron radiation experiments were performed at the BL47XU in the SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (JASRI) (Proposal No 2004B0457-NI-np).

References 1. 2.

Toda, H., Sinclair I., Buffiere J. –Y., Maire E., Connolley T., Joyce M., Khor K.H., Gregson P., Philos. Mag., vol. 83, 2429-2448, 2003. Toda, H., Sinclair I., Buffiere J. –Y., Maire E., Khor K.H., Gregson P., Kobayashi T., Acta mater., vol. 52, 1305-1317, 2004.

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NON-LOCAL PLASTIC-DAMAGE MODEL FOR FAILURE ANALYSIS OF SHEET-METALS M. Brunet, F. Morestin and H. Walter-Leberre LaMCoS, Institut National des Sciences Appliquées, 20 Avenue A. Einstein, 69621 Villeurbanne, France. [email protected] A new damage model which takes account of void shape effect and anisotropy of the matrix material is integrated into the dynamic explicit finite element framework to predict the damage evolution which occurs under crash or stamping process. For the strain localization and failure, the pathological mesh dependence has been overcome by a non-local approach where the evolution equation for the porosity and the equivalent plastic strain is modified by an additional term containing a characteristic internal length. The non-local plastic-damage potential is written as:

)

C

q2 p V y2 (H loc , ’ 2H p )

§ · NV H ¸  (1  q f 2 )  2q1 f cosh¨ 3 ¨ V (H p , ’ 2H p ) ¸ © y loc ¹

0 (1)

The damage model can take into account the three main phases of damage evolution: growth, nucleation and coalescence. To determine the critical porosity f c , the void coalescence failure mechanism by internal necking is considered by using a modified Thomason’s plastic limit-load model on the reference volume element such as: ­ ° ®F °¯

§ RZ / ¨¨ © X  RX

· ¸ ¸ ¹

N

§R ·  G /¨ X ¸ © X ¹

M

½ ª V1 º V1 ° »d ¾ An «1  T V Vy « y »¼ °¿ ¬

(2)

Consistent with (2), the plastic-damage potential (1) is used to calculate the void and matrix geometry changes using the current strain, void volume fraction f and shape factor S. Once the inequality (2) is satisfied, the void coalescence starts to occur and the void volume fraction at this point is the critical value f c . To evaluate the non-local variables (f , H p ) and their gradients at a Gauss point, the partial differential equation of the implicit gradient formulation as: ’ 2H p ( x)  P 2H p ( x)

p  P 2H loc ( x)

(3)

is solved using the integral equation method at the beginning of each time step employing the overlay mesh defined by the Gauss integration points of the underlying shell-element mesh restricted to be in the same plane in order to solved a two-dimensional problem. Once the damage model has been calibrated by an inverse identification technique using the non-local FEM analysis on tensile tests, it can be used to predict the appearance of tearing in any stamping process. In particular, the comparisons between experimental and numerical FLDs calculated with the proposed non-local damage model is shown in Figure 1. The occurrence of ductile rupture has been recognised following the satisfaction of the modified Thomason’s coalescence criterion while the necking (load instability) has been determined when the calculated punch force reaches a maximum. For this Ni-based alloy, the material parameters found are:

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anisotropy: r0 = 1.20; r45 = 1.12; r90 = 0.85, isotropic hardening: V 0 b

1.84, void growth: f 0

0.001 ; S0

0.12 ; nucleation: A 0

547 Mpa; Qf

1891 Mpa;

0.08 , void coalescence: F=0.31;

G=1.23 and O0 1.15 .

Figure 1: Experimental and numerical FLD’s (INCO 718)

References 1.

Pardoen, T., and Hutchinson, J.W.: An extended model for void growth and coalescence, J. Mech. Physics of Solids, Vol. 48(2000), 2467-2485.

2.

Brunet M., Morestin F. and Walter H.: Damage Identification for Anisotropic Sheet-Metals Using a Non-local Damage Model, International Journal of Damage Mechanics, Vol. 13(2004), 35-57.

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A NOVEL TECHNIQUE FOR EXTRACTING STRETCH ZONE FEATURES FROM FRACTOGRAPHS M. Tarafder, Swati Dey, S. Sivaprasad and S. Tarafder National Metallurgical Laboratory, Jamshedpur-831007, India [email protected], [email protected], [email protected], [email protected] The crack tip blunting process leaves an imprint in the form of stretch zone on fracture surfaces during the event of ductile fracture. A schematic representation of the stretch zone in a fractured specimen and a corresponding fractographs is shown in Fig. 1. A typical stretch zone has two components, stretch zone width (SZW) and stretch zone depth (SZD). The SZW is basically the virtual crack extension 'a and SZD is half of the CTOD, G. Stretch zones can be easily identified, when observed under the SEM, since they have visually identifiable boundaries in between the fatigue precracked region and the ductile fracture region

. FIGURE 1. (a) Elevation profile of crack tip zone ( b ) SEM image of fracture surface Previous authors [1-4] have estimated SZW and SZD and have attempted to establish their correlation with the initiation fracture toughness of materials. A typical correlation of Ji with SZW [1] is as following

SZW

Ji 2 k V f tan T



where Vf is the flow stress, 2T is the crack blunting angle and k is a material constant. Sivaprasad et. al [2] have devised a correlation to compute SZD using

SZD

SZT  SZW cos D sin D

(2)

where SZT is the projection of the SZW after rotating the specimen at an angle Dand further used SZD to obtain the fracture toughness of materials. They have estimated SZW and SZT by manual estimation procedure, which is tedious, time consuming and lacks reproducibility and repeatability. This paper reports an image analysis (IA) technique for on-line automatic measurement of stretch zone on ductile fracture surfaces, and applies the technique on Custrengthened HSLA steel for the determination of ductile fracture toughness.

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Fig. 2 shows a schematic diagram of the placement of fracture surface in the SEM at 0o and tilted conditions with four key points identifying the locations of interest. Fig. 2 also includes a typical image signal profile after processing. The schematic is an idealisation, which does not show local uneven topographical features that are present in real specimens. By carrying out simple addition and subtraction operations of the image signals, the spatial co-ordinates of the key points P1, P2, P3 and P4 can be computed.

FIGURE 2. Schematic diagram of 0o and tilted positioning of fracture surface under SEM and the identified key points in the image signals Considering f0(x,y) and fT(x,y) as the post processed image signals of the fracture surface at 0o and tilted conditions respectively and g0(x) and gT(x) are the corresponding vertical density histograms, can be written as y2

g 0 ( x)

¦

y2

f 0 ( x , y ), g T ( x )

y y1

¦

f 45 ( x , y )

y y1

(3)

Assuming no translational shifts in x and z directions after the specimen is tilted, mathematically the following conditions can be stated to identify the key points.

P 4 : Max ^A ( x , y ) P 1 : ^S ( x , y )

g 0 ( x )  g T ( x )`

g T ( x )  g 0 ( x ) ~ 0`

P 2 , P 3 : Min ^S ( x , y )

g T ( x )  g 0 ( x )`

(4)

After identification of the stretch zone boundaries, linear profile in terms of pixels (between P1 and P2 for SZW and P1 and P4 for SZT) are estimated using SZW=F.Zand SZT= F.W where F is the conversion factor from pixel to micron meter and Z and W is the width of the stretch zone in 0o and tilted condition in terms of the number of pixels. It was found that this technique generates reliable data which can be used for prediction of initiation fracture toughness of the HSLA material.

References 1.

Bassim M.N., J. Material Processing Technology, vol 54, 109-112, 1995

2.

Sivaprasad S., Tarafder S., Ranganath V.R., Das S.K. and Ray K.K., Met. Matallurgical and Materials Transactions A, vol 33A, 2002.

3.

Srinivas M., Malakondaiah G. and Rama Rao P., Acta Metall. Matter, vol 41:4, 1301-1312, 1993.

4.

Rogerio de O. Hein L., Ammann J.J. and Nazar A.M.M., Material Characterization, vol 43, 21-30, 1999

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SIMULATION OF FATIGUE CRACK GROWTH BY CRACK TIP BLUNTING P. Hutar and M. Sauzay Commissariat a l’Energie Atomique (CEA) Bat.455, 91 191 Gif-sur-Yvette, cedex France [email protected] The crack tip blunting and re-sharpening on the crack tip is one of the basic mechanisms for fatigue crack growth in ductile metals and alloys, e.g. Laird [1], Neumann [2]. Previous numerical studies of crack tip blunting made by Mc Meeking [3], Needleman and Tvergaard [4] have been carried out for monotonic loading. Subsequently, this kind of analysis has been made for cyclic loading (Gu and Ritchie, Tvergaard and Hutchinson [5]), for the load ratio R=0. It is shown that is possible to obtain fatigue crack growth, which can be comparable with Paris law. Perfect plasticity and a finite element mesh with a small initial radius of the crack tip were used. Because of strong mesh distortion they were applied only three full cycles.

FIGURE 1. Initial mesh of finite elements used for the calculations Recently, Tvergaard [6] made a numerical simulations of the fatigue crack growth for 200 full cycles, using remeshing at several stages of the cyclic plastic deformation, for three different values of the loading ratio. This study is mainly focused on the possibility of modelling this phenomenon in the case of long and physically short cracks. The numerical modelling is based on elastic-plastic finite element analysis with the code CASTEM. The possibility of comparing experimentally obtained results of the fatigue crack growth with the numerical simulation of crack blunting in the first few cycles is studied. Because of practical interest, many authors are interested in finding the ratio between CTOD and fatigue crack growth e.g. Tomkins [7]. Tvergaard [5], [6] proposed a relationship between the cyclic change of CTOD and the growth of fatigue crack in this form:

da dN

ȕ .' CTOD, (1)

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148

where ȕ # 0.33 for the chosen initial radius at the crack tip B and for the material model of perfect plasticity (non-hardening material). The initial radius depends on the applied loading and the yield stress of the material. Our simulation accurately studies this kind of relation, and shows the limits of this ratio. Technical materials have more complex behaviour than can be described by a material model of perfect plasticity. Therefore, in our computations different models of material hardening were used and the effect of the hardening on the crack tip blunting was discussed. For illustration initial mesh of finite elements used for analysis can be seen in Fig.1. The displacement fields are approximated in terms of plane strain 8-noded isoparametric elements. A plate with a small edge crack with initial radius B is used. The crack length is approximately ten 5

times smaller than other dimensions of the specimen. The ratio a/B 10 is used. Around the crack tip was a very fine mesh of finite elements (the size of the smallest elements was approximately a/ 2. 10 7 ). The results presented can contribute to a better understanding of one of the basic mechanisms controlling fatigue crack growth in the case of ductile materials.

References 1.

Laird, C., In Fatigue Crack Propagation, ASTM STP 415, ASTM, Philadelphia, 1967, 131

2.

Neumann, P., Acta Metallurg., vol. 17, 1219, 1969

3.

McMeeking, R. M., J. Mech. Phys. Solids, vol. 25, 357-381, 2004

4.

Needleman, A., Tvergaard, V., ASTM STP 803, Philadelphia, PA, 1983, 80-115

5.

Tvergaard, V., Hutchinson, J.W., Fatigue 2002, vol. 1/5, EMAS, UK, 2002, 107-116

6.

Tvergaard, V., J. Mech. Phys. Solids, vol. 52, 2149-2166, 2004

7.

Tomkins, B., Philosophical Magazine, vol. 18, 1041-1066, 1968

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LOADING RATE EFFECT ON DUCTILE FRACTURE R. Chaouadi SCK-CEN Boeretang 200, 2400 Mol, Belgium [email protected] The Charpy impact test is widely used to monitor the quality requirements of industrial processes. It was also adopted by engineers and scientists to monitor material embrittlement resulting from environmental effects like for example irradiation. In this work, we investigated the effect of loading rate, namely quasi-static versus impact loading, on the ductile fracture behavior. Two low alloyed steels used in the reactor pressure vessel industry were selected, namely A533B and 20MnMoNi55. These steels were extensively characterized from the flow, Charpy impact and fracture toughness properties [1-2]. Figure 1 shows how the loading rate affects the ductile to brittle transition curve for both materials. As can be seen, the major effect of loading rate is located in the fully ductile regime where quasi-static loading requires significantly less energy to full fracture than dynamic (impact) loading. Two temperatures, namely 25°C and 290°C were selected to investigate these loading rate effects. At both temperatures, tensile and crack resistance measurements were performed at both quasi-static and dynamic loading. For the A533B steel, at 25°C, the fracture is not fully ductile and therefore only tests at 290°C were considered for this material. The results are shown in Table 1 for the various materials and conditions. These result clearly show that empirical correlations [3] relating fracture toughness to Charpy impact energy are not applicable without an in-depth analysis. Moreover, the loading rate effects on the crack resistance cannot be solely attributed to the strain rate sensitivity of the material. TABLE 1. Ductile crack initiation toughness.

R. Chaouadi

150

FIGURE 1. Effect of loading rate on the ductile-to-brittle Charpy transition curve.

References 1.

Chaouadi, R. and Fabry, A., In From Charpy to Present Impact Testing, edited by D. François and A. Pineau, Elsevier, 2002, 103-117.

2.

Chaouadi, R., J. Test. and Eval., Vol. 32, No. 6, 469-475, 2004.

3.

Rolfe S.T. and Barsom, J.M., Fracture and Fatigue Control in Structure – Application of Fracture Mechanics, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1977.

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EXPERIMENTAL INVESTIGATION OF SLANT CRACK PROPAGATION IN X100 PIPELINE STEEL S. H. Hashemi, I. C. Howard1, J. R. Yates1, and R. M. Andrews2 The University of Birjand, Department of Mechanical Engineering, Birjand, IRAN 1The University of Sheffield, Department of Mechanical Engineering, Sheffield, UK 2Advantica, Loughborough, UK [email protected] Failure information from full-thickness burst experiments on long distance gas transportation pipelines has shown that unstable fractures propagating in the pipeline axial direction are dominated by ductile slant shearing [1-3]. Different test samples, e.g. Charpy impact [4], drop weight tear test (DWTT) [5] and double cantilever beam (DCB) [6] have been proposed to study the ductile shear crack growth in pipeline steels in a laboratory scale experiment. Because of the design geometry of these specimens, slant crack growth is often preceded by flat fracture in the specimen un-cracked ligament. In this research the slant fracture characteristics of 52cc O.D x 21mm W.T pipeline made from high-toughness steel of grade X100 was investigated using modified compact tension C(T) $ specimens. Two sets of test samples were used in this study; smooth and novel side-grooved 45 slant notch C(T) specimens, see Fig. 1. The latter restraint specimen was used to maintain the

propagating crack in its original 45$ plane.

FIGURE 1. Design geometry of slant C(T) samples: a) smooth, and, b) side-grooved specimen All test specimens were loaded in tensile opening mode I. In each test a crack initiated from an initial 45$ through-the-thickness machined slit, and propagated in slant mode fracture through the specimen ligament. This allowed simulation of the slant crack growth in the laboratory scale close to the real structure. The test data monitored in each experiment was load and crack mouth opening displacement (CMOD). Crack length measurements were conducted using two methods; the current direct potential drop (CDPD), and an optical technique. In the CDPD test the input and output leads were located at the positions such that the Johnson's formula [7] for the relationship between crack length and electric potential was applicable. In the latter a fine square mesh was scored on the side surface of the test sample. The crack length measurements then were monitored using highresolution digital video camera. Fig. 2 is a photograph of the experimental set up

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152

. FIGURE 2. Experimental set up used in slant C(T) testing of X100 pipeline steel From the test results it appeared that the PD method (and Johnson formula, initially developed for crack growth measurement in standard C(T) and 3PB specimens with straight cracks) could be used for slant crack growth estimation. This was validated by comparing the final crack length of the broken specimens in liquid nitrogen with those predicted by the Johnson formula, and with those monitored by the video imaging system used. The load-displacement plots of all test specimens showed substantial load drop after small amounts of ductile slant crack propagation. The optical observation of broken test samples revealed that the fracture surface of both smooth and side-grooved slant C(T) specimens contained traces of quasi-cleavage fracture even though the test temperature was above the material transition temperature. The sharp load drop was associated with this mode of fracture in the specimens tested. From the test data the specific slant fracture energy (in terms of J / mm2 ) was estimated for the X100 steel tested, and shown to be similar to that measured on DCB like specimen for the same class of steel.

References 1.

Rothwell, A. B., In Proceedings of Pipeline Technology, Edited by R. Denys, Elsevier Science, 2000, 387-405.

2.

Demofonti, G., Mannucci, G., Spinelli, C. M., Barsanti, L. and Hillenbrand, H. G., In Proceedings of Pipeline Technology, Edited by R. Denys, Elsevier Science, 2000, 509-520.

3.

Berardo, G. , Salvini, P., Mannucci, G. and Demofonti, G. , In Proceedings of the 2000 International Pipeline Conference, Vol. 1. New York, ASME, 2000, 287-294.

4.

Leis, B. N., Eiber, R. J., Carlson, L. and Gilroy-Scott, A., In Proceedings of the International Pipeline Conference, Vol. II, ASME, 1998, 723-731.

5.

Wilkowski, G. M., Rudland, D. L., Wang, Y. Y., Horsley, D., Glover, A. and Rothwell, B., In Proceeding of IPC’02 4th International Pipeline Conference, Alberta, Canada, 2002, 1-7.

6.

Shterenlikht, A., Hashemi, S. H., Howard, I. C., Yates, J. R. and Andrews, R. M., Engineering Fracture Mechanics, Vol. 71, 1997-2013, 2004.

7.

Johnson, H. H., Materials Research & Standards, Vol. 5, 442-445, 1965.

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ESIS TC8 – NUMERICAL ROUND ROBIN ON MICRO MECHANICAL MODELS : RESULTS OF PHASE III FOR THE SIMULATION OF THE BRITTLE TO DUCTILE TRANSITION CURVE C. Poussard and C. Sainte Catherine Commissariat à l’Energie Atomique, DEN/DMN/SEMI CEA Saclay, Bat. 625P, F-91191 Gif Sur Yevtte Cedex, France [email protected], [email protected] This paper presents the results of a round robin organized by CEA Saclay within the ESIS (European Structural Integrity Society), TC8 (Technical Committee n°8) dedicated to the numerical analysis and the comparison with experimental data. The objective of this round robin (phase III) was to model the ductile to brittle transition curve of the 22NiMoCr37 German RPV (Reactor Pressure Vessel Steel) using elastoplastic damage models. The principle of the round robin is that initial sets of damage parameters are first imposed. Then, contributors are free to adjust and justify their parameters so that a good latch to experimental data may be obtained. A good participation was received for this round robin given the substantial technical efforts that were required to contribute. Ten laboratories including nine disseminated in Europe as well as one laboratory in Asia have contributed. Seven finite element codes have been used and three participants performed full 3D fracture mechanics analyses accounting for ductile crack growth. Six participants contributed to the three steps that were proposed in the specifications. Differences have been obtained between the contributions for which explanations have been suggested. The first step was dedicated to the prediction of a 1TCT specimen at -20°C. For that step, no reference was made to experimental results and the purpose was to compare the codes with each other. The mesh, boundary conditions and critical damage parameters were imposed to the participants and resulted from previous phases of the round robin. Differences have been obtained which have been primarily explained by the fact that participants used different elements, either 8 nodes reduced integration elements or 4 nodes fully integrated elements. For a given element size, this appears to play a major role when predicting ductile crack growth. For the prediction of cleavage fracture, differences were obtained for the plastic volume, due probably to the definition of the threshold used to define the plastic strain but this had no influence when Weibull stresses were compared. The differences were smoothed in step two when comparing the predictions to experimental results and when adjusting critical damage parameters was made. Most contributors agreed to the fact that the initial ductile damage parameters that were supplied to the participants did not allow to predict the ductile crack growth behavior observed in the tests. Larger elements at the crack tip and along the crack growth path and a smaller initial void volume fraction were identified from the computation of 1TCT specimens. The mandatory Beremin parameters used also in preceding phases of the round robin did not lead to satisfactory predictions of the failure probabilities at higher temperatures (-40 and -20°C). The correlation was slightly improved when accounting for a well identified ductile damage model but the results clearly showed that the critical cleavage stress had to be diminished in order to satisfactorily predict the experimental data. Finally, it was found that these models could lead to very good prediction of the transition curve. The correlation was found initially poor when using the initially imposed mandatory ductile and cleavage damage parameters but when identified parameters were used, a good correlation could be obtained within the temperature range covered by the test matrix. The agreement between the computation and the observation was further improved when using a linear dependant critical cleavage stress with temperature. Figure 1 is an example of the quality of the results that can be

154

C. Poussard and C. Sainte Catherine

obtained with the local approach mechanical models over the transition. Between -150°C and 20°C, a perfect match to the experimental data is obtained. At 0°C, the prediction is found to be over conservative since in this example, only a 2D computation was made whilst a full 3D model was required to model correctly ductile crack growth prior cleavage.

FIGURE 1. Prediction of the transition assuming a linearly dependant critical cleavage stress. The results will now be used in order to support an ESIS guideline document entitled Guidance on local approach of rupture of metallic materials, document that describes the state of the art to apply the local approach to crack components. Acknowledgements The authors are very grateful to the round robin participants for the high quality level of the work they have produced for that round robin and the useful discussions that arose when comparing the results. Their patience for obtaining this synthesis is also gratefully acknowledged. The authors also whish to express their gratitude to the GKSS staff in Hamburg and in particular to Wolfgang Brocks, Juergen Heerens, Karl Schwalbe and Ingo Scheider not only for providing the data used in that round robin but also for their continuous and fruitful collaboration within ESIS TC1 and TC8 over the past decade.

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CLOSURE OF A RECTANGULAR SKIN DEFECT VIA THE ADVANCEMENT FLAP C. Antypas, C. Borboudaki, V. Kefalas and D. A. Eftaxiopoulos Department of Mechanics, School of Applied Mathematical and Physical Sciences, National Technical University of Athens Theocaris Building, Zografou Campus, 15773 Athens, Greece [email protected] The article is concerned with the closure of a rectangular skin defect, via the enlongation of the advancement local skin flap. Local skin flaps are skin islands that are stretched, rotated or transposed in order to cover a skin defect, which was created due to the removal of a diseased or injured skin portion. The paper consists of two parts, namely the experimental part and the computational part. In the experimental part, in – vitro tension experiments conducted on piglet skin strips are described. The experimental results yielded the nonlinear stress – strain curves of skin. In the computational part, a stress – strain curve obtained in the experimental part, is used in a finite element model for the closure of a rectangular skin defect via the advancement flap. The skin, the subcutaneous fatty tissue and the underlying muscle tissue are included in the model. The muscle and the subcutaneous tissue mechanical responses, are obtained from the literature. Nonlinear finite element analysis with large deformations is performed in the model. Several stress distributions, within the skin layer, are obtained. Finite element results indicate that stress concentrations at the points where the stitches are done, are created. On the rest of the area of the advancement flap the stress distribution is almost uniform. Borboudaki [1] did in vitro tension experiments on piglet skin strips and the nominal stress – engineering strain curves for the skin were obtained. Antypas [2] did a nonlinear finite element analysis of the closure of a rectangular skin defect, via the advancement skin flap. The skin, the subcutaneous tissue and the underlying muscle were considered as separate materials. The article is based on the work performed in [3] and [4]. For the tension experiments on skin, a male, two month old Duroc piglet, weighing 15 kg, was sacrificed. Immediately after the animal sacrifice, a large single skin portion was removed from the abdominal and the thoracic area of the animal. This skin island, was kept in Ringer’s solution. The fatty tissue was removed from the skin island by using a surgical knife. Then four pairs of dumbbell specimens, i.e. eight specimens overall, were cut from the skin island by using a dumbbell cutter D412 of the ASTM standard. The specimens were kept in Ringer’s solution. Each pair consisted of two strips, taken from symmetric positions, left and right from the two columns of nipples, located in the chest and the abdomen of the animal. Two pairs consisted of longitudinal specimens (long dimension along the spinal cord direction) and the other two pairs consisted of transverse specimens (long dimension perpendicular to the spinal cord direction). Eight simple tension experiments were performed, one for each specimen. The experiments were performed by using an INSTRON 1140 machine. Prior to each experiment, the specimen was placed flat on the working bench, and was regularly rinsed with Ringer’s solution. Two black marker lines were ascribed on each specimen, perpendicular to the longitudinal axis of the specimen. The lines were ascribed by using a drawing ink marker with 0.1mm thick tip and were placed well inside the neck of the dumbbell specimens. The length between the two markers was measured. Afterwards, eight rectangular pieces of emery cloth were glued on the ‘bell’ area of the specimen. The moving grip of the INSTRON 1140 machine was removed and the specimen was attached to the grip. The grip together with the specimen was attached to the machine and the other

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end of the specimen was attached to the other grip. Then the upper grip was displaced such that the length between the marker lines, became equal to the length between them as measured on the working bench. Afterwards, the tension experiment was executed, with a grip displacement velocity of 10mm/s. The experiment was terminated when the specimen slipped out of the grips. A digital video recorder captured the displacement of the marker lines during the experiment and a video editor was used for breaking down the movie into individual frames. By using the number of pixels between the marker lines, the strain was measured at specific times. The strain was corresponded to the tensile force, recorded by the testing machine at specific times. In turn the force was converted to nominal stress via a division by the undeformed cross sectional area of the specimen. For one pair of longitudinal and one pair of transverse specimens, the stress – strain curves were quite close to each other. For the other two pairs of longitudinal and transverse specimens, the stress – strain curves were not close to each other. In the subsequent finite element analysis, a simplified flat three – dimensional model of the advancement skin flap was constructed, by using the commercial package ANSYS 8.0. The skin layer was meshed with shell elements, the subcutaneous tissue was meshed with one dimensional nonlinear truss elements and the underlying muscle tissue was meshed with pentahedral solid elements. The Multilinear Elastic (MELAS) material model of ANSYS was used, where points of the experimental nonlinear stress - strain curve were introduced into the finite element model. Via the MELAS option, only isotropic materials could be modeled. Large displacements were also incorporated in the model. Appropriate displacement constraint boundary conditions were applied, such that the distance between selected nodes on the edge of the skin flap and on the surrounding skin edge, became equal to zero, i.e. these nodes were merged. In this way the stitching process for the closure of a rectangular skin defect during plastic surgery, was simulated. In an area close to the edges of the flap and the surrounding skin, the link elements were removed, for the undermining of skin during plastic surgery to be simulated. Computational results indicated that stress concentrations, at the points where the stitches were placed, were created. On the rest of the area of the advancement flap the stress distribution was almost uniform.

References 1.

Borboudaki C., Experimental and computational study of a skin strip under tension, Diploma Thesis, School of Civil Engineering, National Technical University of Athens, 2004.

2.

Antypas C., A computational study of skin as a composite material – The advancement flap, Postgraduate Thesis, Interscholar Programme of Postgraduate Studies on ‘Computational Mechanics’, National Technical University of Athens, 2005.

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SIMILARITY SOLUTIONS OF CREEP – DAMAGE COUPLED PROBLEMS IN FRACTURE MECHANICS L. V. Stepanova and M. E. Fedina Department of Continuum Mechanics, Samara State University Akad. Pavlov str., 1, 443011, Samara, Russia [email protected] The asymptotic solution to Mode III and Mode I crack problems in a creeping solid in the framework of Continuum Damage Mechanics is presented. The kinetic law of damage evolution is the Kachanov – Rabotnov equation [1]. The damage parameter is incorporated into the power-law creep constitutive equations. Thus the coupled system of damage mechanics – creep theory equations is considered. It is to be expected during such a coupling process that the damage involved gives a great effect on the stress field near the crack tip and when the damage parameter reaches its critical value a totally damaged zone near the crack tip may occur [2-4]. The present contribution is an attempt to obtain asymptotic fields of stress, creep strain rate and continuity near Mode III and Mode I cracks in creeping damaged materials as functions of the similarity variable initially proposed by Riedel [5] under the assumption that the totally damaged zone in the vicinity of the crack tip does really exist. The shape and the characteristic length of the totally damaged zone are not a priori and should be obtained as a part of the solution. The instantaneous response of the materials characterised by the creep power-law constitutive equations and the power-law damage evolution equation is non-linear viscous and the evolution of damage at short times after load application can be analysed under the remote boundary conditions that the stress field must approach the Hutchinson – Rice – Rosengren field of non-linear fracture mechanics. If the HRR-field represents the initial conditions and the remote boundary conditions then dimensional analysis shows that the damage mechanics equations must have similarity solutions [5]. Since the classical continuum mechanics equations can not be valid inside the totally damaged zone the asymptotic solution to the problem is sought at large distances from the crack tip (at large distances as compared with the characteristic length of the totally damaged zone but at yet still small distances as compared with the crack length, with the characteristic length of the cracked body). The asymptotic expansions of the continuity (integrity) parameter

Vij /\

\

and the effective stress

(the stress referred to the surface that really transmits the internal forces) for large

distances R o f from the crack tip, where R is the similarity variable, have the following form

\ ( R , M ) 1  R J g ( 0 ) (M )  R J g (1) (M )  ... ( J , J 1  0 ), V ij ( R , M ) R s f ij( 0 ) (M )  R s f ij(1) (M )  ... ( s , s1  0 ). \ 1

1

(1)

The two-term asymptotic expansion for the effective stress and the three-term asymptotic expansion for the continuity (integrity) parameter are obtained. The construction technique of the far-field stress asymptotics is elucidated. The asymptotic fields allow to find the geometry of the totally damaged zone. The geometry of the totally damaged zone for different values of the material constants is given and analysed (Figures 1 and 2). It is found that the HRR-solution for the creep constitutive equations can not be used as the remote boundary conditions and the actual stress field at infinity is found.

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FIGURE 1. The geometry of the totally damaged zone in the crack tip region of a Mode I crack under plane strain conditions: 1 – the configuration given by the two-term asymptotic expansion of the continuity parameter, 2 – the configuration given by the three-term asymptotic expansion of the continuity parameter.

FIGURE 2. The geometry of the totally damaged zone in the crack tip region of a Mode I crack under plane stress conditions.

References 1.

Kachanov L.M., Introduction to Continuum Damage Mechanics, Martinus Nijhoff, Dordrecht, Boston, 1986.

2.

Zhao J., Zhang X., Engn. Fracture Mechanics, vol. 50, 131-141, 1995.

3.

Zhao J., Zhang X., Int. J. of Fracture, vol. 108, 383-395, 2001.

4.

Astafjev V.I., Grigirova T.V., Pastuchov V.A., In Mechanics of Creep and Brittle Materials, edited by A.C.F. Cocks, A.R.S. Ponter, Elsevier, London. 1991, 49 -61.

5.

Riedel H., Fracture at High Temperature, Springer, Berlin, 1987.

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IMPACT FRACTURE TOUGHNESS DETERMINATION OF DUCTILE POLYMERS BY SPB METHOD J. Wainstein , L. A. Fasce and P. M. Frontini Instituto de Investigaciones en Ciencia y Tecnología de Materiales –INTEMA-, Univ. Nac. de Mar del Plata - CONICET; Juan B. Justo 4302, B7608FDQ, Mar del Plata, Argentina. [email protected] Fracture toughness of ductile materials is often characterized by the J parameter that was developed from the J-integral concept. The determination of a critical value of the J-integral is generally performed through the construction of the resistance curve J-'a of the material. The commonly used method for this purpose is the multiple specimen technique [1] in which several specimens are loaded to obtain different amounts of crack growth. However, this method is very difficult to apply at high rate conditions because of the need of interrupting the test at different crack growth levels. Recently, a new extremely simple single specimen method has been developed from the separation parameter, Spb, and successfully applied in fracture toughness characterization of metals and ductile polymers [1,2]. It consists on the assumption that the load can be separated into two multiplicative functions: the geometry (G) and the deformation (H) functions. The separation parameter, Spb, is defined as the load ratio of a sharp and a blunt notched specimen of the same material, geometry and constraint. Assuming that the load falls in correspondence with stable crack propagation, the load drop after maximum load can be taken as a symptom of crack growth. From the Spb expression (Eq. 1) and counting with at least two calibration points (in order to assess the m parameter in Eq. 1), a simple relationship between the load and the crack growth length can be simply obtained and then the J-'a curve can be evaluated.

S pb

P a ,Q P a ,Q p

b

p

b

Q

§ ap · ¸¸ G p ¨¨ ©W ¹ §a · Gb ¨ b ¸ ©W ¹

Q

§ ap ¨¨ ©W § ab ¨ ©W

m

· ¸¸ ¹ m · ¸ ¹

§ ap ¨¨ © ab

· ¸¸ ¹

m

Q

(1)

The Spb method may appear very similar to the Normalization method; though, Spb method has the appealing advantage of requiring the assumption of only one hypothesis, i.e. a geometry function, which indeed is well known for several specimen configurations. In the proposed Spb method, the load separation principle is applied to total displacement with the advantage of non-subtracting the elastic component of the displacement, which results difficult to evaluate from the loaddisplacement impact records. In this work the capability of the Spb method in determining the impact fracture toughness of ductile polymers is studied. The methodology is assessed for two commercial grade polymers that exhibit ductile impact fracture behavior: acrylonitrile-butadiene-styrene terpolymer ABS (Lustran ABS-640 HR 850) and polypropylene block copolymer PPBC (Tipplen CS 2-8000). Stes containing two records: one of a sharp-notched specimen and one of a blunt notched specimen are employed in the application of the Spb method. Fracture tests are performed at 1m/s in a Fractovis Ceast Falling Weight type machine and they are conducted up to the point of complete failure of the specimen so that the final crack length is not available as a calibration point. In order to determine the “m” parameter in Eq. 1, two points of the load displacement record for which crack lengths are known are used. The first one corresponds to the initial crack length where the Spb

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160

parameter is constant (solid arrow in Fig. 1-b and c); the initial crack length can be measured on the fracture surface of the broken specimen. The second point is taken under the assumption that when the sharp specimen achieves the same crack length as the blunt notched specimen, both are bearing the same load and the Spb parameter is equal to one [3] (dash arrow in Fig. 1-a and c). The steps of the proposed Spb method are illustrated in Fig1.

FIGURE 1. Steps in Spb method for PPBC at 1m/s. a) Load displacement records of sharp and blunt notched samples; b) Spb parameter; c) Estimated crack length. J-R curves arisen from the application of the Spb method for triplicate set of samples are shown in Figure 2. Plane strain fracture toughness values (JIc) derived from the fitted average curves are 7.5 N/mm and 5.4 N/mm for ABS and PPBC, respectively. These fracture parameters will be compared with the fracture toughness parameters evaluated by the essential work of fracture approach (EWF)

. FIGURE 2. J-R curves determined by the Spb method for a) ABS and b) PPBC. The appealing of the Spb method is basically its simplicity. It seems to be applicable for many polymers and it will result helpful for that cases in which the multiple specimen technique is hard to performed such as at high loading rates, high temperatures or aggressive environments.

References 1.

Wainstein J., de Vedia L., Cassanelli A.. Eng. Fracture Mechanics, 70, 2489-2496, 2003.

2.

Wainstein J., Frontini P., Cassanelli A., Polymer Testing, 23, 591-598, 2004.

3.

Kobayashi T., Yamamoto I., Niinomi M., JTEVA, 21, 145-153, 1993.

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A MICRO-TOUGHNESS MODEL FOR DUCTILE FRACTURE K. Srinivasan, Thomas Siegmund and Otmar Kolednik1 School of Mechanical Engineering Purdue University, West Lafayette, IN 47907, U.S.A. 1Erich Schmid Institute of Materials Science, Austrian Academy of Sciences, A-8700 Leoben, Austria [email protected], [email protected], [email protected] Ductile fracture occurs through growth and coalescence of micro-voids that originate at the location of inclusions and precipitates. The plastic work dissipated in these micro-separation processes leading to the creation of a unit fracture surface area is a measure of the micro-toughness of the material. Furthermore, void growth and coalescence processes are accompanied by plastic deformation of the material surrounding the voids. The energy dissipated by the micro-separation processes of void growth and coalescence, and the plastic deformation in the bulk material surrounding the voids together contribute to the overall fracture toughness of the material. Conventional fracture toughness tests fail to individually measure these two very different contributions. As a result, there is limited transferability of fracture toughness test data from the laboratory to an actual structure. To overcome this problem there is a need for measurements that allow for the determination of the micro-toughness in ductile fracture. The transferability of material toughness and crack growth resistance can then be solved with a non-linear analysis model like a cohesive zone model (CZM). If the micro-toughness can be determined experimentally then only the cohesive strength remains a free parameter, and the CZM can then be easily connected to experiments. Furthermore, measurements of micro-toughness are of fundamental interest in the development of materials with improved crack growth resistance. A micro-toughness model using measurements of the ductile fracture surface topology to estimate the plastic work dissipated in the process of the formation of a dimple fracture surface was proposed in [1]. This model provides the micro-toughness, * , (also called the cohesive energy) as

* SV H where V is a flow stress, H is the dimple height, and S is a shape factor [1]. The dimple height can be obtained by topographic measurements performed by taking stereo image pairs in a scanning electron microscope and analyzing them using a digital image analysis system [2]. Detailed investigations of void growth processes reveal that the model of [1] underpredicts the micro-toughness in ductile fracture. This issue is overcome by the present work by developing a new micro-toughness model. The micro-toughness involves the use of accurate expressions for the effective plastic strain,

H , fields and a numerical integration procedure to calculate the micro-toughness. The model incorporates the initial spherical expansion of the void as well as the subsequent lateral void expansion stage. A criterion for the transition from the spherical void growth to a lateral void expansion is incorporated [3], and a criterion on final void link-up based on a critical interligament plastic strain, parameters

*

H , is used. The micro-toughness is then given from the following

*  H , ri , V Y , n, H c

(1)

K. Srinivasan et al.

162 where

ri

is the inclusion size,

V Y yield strength, n hardening. Figure 1(a) depicts predicted

values of the micro-toughness in dependence of the dimple height. Good agreement between the model and corresponding FEM simulations are obtained for the individual stages of void growth, * 1 and * 2 as well as for the total micro-toughness. Practical examples of the application of the micro-toughness model are discussed for two high strength steels (St37 and V720), as well as an aluminium metal matrix composite [4]. The micro-toughness model is also applied to study the effects of dimple size on microtoughness. For dimple sizes approaching the material internal length scale, l, of plasticity (set mainly the dislocation spacing) micro-toughness is calculated through a strain-gradient plasticity model [5] in combination with the micro-toughness model. The material flow stress is then given as V

f (H )  lK with f (H ) the hardening function, and K the strain gradient. Figure 1(b)

demonstrates that for small dimples (dimple radius R0 < 10 Pm) such strain gradient effects need indeed be accounted for in order to accurately predict the micro-toughness. The implications of the finding to inter-granular ductile fracture are discussed.

(a)

(b)

Figure 1: (a) Micro-toughness in dependence of dimple size. (b) Dimple size dependence of micro-toughness, comparison of conventional plasticity and strain gradient plasticity.

References 1.

Stüwe, H.P., Eng. Fract. Mech., vol. 13, 231-236, 1980.

2.

Stampfl, J., Scherer, S., Gruber, M. and Kolednik, O., Appl. Phys., vol. A63, 341-346, 1996.

3.

Pardoen, T. and Hutchinson, J.W., J. Mech. Phys. Solids, vol. 48, 2467-2512, 2000.

4.

Miserez, A., Rossoll, A. and Mortensen, A., Acta Mater. vol. 52, 1337-51, 2004.

5.

Huang, Y., Qu, S., Hwang, K.C., Li, M., Gao, H., Int. J. Plast., vol. 20, 753-782, 2004.

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CRACK COALESCENCE MODELLING OF FSW JOINTS A. Ali, M. W. Brown1 and Chris A. Rodopoulos2 Department of Mechanical and Manufacturing Engineering Faculty, Putra University Malaysia, 43400, Serdang Selangor , Malaysia 1Department of Mechanical Engineering University of Sheffield , Sir Frederick Mappin Building, Mappin Street Sheffield S1 3JD,United Kingdom 2Structural Materials and Integrity Research Centre, Materials and Engineering Research Institute, Sheffield Hallam University, City Campus, Howard Street, United Kingdom [email protected], [email protected], [email protected] In the present work, Friction Stir Welds (FSW) of 2024-T351 aluminium alloys is characterised in terms of macrostructure, microstructure, hardness, precipitate distribution, and weld residual stress. Cyclic properties and fatigue endurance of the FSW joints are also investigated and discussed. Critical areas for natural fatigue crack initiation in FSW are pinpointed. The fatigue mechanism in FSW is identified to follow a multiple crack coalescence nature (Figure 1). The number of cracks participate in coalescence and the resulting crack growth rate is governed by the dynamic distance between the crack tips from crack initiation to coalescence. The above represents a complex condition for modelling. Based on crack growth and characterisation of FSW joints, a modified version of the HobsonBrown [1-3] is adopted. The good correlation achieved between the experimental data and the model predictions is shown in Figure 2. The model can successfully handle multiple cracking and coalescence as well as modelling crack growth within residual stress fields. The model follows the damage tolerance design philosophy, which is widely accepted in aircraft manufacturing. The damage tolerance approach incorporates knowledge of fatigue crack detection, initial crack length, propagation direction, fatigue crack growth rate and maximum crack length that leads to inspection time intervals.

Figure 1. Replicas images for LCF of 2024-T351 AL Alloy FSW polished mirror specimen at 300MPa applied stress with load ratio R=0.1 showing the coalescence of cracks.

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Figure 2. Life prediction of FSW 2024-T351 Al Alloy polished mirror.

References 1.

P. D. Hobson, M.W. Brown., E. R. de Los Rios, Two phases of short crack growth in a medium carbon steel. Behaviour of shorth fatigue crack(Edited by K. J. Miller & Eduardo), 1986: p. 441-459.

2.

Shaikh, Z., Initiation, Propagation and Coalescence of Short Fatigue Crack in AISI 316 Stainless Steel at 200C and 5500C. PhD. Thesis, Sheffield University, 1991.

3.

Gao, N., M. W. Brown, Short Crack Coalescence and Growth in 316 Stainless Steel Subjected to Cyclic and Time Dependent Deformation. Fatigue and Fracture Engineering Material Structure, 1995. 18(12): p. 1423-1441.

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FATIGUE CRACK INITIATION IN A TWO PHASE %-METASTABLE TITANIUM ALLOY: INFLUENCE OF MICROSTRUCTURAL PARAMETERS A. Lenain, P.J. Jacques and T.Pardoen Département des Sciences des Matériaux et des Procédés, Université catholique de Louvain, IMAP, Place Sainte Barbe 2, B-1348, Louvain-la-Neuve, Belgium [email protected], [email protected], [email protected] A new generation of DEtitanium alloys with enhanced performance over density ratio is currently receiving lots of attention from the aerospace industry. One of the critical parameter is the fatigue resistance in the both low and high cycle fatigue (LCF and HCF) regimes, in particular the crack initiation. Fatigue initiation is strongly influenced by several characteristics of the microstructure such as grain size, grain orientation and misorientation (e.g Jin et al. [1]). Up to now, the initiation of fatigue cracks in the new low cost beta (LCB Ti alloys) has been characterised only in the case of a fully E microstructure (Hu et al. [2], Krupp et al. [3], Floer et al. [4]). Furthermore, hardly anything can be found in the literature on the fatigue crack initiation in multiphase Ti-based microstructures. This study aims at understanding the couplings between cracking initiation and microstructural features in the DE TIMETAL LCB titanium alloy under cycling loading. Fatigue tests were carried out on notched specimens presenting either equiaxed (Fig. 1 (a)) or acicular (Fig. 1(b)) morphologies. The first microstructure is obtained by hot rolling and subsequent annealing at 760°C and the second one is obtained by continuous cooling from 810°C at a speed rate of 2°C/min. These two microstructures were first characterized by SEM, XRD, EBSD and TEM. Fatigue tests are regularly stopped and sheet specimens are observed with the FEG-SEM. Results, obtained on the equiaxed microstructure (Fig. 1 (a)), show that slip lines appears, mostly in the E grains (Fig. 2 (a)). The density increases with the number of cycles. These slip lines constitute privileged damage sites. The orientation of the E grains in which slip lines first appear has been determined. Fig. 2 (b) shows that there is a misorientation profile across two gliding lines in a E grain which is explained by the lattice rotation due to a deformations gradient into the grain.

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References 1.

1. Jin O., Mall S., Materials Science and Engineering A, vol 359, p. 356-367, 2003.

2.

Hu Y.M., Floer W., Krupp U., Christ H.-J., Materials Science and Engineering A, vol. 278, p. 170-180, 2000.

3.

Krupp U., Floer W., Lei J., Hu Y., Christ H.-J., Philosophical Magazine A, vol. 82, No 17/18, p. 3321-3332, 2002.

4.

Floer W., Krupp U., Christ H.-J., Schick A., Fritzen C.-P, In Proceedings of the Eighth International Fatigue Congress, edited by A.F. Blom, Stockholm, 2002, p. 2369-2376.

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EFFECTS OF SPECIMEN TYPE, SIZE AND MEASUREMENT TECHNIQUES ON FCGR B. Kumar and J. E. Locke National Institute of Aviation Research & Wichita State University 1845. N Fairmount St, Wichita KS 67260 [email protected], [email protected] The literature on fatigue and fracture is extremely extensive, mainly due to the large number of variables involved in the process. It is not possible to look at all the possible variables involved in the fatigue process. The present study is focussed on some of the aspects involved in generating fatigue crack growth data namely: specimen type, size, measurement techniques and test methods. Schjive [1] mentioned several reasons for conducting fatigue test programs such as: comparative experiments; compiling basic material data; verification of prediction models and research on fatigue and fracture phenomena. The choice of specimen type is usually determined by specimen production; ease of carrying out experiments, reproducibility, accuracy of test results, and comparability to other test programs. The specimen types that have been and are being investigated can be classified into the following types: 1

Symmetric specimens a. Middle crack tension specimen M(t) b. Double edge notch tension specimen

2

Asymmetric specimens a. Compact tension C(t) specimens b. Eccentrically loaded single edge coupon ESE (t)

The specimen width’s being considered are 2.00” & 3.00” for both the thin and thick sheet materials. The thicknesses range from 0.040” to 0.25”. The material’s being investigated are are 2024-T3 & T3511, 7050-T7451, 7075-T6 &T7351 and 7475-T7351 Aluminum alloys. They were so chosen as they are widely used by the aircraft industry. The test data has been generated using several different measurement techniques: optical microscope, clip gage, Fractomat™ based Krak gages, and the ACPD system to monitor crack growth. All these instruements provide crack growth resolution higher than required by ASTM 647E. The figures 1 & 2 show the crack length measurement data for 7475 and 7050 Al alloys. Though there seems to be some variation in the reading between the optical microscope and the clip-gage. We are testing some thicker specimens to see if we still see a difference between them. There was very good agreement with the Krak Gage and the optical reading. The differences as a result of the measurements are being analyzed and the results will be presented in da/dn versus Kmax or K effective.

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Figure 1 & 2: Crack length versus number of cycles for Al 7475 and 7050 (t = 0.10”) ESE (t) specimen using clip gage, optical microscope and Krak Gages. There are several crack initiation techniques recommended, and their subsequent effect on crack propagation data is still a source of concern and debate. Initial testing using the guidelines provided in ASTM 647E, which recommend crack initiation to occur in no less than 1.0 x105 cycles has been followed. Crack growth data shows considerable variability near the threshold regime Marci [2 & 3], this is because of the effects of the R-ratio, testing methods and specimen types. It would seem that the differences in the data generated is dependent on of the above mentioned variables. Though all the variables are beyond the scope of this investigation we are will conduct some limited testing to see the effects of the testing methods. Most of the testing used in this investigation is based on the constant Pmax loading with two stress ratio’s R =0.5 and R =0.1. The K reducing method to determine FCGR is also planned. Finally results from the testing of the M(t) , C(t), ESE(t) and the DENT double edge notch specimens using different techniques will be reviewed and presented.

References 1.

J. Schjive, “Fatigue Specimens for Sheet and Plate Material”, Fatigue & Fracture of Engineering Materials & Structures, vol 21, pp 347-357, 1998.”

2.

G., Marci, D. E., Castro, V., Bachmann, “Fatigue Crack Propagation Threshold”, Journal of Testing and Evaluation JTEVA, vol. 17, No. 1, Jan. 1989.

3.

G., Marci, “Non-propagation conditions (Kth) and Fatigue Crack Propagation Threshold (KT)”, Fatigue Fracture Engineering Mater. Struct. vol. 17, No 8, pp 891-907, 1994.

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THE EFFECT OF STRESS RATIO ON FATIGUE SHORT CRACKING C. A. Rodopoulos and S.-H. Han Structural Materials and Integrity Research Centre, Materials and Engineering Research Institute, Sheffield Hallam University, City Campus, Howard Street, United Kingdom [email protected] Structural Safety Group, Korea Institute of Machinery & Materials, 171 Jang-dong, Yusung-Gu, Daejeon, 305-343, Republic of Korea [email protected] Short or Stage I crack growth represents a unique case where the Paris-Erdogan Linear Elastic Fracture Mechanics model fails to predict crack growth and hence fatigue life. The propagation rate of short cracks has been found in numerous works and for a variety of materials to be significantly higher than that predicted by the aforementioned model [1,2]. Yet, there is a strong relation between the material and the extent of short cracking. In general, aluminium alloys exhibit a much larger short cracking potential to high strength steels. In addition, stress ratio has also been found to play an important role on such phenomenon [3]. In brief, the extent of short cracking has been found to decrease with the stress ratio and even disappearing after a particular value [4]. In a number of papers Rodopoulos and co-workers argued that the phenomenon depends on the ratio between the fatigue limit and the cyclic yield stress [5], as shown in Figure.1.

FIGURE.1: Extent of fatigue short cracking (iint) versus the ratio between fatigue limit and cyclic yield stress. Such argument was based on examining the point where the transition line between a Stage I and a Stage II (long crack) crosses the line representing transition between a propagating and a non-propagating crack (Kitagawa-Takahashi diagram), see Figure 2.

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FIGURE.2: Condition for evaluating the extent of short cracking. The solid line represents the transition between short and long crack growth and the dashed line represents conditions for crack arrest. In this work, a sensitivity analysis is presented after the above transition lines have been modified to include the effect of stress ratio. The work concludes with the development of material maps versus stress ratio and the tendency towards short cracking.

References 1.

Pearson, S. Engng., Fract. Mech. Vol. 7, 235-247, 1975.

2.

Morris, W. L. Metall. Trans., A84, 589-596, 1976.

3.

Edwards, P. R., Newman, J.C. AGARD R-767, 1990.

4.

C. A. Rodopoulos, E. R. de los Rios, Facta Universitätis, Series Mechanics, Vol. 3, 13, 647655, 2003.

5.

C. A. Rodopoulos and E. R. de los Rios, Inter. J. of Fatigue, 24, 719-724, 2002.

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DWELL-FATIGUE BEHAVIOUR OF A BETA-FORGED TI 6242 ALLOY P. Lefranc, C. Sarrazin-Baudoux and V. Doquet2 LMPM – UMR CNRS 6617, ENSMA, 86961 Futuroscope-Chasseneuil Cedex, France 2LMS, Ecole Polytechnique, Palaiseau, France [email protected], [email protected], [email protected] For over three decades, gas turbine industries have been confronted to the phenomenon of ambient temperature dwell fatigue sensitivity in titanium alloys. This effect consists of a reduction of fatigue lives due to the introduction of dwell periods at the peak stress of the cyclic loading. Up to now, no real mechanism can explain such behaviour. During the last three decades, many studies [1] were performed to investigate the influence of parameters such as microstructure, temperature, dwell period's length and hydrogen content on this dwell-fatigue behaviour. Characteristic features are a significantly increase in dwell sensitivity with a coarse lamellar microstructure or with an increase in hydrogen content and the disappearance of dwell susceptibility in the temperature range of 150°C and 200°C. This paper deals with a study of the influence of microstructural anisotropy on the dwellfatigue behaviour and with the influence of the dwell period introduction at the peak stress of the cyclic loading on the crack initiation. So, cyclic and two minutes dwell tests were performed at room temperature on a near alpha Ti-6242 forged above the beta transus. This kind of forging plus heat treatments lead to a coarse lamellar microstructure either aligned in prior beta grains or basket weaved microstructure. Cylindrical specimens used in this study have a utile length of fifteen millimetres and a diameter of four millimetres. Tests were conducted at different stress levels leading to lives ranging between 104 to 105 cycles. Some specimens were instrumented with acoustic detection gages in order to detect initiation. The results show that a same dwell life debit ranging between 3:1 and 5:1 can be noticed for the both specimen orientations. But one of the specimen orientations has shown cyclic and dwell lives two times greater than the other one. Specimens with the weaker cyclic and dwell lives have also shown up a lot of cracks along its external surface. Finally, MEB observations have been performed in order to precise the cracking process. The fracture surface morphologies for cyclic and dwell loading are respectively characterised with a particular attention to the localisation of the ignition sites. Then, these morphologies are related to the crack growth rate as determined from striations spacing and using relationships from the literature which relate the crack propagation rate to the stress intensity factor or the local plastic deformation for short and long cracks. The mechanisms controlling the dwell effect are finally discussed on the basis of these results and observations confronted to the available literature [1-6].

References 1.

M. R. Bache. A Review of Dwell Sensitive Fatigue in Titanium Alloys : The Role of Microstructure, Texture and Operating Conditions, International Journal of Fatigue, Vol. 25, pp 1079-1087, 2003.

172

P. Lefranc et al.

2.

D. Eylon,, J. A. Hall., Fatigue behaviour of E-processed titanium alloy IMI 685, Metallurgical Transactions, Vol. 8A, pp. 981-990, 1977

3.

W. J. Evans, C. R. Gostelow. The effect of hold time on the fatigue properties of D/Eprocessed titanium alloy, Metallurgical Transactions, Vol. 10A, pp .1837-1846, 1979.

4.

J. E. Hack and G. R. Leverant. The influence of microstructure on the susceptibility of titanium alloys to internat hydrogen embrittlement, Metallurgical Transactions, Vol. 13A, pp. 1729-1738, 1982.

5.

M. R. Bache. M. Copet, H. M. Davies, W. J. Evans and G. Harrison Dwell sensitive fatigue in a near D titanium alloy at ambient temperature, International Journal of Fatigue, Vol. 19, Sup. No l, pp S83-S88, 1997.

6.

M. E. Kassner, Y. Kosaka and J. A. Hall. Low-cycle dwell-time fatigue in Ti-6242, Metallurgical and Materials Transactions, Vol. 30A, pp. 2383-2389, 1999.

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INVESTIGATION INTO FATIGUE LIFEOF WELDED CHEMICAL PIPELINES Cz. Goss and L. Sniezek Military University of Technology 00-908 Warszawa, ul. Kaliskiego 2, Poland [email protected] Industrial pipelines, in particular the ground-based and overhead ones within any chemical works, demand special attention owing to hazards to the employees, population in the surrounding area, and environment. Hazards are greatest while transferring dangerous media between manufacturing departments and during the storage thereof. Hence, there is a permanent need to deal with the problems of pipeline strength [1-2]. Failures/damages are usually attributable to, e.g. corrosion, design errors, flaws, and welding notches. The latter ones are closely related with any discontinuities and changes in the shape of the pipeline’s cross-section, which often become potential locations of crack initiation due to stress concentrations. The states of strain and stress in the bottom of a welding notch, i.e. the point of fatigue cracking initiation, are determined with account taken of the fact that the material can get plasticized even if the rated stresses (beyond the notch) are lower than the yield point of the steel. Such being the case, one should aim at defining the effort of the material in the region of the welding notch [3-4]. In the course of dimensioning the welded joints within the range of low-cycle fatigue strength, the so-called ‘notch-bottom method’ is used. In the bottom of the notch there are stress and strain concentrations occurring at the same time. They can be produced owing to some change(s) in the shape of the joint itself and the shape of the weld; also, due to welding defects in the forms of undercuts, complete fusion, no weld penetration, and to residual stress that remains after manufacturing processes needed to fabricate the structure, e.g. after cutting, bending, welding, etc. The effort in the bottom of the notch (in a transverse weld this would be the so-called line of fusion, i.e. the native material and that of the weld penetrating each other) is practically found by means of computations only. Estimated were pipelines made of the 1H18N9T steel: those after thirty years’ service, and the ‘new’ ones. Chemical compositions of the steel used to construct these pipelines are shown in Table 1. Table 2 presents static and cyclic mechanical properties of the steel.

TABLE 1. Chemical composition of the 1H18N9T steel. Pipeline

C

Si

Mo

Ti

Cr

Mn

Ni

% by weight „old”

0,05

0,64

0,21

0,63

18,5

1,2

9,8

„new”

0,04

0,8

0,4

0,4

17,88

1,8

8,89

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TABLE 2. Material properties.

The computational model presented in the paper provides capability to determine the effort of the material (i.e. of the steel used to manufacture the chemical pipeline) in the area of the welding notch. On the grounds of both the literature data and experimental work carried out by the Authors, analytical dependences have been formulated to calculate then the elastic-plastic range of strain in welding notches in pipelines operated for thirty (30) years, and in the ‘new’ ones. Computations were made with the strain criterion applied, i.e. the effort of the material in the welding-notch area was determined. A comparison between the range of strain in the welding notch (with the range of nominal stresses assumed) and the destructive strain of steel characterised with the computational range of strain has been accepted as the basis to calculate load capacity of welded joints for the low-cycle range. Some formulae have been suggested in the paper to calculate computational, low-cycle fatigue strength expressed with the range of total strain for a pre-set number of loading cycles. On these grounds formulae have been introduced to facilitate computations of service lives of pipelines. The service lives are defined with the number of loading cycles Nf up to the crack initiation, with the range of nominal stresses in the pipeline coating assumed to be 'VN. The calculated values of fatigue lives for pipelines after many years’ operational use, with R = 0,1 assumed, are lower by 60 - 80% as compared to ‘new’ pipelines.

References 1.

DeWolf G. B.: Process Safety Management in the Pipeline Industry: Parallels and Differences Between the Pipeline Integrity Management (IMP) rule of the Office of Pipeline Safety and the PSM/RMP Approach for Process Facilities. Journal of Hazardous Materials. vol. 104, 169-192, 2003.

2.

Papadakis G. A.: Major Hazard Pipelines: a Comparative Study of Onshore Transmission Accidents. Journal of Loss Prevention in the Process Industries. vol. 12, 91-107, 1999.

3.

Samuelsson J.: Design and Analysis of Welded High Strength Steel Structures. EMAS. Stockholm, Sweden, 2002.

4.

Maddox S.J.: Fatigue Strength of Welded Structures. Second edition. Albington Publishing, Albington, 1991.

The testing work has been done and will be continued under the Research Project No. 5 TO7B 031 25, with financial support of the Committee for Scientific Research (KBN) in the years 2003-2006.

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DIFFERENT ANALYTICAL PRESENTATIONS OF SHORT CRACK GROWTH UNDER ROTATION-BENDING FATIGUE D. Angelova and A. Davidkov Donka Angelova – Professor, University of Chemical Technology and Metallurgy-Sofia (UCTM), 8 Kl. Ohridsky Blvd., 1756 Sofia, Bulgaria, e-mail: [email protected] Aleksander Davidkov – Research Fellow, Institute of Metal Science, Bulgarian Academy of Sciences, 67, Shipchensky Prohod Blvd.,1574 Sofia, Bulgaria, e-mail: [email protected] Although the enormous progress in fatigue investigations and the understanding achieved during the last years, fatigue phenomenon stays as an important problem concerning strength of metals, their life and structural integrity of engineering constructions. One method which is very useful, informative and easy for application is that of investigation of short fatigue-crack growth by replica monitoring of surface crack propagation from the initiation to failure. In our case, this method includes short-crack rotation-bending (R-B) experiments and length measuring of propagating crack a at some cycles N on smooth hour-glass specimens subjected to different frequency and symmetric cycling loading, Table 1. Material under investigation is a rolled lowcarbon, low alloyed steel (RLCLAS), mostly used for off-shore applications and in shipbuilding, marked as 092 according to the Bulgarian Construction Steel Standard. Experimental conditions under in-air R-B are the following: specimen 1 (Stress range , MPa – 620, Frequency f, Hz – 11), and respectively: specimen 2 (620, 11), specimen 3 (580, 11), specimen 4 (620, 6.6). The experiments are carried out on a table-model machine for R-B fatigue, FATROBEM– 2004, newly designed, constructed and assembled in the Laboratory of Plastic Deformation of UCTM. The machine is shown on Fig. 1 and its work described in Davidkov [1].

FIGURE 1. Test apparatus scheme: electric engine 1, driving belt 2, ball-bearing unit 3, leading shaft 4, corrosion box 5, specimen 6, leaded shaft 7, device for circulation and aeration of corrosion agent 8, working box 9, device for loading and load changing 10, counter 11. A model “short crack growth-rate, da/dN – crack length, a” under cyclic R-B fatigue – Eq. (1) – comprises parabolic-linear presentation of the three regimes of crack propagation (I SFC – short fatigue crack, II PhSFC – physically small and III LFC – long crack), and analytical determination of microstructural barriers d1 and d2, at which cracks are slowing down and stop [1]; a0 and af – the initial and final crack size, A, B, C – coefficients depending on metal nature I SFC {a(a0 , d1]} and II PhSFC {a[d1 , d2]}:

da dN

Aia 2  Bia  Ci , i=1, 2;

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176

III LFC { a[d2 , af )}:

da dN

A3 a B3

(1)

The basic model functions from (1) are corrected for each regime, considering the highest crack growth rates, and presented in Fig. 2 as a parabolic-linear family 1.

FIGURE. 2. Different presentation of fatigue data: a. Corrected dependences “Crack growth rate, da/dN – crack length, a” o Family 1; and b. “Crack growth rate, da/dN – surface energy, 'W ” o Line 2 An alternative approach to already described, classical way of treating fatigue comprises a new function W, and a new presentation of experimental data in parameters dN / da , 'W . The function 'W discussed for the first time in Angelova [2, 3] has a dimension of surface energy per second and unity of crack size, and leads to a linear presentation of fatigue data, da/dN– 'W o Line 2 shown as thick line in Fig. 3. The scatter band is indicated by fore thin lines at a condition of excluding two distant points from Family 1; the inner thin lines correspond to ½ and 2 folds of da/ dN, and the outside ones - to 0.4 and 2.5. Such a precision makes it possible to use the presentation

da/dN– 'W at a lesser number of the measurements (recordings) made under every fatigue test, especially at high correlation coefficient which in our case is fcor>0.8. Afterwards a transition to the presentation “da/dN – a” showing much larger scatter would not be difficult.

References 1.

Davidkov A., Angelova D., In Proceedings of the 2-nd International Conference “Deformation, Processing and Structure of Materials”, Belgrade, May 2005, 173-178.

2.

Angelova, D., In CD Proceedings of ECF13, Abstracts, San Sebastian, September 2000, 128.

3.

Angelova, D., In Proceedings of the ECF14, Vol. 1, Cracow, September 2002, 89-97.

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VARIABLE AMPLITUDE LOAD INTERACTION IN FATIGUE CRACK GROWTH FOR 2024-T3 ALUMINIUM ALLOY D. Kocanda, S. Kocanda and J. Torzewski Military University of Technology Kaliskiego 2 Str., 00-908 Warsaw, Poland [email protected] Special needs that concern fatigue damage of aircraft components require undertaking the investigations of fatigue crack growth in aerospace alloys and finding the correlation between the images of fracture surface and the accumulated damage due to applied load. Importance of fractography supporting the analysis of failure cases of real structures was pointed out among others by J. Schijve in his recently published book [1]. In order to check the capability of the reconstruction of load-time history on the basis of fractographic analysis extensive research program was developed for 2024-T3 Aclad aluminium alloy sheet subjected to different variable amplitude loads [2]. The paper presents the results both of fatigue crack growth response and the microfracture analysis for the CCT specimens (400x100x3 mm) under two similar loads LHL (low-high-low) and FAF (flight-after-flight) (Fig. 1a and b). These loads are employed when simulating the flight loads of the lower skin aircraft wing structure.

FIGURE 1. Loading of type LHL (a) and type FAF (b) Load sequence LHL contains 2400 cycles whereas FAF sequence counts 240 cycles of the stress levels just the same the LHL load. However, these loads differ either from the number of cycles in the particular load blocks, thereby the number of overloads, or the order of the load blocks in the program. Employing these two load programs we can learn the influence of the load shape on the crack growth rate and the lifetime of a component as well. Crack growth rate behaviour in 2024-T3 alloy was analyzed either on the surface or in the depth of the samples and performed on the diagrams. The extension of crack depth was estimated on the basis of fractographic analysis with the help of SEM or TEM microscopes. In many cases the effect of multiple overloads that intersperse the baseline cycles is not clearly visible on the typical experimental plot da/dN as function of 'Keff. More details of crack retardation and acceleration associated with the overloads provide the microfracture analysis done with the help of TEM microscope. Figure 2 performs the micrographs which illustrate the systems of fatigue striations on the fracture surface under LHL and FAF load sequences. Microfracture analysis revealed a big variation of crack growth rate within the particular load sequences. The courses of local crack growth rate, affected by one load program of LHL type (Fig. 3a) and FAF type (Fig. 3b) against crack length are shown in Figure 3. Crack growth rates were estimated on the basis of fatigue striations spacing referred to the particular blocks of loading. Further analysis proved that under LHL program the period of crack propagation covers less than 10% of load program duration

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whereas in the case of FAF program 26% of total time is devoted to crack propagation. Well, most time of the load program duration is associated with the crack arrest or crack growth at very low rate. This crack behaviour results from the plastically induced crack closure effect as well as the crack penetration through the plastic zones associated with the overloads.

FIGURE 2. TEM (a) and SEM (b) micrographs illustrate the fatigue striation systems on the fracture surface that are associated with LHL program (a) and FAF program (b).

FIGURE 3. Variation of crack growth rates in microscopic scale for 2024-T3 alloy within one load sequence of LHL (a) and FAF (b) loadings against crack length, respectively. For prediction the crack growth under VA loading and estimation the fatigue life of a component was elaborated a deterministic approach. The crack retardation model is based on the Wheeler model.

References 1.

Schijve , J., Fatigue of structures and materials, Kluwer Academic Publishers, 2001.

2.

Kocanda D., Kocanda S. and Torzewski J., Archive Mech. Engineering, vol. LI, No 3, 361376, 2004.

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AN INVESTIGATION ON THE FATIGUE PERFORMANCE OF HYDRAULIC GATE WHEELS D. Polyzois and A. N. Lashari Department of Civil Engineering, University of Manitoba 15-Gillson St., Winnipeg, MB, R3T 5V6, Canada [email protected] Manitoba Hydro currently owns fourteen hydro power generating stations with a total capacity of over 7500 MW. Both emergency intake gates and spillway gates are used in each. These are fixedwheel gates with wheels mounted on both sides which roll on roller paths. Environmental corrosion along with high wheel loads cause differences in the profile of the roller path surface. Combined with the relatively high torsional stiffness of the gate end girders, a condition of wheel load redistribution occurs where some wheels are relieved of load while others are loaded beyond their maximum design values. These loads can be as high as two to three times larger as the original design loadings. Failure of one wheel could jeopardize the overall operation of the gate. Currently, the design of gate wheels and roller paths do not consider the fatigue life of these elements. Metal fatigue is a process resulting in failure or damage of a component subjected to repeated loading. Although failure by progressive fracture is often associated with localized tensile stresses, fatigue cracks can also occur on the plane of maximum shearing stresses. In the case of wheels or wheels used in spillway or control gates, contact stresses on or somewhat beneath the surface of the contact surface can cause failure of one or both of the bodies. In this case, since the contact point changes as the gates open and close, the contact stresses are repeated over many times, a situation that could eventually lead to fatigue failure. Usually, failure starts as a localized fracture just below the surface of contact where the shearing stress is high and progresses outwardly under the influence of the repeated wheel loads. Contact stresses can also cause pitting at the surface of contact, as shown in Fig. 1. An experimental investigation was carried out at the University of Manitoba in Winnipeg, Canada, which involved the testing of three wheels and six roller path plates under cyclic loading. The wheels were 838.2 mm in diameter while the roller path plates were 381 x 177.8 x 50.8 mm. One of the wheels was made of cast iron while the other two were made of forged steel. The material in two of the roller path plates was ASTM C 1040 with no heat treatment. The material in the other plates was ASTM C 1045 with heat treatment. A unique test set up, shown in Fig. 2, was designed and constructed for this special fatigue type of testing. The average Brinell Hardness Number (BHN) for plates P1 and P2, which were not heat treated, was 291, whereas, for the rest of the roller path plates, which were heat treated, the average BHN was 364. The hardness for the cast iron wheel varied from 391 BHN at the rolling surface to 219 BHN at 38 mm away from the rolling surface while hardness for forged steel wheel (R2) varied from 373 BHN at the rolling surface to 326 BHN at 63 mm away from the rolling surface. The hardness for the other forged steel wheel (R3) varied from 473 BHN at the rolling surface to 428 BHN at 38 mm away from the rolling surface.

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The wheels were subjected to a radial load of, approximately, 825 kN that remained fairly constant while the wheels were “rolled” over the roller path for up to one million cycles. The tensile strain on the cast iron wheel ranged from 103 µ to 2057 µ while the tensile strain on the forged steel ranged from 4 µ to 206 µ. Tensile strains were observed in almost all the strain gauges installed on all roller path plates. Roller path plates P1 and P2, which were not heat treated, exhibited a maximum indentation of 1.48 mm and 1.21, respectively, after one million cycles. Roller path plates P3 and P4 recorded a very low indentation depth of 0.03 mm and 0.11 mm, respectively. The other four roller plates were heat treated and suffered a much smaller surface indentation which ranged from 0.02 to 0.11 mm after 400,000 cycles. Clearly the test results demonstrated that cast iron wheels performed very poorly under fatigue loading while heat treated forged steel wheels performed well.

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A MICROMECHANICAL MODEL FOR CRACK INITIATION IN HIGH CYCLE FATIGUE OF METALLIC MATERIALS Vincent Monchiet, Eric Charkaluk and Djimedo Kondo Laboratoire de Mécanique de Lille, UMR CNRS 8107, Université Lille 1, France [email protected], [email protected], [email protected] Most of structural components resisting to high cycle fatigue are subjected to a multiaxial state of stress. Since fatigue cracks generally initiate and propagate in a plane of maximal shear stress (stage I), the first approaches of Crossland and Sines considered the octahedral plane and their criteria are based on the amplitude of the second invariant of the deviatoric stress tensor. In order to take into account the mean stress, these authors postulated also a linear combination of J 2 and the hydrostatic part of the stress tensor. It is now widely recognized that under high cycle loadings conditions, metals fracture is the result of the strain localization in some unfavorably oriented grains undergoing plasticity. Dang Van, followed by Papadopoulos and others, had proposed a multiscale framework which leads to a sufficient condition for non nucleation of cracks under high cycle loading. This condition is ensured by elastic shakedown at the grain scale (see the representive elementary volume on Fig. 1). Nevertheless, microplastic activity alone cannot explain the role of pressure on the fatigue limit and a generalized multiaxial fatigue limit depending on the hydrostatic pressure is due. So far, this is the proposal already suggested by Papadopoulos in his generalized multiaxial fatigue limit.

FIGURE 1 : Representative Elementary Volume (RVE) To support this type of modelling, we propose in the present study to incorporate some observed damage mechanisms (reported in literature for materials involving faced-centred-cubic structures) in the multiscale approach of Dang Van. The characteristics of the study lies in the consideration of the scale of Persistent Slips Bands (PSB) at which appear the damage micromechanisms. Actually, the PSB constitute preferential sites for fatigue cracks nucleation. The outline of the study is as following : 1

we first propose a simple model for the grain behavior under high cycle loading : microplasticity and microdamage mechanisms (induced by micro-cavities growth) are incoprorated in this grain level model. The monocrystal plastic behavior is described by the a Schmid's law with a linear isotropic hardening and non linear kinematics hardening law, the later being based on the effective plastic slip. On the basis of experiments by Antonopoulos et al. (1976) and Esseman et al. (1982), damage along PSB is associated to the production of vacancies (which is responsible of irreversible volume change) and non spherical microvoids nucleation and growth into these localized bands. The model is completed by adopting the crack nucleation condition proposed by Antonopoulos et

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al.(1976) according to which a crack nucleates at the PSB-matrix interface when the total strain along the PSB reaches a critical value. At the grain level, a crack nucleation criterion is then derived and allows to determine the local condition for fatigue limit. 2

a second part of the study deals with non linear homogenization techniques allowing to translate the local crack nucleation criterion into a macroscopic fatigue criterion. Different non linear homogenization schemes are considered : Lin-Taylor model, Sachs scheme and Kroner's accomodation law. The consideration of such simple schemes is justified by the fact that in high cycle fatigue context, plasticity is localized in one or few grains.

An illustration of the micro-macro approach in the case of macroscopic affine loadings is presented on Fig. 2 ; this clearly shows the capability of the model to take into account the effect of the pressure. Besides, the fatigue limit appears to be independent of the mean shear stress.

FIGURE 2 : Affine torsion-tension loadings. Amplitude of the normalized shear stress

Ta as W0

function of the normalized mean pressure. Comparison of the predictions of two homogenization schemes (Sachs, Eshelby-Kroner).

References 1.

J. G. Antonopoulos, L. M. Brown, A. T. Winter. Vacancy dipoles in fatigued copper. Philosophical Magazine, Vol. 34, No. 4, pp. 549-563, 1976.

2.

M. Berveiller, A. Zaoui. An extension of the self-consistent scheme to plastically flowing polycrystals. J. Mech. Phys. Solids, Vol. 26, pp. 325-344, 1979.

3.

U. Essmann, U. Gosele, H. Mugrhabi. A model of extrusions and intrusions in fatigued metals. I. Point-defects production and the growth of extrusions. Philosophical Magazine A, Vol.44, No. 2, pp. 405-426, 1991.

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COMPARATIVE ANALYSIS OF TWO MODELS FOR EVALUATING FATIGUE DATA Enrique Castillo, Antonio Ramos2, Manuel Lopez-Aenlle2, Alfonso Fernandez-Canteli2 and Roland Koller3 ETSICCP, University Cantabria, Avda. de los Castros s/n, 39005 Santander, Spain. 2EPSIG, University Oviedo, Campus de Viesques, 33203 Gijón, Spain. 3EMPA, Überlandstr. 129, 8600 Dübendorf, Switzerland. [email protected], [email protected], [email protected] The optimization of fatigue programs comprising planning, testing and results evaluation is an issue of paramount importance for material and testing laboratories and a recursive subject in the literature which research groups dealing with fatigue design are long concerned with. There is a general belief that no specific model fulfils in a satisfactory way all these functions, i.e. a model to be considered acceptable by the community. Nevertheless, the up-and-down method, despite its limitations, finds a good recognition by both, research groups related to the academy as well as to the testing laboratories. This can be due to the simple test strategy and evaluation technique implied in the practical application of the up-and-down method, which is easy to understand and to apply in practice. The limited information supplied in this methodology, consists in the determination of the probabilistic stress range for a certain limit number of cycles, here denoted as pseudo endurance limit, which is, generally, considered, although unjustifiably, sufficient for practical design [1,2]. Among the inconsequences of the up-and-down method we find the assumption of a normal (or log-normal) distribution function for the variation of the stress range for given number of cycles, which is not suppported by statistical analysis of real data [3]. Further, data results corresponding to the long life fatigue region, i.e., that properly involved in the up-and-down method, is to be completed by additional results in the medium life fatigue region if the whole S-N field is required to be considered in the current fatigue life design. In this paper, an alternative fatigue test strategy and the subsequent parameter estimation from data results is proposed for use. The procedure is based on a regression Weibull model comprising the whole S-N field, as developed by Castillo et al. [4]. The model enables us to incorporate specimens of different lengths into the analysis [5]. Firstly, the two models considered here, that based on the up-and-down methodology and the regression model proposed by the authors, are introduced and discussed. The possibility of considering a Weibull distribution for the stress range in the up-and-down methodology, leading to the so-called Weibull-up-and-down model, is justified and proposed. The experimental program carried out at the EMPA (Swiss Federal Laboratories for Materials Testing and Research) is also presented (see Fig. 1). Thereafter, a comparative analysis of the fatigue results obtained in the frame of this program is performed using both methodologies. The applicability and reliability resulting from both procedures is then analyzed and the advantages and shortcomings of both methods are discussed. Finally, the conclusions of this investigation are presented.

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FIGURE 1. Adjusting fatigue data of 42CrMo4 steel using the proposed regression model .

References 1.

Deubelbeiss E., Materialprüfung, Vol. 16, 240-244, 1974

2.

Hück, M., Schütz, W., Zenner, H., Industrieanlagen Betriebsgesellschaft mbH, ReportB-TF742B, 1974.

3.

Castillo, E., Fernández Canteli, A., Esslinger, V., Thürlimann, B.,IABSE Periodica 1/1985, IABSE Proceedings 82/85, 1-40, 1985.

4.

Castillo, E., Fernández Canteli, A., Int. Journal of Fracture Nr. 107, 117-137, 2001.

5.

Castillo, E., López-Aenlle, M., Ramos, A., Fernández-Canteli, A., Esslinger ,V., Kieselbach, R., Int. J. of Fatigue. Submitted to evaluation.

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ASSESSMENT OF DAMAGE AT NOTCH ROOT OF THICK PLATES E. C. G. Menin and J. L. de A. Ferreira University of Brasília - UnB, Mechanical Engineering Department, GAMMA Research Group Campus Univ. Darcy Ribeiro, Asa Norte, Brasília, Brazil, 70940-910; 55-61-3073706 R. 213 [email protected], [email protected] Heavily loaded structural components may present local yield at stress concentrators, such as, notches and geometrical discontinuities [1]. In cases involving cyclic loads, the presence of local plasticity could lead to the nucleation and propagation of fatigue cracks and complete fracture of the components [2, 3]. In such cases, the strain life approach should be used to evaluate fatigue damage, making it necessary to perform an elastoplastic analysis of stresses and strains at the proximities of these stress concentrators. Due to reduced computational effort requested, approximated models are widely used with that purpose. The most used are the ones proposed by Neuber [4], Seeger et al. [5], Glinka [6] and Ye et al. [7]. One factor that complicates the use of these approaches consists in the evaluation of stress concentration problems, by most part of the specialized literature, as plane approximation problems that do not take into account the variations in the stress-strain field configuration along the thickness of the components, as these become larger in magnitude. To corroborate the importance of such 3D analysis, several numerical and experimental studies have been published indicating that the stress field near the geometrical discontinuities varies along the notch root, as components become thicker [8]. In such cases, 2D values of Kt and stress/strain plane approximations should be carefully evaluated when associated to local strain models in order to correctly estimate local levels of solicitations at the notch root of thick components. In that sense, this study presents examples of the difficulties associated to the use of local strain approximated models when evaluating cases involving notched components presenting expressive values for the ratio between thickness and notch root radius, or dimensionless thickness, t/r. A preliminary linear elastic behavior analysis for the variation of Kt and the displacement constraint level of points along the notch root was performed using 3D FEM. After that, elastoplastic analyses were performed by means of the most used local strain models, as well as, finite element 3D models and 2D approximation. These simulated the local behavior at the root of different geometries and types of steel associated to two cases of study, exemplified on Tables 1 and 2. TABLE 1. Notch geometries and materials.

TABLE 2. Mechanical and fatigue properties

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The results obtained for the linear elastic domain analysis of the cases of study made it possible to evaluate the stress constraint level of points at the notch root of the stress concentrators, as well as, the behaviour of Kt for components with different values of t/r tending to zero and to determine the reliability and coherence of the use of 2D values of this factor to describe the stress concentration phenomena. The results presented for the elastoplastic analysis of the two cases of study made evident the difficulties associated to the use of local strain approach in cases involving components with expressive values of the dimensionless thickness. Among these are the ones associated to the determination of correct values of Kt and the constitutive curve constants to be used along with the local strain models, the determination of the points subjected to the most severe conditions, as well as, the type of bi-dimensional approximation to be used with FEM. The analysis results suggested the necessity of 3D FEM evaluation to determine in a precise way the local strain and fatigue life of components with expressive values of t/r. Moreover, the results made evident that, in the impossibility to use such practice, one should be careful when using plane stress and strain approximations and 2D values of Kt because these could present divergences with respect to the real conditions evaluated for the models.

References 1.

Peterson, R.E. (1997), Stress Concentration Factors, Ed. John Wiley & Sons, EUA.

2.

Filippini, M. (2000), “Stress gradient calculations at notches”, Int. Journal of Fatigue, 22, 397-409.

3.

Visvanatha, S.K., Straznicky, R.L. e Hewitt, R.L. (2000), “Influence of strain estimation methods on life prediction using the local strain approach”, Int. Journal of Fatigue 22, 67581.

4.

Neuber, H. (1961), “Theory of stress concentration for shear-strained prismatical bodies with arbitrary nonlinear stress-strain law”, Journal of Applied Mec., 28.

5.

Seeger, T.H. e Heuler, P. (1980), “Generalised application of Neuber’s rule”, Journal of Testing and Evaluation, 8, 199-204.

6.

Glinka, G. (1985), “Energy density approach to calculation of inelastic strain-stress near notches and cracks”, Eng. Fract. Mechanics, 22(3), 485-508.

7.

Ye, D., Matsuoka, S., Susuki, N. e Maeda, Y. (2003), “Further investigation of Neuber’s rule and the equivalent strain energy density (ESED) method”, Int. J. of Fatigue, 22, 675-681.

8.

Zhenhuan L., Wanlin, G. e Zhenbang, K. (2000), “Three-Dimensional elastic stress fields near notches in finite thickness plates”, Int. Journal of Solids and Structures, 37, 7617-7631.

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FATIGUE STRENGTH PREDICTION OF SPOT-WELDED JOINTS USING SMALL SPECIMEN TESTING Eisuke Nakayama, Manabu Fukumoto, Mitsuo Miyahara, Kazuo Okamura, Hiroki Fujimoto and Kiyoyuki Fukui1 Corporate Research & Development Laboratories, Sumitomo Metal Industries, Ltd., 1-8, Fuso-Cho, Amagasaki, Hyogo 660-0891, Japan 1Steel Sheet, Plate, Titanium & Structural Steel Company, Sumitomo Metal Industries, Ltd., 1-8-11, Harumi, Chuo-ku, Tokyo 104-6111, Japan [email protected] It is well known that fatigue strength of spot weld of high strength steel sheet is not improved, compared with that of mild steel sheet. In this study, the governing factors and the effects of steel grade on fatigue strength of spot weld is investigated. Firstly, small specimens with total length of less than 3mm are taken from the spot weld of mild steel sheet (270MPa-grade) and high strength steel sheet (590MPa-grade). And then, tensile and high cycle fatigue properties are individually evaluated by newly-developed testing technique. Secondly, finite element analyses of tensile-shear specimen of spot-welded joints under cyclic loading are carried out and fatigue limit of the joints are predicted, using the above-mentioned local material strength properties and considering welding residual stresses around spot weld. Predicted results are nearly equal in both steels, which coincides with experimental results. It is found that fatigue strength of HAZ, which is the crack initiation site in joint, of 590MPa-grade steel is higher than that of 270MPa-grade steel. However, residual stress in 590MPa-grade steel is also higher and this may be one of the reasons why 590MPa-grade steel exhibits little improvement in fatigue strength of the joint over 270MPa-grade steel.

FIGURE 1. Shape and dimensions of fatigue specimen (unit:mm).

FIGURE 2. S-N diagrams of HAZ specimen.

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A THERMO-MECHANICAL MODEL FOR RANDOM BRAKING OF MACHINE COMPONENTS F. Loibnegger, H.P. Rossmanith1 and R. Huber Vienna University of Technology Institute for Testing and Research in Materials Technology, Karlsplatz 13, A-1010 Vienna 1Institute of Mechanics and Mechatronics, Wiedner Hauptstr. 8-10/325, A-1040 Vienna [email protected], [email protected], [email protected] This contribution presents a hybrid analytical-numerical treatment of the thermo-mechanical model for the analysis of the braking process of rotating machine parts such as wheels, etc. The machine parts have the shape of a thick disk. These disks are repeatedly frictionally disk-braked at random sequences of time instants. As the loading is rather severe, the stresses during braking and subsequent cooling reach the plastic limits in compression and tension, respectively. Hence, the loading may cause conditions similar to those encountered in shake-down phenomena. The thick disk is assumed to contain initial compressive and tensile stresses as a result of inappropriate heat treatment after forging and due to press-fitting the disk on the axis. In addition, the disk is allowed to develop and extend radial surface cracks within the annular brake regions. The shapes of these surface cracks initially are semi-elliptical, but vary largely, depending on the loading sequences and the existing residual stress fields after cyclic straining [1]. Under certain loading conditions and random sequences of brake phenomena, the circumferentially distributed and radial oriented cracks may exhibit accelerated crack growth in axial direction and in a few cases cracks may even emerge on free rim surfaces. A thermo-elasto-plastic fracture mechanical analysis was performed, based on a finite element analysis. The crack was locally modelled as a semi-circular surface crack which was allowed to propagate at variable velocities along the surface and into the material. Linear elastic fatigue type crack advance was assumed during the cooling phase after braking. It was detected, that the distribution of residual stresses had a decisive influence on the stability behaviour of fatigue cracks. It could be shown that the extension of cracks on the surface along the circumferential direction was controlled by the residual stresses, ultimately leading to crack arrest. The large tensile circumferential stresses within the brake region are balanced by the residual compressive stresses in the rim and hub regions. Results indicate that the actual load is depending on the randomness and characteristics of the braking events. The speed of directional crack advance also depends on the style and the loading sequence. Safe life – time diagrams could be constructed for the use of the rotating machine parts [2]. These safety diagrams clearly demonstrate the effect of the initial crack size on the arrest behaviour of the observed crack and the remaining life time of the structure. This paper discusses in detail the various steps of the very complex analysis [3] and at each stage indicates alternative routes and avenues for improvement of the analysis while still keeping the amount of numerical calculations at bay. A practical example will be demonstrated.

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References 1.

Rolfe S.T. & Barsoum, J.M., Fracture and Fatigue Control in Structures - Applications of Fracture Mechanics, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1977.

2.

Anderson T.L., Fracture Mechanics - Fundamentals and Applications. CRC Press, Boca Raton, USA, 1991.

3.

Gdoutos, E.E., Rodopoulos, C.A. & J.R. Yates : Problems of Fracture Mechanics and Fatigue - A Solution Guide, Kluwer Academic Press Publishers, 2003.

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LIFETIME CALCULATION OF RAILWAY WHEEL STEELS BASED ON PHYSICAL DATA F. Walther and D. Eifler Institute of Materials Science and Engineering University of Kaiserslautern, P.O. Box 3049, D-67653 Kaiserslautern, Germany [email protected], [email protected] Higher speeds in passenger traffic and higher axle loads in freight traffic cause a substantial increase of the mechanical load of railway wheels. To develop and verify fatigue criteria and lifetime calculation methods, a reliable fatigue data base of highly loaded wheels steels, in particular under near-service loading conditions, is required. Fatigue tests with variable maximum stresses were performed at ambient temperature on servohydraulic testing systems with specimens of the wheel steels R7 (SAE 1055) and B6 (SAE 1070) according to UIC standards. The specimens were taken from different depth positions of the rim of original railway wheels. Due to the industrial heat treatment and the size of the components microstructural gradients are unavoidable [1, 2]. In addition to the plastic strain amplitude Ha,p from mechanical stress-strain-hysteresis measurements, changes of the specimen temperature 'T and the electrical resistance 'R during cyclic loading were considered. The integral temperature and resistance data can be used to evaluate continuously the fatigue behaviour under variable amplitude loading. Besides the specimen geometry and temperature, the resistance depends on the specific resistance of the material and changes in a characteristic manner as a function of the defect density in the material. To describe proceeding fatigue damage, the resistance can be measured as a reference value at the beginning and during a fatigue test as well as in load-free states [1, 2].

FIGURE 1. Variable amplitude loading with constant amplitude (measuring) sequences. The basic idea of the new testing procedure developed at the Institute of Materials Science and Engineering is to combine near-service load spectra with periodically inserted measuring sequences with a constant amplitude below the endurance limit. With this method (Fig. 1) reliable information about proceeding fatigue damage under near-service loading can be obtained on the basis of Ha,p, 'T and 'R. In representative cyclic ‘deformation’ curves the mean values of these physical quantities are plotted as a function of the number of cycles N*. N* was calculated by multiplication of the frequency and the time of experiment. The random signal was generated by a combination of a White Noise and a Gauss distribution. After normalising the random signal to values between -1 and 1 it was multiplied with the maximum stress. Cyclic softening and hardening processes were observed for random loading experiments with maximum stresses of 400 MPa d Vmax d 800 MPa (Fig. 2), comparable to single-step tests. An

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increasing maximum stress leads to higher measured values in an unique manner and consequently shorter lifetimes. The physical quantities Ha,p, 'T and 'R are directly correlated with microstructural details. The test with Vmax = 400 MPa was stopped without specimen failure.

FIGURE 2. Representative cyclic Ha,p-, 'T- and 'R-curves for random loading, R7. Furthermore, the new testing procedure allows to establish lifetime calculation methods for near-service loading. To derive a physically-based lifetime calculation (PHYBAL), 'T and 'R were used equivalently to Ha,p in Morrow and Manson/Coffin curves. Using the mathematical descriptions of these curves, S,N curves according to the Basquin equation can be calculated. The lifetimes calculated on the basis of the plastic strain amplitude, the temperature and the resistance agree very well with the experimentally determined lifetimes [3].

References 1.

Walther, F., Eifler, D., Mater. Sci. Eng. A 387-389, 481-485, 2004.

2.

Walther, F., Eifler, D., In Proceedings of the 11th International Conference on Fracture, edited by A. Carpinteri, Turin, No. 3944, 2005, 1-6.

3.

Starke, P., Walther, F., Eifler, D., PHYBAL - A new method for lifetime prediction based on strain, temperature and electrical measurements, Int. J. Fatigue, 2005, in press.

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FATIGUE CRACK PROPAGATION OF SUPER-DUPLEX STAINLESS STEEL AT DIFFERENT TEMPERATURES G. Chai and S. Johansson Sandvik Materials Technology, R&D Centre 811 81 Sandviken, Sweden Linköping University, Department of Mechanical Engineering SE 581 83 Linköping, Sweden [email protected], [email protected] The fatigue crack propagation behaviour in an austenite-ferrite two phase super-duplex stainless steel (SDSS) (UNS S32750) has been investigated at temperatures from –50ºC to 150qC. Two material conditions (as delivered condition-AD and aged condition (475 ºC/4h)) and two stress ratio values (R=0,1 and 0,5) were used. The fatigue crack propagation rate, threshold value, closure and fracture behaviour have been studied. The fatigue crack propagation of this alloy at –50ºC shows a tendency of lower crack propagation rates at small stress intensity factor range, but higher rates at higher stress intensity factor range, and a higher crack propagation threshold value comparing with those at RT. The crack propagation rates at 150ºC are similar to those at RT, and the crack propagation threshold value is also higher than that at RT, but smaller than that at –50ºC. The ageing of the alloy or an increase in R value increases crack propagation rate, but decreases the threshold value (Figure 1).

FIGURE 1. Influence of temperature, material and stressconditions on crack propagation behaviour of a DSS material This alloy shows rather high fatigue crack propagation threshold values 'Kth (Table 1). It was found that it is mainly due to the fact that this two phase material has large crack closure, especially at low and high temperatures (Table 1). The following two phenomena observed may give some explanations. One is type of “crack-bridges” occurred in the softer phase (Figure 2a). Compressive residual stresses in this phase were measured after the fatigue testing. This may indicate that fatigue crack closure can be induced by residual stresses. The other is type of “fracture mismatch” observed near the threshold regime. The fracture changes its pattern or directions when a crack propagates from one phase to another (Figure 2b). This may increase the surface roughness induced closure.

194

G. Chai and S. Johansson

TABLE 1. Influence of temperature on the closure and effective threshold values.

*: from da/dN measurements; **: from closure measurements. '.cl: closure value; 'Keff effective threshold value.

th

:

FIGURE 2. (a). Residual stress induced closure; (b). Fracture mismatch from austenite phase Jto ferrite phase D The higher effective threshold value 'Keff th at 150qC, which can not be explained by the classic theories, was further investigated. It may be attributed to dynamic strain ageing. A transition from cleavage fracture to facet fracture was observed near the threshold values in the as delivered material at -50qC and in the aged material at RT. The possible mechanisms were discussed. Key words: Super duplex stainless steels, Fatigue crack propagation behaviour, Fatigue crack closure, Temperature, Fracture.

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TRANSITIONS OF FATIGUE CRACK INITIATION FROM SURFACE, SUBSURFACE TO SNDFCO G. Chai Sandvik Materials Technology, R&D Centre, 811 81 Sandviken, Sweden [email protected] As known, fatigue crack initiation mainly starts at surface defects at high stress or strain amplitudes, but shifts to pre-existing subsurface defects such as inclusions or pores at low stress amplitudes or in the very high cycle fatigue regime [1]. Recently, it was reported that fatigue crack initiation could occur in non-defect existing areas and form a subsurface non-defect fatigue crack origin (SNDFCO) [2]. Figure 1 shows a summary of these three phenomena.

FIGURE 1. Three types of fatigue crack initiation; (a). From a surface defect; (b). From a subsurface inclusion; (c). From subsurface non-defect fatigue crack origin (SNDFCO). This paper gives a discussion on the transition mechanisms of fatigue crack initiation from surface defects, subsurface defects to subsurface non-defect fatigue crack origins in some two phase or multiphase steels. It was found that surface crack initiation mainly is caused by extrusion and intrusion of slip bands at the specimen surface, where the applied stresses are higher than the elastic limit of the material (Figure 2a). The occurrence of subsurface crack initiation is caused by localised cyclic plastic deformation or dislocation slipping processes around the subsurface defects due to stress concentrations (Figure 2b). The formation of SNDFCO in some two phase alloys is also a cyclic plastic deformation process. Although the stresses applied are lower than the elastic limit of the material, but they can be higher than the elastic limit of the softer phase. This leads to the occurrence of cyclic plastic deformation in this softer phase, which causes the damage and then the formation of micro or short cracks in the softer phase (Figure 2c) or at the grain boundaries or corners due to the stress concentration by dislocation pileups.

G. Chai

196

FIGURE 2. Transition mechanisms of the fatigue crack initiation from the surface, subsurface to subsurface non-defect fatigue crack origin; (a). Extrusion and intrusion of slip bands at the specimen surface; (b). Slip band formed near the subsurface defect; (c). Short cracks formed in the softer phase. The formation of SNDFCO is a crack propagation process, which is controlled by microstructure mechanics. The crack propagation transition from stage I to stage II leads to the formation of SNDFCO. The size and morphology of the SNDFCO strongly depend on the applied stresses. The size of the SNDFCO increases and their fracture morphology changes from more ductile to facet when the applied stresses decrease. Key words: Fatigue crack initiation, Subsurface non-defect fatigue crack origin (SNDFCO), Fracture, Two phase alloys, Dislocation slip band.

References 1.

Murakami, Y., Metal Fatigue: Effect of small defects and non-metallic inclusion, Elsevier Science Ltd, 2002.

2.

Chai, G., In Proceedings of the Third International Conference on Very High Cycle fatigue, edited by T. Sakai and Y Ochi, Kusatsu, 2004, 24-31 and 374-381.

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SURFACE FATIGUE OF GEAR TEETH FLANKS G. Fajdiga, M. Sraml and J. Flasker University of Maribor, Faculty of Mechanical Engineering Smetanova ulica 17, SI-2000 Maribor, Slovenia [email protected] Mechanical behaviour of various machine elements, such as gears, brakes, clutches, rolling bearings, wheels, rails, and screw and riveted joints, are influenced by interaction between contact elements and surfaces. Surfaces in rolling and/or sliding contact are exposed to material contact fatigue. Contact fatigue can be defined as a kind of damage caused by changes in the material microstructure which results in crack initiation followed by crack propagation, under the influence of time-dependent rolling and/or sliding contact loads. The contact fatigue process can in general be divided into two main parts: •

initiation of micro-cracks due to local accumulation of dislocations,high stressesat local points, plastic deformation around inhomogeneous inclusions or other imperfections in or under the contact surface;

•

crack propagation, which causes permanent damage to a mechanical element.

In this paper the pitting phenomenon of gears is addressed and the developed numerical model is used for determination of pitting resistance, i.e. the service life of gear teeth flanks. The initiation of fatigue cracks represents one of the most important stages in the pitting process. The position and mode of fatigue crack initiation depends on the microstructure of the material, the type of the applied stress and micro- and macro-geometry of the specimen, Cheng [1]. The crack initiation periods can be very different and cracks can be initiated either on or under the surface, depending on a different combination of rolling and sliding contact conditions, Kaneta [2]. In general, gear teeth pitting may be initiated on sub-surface or surface. Sub-surface pitting initiation can be observed in high quality gears made of alloy steel, with smooth contact surfaces and good lubrication, where the large shearing sub-surface stresses due to contact loading initiate substantial dislocation motion, which governs the crack initiation process, Glodež [3]. Surface pitting initiation is common in industrial gears, which have rougher surfaces and are made of ordinary construction steels. The surface pitting is strongly influenced by surface roughness and other surface defects, like machining marks, large notches, inclusions, etc. The surface cracks may also appear as a consequence of thermal treatment of the material due to residual stresses. This paper considers only the second mechanism of gear pitting, i.e. surface pitting. The process of surface pitting can be visualized as the formations of small surface initial cracks grow under repeated contact loading. Eventually, the crack becomes large enough for unstable growth to occur, which causes the material surface layer to break away. The resulting void is a surface pit (Fig. 1). The number of stress cycles N required for pitting of a gear teeth flank to occur can be determined from the number of stress cycles Ni required for the appearance of the initial crack in the material and the number of stress cycles Np required for a crack to propagate from the initial to the critical crack length, when the final failure can be expected to occur: N

Ni  N

p

(1)

G. Fajdiga et al.

198

FIGURE 1. Typical surface pits on gear tooth flank. This paper describes a computational model for contact fatigue crack initiation and crack propagation in the contact area of gear teeth flanks. The purpose of the present study is to present, firstly, a model for prediction of contact fatigue initiation, which is based on continuum mechanics, real cyclic contact loading and specific material fatigue parameters. The material model is assumed as homogeneous, without imperfections such as inclusions, asperities, roughness, residual stresses, etc., as often occur in mechanical elements. A moving contact load is often used for simulation of the cyclic loading in fatigue crack initiation and propagation analyses on mechanical elements (simulation of meshing of gears) Fajdiga [4]. The second part of the computational model is a crack propagation model based on appropriate short fatigue crack growth theories Navarro [5], Sun [6]. The model attempts to account for the different parameters influencing the crack propagation process (Hertzian contact pressure, friction between contacting surfaces, fluid trapped in the crack, meshing of gears, etc,) leading to pitting, starting from the initial surface fatigue crack to the critical crack length, when the occurrence of a surface pit is expected. The results of the computations can be used to predict the time required for the development of pits, i.e. the service-life of gears with regard to pitting [4].

References 1.

Cheng W., Cheng HS., Mura T., Keer LM. Micromechanics modelling of crack initiation under contact fatigue. ASME Journal of Tribology; 116: 2-8, 1994.

2.

Kaneta M., Yatsuzuka H., Murakami Y. Mechanism of crack growth in lubricated rolling/ sliding contact. ASLE Transactions; 28: 407-414, 1985.

3.

Glodež S., Ren Z., Flašker J. Simulation of surface pitting due to contact loading. International Journal for Numerical Methods in Engineering; 43: 33-50, 1998.

4.

Fajdiga G., Flašker J., Glodež S. and Ren Z. Numerical simulation of the surface fatigue crack growth on gear teeth flanks, Journal of Mech. Engineering 46(6), 359-369, 2000.

5.

Navarro A. and Rios E.R. Short and long fatigue crack growth- a unified model, Philosophical Magazine, 57, 15-36, 1988.

6.

Sun Z., Rios E.R. and Miller K.J. Modelling small fatigue cracks interacting with grain boundaries, Fatigue Fract. Engng Meter, 14, 277-291, 1991.

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FATIGUE AND FRACTURE PROCESSES IN HIGH PERFORMANCE PM TOOL STEELS G. Jesner, S. Marsoner1, I. Schemmel2 and R. Pippan3 Materials Center Leoben Forschung GmbH Franz-Josef-Strasse 13, 8700 Leoben, Austria [email protected] 1Materials Center Leoben Forschung GmbH Franz-Josef-Strasse 13, 8700 Leoben, Austria [email protected] 2Boehler Edelstahl Ges.m.b.H Mariazeller Strasse 25, 8605 Kapfenberg, Austria [email protected] 3Erich Schmid Institute for materials science of the Austrian academy of sciences Jahnstrasse 12, 8700 Leoben, Austria [email protected] For cold forging applications often high performance PM – tool steels were applied. The tools are cyclically repeated loaded to very high stresses by the forging process. The stresses are often significantly larger than the yield stress. This will result in a local plastic deformation, crack initiation, crack propagation and finally to the failure of the tools. It is important to know the fatigue behaviour of these types of steels to get information about the life time of such tools. From microstructural point of view the investigated steels can be considered as MMC with primary carbides with the size of a few microns and a martensitic matrix consisting of secondary carbides. By heat treatments the strength of the matrix can be varied over wide range. Microstructures with low and high primary carbide content and an extreme variation in hardness – i.e. a large variation in the matrix microstructure are investigated. The fatigue crack propagation curve and the threshold of stress intensity range fatigue crack growth curves were determined for different stress ratios in such tool steels with different microstructures and heat treatment. Fig. 1 shows as an example the micrographs of two selected steels. The different fatigue and fracture mechanism and the influence of the design of the microstructure as well as the mechanical properties of the matrix will be discussed.

FIGURE 1. Microstructure of two selected high performance tool steels.

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NOTCH AND DEFECT SENSITIVITY OF ADI IN TORSIONAL FATIGUE B. Atzori and G. Meneghetti Department of Mechanical Engineering, University of Padova Via Venezia, 1 – 35131 Padova (Italy) [email protected] Recently Atzori et al. [1,2] analysed the sensitivity to defects and to standard notches in axial fatigue of metallic materials commonly adopted in manufacturing engineering components and structures, like steels and aluminium alloys. As a result of the proposed approach, the effect of any kind of geometrical discontinuity on the fatigue limit can be treated, such as small defects, cracks, sharp notches or crack-like notches and standard rounded notches characterised by an arbitrary notch tip radius and notch opening angle. Two material parameters are needed, i.e. the material fatigue limit and the threshold value of the Stress Intensity Factor.

FIGURE 1. plot of the torsional fatigue limit for components weakened by V-notches. In the present work such an approach has been extended from axial fatigue to torsion fatigue and can be summarised by means of the diagram presented in Fig. 1, where the fatigue limit in terms of nominal shear stress range referred to the gross section 'Wg,th is reported as a function of an effective dimension of the component aeff defined as: 1

aeff

§ K 3 · 1O3 ¨ ¸ ¨W ¸ © g ¹

(1)

being K3 the Notch-Stress Intensity Factor for mode III loading evaluated for the same component but imposing a notch tip radius equal to zero, Wg the nominal shear stress evaluated on the gross section and O3 is the degree of singularity of the local stress field, which depends on the notch opening angle. Three regions can be schematically singled out divided by two length parameters, namely

a 0V t ,

*V which is a material parameter, and a t , which depends also on the

elastic stress concentration factor Ktg for torsion. If aeff < a

V 0 t,

then the presence of a (small) notch

does not lower the fatigue limit with respect to the material torsional fatigue limit. If

a 0V t 540oC temper > 620oC temper. For the three tempered conditions with plasma-nitriding, the differences of fatigue life were significantly decreased and the strain-life curves almost merged together. Furthermore, due to the formation of brittle Fe4N compounds on the specimen surface easily resulting in crack initiation, the fatigue life was apparently decreased after plasma-nitriding for each tempered condition. Fractography observations indicated that all of the fatigue fracture surfaces for the plasma-nitrided specimens exhibited a common fracture mode dominated by brittle cracking with no obvious crack initiation sites. In addition, the LCF lifetime data generated under seven different treatment conditions for the given DIN 1.2367 tool steel are well correlated with a yield-strength-normalized Smith-Watson-Topper (SWT) parameter in a log-log linear relationship, proposed by Lin and Chu [7], for which the correlation coefficient, r2, is up to 0.83.

References 1.

Mebarki, N., Delanges, D., Lamesle, P., Delmas, F. and Levaillant, S., Mater. Sci. Eng. A, vol. 387-389, 171-175, 2004.

2.

Barrau, O., Boher, C., Gras, R. and Rezai-Aria, F., Wear, vol. 255, 1444-1454, 2003.

218

C. C. Liu et al.

3.

ASTM E606-80, Annual Book of ASTM Standards, vol. 3.01, 609-615, 1991.

4.

Bannantine, J. A., Comer, J. J. and Handrock, J. L., Fundamentals of Mental Fatigue Analysis, Prentice-Hall Press, New Jersey, 1990.

5.

Nakagawa, H. and Miyazaki, T., J. Mater. Sci., vol. 34, 3901-3908, 1999.

6.

Mar, S., Li, Y. and Xu, K., Surf. Coat. Tech., vol. 137, 116-121, 2001.

7.

Lin, C. K. and Chu, C. C., Fatigue Fract. Eng. Mater. Struct., vol. 23, 545-553, 2000.

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IMPACT TESTING A CAPABLE METHOD TO INVESTIGATE THE FATIGUE RESISTANCE K. David, P. Agrianidis, K. G. Anthymidis1 and D. N. Tsipas2 Department of Mechanical Engineering, Technological University of Serres, Terma Magnesias str., GR 62124, Serres, Greece 1Serres Applied Research Center, Terma Magnesias str., GR 62124, Serres, Greece 2Department of Mechanical Engineering, Aristotle University of Thessaloniki, 54006, Thessaloniki, Greece [email protected] The modern power generation steam turbines are being designed to have higher efficiencies and to meet the stringent environmental regulations, ensuring plant reliability, availability and maintainability without compromising cost. High efficiencies can be achieved by higher temperatures. Therefore, the operating temperature is expected to rise from 550oC to 650oC and from the material perspective to implement turbine components protected by spallation and oxidation resistant coatings. To guarantee the reliability of coated steam turbines components used in power plants, the lifetime assessment of the coatings and their failure prediction become very important. Microhardness, scratch adhesion and pin-on-disc sliding tests are commonly used for rapid evaluation of the mechanical properties of coatings. However, they do not model the dynamic cyclic impact fatigue. Recently the impact test method has been introduced as a convenient experimental technique to evaluate the fatigue strength of coatings being exposed in alternate impact loads, Bouzakis et al. [1]. According to this method a coated specimen is exposed to a cyclic impact load. The superficially developed Hertzian pressure induces a complex stress field within the coating, as well as in the interfacial zone. Both these stress states are responsible for distinct failure modes such as a cohesive or adhesive one. The exposure of the layered compounds against impulsive stresses creates the real conditions for the appearance of coating fatigue phenomena based upon structural transformation, cracking generation and cracking growth, which are responsible for the gradual microchipping and the degradation of the coating. The objective of this experimental study was to investigate the influence of the impact stress fields on the performance and fatigue strength of thermal spray HVOF coatings. Furthermore, the overall aim of the current research was to prove the reliability of the impact test, as a new testing method, to assess the coating lifetime against fatigue, to interpret the failure modes of coatings, and thereby to exam its capability, whether this non-standard test can be used as a useful method for the development and optimisation of fatigue resistant coatings working under impact loading. Figure 1 shows the impact test rig where the experiments have been conducted.

K. David et al.

220

FIGURE 1. The impact test rig. The stress strain problem related to the impact test is the Herzian contact, which develops between the spherical indentor (carbide ball) and the examined layered space. The contact load leading to coating fatigue fracture was recorded in fatigue-like diagrams (endurance strength curves) versus the number of impacts. Gradual intrinsic coherence release and coating microchipping or abrupt coating fracture and consequent exposure of the substrate material designate the coating failure. The coating failure mode and its extent were assessed by SEM observations and EDX analysis. In case of relatively tough coating microstructure with high wear resistance as the WC-CoCr thermal spray coating is, the coating layer sustains the cyclic impacts without any sign of cohesive delamination failure. Instead of that, only superficial abrasive wear and spalling failure has been observed (Fig 2). This behaviour can be attributed to the improved fracture toughness of this coating.

FIGURE 2. WC-CoCr coating failure initiation (cohesive failure mode) and microhardness measurement of the layered compound.

References 1.

Bouzakis, K., Vidakis N. and David, K., J. of Thin Solid Films, vol. 351, 1-8, 1999.

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COMPARATIVE ASSESSMENT OF FATIGUE-THRESHOLDS ESTIMATED BY SHORT AND LONG CRACKS K. K. Ray, N. Narasaiahb and S. Tarafderb Department of Metallurgical and Materials Engineering, Indian Institute of Technology, Kharagpur-721302, India, b National Metallurgical Laboratory, Jamshedpur-831007, India. [email protected], [email protected], [email protected] The safe life design philosophy of structural components is based on the knowledge of the fatigue threshold for long cracks ('Kth). The emergence of the concept of short cracks, its numerous experimental verification and the continued studies on its growth behaviour over the past years have brought forward challenges to the basis of the safe life design philosophy. However, short cracks interestingly exhibit either single or multiple-thresholds. But prior investigations related to the determination and examinations of fatigue threshold for short cracks ('Kthsc) in structural materials are limited in number. In an earlier communication [1], the largest value amongst the detected thresholds associated with short cracks has been referred as “near long crack fatigue threshold” (NLFTH) and the magnitude of NLFTH has been hypothesized as close to the fatigue threshold obtained from long crack experiments as illustrated using Fig.1. This investigation aims to explore the magnitudes of 'Kthsc and 'Kth for a few steels, to determine the NLFTH values for these materials and finally to make a comparative assessment of NLFTH with their corresponding 'Kth values.

Fig.1 Schematic view of the critical crack length at the transition between short and long crack and their fatigue thresholds. The points B and C are the thresholds for short and long cracks. The point D (in part a) or B and C (in part b) indicates the transition length [1]. Experimental investigations on short crack growth behaviour and measurement of long crack fatigue thresholds have been carried out using some recently developed specimens [1-3] which can be coupled to rotating bending machine for the convenience of carrying out fatigue tests at relatively high frequency. Schematic configurations of these specimens are shown in Fig.2.

Fig.2 Configuration of specimens used for (a) short crack and (b) long crack growth experiments.

K. K. Ray et al.

222

The experiments have been carried out on four plain carbon steels and the generated data of crack growth rates against stress intensity factor range have been analyzed to examine the threshold values, 'Kth, 'Kthsc and NLFTH. The magnitudes of 'Kth have been estimated by load shedding procedure whereas the magnitudes of 'Kthsc have been evaluated from the short crack growth behaviour. An alternative set of experiments has been conducted to examine the appropriateness of the 'Kth values obtained using the new specimen configuration by comparison with standard conventional tests using compact tension specimens. Some typical results on 'Kth, 'Kthsc and NLFTH are depicted in Fig.3. The fatigue crack growth studies have been supplemented with characterization of the microstructure, hardness and tensile property of the selected steels. In addition, the effect of the associated microstructures on the investigated short crack paths has been carefully examined. The transition of short to long crack in the investigated steels was found to be dependent on the nature of the short cracks. But, the maximum fatigue threshold values obtained from short crack growth experiments on various specimens were found to be independent of the nature of the short cracks. This maximum values of 'Kthsc, referred here as NLFTH for short cracks are interestingly found to be in good agreement with their corresponding 'Kth values. The short cracks are considered to be un-influenced by the crack closure effect, whereas the long cracks considered in these experiments are observed to have little effect due to crack closure at R =-1. These aspects are considered to lead the above agreement. The current observations can be supported by some earlier reports of James and Knott [4], Sadananda and Vasudevan [5] and Taylor [6].

References 1.

Ray K. K., Narasaiah N., and Sivakumar R., Mater. Sci. Engg. A, vol. 372, 81-90, 2004.

2.

Narasaiah N., Initiation and growth of cracks near fatigue threshold in plain carbon steels, Ph.D Dissertation, IIT, Kharagpur, India, 2004.

3.

Narasaiah N. and Ray K. K, Role of microstructure on short crack propagation and its threshold, Paper No. 5075, ICF11, Turin , Italy, 2005

4.

James M. N. and Knott J. F., Fat. Fract. Eng. Mater. Struct., vol.8, 177-183, 1985

5.

Sadananda K. and Vasudevan A. K. , Int. J. Fatigue. vol.19, S99-103

6.

Taylor, D., Fatigue Thresholds, Butterworths and Co., London, p-135 1989.

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SCANNING ELECTRON MICROSCOPE MEASUREMENTS OF CRACKOPENING STRESS ON FATIGUE CRACKS EXPOSED TO OVERLOADS L. Jacobsson and C. Persson Materials Engineering, Lund University, Sweden Box 118, 221 00 Lund, Sweden [email protected] A fatigue crack exposed to an overload change the characteristics of propagation due to the enlarged plastic zone at the crack tip. The residual stresses in the material surrounding the crack tip lead to a crack closure phenomenon, and when the global applied stress gives a zero stress at the crack tip, the crack start to open. The enlarged plastic zone changes the crack closure and opening stresses that affect the effective stress intensity factor that is a measure of the stresses acting at the crack tip. To measure the global stress when the crack tip starts to open, different techniques are used. The use of a travelling microscope gives visual observations of the crack, and the observations can be done to detect when the crack opens. The compliance-offset method is used to measure the crack closure stress from the reload compliance curve that is produced from an extensometer measuring the displacement in the crack mouth. Variations in the potential drop signal throughout a load cycle are used by Andersson et al. [1] to identify opening and closure stresses. Shimojo et al. [2] uses an electrochemical technique to detect the creation of fresh surface within the crack. They discovered that the plastic zone expand more in the region with plane stress condition close to the surface after an overload, and when material was removed from the surface both the retardation of the crack propagation rate and crack closure decreased. During in-situ fatigue crack experiments Halliday et al. [3] observed differences in crack closure stresses and near tip COD for the load conditions R = 0.05 and -1. They dismiss the influence of mechanisms such as crack tip blunting and strain hardening. The aim of this study were to make more exact measurements of crack opening and closure stresses and crack shape very local around the crack tip to find relations to the crack propagation rate after an overload. This was done from high-resolution scanning electron microscope images that were analyzed with an image analysis program. Experiments with different R-values and overload ratios were performed. To detect the crack shape and the crack opening and closure stresses, an image analyzing technique is used together with in-situ fatigue crack propagation experiments within a scanning electron microscope. Throughout the load cycle, high-resolution images are taken of the crack. A selected spot in one image can be re-found with a cross-correlation algorithm in images at other stress conditions. With this technique the displacement field around the crack is determined throughout the load cycle and the stresses when the crack opens and closes can be accurately measured. Also, the crack shape and compliance curve were determined. In fig. 1 a) the compliance curve is plotted where displacements are measured a few micrometers from the crack tip and fig. 1 b) show the crack shapes, from the crack tip to 0.1 mm, for increasing loads.

L. Jacobsson and C. Persson

224

FIGURE 1. a) Compliance curve where the displacements are measured at the crack tip. (o) increasing load, () decreasing load. b) Crack shapes for different applied loads.

References 1.

Andersson, M., Persson, C., Melin, S., ICF 9, 2003

2.

Shimojo, M., Chujo, M., Higo, Y., Nunomura, S., Int. J. Fatigue, vol. 20, no. 5, 365-371,1998

3.

Halliday, M.D., Zhang, J.Z., Poole, P., Bowen, P., Int. J. Fatigue, vol. 19, no. 4, 273-282, 1997

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PROPAGATION PATH AND FATIGUE LIFE PREDICTIONS OF BRANCHED CRACKS UNDER PLANE STRAIN CONDITIONS M. A. Meggiolaro, A. C. O. Miranda1, J. T. P. Castro and L. F. Martha2 Dept. Mech. Eng., 1Tecgraf, 2Dept. Civil Eng., Pontifical Catholic University of Rio de Janeiro Rua Marquês de São Vicente 225, Gávea – Rio de Janeiro, RJ, Brazil 22453-900 [email protected], [email protected], [email protected], [email protected] Fatigue cracks can significantly deviate from their Mode I growth direction due to the influence of overloads, multi-axial stresses, micro structural inhomogeneities such as grain boundaries and interfaces, or environmental effects, generating crack kinking or branching (Lankford and Davidson [1]). The stress intensity factors (SIF) associated to branched fatigue cracks can be considerably smaller than that of a straight crack with the same projected length, causing crack growth retardation or even arrest, as discussed by Suresh [2]. This mechanism can quantitatively explain retardation effects even when plasticity induced crack closure cannot be applied, e.g. in high R-ratio fatigue problems under plane strain conditions. Analytical solutions have been obtained for the SIF of some branched cracks, however numerical methods such as the ones presented in Miranda et al. [3] are the only means to predict the subsequent curved propagation behaviour. In this work, a specialized Finite Element program is used to calculate the propagation path and associated SIF of bifurcated cracks. The numerical calculations are validated through experiments on 4340 steel ESE(T) specimens. A total of 6,250 FE calculations are used to fit empirical equations to the process zone size and crack retardation factor along the curved crack branches. The bifurcation simulations include several combinations of bifurcation angles, branch asymmetry ratios, crack growth exponents, and even considers interaction between crack branching and other retardation mechanisms such as crack closure, assuming the crack opening level is well known. It is shown that very small differences between the lengths of the bifurcated branches are sufficient to cause the shorter one to eventually arrest as the longer branch returns to its preoverload conditions, see Fig. 1. The process zone size is found to be smaller for lower bifurcation angles and for branches with greater asymmetry, in both cases due to the increased shielding effects on the shorter branch. Higher crack closure levels also result in smaller process zones, because the shorter branch is more easily arrested due to the reduction in its stress intensity range. However, a competition between smaller process zone sizes and lower growth rates of the longer branch takes place to determine the real effect of combined bifurcation and closure. The proposed equations can be readily used to predict the propagation behaviour of branched cracks in an arbitrary structure, as long as the process zone is small compared to the other characteristic dimensions. From these quantitative results, it is shown that crack bifurcation may provide a sound alternative mechanistic explanation for overload-induced fatigue crack retardation on structural components.

M. A. Meggiolaro et al.

226

FIGURE 1. Bifurcated crack propagation behaviour.

References 1.

Lankford, J., Davidson, D.L. Advances In Fracture Research, vol. 2, 899-906, 1981.

2.

Suresh, S., Fatigue of materials, Cambridge University Press, U.K., 1998.

3.

Miranda, A.C.O., Meggiolaro, M.A., Castro, J.T.P., Martha, L.F., Bittencourt, T.N., Engng. Fracture Mechanics, vol. 70, 1259-1279, 2003.

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SHORT CRACK EQUATIONS TO PREDICT STRESS GRADIENT EFFECTS IN FATIGUE M. A. Meggiolaro, A. C. O. Miranda1, J. T. P. Castro and J. L. F. Freire Dept. Mechanical Engineering and 1Tecgraf, Pontifical Catholic University of Rio de Janeiro Rua Marquês de São Vicente 225, Gávea – Rio de Janeiro, RJ, Brazil 22453-900 [email protected], [email protected], [email protected], [email protected] It is well known that the notch sensitivity factor q can be associated with the presence of nonpropagating cracks. Such cracks are present when the nominal stress range 'Vn is between 'V0/Kt and 'V0/Kf, where 'V0 is the fatigue limit, Kt is the geometric and Kf the fatigue stress concentration factors of the notch. Therefore, in principle it is possible to obtain expressions for q if the propagation behaviour of small cracks emanating from notches is known. Several expressions have been proposed to model the dependency between the threshold value 'Kth of the stress intensity range and the crack size a for very small cracks, see Chapetti [1]. Most of these expressions are based on length parameters such as El Haddad-Topper-Smith’s a0 [2], estimated from 'Kth and 'V0, resulting in a modified stress intensity range 'K I

'V

ʌ( a  a 0 )

, a0

1 § 'K th · ¨ ¸ S © 'V 0 ¹

2

(1)

which is able to reproduce most of the behaviour shown in the Kitagawa-Takahashi plot. Yu et al. [3] and Atzori et al. [4] have also used a geometry factor D to generalize the above equation to any specimen, resulting in

'K I

D ˜ ' V ʌ( a  a 0 )

a , 0

1 § 'K th · ¨ ¸ S © D ˜ 'V 0 ¹

2

(2)

Peterson-like expressions are then calibrated to q based on these crack propagation estimates. However, such q calibration is found to be extremely sensitive to the choice of 'Kth(a) estimate. In this work, a generalization of El Haddad-Topper-Smith’s equation, which better correlates with experimental crack propagation data collected from Tanaka et al. [5] and Livieri and Tovo [6], is proposed:

' K th 'K 0

ª § a ·n / 2 º «1  ¨ 0 ¸ » «¬ © a ¹ »¼

1 / n

(3)

where 'K0 is the threshold stress intensity factor for a long crack with load ratio R = 0. In the above equation, n is typically found to be between 1.5 and 8.0, see Fig. 1. Clearly, Eqs. (1) and (2) are obtained from Eq. (3) when n = 2.0.

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FIGURE 1. Ratio between long and short crack propagation thresholds as a function of a/a0. Equation (3) is used in a Finite Element program to evaluate the behavior of cracks emanating from circular and elliptical holes. For several combinations of notch dimensions, the smallest stress range necessary to both initiate and propagate a crack is calculated, resulting in expressions for Kf and therefore q. It is found that the q estimates obtained from this generalization better correlate with experimental crack initiation data. Expressions for the maximum admissible flaw sizes at a notch root are also obtained.

References 1.

Chapetti, M.D., Int. J. of Fatigue, vol. 25, 1319–1326, 2003.

2.

El Haddad, M.H., Topper, T.H., Smith, K.N., Engng. Fract. Mech., vol. 11, 573-584, 1979.

3.

Yu, M.T., DuQuesnay, D.L., Topper, T.H., Int.J.Fatigue, vol. 10, 109-116, 1988.

4.

Atzori, B., Lazzarin, P., Meneghetti, G., Fatigue Fract. Engng. Mater.Struct., vol. 26, 257267, 2003.

5.

Tanaka, K., Nakai, Y., Yamashita, M., International J. of Fracture, vol.17, 519-533, 1981.

6.

Livieri, P., Tovo, R., Fatigue Fract. Engng. Mater.Struct., vol. 27, 1037-1049, 2004.

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FATIGUE BEHAVIOUR OF PRE-STRAINED TYPE 316 STAINLESS STEEL Masayuki Akita, Masaki Nakajima1, Keiro Tokaji2 and Yoshihiko Uematsu2 Faculty of Eng., Gifu Univ., 1-1 Yanagido, Gifu 501-1193, Japan 1 Dept. of Mech. Eng., Toyota National College of Technology, 2-1 Eisei-cho, Toyota 471-8525, Japan 2 Dept. of Mech. and Systems Eng., Gifu Univ., 1-1 Yanagido, Gifu 501-1193, Japan [email protected] Type 316 stainless steel has excellent corrosion resistance, which has been widely used for machine components and structures. Materials are usually subjected to plastic deformation by processing or forming. Therefore, it is very important to understand the effect of pre-strain on fatigue behaviour (Radhakrishnan and Baburamani [1], Yokotsuka and Ikegami [2]). The present paper describes the fatigue behaviour of pre-strained 316 stainless steel. Rotating bending fatigue tests have been performed using specimens subjected to tensile pre-strains and the fatigue behaviour was discussed. The material used is a 316 stainless steel with a diameter of 16 mm. The chemical composition (wt.%) is C: 0.04, Si: 0.23, Mn: 1.33, P: 0.33, S: 0.03, Ni: 10, Cr: 16.9, Mo: 2.01. The material was solution treated at 1353 K for 1 h. After solution treatment, two different tensile pre-strains of 5 % and 15 % were given to the material from which hourglass-shape fatigue specimens with a diameter of 5 mm were machined. Vickers hardness was 137HV for the virgin specimen, 177HV for the 5% pre-strained specimen and 214HV for the 15% pre-strained specimen. Before fatigue test, specimens were mechanically polished by emery paper.

FIGURE 1. S-N diagram. Fatigue tests were performed using cantilever-type rotating bending fatigue testing machine operating at a frequency of 53 Hz. Crack initiation and small crack growth were monitored with replication technique. After experiments, fracture surfaces were examined in detail by a scanning electron microscope (SEM). The S-N diagram is shown in Fig.1. It can be seen that fatigue strength increases with increasing pre-strain level. Only a slight increase in fatigue strength can be seen in the 5% prestrained specimens, while a very large increase is attained in the 15% pre-strained specimens. The fatigue limits of the virgin, 5% pre-strained and 15% pre-strained specimens are 300 MPa, 320

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MPa and 380 MPa, respectively. Fatigue tests were continued to 108 cycles, but no failure took place. Based on the observation of crack initiation and growth, the increase of fatigue strength due to pre-strain was attributed to increased crack initiation resistance, because small crack growth was not affected significantly by pre-strain. Figure 2 illustrates the results of stress-incremental fatigue tests. Experiments were started from the stress level of 20 MPa lower than the fatigue limit for each specimen. When the specimens were not fractured until 107 cycles, then the stresses were raised by 20 MPa. As seen in the figure, the fatigue limits are increased significantly in the virgin and 5% pre-strained specimens (27% and 25% increase, respectively), while no increase is seen in the 15% pre-strained specimen, suggesting that the coaxing effect depends on the initial condition of specimens. The hardnesses of fractured specimens were increased remarkably in the virgin and 5% pre-strained specimens, while a slight increase in the 15% pre-strained specimen. Therefore, the coxing effect is strongly related to the ability of work hardening during stress cycling.

FIGURE 2. Stress-incremental fatigue test results.

References 1.

1. Radhakrishnan, V.M. and Baburamani, P.S., Mater. Sci. Eng., 17, 283-288, 1975.

2.

2. Yokotsuka, T. and Ikegami, K., J. Soc. Mat. Sci., Japan, 48, 38-43, 1999.

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THE INFLUENCE OF CONSTRAINT ON FITTING FATIGUE CRACK GROWTH DATA M. Carboni and M. Madia Politecnico di Milano Via La Masa 34, I-20156 Milano, Italy [email protected], [email protected] Fracture mechanics, in terms of crack propagation, is one of the most popular approaches for life prediction of components and structures subjected to fatigue loads. Experimental tests (as an example for a structural steel see Fig. 1) are carried out in order to quantify crack growth rates and thresholds.

FIGURE 1. Typical experimental results obtained from fracture mechanics tests on a structural steel. The obtained results, together with dedicated numerical analyses, are used in the calibration process of crack propagation analytical models, such as the Strip-Yield model (Newman [1]) able to keep into account the crack closure phenomenon. These kind of empirical models, initially introduced for aeronautical applications, are included in widespread life prediction softwares, such as AFGROW [2] and NASGRO [3], which adopt, as propagation law, the so-called “NASGRO Equation”

da dN

§ 1 ª§ 1  f · º ¨© 'K » C «¨ ¸ ¬© 1  R ¹ ¼ § ¨1  © n

p

' K th · ' K ¸¹ q K max · ¸ K crit ¹

(1)

where the parameter “f” is named “Newman’s closure function” and is a function a the constraint factor “D” [1] used to introduce in the calculations the real 3D stress field at the crack tip. The existing software incorporate numerical procedures for fitting parameters of Eq. (1) by using da/dN data without any explicit reference to test conditions. On the other hand, fatigue crack growth data obtained with different experimental conditions (specimen type, maximum applied stress) are also differing in D at the crack tip and so the direct fitting of Eq. (1) is not correct. In this paper we examine a set of crack growth data obtained onto a mild structural steel with different specimens (SE(B) and C(T)) from the point of view of constraint factor at the crack tip. In particular, constraints have been analysed with a series of detailed FEM analyses (Fig. 2).

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Results have allowed us to show how apparently conflicting data (especially in terms of 'Kth) can be re-analysed considering D factors at the crack tip in the different tests.

FIGURE 2. Analysis of the constraint factor at the tip of a SE(B) specimen

References 1.

Newman, J. C. Jr., ASTM STP 748, 53-84, 1981.

2.

Anonymous. 2001, NASA Technical Report JSC-22267B, Website: www.nasgro.swri.org, 2001.

3.

Harter, J. A., U.S. Air Force Research Laboratory Technical Report AFRL-VA-WP-TR-2002XXX, Website: http://afgrow.wpafb.af.mil, 2002.

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ATOMIC FORCE MICROSCOPY OF LOCAL PLASTIC DEFORMATION FOR TEMPERED MARTENSITE Masao Hayakawa, Saburo Matsuoka1 and Yoshiyuki Furuya Materials Information Technology Station, National Institute for Materials Science (MITS/NIMS), 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan 1Faculty of Engineering, Kyushu University, Fukuoka, Japan [email protected] An AFM technique established for observing two types of fine and complicated tempered martensite structures was developed into a technique for quantitatively evaluating local plastic deformation near tensile yield points. Surface steps with 5-40 nm were observed in locally deformed martensite blocks near prior austenite grain boundaries. The material used was JIS-SCM440 steel (containing of 0.40%C, 0.25%Si, 0.79%Mn, 1.12%Cr, 0.17%Mo; mass%). The 7.75 mm-diameter bar was austenized for 720 s at 1323 K, and then rolled at 1048-1053 K to the total area reduction was 50% as a modified-ausforming treatment [1]. The bar was tempered for 10 s at 803 K by induction heating. (This was called MAQT; Modified-Ausformed-Quenced and Tmepered.) Another bar was austenized for 0.9 ks at 1153 K and then tempered for 1.8 ks at 673 K. (This was called CQT; Conventional Quenched and Tempered.) Tensile strength showed the same value of 1580 MPa. AFM observation was conducted under the tapping mode in the atmosphere. The detail of an AFM observation method is described in the reference [2]. Briefly, the method is: 1) taking AFM images of an electropolished surface (see Figs. 1(a) and 2(a)); 2) taking AFM images of the same location after the tensile test (tensile plastic strain: 0.2, 0.4, 0.6%, respectively) after finding the position using a micro-Vickers indent as a reference mark (see Figs. 1(b) and 2(b)); 3) Finally, prior austenite grain boundaries in the chemically corroded surface were identified. Figures 1(a) and 2(a) show AFM images of the electropolished surfaces for MAQT and CQT before the tensile test, respectively. The black and white contrast in the images show the level differences on the surface attributable to differences in crystal misorientation with high-angle boundaries. Therefore, each strip of uniform brightness corresponds to a martensite block that has a high-misorientation-angle boundary. The mean block widths were 0.38 and 0.49 m for MAQT and CQT, respectively. Cementite particles, which project out from the base metal, are shown as white spots. Figures 1(b) and 2(b) are images created by superimposing prior austenite grain boundaries on the AFM images of the electropolished surfaces for MAQT and CQT after the tensile tests, respectively. The horizontal direction is the tensile loading direction. The local plastic deformation occurred in relative large blocks near prior austenite grain boundaries. The surface steps caused by local deformations in MAQT were lower than in CQT, since the martensite blocks in MAQT were finer than in CQT. The values of the surface steps corresponded to the number of pile-up dislocation at block boundaries.

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FIGURE 1. AFM images of the electropolished surface before and after the tensile test in (a) plastic strain 0% and (b) 0.6% for MAQT. Prior Ȗ grain boundaries were shown in (b).

FIGURE 2. AFM images of the electropolished surface before and after the tensile test in (a) plastic strain 0% and (b) 0.6% for CQT. Prior grain boundaries were shown in (b).

References 1.

Yusa S., Hara T., Tsuzaki K. and Takahashi T., CAMP-ISIJ vol.12, 1296, 1999

2.

Hayakawa M., Matsuoka S. and Tsuzaki K., Mater. Trans., vol. 43, 1758-1766, 2002

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IMPROVEMENT OF FATIGUE STRENGTH DUE TO GRAIN REFINEMENT IN MAGNESIUM ALLOYS Mitsutoshi Kamakura, Keiro Tokaji1, Hideaki Shibata2 and Norikatsu Bekku3 Graduate Student, Gifu Univ., Yanagido, Gifu 501-1193, Japan 1Dept. of Mech. Systems Eng., Gifu Univ., Yanagido, Gifu 501-1193, Japan 2Gifu Prefectural Research Institute, Oze, Seki 501-3265, Japan 3Honda Material Industries, Inc., Yokohira, Ooi-machi, Ena 509-7201, Japan [email protected] Magnesium (Mg) alloys are very attractive materials for structural applications because of excellent specific strength. However, their absolute strengths are insufficient, thus it is necessary to further improve the mechanical properties, particularly fatigue strength. One of the methods for improving mechanical properties is grain refinement, but studies on grain refinement in Mg alloys are very limited (Yamashita et al. [1], Kumar et al. [2]). The purpose of the present study is to achieve grain refinement due to controlled extrusion and associated improvement of fatigue strength in wrought Mg alloys. First, grain refinement due to extrusion was studied and then the fatigue behaviour of the extruded materials was discussed. Billets (grain size: 200-250Pm) of AZ61A and AZ31B were extruded at an extrusion ratio of 67. The most important parameter influencing grain refinement is working temperature that was controlled to be low (L), middle (M) and high (H) temperatures. The microstructures on the cross section in AZ61A and AZ31B are shown in Figs1 and 2, respectively. In both alloys, grain size decreases with decreasing working temperature and grain refinement is much more remarkable in AZ31B. The average grain sizes are 12.1Pm, 12.7Pm and 5.8Pm for AZ61A-H, AZ61A-M and AZ61A-L, 7.4Pm, 2.9Pm and 2.1Pm for AZ31B-H, AZ31B-M and AZ31B-L, respectively.

FIGURE 1. Microstructures in AZ61A: (a) AZ61A-H, (b) AZ61A-M, (c) AZ61A-L.

FIGURE 2. Microstructures in AZ31B: (a) AZ31B-H, (b) AZ31B-M, (c) AZ31B-L.

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FIGURE 3. S-N diagram.

FIGURE 4. Grain size dependence of proof stress and fatigue strength. Rotary bending fatigue tests were performed in laboratory air using smooth specimens of the extruded materials in both alloys. The S-N diagram is shown in Fig.3. In AZ61A, the grain size dependence of fatigue strength is less remarkable, but the fine-grained material (AZ61A-L) exhibits slightly higher fatigue strength in long life regime. On the other hand, in AZ31B, fatigue strength increases with decreasing grain size. Based on observation of crack initiation and growth, such grain size dependence of fatigue strength in AZ31B resulted from both improved crack initiation resistance and small crack growth resistance. Proof stress and fatigue strength at 107 cycles are represented in Fig.4 as a function of grain size, where both strengths were expressed properly with the Hall-Petch relation in AZ31B, but not in AZ61A.

References 1.

1. Yamashita, A., Horita, Z. and Langdon, T.G., Mater. Sci. Engng, A300, 142-147, 2001.

2.

2. Kumar, N.V.R., Blandin, J.J., Desrayaud, C., Montheillet, F. and Suéry, M., Mater. Sci. Engng, A359, 150-157, 2003.

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A UNIFIED FATIGUE AND FRACTURE MODEL APPLIED TO STEEL WIRE ROPES M. P. Weiss, R. Ashkenazi and D. Elata Faculty of Mechanical Engineering, Technion IIT Haifa 32000, Israel [email protected], [email protected], [email protected] The behavior of short and very short fatigue cracks, emanating from so called “smooth” specimens with stress concentrations has been an intriguing research topic for a long time. It is well known that micro-cracks are embedded in the surface of any smooth specimen and are created during the manufacturing process. A few of these micro-cracks will eventually propagate due to fatigue loads and will become major cracks. Due to a combination of high local stresses and stress concentrations, the short cracks are the first to become the major cracks and eventually cause failure. A quantitative two-term model for a step by step simulation of crack propagation from very short cracks to fracture has been proposed by one of the authors, Weiss [1] and Weiss and Hirshberg [2]. The model is based on the Fatigue Diagram that segregates the whole fatigue and fracture domain into 6 unique zones, and relates each zone to a known fatigue and/or fracture regime. Zone 4 in the diagram is the most prevalent in industry, as it is so bounded that the stress amplitudes are higher than the endurance stress, but lower than the elastic limit, and the stress intensity factor ranges are higher than the threshold and lower than the fracture toughness. Most metal parts and structures that are loaded by alternating loads, finally break down in this zone, either by gross yielding or by critical crack propagation. In this zone the superposition of two fatigue crack propagation rules is used. In the current study, the model is described, discussed and enhanced and is shown to be applicable to fatigue failure in single wires of steel wire ropes in general and specially in nonrotating tower crane wire ropes. In its service life a wire rope is subjected to fluctuating tension loading and to bending over sheaves. The bending stresses along the individual double helix wire are strongly dependent on the sheave-to-wire diameters ratio and on the arrangement of the reeving system. Predicting the fatigue life of a wire rope is considered as an essential objective for users and manufacturers. Generally, the failure of the individual wire is caused due to an initial crack that propagates to a critical length. In order to improve the safety level in hoisting appliances, the development of a model that will reliably predict the fatigue life and the safe service life of the rope, is needed. Moreover, a reliable model based on all the stress affecting factors, will considerably reduce complex and expensive experimental study. In this study a new approach to simulate the fatigue life of individual wires within a wire rope, that is subjected to tension-tension and bending over sheave is presented. The model is based on the two-term fatigue propagation model [1] and on a new analysis of the stresses that simulates bending and tension stresses that are generated along the double helix wire within a rope, as shown by the authors, Elata et al. [3]. It is assumed that initial flaws that were generated during the cold drawing manufacturing process exist in the individual wire. Several of these flaws (initial cracks) are located at critical sites where tension and bending stresses are maximal. Once the hoisting cycle is defined by means of the rain-flow method, it is converted to an “equivalent” loading cycle with a completely reversed loading (R=-1) by employing the Gerber parabolic line. The growing of the assumed initial crack is then simulated according to the appropriate zone on the fatigue

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diagram [1]. Material parameters are calibrated according to experimental fatigue data that was measured on eutectoid steel wires. An un-lubricated rope is assumed. Accordingly, relative displacements between adjacent wires are not permitted. The stress simulation model fully considers the configuration of the straight and bent double helix wire. The fatigue life of individual wires within an 18u7 non rotating rope are simulated for various reeving systems, D/d ratios and tension loads. This type of rope is mainly in use in tower crane applications. The theoretical results were tested on regular, industrial wires, using a specially built tension apparatus, that is free to rotate on one side, so that the twisting moments and deformations, that are generated in tension, can be measured. The results of the stresses were found to be close to the analytical predictions. Fatigue life was found to be in good agreement with Feyrer 's [4; 5] experimental prediction formula. Moreover, simulation results predict extensive fatigue deterioration of the wires within the inner strand layer, under free end attachment using a swivel, just as is customary in many tower cranes. The model quantitatively emphasizes the strong dependence of the fatigue life on the quality of the surface finish of the wires, namely on the residual micro-cracks that were generated during the deep drawing plastic deformation, in the diameter reduction process of the single wires in manufacturing. The new approach may be applied to predict the fatigue life of a complicated cross section of a rope within a hoisting system. Moreover, the model will extensively reduce expensive experimental study and can also be used to design better wire configurations. The demonstrated application in wire ropes is just one example for the use of the two-term model in fatigue life prediction of complicated mechanical parts underd different stress combinations and histories.

References: 1.

Weiss M.P., Int. J. of Fatigue, Vol. 14, No. 2, pp. 91-96, 1992

2.

Weiss M.P. and Hirshberg Z., Fatigue & Fracture of Engineering Materials & Structures, Vol. 19, No. 2\3, pp. 241-249, 1996

3.

Elata D., Eshkenazy R and Weiss M.P., International Journal of Solids and Structures, 2004, Vol 41 /5-6, pp. 1157-1172

4.

Feyrer K., Drahtseile, Springer-Verlag Berlin, Heidelberg, 1994

5.

Feyrer K., Wire, vol. 45 (2) pp.99-103, 1995

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CORRELATION BETWEEN PARIS’ LAW PARAMETERS BASED ON SELFSIMILARITY AND CRITICALITY CONDITION A. Carpinteri and M. Paggi Department of Structural and Geotechnical Engineering, Politecnico di Torino Corso Duca Degli Abruzzi 24, 10129 Torino, Italy [email protected], [email protected]

Fatigue crack growth data are usually presented in terms of the crack growth rate, d a / d N , and the stress-intensity factor range, ' K . The typical fatigue crack propagation curve is shown in Fig.1, where Region I is referred to as the near-threshold region, Region II as the power-law region and Region III as the rapid crack propagation region where

K max o K IC and crack growth

instability occurs. In Region II the Paris’ equation (Paris and Erdogan [1]) provides a good approximation to the majority of experimental data:

da dN

C ('K )m (1)

where C and m are empirical constants usually referred to as Paris’ law parameters.

FIGURE 1. Scheme of the typical fatigue crack propagation curve. Point CR corresponds to the onset of crack growth instability. From the early 60’s, research studies have been focused on the nature of the Paris’ law parameters, demonstrating that C and m cannot be considered as material constants. In fact, they depend on the testing conditions, such as the loading ratio R (Radhakrishnan [2]), on the size of the specimen (Barenblatt [3]), and, as pointed out very recently, on the initial crack length (Spagnoli [4]). However, an important question regarding the Paris’ law parameters still remains to be answered: are C and m independent of each other or is it possible to find a correlation between them based on theoretical considerations? Concerning this point, it is important to take note of the controversy about the existence of a correlation between C and m in the Literature (Radhakrishnan [5], Cortie [6], Bergner and Zhouar [7]). However, a very consistent empirical relationship between the Paris’ law parameters is usually represented by the following formula [5]:

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240

C

AB m

,

(2)

where parameters A and B depend on the material being studied and are obtained from a best-fit procedure on experimental data. In the present paper, the correlation existing between the Paris’ law parameters is derived on the basis of theoretical arguments. To this aim, both self-similarity concepts [3] and the condition that the Paris’ law instability corresponds to the Griffith-Irwin instability at the onset of rapid crack growth (see point CR in Fig.1) are profitably used. Comparing the functional expressions derived according to these two independent approaches, a relation between the Paris’ law parameters C and m formally similar to Eq.(2) is proposed. Parameter A is found to be dependent on the ultimate size of the inelastic zone ahead of the crack tip and on the Carpinteri’s brittleness number (Carpinteri [8]). On the other hand, parameter B turns out to be dependent on the loading ratio and on the critical stress-intensity factor. The main consequence of these relations is that only one macroscopic parameter is needed for the characterization of damage during fatigue crack growth. An experimental assessment of this new correlation is proposed for a wide range of materials including steels, Aluminium alloys, epoxy resins with liquid-filled urea-formaldehyde microcapsules and polymer/silica interfaces. The effect of the loading ratio on the parameter C is also deeply discussed. A good agreement with experimental data is achieved, showing the effectiveness of the new proposed correlation.

References 1.

Paris P.C. and Erdogan F., J. Basic Engineering, vol. 85D, 528-534, 1963.

2.

Radhakrishnan V.M., Engineering Fracture Mechanics, vol. 11, 359-372, 1979.

3.

Barenblatt G.I., Scaling, self-similarity and intermediate asymptotics, Cambridge University Press, Cambridge, 1996.

4.

Spagnoli A., Mechanics of Materials, vol. 37, 519-529, 2005.

5.

Radhakrishnan V.M., Engineering Fracture Mechanics, vol. 13, 129-141, 1980.

6.

Cortie M.B., Engineering Fracture Mechanics, vol. 30, 49-58, 1988.

7.

Bergner F. and Zouhar G., International Journal of Fatigue, vol. 22, 229-239, 2000.

8.

Carpinteri A., Materials and Structures, vol. 14, 151-162, 1981.

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THERMO-MECHANICAL FATIGUE LIFETIME ASSESSMENT WITH DAMAGE-PARAMETERS, ENERGY-CRITERIONS AND CYCLIC-JINTEGRAL CONCEPTS M. Riedler, R. Minichmayr, G. Winter and W. Eichlseder2 University of Leoben, Christian Doppler Laboratory for Fatigue Analysis Chair Mechanical Engineering2 Franz-Josef-Str. 18, A-8700 Leoben [email protected] The simulation of the thermo-mechanical fatigue (TMF) behaviour of cylinder heads is an important design step in the automotive industry. The steady rise of engine power and the demand of lightweight construction with a concurrent enhanced reliability require an optimised dimensioning process. The goal of this paper is to apply classical damage parameters, plastic and total energy criterions and cyclic J-integral concepts for a thermo-mechanical lifetime assessment of aluminium and cast iron alloys. Many of the empirical models are strain based criterions like the Manson-Coffin [1-2] criterion with numerous modifications. Criterions based on damage parameters try to find a correlation between the number of cycles to failure and loading parameters. The fracture mechanical view allows e.g. with cyclic J-integrals a description of the TMF lifetime. Cumulative models, as the Chaboche [3] models, try to cumulate the damage for each cycle, therefore they need a lot of computing time for complex structures. The use of submodels is one possibility of using them for a TMF lifetime assessment of cylinder heads. Another method is the accumulation of the specific damage parts (pure fatigue, oxidation, creep), as e.g. Miller [4] (accumulation of crack propagation rates) or Neu/Sehitoglu [5] (accumulation of damage rates) do it. Microstructural methods have a physical background, but are often difficult to use for a TMF lifetime estimation. It is shown in previous work (Riedler [6]), that energy based criterions are qualified for TMF lifetime approaches. Due to the interplay of strain and stress values at a TMF loading they are able to account for more specific influences as well as their interactions. The general energy based lifetime criterion is as follows: 'W

e ˜ f ('We )  p ˜ f ('W p )

,

Nf

A ˜ 'W  B

(1)

The specific energy is the sum of an elastic and plastic energy function, whereas both are characterised with strain and stress parameters, as e.g. amplitude, maximum, minimum or effective values. A power law is used to describe the dependency of the lifetime. The plastic energy criterion W1 [6] is best suited for the very ductile Al-alloy AlCuBiPb to account for the influences of a varying maximum temperature, dwell time, mean strain, pre-ageing and ageing in service time. The classical damage parameter according to Smith-Watson-Topper [7] gives the best result for the ductile aluminium cast alloys AlSi7MgCu0.5 and AlSi8Cu3. For inductile materials like alloy AlSi6Cu4 a criterion based on fracture mechanics in the manner of a cyclic J-integral approach according to Tomkins [8] provides the best TMF lifetime estimation result. A TMF lifetime assessment for the different materials investigated shows a reasonable scatter of about 2.5, see Fig. 1. Since only the Tomkins approach as a sum of an elastic and plastic energy part [8]:

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242

'J

2 § S ˜ V max 2S ˜ V max ˜ 'H p  a ˜¨ ¨ E 1  n' ©

· ¸ N f ¸ ¹ ,

§ 'J · A˜¨ ¸ © a ¹

B

(2)

which is a special type of Equ. (1), never gives a rank worse than five (of ten investigated criterions) for the different materials researched, a standard deviation minimisation process to determine an appropriate energy definition based on Equ. (1) is executed. This allows us to describe the TMF life of different materials and material properties with an improved accuracy.

FIGURE 1. Simulation of the TMF lifetime.

References 1.

Manson, S.S, Behaviour of materials under conditions of thermal stress, NACA Report No. 1170, 1954.

2.

Coffin, L.F, Trans. ASME, vol. 76, 931-950, 1954.

3.

Lemaitre, J. and Chaboche, J.L., Mechanics of solid materials, Cambridge Univ. Press, 1990.

4.

Miller, M.P., McDowell, D.L., Oehmke, R.L.T. and Antolovich, S.D., In Proceedings of Thermo-Mechanical Fatigue Behaviour of Materials, ASTM STP 1186, edited by H. Sehitoglu, Philadelphia, 1993, 35-49.

5.

Neu, R.W. and Sehitoglu, H., Metals Trans. A, vol. 20A, 1989, 1755-1767 and 1769-1783

6.

Riedler, M.: PhD Thesis, University of Leoben, 2005.

7.

Smith, K.N., Watson, P. and Topper, T.H., J. of Materials, vol. 5, No. 4, 767-778, 1970.

8.

Tomkins, B., Sumner, G. and Wareing, J., In Proceedings of International Symposium on Low Cycle Fatigue Strength and Elasto-Plastic Behaviour of Materials, edited by K.-T. Rie and E. Haibach, DVM, Berlin, 1979, 495-508.

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PREDICTING FATIGUE CRACK RETARDATION FOLLOWING OVERLOAD CYCLES Marcos V. Pereira, Fathi A. Darwish1, Arnaldo F. Camarao2 and Sérgio H. Motta3 Department of Materials Science and Metallurgy / Catholic University of Rio de Janeiro Rua Marquês de São Vicente 225, Rio de Janeiro / RJ, CEP 22453-900, Brazil 1Fluminense Federal University Rua Passo da Pátria 156, Niterói / RJ, CEP 24210-240, Brazil 2GEP / ArvinMeritor CVS Av. João Batista 825, Osasco / SP, CEP 06097-900, Brazil 3Technology Division / Brasilamarras Rua Eng. Fábio Goulart 40, Niterói / RJ, CEP 24050-090, Brazil [email protected], [email protected], [email protected], [email protected] Dating back to the beginning of the seventies, a number of models have been proposed to predict fatigue crack growth rate under variable amplitude loading. This effort was motivated by earlier observations that the application of an overload is followed by crack growth retardation over a crack length increment. The model of Willenborg, which belong to the group of yield zone models, incorporate interaction effects and is characterized by introducing crack tip plasticity. Although interaction models are generally considered to be applicable for high strength alloys with limited ductility, empirical verification of the predictions made by these models is rather limited. Accordingly, the present study was initiated in an effort to test the validity of the Willenborg model for predicting fatigue crack growth retardation in an R3 grade structural steel following the application of overload cycles. As this grade steel is used for fabricating offshore mooring chains, the study was extended to also include flash welded joints taken from the chain links. CT specimens were machined from both the base metal as well as from the welded joints and a number of these specimens were subjected to a heat treatment that involved quenching and tempering. The CT specimens, both heat treated and untreated, were fatigue tested under constant amplitude (CA) loading in order to establish the typical da/dN versus K curves. During CA fatigue loading, some specimens in different material conditions, were subjected to single and multiple overloads applied at a given crack length, and crack growth rate da/dN was followed as a function of K, evidencing the retardation in crack propagation over an interval of crack length. Crack propagation rate da/dN within the delay period was predicted by Willenborg model and then compared with the experimental data. Finally, the results are presented and discussed focusing on the comparison between the predictions made by the model in light of the experimental data.

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FIGURE 1. Variation of crack size (a) with the number of cycles (N) for flash welded joint after overloading.

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FATIGUE CRACK GROWTH AT NOTCHES CONSIDERING PLASTICITY INDUCED CLOSURE Jutta Bruening, Olaf Hertel, Michael Vormwald and Georgios Savaidis Technische Universität Darmstadt, Materials Mechanics Group Petersenstraße 12, D-64287 Darmstadt, Germany [email protected] [email protected] [email protected] Aristotle University Thessalonica, Division of Mechanical Engineering, Laboratory of Machine Elements and Machine Design GR-54124 Thessalonica, Greece [email protected] Classical fatigue analyses discriminate between technical crack initiation (crack length of about 1mm) and crack propagation stages. The stage of crack initiation, however, is itself dominated by the growth of short fatigue cracks. Based on the assumption that a fatigue life to initiate a microstructurally short crack of dimensions in the order of 10Pm may be neglected Dankert et al. [1] have proposed a so-called unified elastic-plastic model for fatigue crack growth evaluation which describes the whole fatigue life (technical crack initiation and stable crack growth) of notched and unnotched components by integrating an appropriate crack growth law. In the meantime this model has entered a guideline for the proof of the strength of components [2]. The present paper reports on the results of an investigation on this model which led to an improvement of the model’s assessment of effective ranges of the crack driving force (i.e. the JIntegral). Furthermore, a generalization enabling its application for arbitrary notch situations is presented. Additionally, new results are shown of comparisons of experimentally determined and calculated crack growth curves as well as life curves for both the initiation of a technical crack (crack depth 1mm) and the final failure . The basic modules of the model are the following: The range of the cyclic J-integral is taken as the relevant crack driving force. This is essential because generally short fatigue cracks grow in a notch field where elastic-plastic conditions prevail in the uncracked situation. Therefore, the limits for the application of the linear fracture mechanics are violated. Nevertheless, the special case of the linear fracture mechanics based calculation (negligible cyclic plastic deformation) is incorporated. Approximation formulas for the J-integral of semi-elliptical and quarter-elliptical surface cracks as well as through-the-thickness cracks in components with elliptical notches are presented. A procedure for assessing cracks in arbitrarily notched components is outlined such that this problem can be reduced to the solved case with elliptical notches. Effective ranges are considered exclusively. This means that only the range between the crack closure level and the peak level of a cycle is taken to calculate the J-integral range. The approximation formulas for the crack opening level are taken as proposed in the literature by Dankert et al. [1] and Savaidis and Dankert [3]. however, the reference load for cyclic loading is taken to arrive at appropriate effective Jintegral ranges instead of its monotonic counterpart. A Paris-type crack growth equation is formulated in terms of this effective J-integral range. Integration of this equation leads to the crack growth curves and fatigue lives.

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The integration starts at a suitably chosen initial crack length. The relevant criterion is that the integration starting at this very initial crack length will result in the material’s strain-life curve for the special case of an unnotched material specimen. Variable amplitude loading is taken into account by identifying cycles according to the rainflow algorithm. Saal [4] has performed well documented experiments on the initiation (technical crack size 1mm) and growth of fatigue cracks in notched plates of low alloyed steel. The comparison of the life curves with the corresponding curves calculated by applying the improved unified model reveals the reasonable accuracy of the model. The differences of the new results compared to those of the original model are exemplified.

References 1.

M. Dankert, S. Greuling, T. Seeger. A Unified Elastic-Plastic Model for Fatigue Crack Growth at Notches Including Crack Closure Effects.Symposium on Advances in Fatigue Crack Closure Measurement and Analysis, San Diego, Calif., 1997, ASTM, 1999, STP 1343, S.480

2.

FKM-Richtlinie ”Bruchmechanischer Festigkeitsnachweis”, 2. Auflage, VDMA Verlag GmbH, Frankfurt am Main, to be published 2005

3.

G. Savaidis, M. Dankert, T. Seeger, An analytical procedure for predicting opening loads of cracks at notches. Fatigue and Fracture of Engineering Materials and Structures, 1995, 18(4), S. 425-442

4.

Saal, H., Einfluß von Formzahl und Spannungsverhältnis auf die Zeit- und Dauerfestigkeit und Rißfortschreitungen bei Flachstäben aus St52, Heft 17, Institut für Stahlbau und Werkstoffmechanik, Technische Universität Darmstadt, 1971

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INFLUENCE OF MICROSTRUCTURE ON FATIGUE PROPERTIES OF NIBASE SUPERALLOY AT ELEVATED TEMPERATURE QY. Wang , Y. Matsuyama1, N. Kawagoishi1, M. Goto2 and K. Morino3 Sichuan University, Chengdu 610065, China 1Kagoshima University, 1-21-40 Korimoto, Kagoshima, Japan 2Oita University, 700 Tannoharu Oita, Japan 3Tokuyama College of Technology, 3538 Kume Takajyo Shunan, Japan [email protected], [email protected], [email protected], [email protected] Ni-base superalloys are used under sever conditions like a high temperature or sever corrosive environment because of their superior properties on corrosion, creep, static strength at high temperatures and so on. Therefore, many studies on creep and fatigue properties of the alloy have been carried out, e.g. Brown and Hicks [1]. Recently, it is very important to know the fatigue properties in long life region, because machines and structures are used for long-term from the point of view of environmental and economical demands. However, most of the studies on fatigue were very limited within the short life up to107cycles. It is reported that fracture occurs from an internal inclusion in long life region in many high strength steels and surface treated steels, while surface fracture occurs in short life region, e.g. Murakami et al. [2]. Moreover, the fatigue properties may be influenced by microstructure. However, the mechanism and the evaluation method for fatigue life of internal fracture are not clarified. In the present study, fatigue properties of Inconel 718 and the influence of grain size on the properties were investigated in the wide region of fatigue life until 108 cycles at room temperature and 500 under rotating bending. Fatigue tests were carried out using materials with two kinds of grain sizes, about 20m and 100m. Table 1 shows the mechanical properties of the materials. Prior to fatigue tests, all the specimens were electro-polished about 20m from the surface layer. Observations of the change in the surface state of a specimen due to stress repetitions and fracture surface were carried out under an optical microscope using plastic replication technique or under a scanning electron microstructure (SEM) directly. Fig. 1 shows S-N curves. Fatigue strength is high in the fine grain at both temperatures, especially at 500. Although, all the fracture originated from the surface except for the fine grain at 500 in long life region, resulting duplex S-N curve. Fig. 2 shows crack growth curves. There is no or little differences in the crack initiation life

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248

and the growth rate of a larger crack between the fine grain and the coarse grain at both temperatures. However, the growth rate of a crack smaller than about 200m is higher in the coarse grain than in the fine grain at room temperature. This is caused that the crack length initiated is larger in the coarse grain than in the fine grain. On the other hand, a definite suppression of a crack growth at 500, when a crack is small. The suppression is caused by oxide induced crack closure at 500. These are main reasons for the difference in the influence of grain size on the fatigue strength at both temperatures.

References 1.

Brown, C.W. and Hicks, M.A., Int. J. Fatigue, vol. 4, 73-81, 1982

2.

Murakami, Y., Yokoyama, N. N. and Nagata, J., Fatigue Fract. Engng. Mater. Struct., vol. 25, 735-746, 2002

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MODDELLING FATIGUE CRACK CLOSURE USING DISLOCATION DIPOLES P. F. P. de Matos and D. Nowell University of Oxford, Oxford, UK [email protected], [email protected] Over the past 30 years the study of fatigue crack closure has been one of the most challenging research topics in fatigue crack growth. This phenomenon was first noticed by Elber [1] and then has been documented by several researchers, both experimentalists and analysts. Different closure mechanisms have been observed, although the primary mechanism of closure seems to be plasticity-induced. One of the reasons why fatigue crack closure has been so extensively studied is because of the need of predicting fatigue lives of structural components, e.g. aircraft industry. It has been proved that fatigue crack closure plays an important role in crack growth rates together with load ratio and load history. To quantify the crack closure effect, different techniques can be used, e.g. experimental, numerical and analytical. Usually experimental techniques are not used for practical purposes as they are time consuming and because of the high cost of the experimental work. Numerical techniques such as FEM modelling have been successfully used to model crack closure. However they are time consuming since elasto-plastic models are required to accurately model the plastic deformation ahead the crack tip and the plastic wake. Usually FEM results are dependent on the level of mesh refinement, crack-tip node release scheme etc. Concerning the analytical techniques different approaches can be used. A novel technique was developed by Newman [2], his model is based on the Dugdale model but was modified to leave deformed material on the wake of the advancing crack. This model is dependent on an empirical constraint factor which is used to establish the link between the plane stress and plane strain condition. Furthermore, yield strip models are only suitable to model cracks under plane stress; therefore the use of this constraint factor for modelling plane strain is only an approximation since the deformation mechanism is completely different. In the present paper a quadratic programming technique is used to model fatigue crack closure. The model herein used was developed by Nowell [3] for modelling fatigue cracks under plane stress. In the present paper we are going to show how this model can be changed to model crack closure under plane strain conditions. In the original model, Nowell [3] used displacement discontinuity opening dipoles (see FIGURE 1) to model both crack and plastic region ahead of the crack tip. For modelling crack closure under plane strain this model was changed in order to take into account the different deformation mechanism. Sliding dislocation dipoles were collocated along the planes of maximum shear stress to quantify the plastic deformation along these planes and at the tip of the crack. Initial results compare well with those given by Kanninen and Atkinson’s [4] superdislocation model for the case of a static crack, FIGURE 2. The aim of the present paper is to investigate the deformation of the crack tip in both deformation modes plane stress and plane strain. The results are compared with different methods, e.g. FEM and Newman model [2]. The case of more general loading conditions under plane strain will be discussed.

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250

FIGURE 1. a) Opening and sliding dislocation dipoles; b) Dipole displacement field.

FIGURE 2. Crack tip opening displacement. Present model vs Kanninen and Atkinson [4].

References 1.

Elber W., Engineering Fracture Mechanics, vol. 2(1), 37-44, 1970

2.

Newman Jr. J.C., ASTM STP, vol. 748, 53-84, 1981.

3.

Nowell D., Fatigue & Fracture of Engineering Materials & Structures, vol. 21(7), 857-871, 1998.

4.

Kanninen M.F. and Atkinson C., International Journal of Fracture, vol. 16(1), 53-69, 1980.

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COMPARISON BETWEEN FATIGUE CRACK GROWTH MODELLED BY CONTINOUS DISLOCATION DISTRIBUTIONS AND DISCRETE DISLOCATIONS P. Hansson, S. Melin and C. Persson1 Division Mechanics, 1Division of Materials Engineering Lund Institute of Technology, Box 118, SE-22100 LUND [email protected] Short fatigue cracks are known to have a growth behaviour different from that of long cracks, the latter well predicted by linear elastic fracture mechanics. Short cracks can grow at high rates at load levels well below the threshold value for long cracks, before entering into the long crack region, or arrest and become nonpropagating cracks. The growth behaviour of short cracks is strongly influenced by the microstructure of the material, such as grain boundaries and direction of slip planes within the grains, as well as of local plasticity around the crack tip. Microstructurally short cracks, typically shorter than a few grains, grow in a single shear mechanism along specific slip planes within the grains, cf. Suresh [1], leading to a zigzag crack path, cf. Fig.1.

FIGURE 1. Zigzag shaped edge crack. For low growth rates, in the order of a few burgers vectors per cycle, it is important to account for the discrete dislocations within the material. Studies taking the nucleation, movement and annihilation of discrete dislocations along specific slip planes into account have been performed by Riemelmoser et al. [2] to study the cyclic crack tip plasticity for a long mode I crack. A similar model have also been developed by Bjerken and Melin [3] to study the influence of grain boundaries on a short propagating mode I crack, subjected to fatigue loading. Another approach was used by Krupp et al. [4] to study the propagation of short cracks in a duplex steel. In this model, the plastic zone was described by dislocation elements distributed along the slip planes, and the crack growth rate was assumed to be determined by the crack tip shear displacement. In this study, the propagation of a short edge crack, situated within one grain in a bcc material subjected to fatigue loading is modelled using a dislocation formulation. The external boundary, defined as the free edge and the crack itself, is modelled by dislocation dipole elements, consisting two glide dislocations and two climb dislocations, allowing the crack surfaces to both open and shear. The plasticity is modelled by a continuous distribution of dislocation elements along the slip planes, allowing the slip planes only to shear. The grain boundary is treated as an impenetrable hinder for the dislocations, and the crack is assumed to be the only dislocation source in the initially dislocation free material. A schematic description of the model is seen in Fig. 2.

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As the applied load exceeds a certain critical value, cf. [5], dislocations will nucleate at the crack tip or a corner point of the crack, forming plasticity along the slip planes. As the load is increased, the plastic zone is increased until maximum load is reached and the load is reversed. During unloading dislocations will move back towards the crack and annihilate, resulting in crack growth in the corresponding direction under the assumption that no healing of the crack surfaces is allowed. To describe the plasticity with continuous dislocation distributions instead of with discrete dislocations as used in earlier studies by Hansson and Melin [5], creates a more efficient model as regards to computational time, which, in turn allows for simulations at higher growth rates and growth through additional grains. Though, the approach results in decreasing accuracy in describing the plastic zone and loss of physically correct dislocation distribution as compared to the approach in [5].

FIGURE 2. Schematic description of the model.

References 1.

Suresh, S. Fatigue of Materials, second edition. University Press, Cambridge, 1998.

2.

Riemelmoser, F.O, Pippan, R. and Kolednik, O. Cyclic crack growth in elastic plastic solids: a description in terms of dislocation theory. Computational Mechanics, 20:139-144, 1997.

3.

Bjerkén, C. and Melin, S. A study of the influence of grain boundaries on short crack growth during varying load using a dislocation technique. Engineering Fracture Mechanics, 71(15):2215-2227, 2004.

4.

Krupp, U., Düber, O., Christ, H.-J. and Künkler, B. Application of the EBSD technique to describe the initiation and growth behavior of microstructurally short fatigue cracks in a duplex steel. Journal of Microscopy., 213(3):313-320, 2003.

5.

Hansson, P. and Melin, S. Dislocation-based modeling of the growth of a microstructurally short crack by single shear due to fatigue loading. Int Jnl of Fatigue, 27:347-356, 2005.

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FATIGUE EVALUATION CONSIDERING THE ENVIRONMENTAL INFLUENCE USING A MONITORING SYSTEM R. Cicero, I. Gorrochategui and J. A. Alvarez University of Cantabria E.T.S. Ingenieros de Caminos, Av/Los Castros s/n, 39005, Santander, Spain [email protected] The Nuclear Power Plants were designed for an initial life of 40 years, however nowadays, is under study the possibility of its life extension. This process requires, among other issues, the analysis of all the time limited aging calculations to the life period of the original design. A typical case of this kind of calculations are the fatigue evaluations. In early designs fatigue damage was not considered in the Nuclear Power Plants. Once it was introduced, the fatigue damage evaluation was carried out based uniquely on stress considerations, being necessary to demonstrate that the fatigue damage was lower than the unity. Along the years, new considerations have been introduced like the variation of the material properties with the temperature, new computer applications and programs to calculate the stresses in components with higher accuracy, as well as the possibility of implementing monitoring systems to register all the real transients that occur in the Nuclear Power Plants, and therefore, allowing a more realistic evaluation of the fatigue damage. With all these new elements, it has been being demonstrated that the fatigue damage is always lower than one even considering a life of 60 years. In the last years, it has been observed the influence of the environment where the components are submerged on the fatigue damage [1] and methods have been developed to estimate this effect. A first analysis of fatigue, considering the environmental effect [2], extrapolating the number of cycles linearly and applying correction factors for the environmental effect, can lead to the result that the fatigue damage in some components for 60 years of life is higher than one, and then they are in a critical situation of fatigue failure. For these reasons, nowadays it becomes necessary to focus the resources on the development of new more precise evaluation methods of the environmental influence. These new methods have to take into account the changes that occur during the transients (temperature, O2 concentration...), the composition of the affected materials, the loading process... One possible solution for the fatigue damage evaluation could be the implementation of a monitoring system that registers the environmental real conditions and the type of loading in each moment [3, 4]. In this way, it would be possible to establish an accurate approach with the possibility of a life extension till 60 years, as for this degradation mechanism is referred. This work illustrates this methodology through its application to a real case.

References 1.

NUREG/CR-6260, Application of NUREG/CR-5999 Interim Fatigue Curves to Selected Nuclear Power Plant Components.

2.

Mehta, H.S. and Gosselin, R.S., Environmental factor approach to account for water effects in pressure vessel and piping fatigue evaluations. Nuclear Engineering and Design 181, 1998

254

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3.

Stevens G.L., Deardorff F.A. and Gerber. A.D., Fatigue Monitoring for Demonstrating Fatigue Design Basis Compliance.

4.

D. Pando, J. A. Alvarez and I. Gorrochategui, On the use of a monitoring system for fatigue usage calculations, Engineering Failure Analysis. 2004. Vol. 11, 765-776.

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THERMAL FATIGUE CRACK INITIATION AND PROPAGATION BEHAVIOR OF STEELS FOR BOILER S. Aoi, T. Marumiya, R. Ebara, T. Nishimura and Y. Tokunaga Department of Advanced Materials Science, Kagawa University 2217-20Hayashi-cho, Takamatsu-city,Kagawa,761-0396,Japan [email protected] Miura Institute of Research & Development, 7 Horie-cho,Matsuyama-city,Ehime,799-2696, Japan Miura Co.,Ltd., 7 Horie-cho,Matsuyama-city,Ehime,799-2696, Japan Thermal fatigue tests were conducted for SB410 steel and SUS310S steel for boiler. A laboratory made thermal fatigue testing apparatus was used. This apparatus consisted principally of a heating device using oxygen and LPG gas, a temperature control device for the heated zone and a rapid cooling device for the specimen. During thermal fatigue tests the heating and cooling cycles were repeatedly loaded on the specimen placed on the specimen holder. City water was used as a cooling medium. The heating temperatures were 673K, 773k and 873K,and cooling water was sprayed on to the specimen surface through a nozzle. As it was difficult to measure the surface temperature of the specimen, small holes for a thermocouple were prepared to measure the temperature of the notch during the thermal fatigue tests. Thus the measured temperatures were used as the testing temperatures. The plate specimens with an electric discharged notch at

Figure 1.Thermal fatigue test specimen the bottom of the mechanical U notch. The thicknesses of the specimens were 24mm and 12mm.The thermal fatigue crack initiation tests and thermal fatigue crack propagation tests were conducted up to 100 cycles for specimens with 24mm thick and 300 cycles for specimens with 12 mm thick. Figure 1 shows the figure and the size of the thermal fatigue test specimen. The thermal fatigue crack length was measured at every ten cycles by use of a viewing microscope with magnification of 20 after interrupting thermal fatigue tests. The thermal fatigue cracks were examined by an optical microscope and thermal fatigue fracture surfaces were examined by a JEOL scanning electron microscope (JSM5500S). Figure2 shows crack propagation curves for SB410 steel with 12mm thick. The higher the testing temperature the smaller the number of heat cycles is. The higher the testing temperature the faster the crack propagation rate is. The same phenomenon was observed for SUS310S. The thermal fatigue crack propagation rate of SB410 steel was faster than that of SUS310S steel. Plural thermal fatigue cracks were observed on the bottom of the electric discharged notch for SB410 steel. The crack branching was observed on the

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specimen tested at 873K. Striation was observed on fracture surfaces of SB410 steel. Striation was predominant on fracture surfaces of SUS310S. The striation spacing per cycle ,S obtained from the measured striation spacing S versus K curve was well coincident with the da/dN K curve in the high crack propagation rate. It can be concluded that thermal fatigue crack of boiler steels propagate in association with striation.

Figure2. Thermal fatigue crack propagation curves of SB410 steel with 12mm thick

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RECENT DEVELOPMENTS IN FATIGUE CRACK GROWTH R. Jones , S. Pitt1, and E. Siores2 Cooperative Research Centre for Railway Engineering, Department of Mechanical Engineering, P.O. Box 31, Monash University, Victoria, 3800, Australia. [email protected] 1Air Vehicles Division, Defence Science and Technology Organisation, 506 Lorimer Street, Fishermans Bend 3207, Australia, [email protected] 2Centre for Materials Research and Innovation, Bolton University,Deane Road, Bolton , BL3 5AB, England, [email protected] Recent research [1 - 3] has shown that the Frost Dugdale law [4] can be applied to a wide class of engineering problems, and that for complex load spectra the crack growth rate per loading block da/dB is essentially a linear function of a, see Figure and [1] for more details. These findings together with the realisation that “in the threshold regime, there is something missing either in the model”, see [5], led to the conjecture [1-3] that in Region I the crack growth rate can be expressed in the form: da/dN = C ( a/a*)(1-m/2) ('K) m

(1)

which for small cracks integrates to give the Frost-Dugdale relationship, viz: a = ao e EN

(2)

Figure 1: Crack growth rates for A7 wing, from [1, 3]. where N is the number of cycles, E is a parameter that is geometry, material and load dependent, a is the crack depth and, a0 is the initial size of the defect. This paper presents a large number of examples to show that this relationship is also true for both over and underloads, see Figs 2 and 3 which present the experimental results presented by Liu and Dittmer [6] and Schijve and Broek [7] respectively. This methodology has been linked with NASTRAN and is used, in conjunction with a finite element model of the F-111 wing, to predict crack growth in the 1969 F111 wing test, which was performed in the US as part of the F-111 certification program.

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References 1.

Barter S., Molent L., Goldsmith N. and Jones R., 2004, "An Experimental Evaluation Of Fatigue Crack Growth", Journal Engineering Fracture Mechanics, 2004.

2.

R. Jones, S. Barter, L. Molent and S. Pitt, "Crack growth at low K's and the Frost Dugdale law", Journal Chinese Institute of Engineers, Special Issue in Honour of Professor G. C. Sih, 27, 6, 869-875, 2004.

3.

L. Molent, R. Jones, S. Barter, and S. Pitt, “Recent Australian Developments In Fatigue Life Assessment”, Submitted International Journal of Fatigue, April 2005.

4.

N. E. Frost and D. S. Dugdale, “The propagation of fatigue cracks in test specimens”, Journal Mechanics and Physics of Solids, 6, pp 92-110, 1958.

5.

J.C. Newman Jr., A. Brot, C. Matias, “Crack-growth calculations in 7075-T7351 aluminum alloy under various load spectra using an improved crack-closure model”, Engineering Fracture Mechanics 71 (2004) 2347–2363, 2004.

6.

F. Liu and D. F. Dittmer, “Effect of multi-axial loading on crack growth”, AirForce Flight Dynamics Laboratory, Air Force Systems Command, AFFDL-TR-78-175, Volumes I – III, September 1978.

7.

J. Schijve and D. Broek, “Crack Propagation Based on a Gust Spectrum with VariableAmplitude Loading”, Aircraft Engineering, 34, pp. 314-316, 1962.

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CRACK CLOSURE EFFECTS IN A CRACKED CYLINDER UNDER PRESSURE J. Zhao, R. Liu, T. Zhang1 and X. J. Wu2 Department of Mechanical and Aerospace Engineering, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario, Canada K1S 5B6, [email protected] 1Department of Mathematics, Northeastern University, Shenyang, Liaoning, P.R. China 110004, [email protected] 2Institute for Aerospace Research, National Research Council Canada, 1200 Montreal Road, Ottawa, Ontario, Canada K1A 0R6, [email protected] The circumferential stress varies through the wall thickness when a cylinder is subjected to internal or external pressure. Internal pressure will induce tensile circumferential stress while external pressure compressive stress, in terms of the thick-walled cylinder theory [1]. The resultant stress due to the synergetic contribution of internal and external pressure may be tensile at the inner surface and compressive at the outer surface or vice versa in some cases, depending on the load levels, which would lead to crack-face closure at the compressive edges when the cylinder contains an axial crack. Historically, crack problems in shells were formulated in terms of either the classical theory [2] or the transverse shear theory [3], which were all based on the linearized shallow shell theory [4-6]. However, one deficiency of these solutions is that the crack face interpenetration or overlap was allowed at the compressive edge when a bending load was involved, which is physically unrealistic. In reality, crack-face closure on the compressive edge may occur when a shell or plate containing a through-the-thickness crack is subjected to bending load. The present research is aimed to develop a formulation for the determination of stress intensity factor for a cylinder containing an axial crack, which incorporates the effect of the crackface closure. According to the formulation developed by Delale and Erdogan [7-9], the problem of a cracked shell subjected to membrane force and bending moment can be reduced to a pair of coupled singular integral equations,

 dW  1>k K,W G W  k K,W G W @dW ³ 11 1 12 2

1GW 1

³

1W K

2SF1K ,

1

h 1Q 2 G2W dW  ³>k21K,W G1W  k22K,W G2W @dW 2S F2 K , 4 ³ a O0 1 W K 1 1

(1a)

1

(1b)

1

³ G W dW i

1

where

K

0, (i = 1, 2)

(1c)

y / a , -a < y < a, and G1 and G2 denote the derivatives of the crack-face normal

displacement, u(0+, K), and the crack face rotation, E(0+, K), respectively,

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G1 K



w u 0 ,K wK

G2 K

and



w E 0 ,K . wK

(2)

The simulation of the crack-face closure is achieved by introducing a contact force at the compressive edge so that in the closure region the normal displacement of the crack face at the compressive edge must remain equal or greater than zero, that is,





u 0  ,K r

h E 0  ,K t 0 2a





(3)

Due to the curvature effect of shell crack-face closure may not always occur on the entire length of the crack, depending on the geometry of the shell and the nature (direction) of bending load. The closure regions will be determined as a mixed-boundary value problem through an iterative process such that either the normal displacement at the compressive edge is equal to zero or the contact pressure is equal to zero. The stress intensity factor at the crack tip is due to the synergetic contribution of membrane and bending effects, which is evaluated by Delale and Erdogan [8], k I z



E a 2

z ª º «¬ g 1 1  a g 2 1 »¼

(4)

which shows that the stress intensity factor varies through the shell wall thickness. The results demonstrate that due to the curvature effect the crack closure behavior in shells differs from that in flat plates. Full-length closure always occurs in flat plates, but it is not a case in shells. Partial closure may occur in shells, depending on the shell geometry and the bending load direction. It is found that crack-face closure greatly reduces the bending component but increases the membrane component of the stress intensity factor. The crack-face closure prevents the penetration of the crack faces at the compressive edges physically when a cracked shell is subjected to bending load, which leads to a zero value of the stress intensity factor at the closure edge.

References 1.

Benham, P.P., Crawford, R.J. and Armstrong, C.G., Mechanics of Engineering Materials, Longman Group Limited, Singapore, 1996.

2.

Reissner, E., in Proceedings of the First Symposium on Naval Structural Mechanics, 1958, 74-113.

3.

Sih, G.C. and Hagendorf, H.C., Plates and Shells with Cracks, Sih, Noordhoff Int Pub, 1977.

4.

Reissner, E., J. Math. Phys., vol. 25, 80-85, 1946.

5.

Reissner, E., J. Math. Phys., vol. 25, 279-300, 1946.

6.

Nagdi, P.M., Quart. Appl. Math., vol. 14, 331-333, 1956.

7.

Delale, F. and Erdogan, F., Quart. Appl. Math., vol. 37, 37:239-258, 1979.

8.

Delale, F. and Erdogan, F., Int. J. Solids Struct., vol. 15, 907-926, 1979.

9.

Delale. F. and Erdogan, F., Eng. Fract. Mech., vol. 18, 529-544, 1983.

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AN EXPERIMENTAL STUDY OF TEARING-FATIGUE INTERACTION Peter Birkett, Michael Lynch and Peter Budden1 Serco Assurance, Birchwood Park, Warrington, Cheshire, WA3 6AT, UK 1British Energy Generation Ltd., Barnett Way, Barnwood, Gloucestershire, GL4 3RS, UK [email protected] Structural integrity assessments of defects in components under cyclic loading typically add the individual contributions to crack extension from tearing and fatigue, calculated using the Jresistance (JR) curve and fatigue crack propagation data, respectively. This approach, with the limiting crack size determined by an instability analysis, is employed in the widely used R6 defect assessment procedure [1]. However, it is likely that under conditions of variable or severe cyclic loading, the fatigue crack growth rate can be retarded or enhanced by tearing occurring within the fatigue cycles. Similarly, crack extension due to tearing can be affected by prior fatigue crack growth. An experimental and analytical programme is in progress designed to explore tearingfatigue interaction, and to refine and validate R6 advice, using load-history transients typical of those considered in nuclear reactor pressure vessel (RPV) assessments.

FIGURE 1. A typical load-crack mouth opening displacement trace for a tearing fatigue test. In the programme, transients with tearing and fatigue components were applied to standard fracture toughness test specimens and the resulting crack extension behaviour was compared with predictions made using the R6 methodology. A ferritic RPV steel was used, but an austenitic steel was also used for some tests. Baseline fatigue crack growth rate data were determined at relevant R-ratios and temperatures. The baseline JR curve was defined at ambient temperature and 288ºC using standard test procedures. Fifty-eight tearing-fatigue (TF) tests were performed, consisting of a series of pre-defined fatigue stages separated by monotonic loading stages. The parameters varied included: R-ratio (-1.1 to +0.8); temperature (ambient, 288ºC,); ‘’ and ‘’ factors (ratios of the maximum and minimum cyclic loads to the most recent tearing load); specimen thickness (15mm to 40mm); and the numbers of cycles and stages. Fig. 1 shows a typical load-displacement curve for a test loaded to P1 followed by fatigue cycling between DP1 and EP1, a further tear to P2, and so on. The tests were analysed to estimate the crack length at each stage of the test. Fig. 2 shows a plot of the estimated and measured crack growth values at the end of each test. The majority of points fall above the 1:1 reference line, indicating that estimated values are conservative. However, a significant number of points fall below the line and were found to relate mainly to thinner specimens. The analyses were refined by (i) increasing the estimated tearing crack growth incrementally, rather than assuming that tearing recommences at the start of the JR

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curve, and (ii) using an enhanced fatigue crack growth law at high K values. These refinements decreased conservatism. Sensitivity studies were also carried out in order to examine how the estimated crack growth was affected by changes in the limit load solution, fatigue crack growth law and JR curve. Further analysis used crack driving force

FIGURE 2. Comparison of estimated versus measured crack growth for tearing-fatigue tests. diagrams to carry out ductile tearing analyses, from which maximum allowable crack sizes at instability were obtained. Three alternative J-estimation schemes were used, R6 Options 1 and 2 and the GE-EPRI approach. The results indicated that: (i) the R6 guidance on tearing-fatigue generally gave conservative estimates of tolerable crack size compared with the measured crack sizes from the TF tests, with those based upon the GE-EPRI scheme being the least conservative; (ii) simple addition of tearing and fatigue crack growth components did not always give conservative estimates of crack growth, compared with the crack sizes measured; (iii) the use of the tolerable crack size from EPRI as a limiting crack size value for the simple addition of tearing and fatigue crack growth components was conservative for the thicker specimens, but may not be for the thinner specimens and (iv) the simple addition results were sensitive to relatively small changes in the definitions of the JR curve and Paris Law.

References 1.

R6 – Revision 4, Assessment of the Integrity of Structures Containing Defects, British Energy Generation Ltd, Amendment 3, 2004.

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SIF SOLUTIONS FOR CRACKS IN RAILWAY AXLES UNDER ROTATING BENDING S. Beretta, M. Madia, M. Schodel and U. Zerbst1 Politecnico di Milano, Dipartimento di Meccanica, Via La Masa 34, 20156 Milano 1GKSS Research Center Geesthacht GmbH Max Planck Straße, 21502 Geesthacht, Germany Railway axles are designed for infinite life. However, in order to correctly manage the few failures detected in service [1] for this safety component, there has been an increasing attention to damage tolerance analysis and determination of inspection intervals for railway axles [2]. Among the different input parameters of a damage tolerance analysis, a wide knowledge of SIF solutions for railway axles is not available because of the presence of an effect induced by rotating bending upon the SIF at the surface crack tip of a growing crack (Fig. 1.a and 1.b): K is higher in rotating bending than in plane bending and in particular there exists an angle T0 such that K(T0)=max{K(T)}. The only solutions available for this kind of problem are the ones by Carpinteri et al. [3,4] who obtained combined SIF solutions obtained under plane bending at T = 0° and T = 90° for calculating SIF in smooth bars.

Figure 1. Schemes adopted for the analyses: a) scheme of the crack; b) scheme of the rotating bending and explanation of the superposition of the effects (M’X and M’Y). In order to analyze this problem, a series of SIF solutions for some typical notches (named as T-notch, U-notch and S-transition) [5] of railway axles under plane and rotating bending were carried out. In particular the effect of rotating bending upon cracks in axle body and near the press-fittings is investigated. Considering the three different notches, K values have been calculated for different crack depths and shapes, taking into account different rotation angles for the axle. In particular analyses for T = 0° and T = 90° resulted to be useful to determine the behavior of K for different rotation angles. By this point of view, the results show that SIF of surface cracks onto axle body, under rotating bending, can be obtained as a simple superposition of the effects of the two bending moments (M’X and M’Y) acting on the crack (Fig. 1.b). This simple approximation works well also for cracks near press-fittings (Fig. 2.a). It is very interesting to compare SIF for cracks at S-transition obtained with press-fitting and with a tied connection (Fig. 2.b). While there is no significant effect for tip A, SIF at point B with press-fitting is approx. 25% higher than the one obtained with the tied connection: this fact seems to be due to a

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different stress distribution at the notch root. It is of some importance to remark that this result shows that the evaluation of SIF near (or at) the press-fittings has to be carried out considering the effective load transfer and SIF solutions for axle body cannot be directly applied.

Figure 2. Results in terms of SIF at S-transition for a crack with a/D = 0.1267 and a/b = 0.736 (Snom = 107 MPa): a) superposition of the effects vs. FEM in case of press-fitting; b) comparison of FEM results for tied-contact and press-fitting.

References 1.

Smith, R. A. and Hillmansen, S., “A brief historical overview of the fatigue of railway axles”, Proc. Instn Mech. Engrs, 218 (2004).

2.

Zerbst, U. Vormwald, M. Andersch, C. Mädler, K. and Pfuff, M., “The development of a damage tolerance concept for railway components and its demonstration for a railway axle”, Engng Fract. Mech., 72, 209-239 (2005).

3.

Carpinteri, A. and Brighenti, R., “Part-through cracks in round bars under cyclic combined axial and bending loading”, Int. J. Fatigue, 18, 33-39 (1996).

4.

Carpinteri, A. Brighenti, R. and Spagnoli, A., “Surface flaws in cylindrical shafts under rotary bending”, Fatigue Fract. Engng Mater. Struct., 21, 1027-1035 (1998).

5.

EN 13261, “Railway applications – Wheelsets and bogies – Axles – Product requirements”, CEN, September 2003.

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MECHANICAL CHARACTERIZATION OF SINGLE CRYSTAL BARS WITH CAPACITOR DISCHARGE WELDING AND LASER CLADDING Samanta Chiozzi, Vito Dattoma and Francesco W. Panella Dipartimento di Ingegneria dell’Innovazione, Università degli Studi di Lecce Via per Arnesano, 73100 Lecce, Italy [email protected], [email protected], [email protected] The efficiency of gas turbine systems used for energy production and for aeronautical engines construction can be improved through the elevated thermo-mechanical capabilities of advanced materials employed for blades production. It is well known in fact, the importance to increase the turbine inlet temperature; this temperature is limited by the highest working temperature of steels and super-alloys of which blades and rotor are made. Therefore it is necessary to study the employment of new materials more resistant to high temperatures. Actually two different ways are being employed to reach the above results: the application of stators and rotors cooling systems or the substitution of ordinary steels with more resistant high temperature superalloys. Both methods are valid, but the first one is less preferred by aeronautical industries because it needs the blade profile modification to facilitate the inside cooler circulation, affecting the blade efficiency and increasing the total weight [1]. Among the innovative materials currently under study, multicrystal and Single Crystal Nickelbase superalloys allow the theoretical achievement of 1300°C without damage and with the ability to withstand high loads if compared with the ordinary materials and they are being strongly considered for the future aeronautical engines. Single Crystal superalloys are of particular interest since they have the advantage to avoid the presence of microstructural discontinuities originated by the grain edges and the sites of precipitates concentration, which in multicrystal superalloys generally represent the zone of crack initiation and propagation [2,3]. In the present work the static behavior of Single Crystal Nickel-base superalloy CMSX-4 has been analyzed, performing deep mechanical and microstructural characterization, necessary to establish in detail the superalloy behaviour at the expected service stresses. Tests have been performed both at room and working temperature (about 800°C), comparing base material, CD welded and Laser Clad cylindrical bars. The microstructure has been successively analyzed through investigations performed with the optic microscope and the scanning electron microscope (SEM) observations. The micrographic analysis concerned base material and as-welded specimens; this way the microstructural modifications and the Heat Affected Zones have been studied as well as the interaction between the weld material layers and parent metal. The mechanical and microstructural characterization for “as welded” material is needed because of the requirement to develop advanced technologies for the repair of damaged blades, particularly in the case of blisks, constituted of blading and rotor in one piece. The Capacitor Discharge Welding (CDW) technique is particularly suitable because it allows the removal of the damaged part and the subsequent substitution of a new blade without the replacement of the whole block and additional machining; it allows to achieve extremely thin welded joints with narrow Heat Affected Zones, in order to avoid stress concentration effects at the weld toe and to reach good material continuity [4-7]. Actually the CDW process for aeronautical applications is under analysis, since it is not yet employed in production lines because of the lack

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of enough experimental tests on advanced materials with the involved welding parameters. Laser cladding is an highly flexible repair technique which is already applied for the aero engine industry [8]. In this work the first welding trials on Single Crystal specimens have been analyzed in order to establish the mechanical properties decay of a single crystal welded component, but also the microstructural modifications of the parent material after the welding process in relation to the used technological parameters had to be investigated. Static test results reveal acceptable structural abilities of the welded joints, but it is not possible to compare them with other data since in literature very few works about CMSX-4 can be found. Laser clad specimens show excellent tensile strength and higher yield behavior than those obtained with CD welded joints; the welding parameters and the heat treatments have not yet optimized and the welded material distribution and microstructure shell improove in the next experiments.

References 1.

Gell, M., Duhl, D.N. and Giamei, A.F., The development of Single Crystal superalloy turbine blades, Pratt & Whitney Aircraft Group, Superalloys, 1980, 205-214.

2.

Hemmersmeier, U. and Feller-Kniepmeier, M., Element distribution in the macro- and microstructure of nickel base superalloy CMSX-4, Material Science and Engineering A374, 2004.

3.

Wagner, A., Shollock, B.A. and McLean, M., Grain structure development in directional solidification of nickel-base superalloys, Material Science and Engineering A256, 1998.

4.

Chiozzi, S., Dattoma, V. and Panella, F.W., First results on the mechanical behaviour of CDW welded superalloys, 5th International Conference on Fatigue and Fracture, Bari-Italy, 9-10 May 2005.

5.

Casalino, G., Dattoma, V., Ludovico, A. and Panella, F.W., Numerical model for Capacitor Discharge Welding, 13th DAAAM International Symposium, Vienna-Austria, October 2002.

6.

Alley, R.L., ASM Handbook, Vol. 6: welding brazing and soldering Capacitor Discharge Study Welding”, American Welding Society, 1991.

7.

Dattoma, V. and Panella, F.W., Studio della resistenza su saldature CDW di barre in acciaio AISI 304, XXXII Convegno AIAS, Salerno-Italy, 3-6 September 2003.

8.

Richter, K.H., Orban, S. and Nowotny, S., Laser Cladding of the Titanium Alloy Ti6242 to restore damaged blades, XXIII International Congress on Applications of Lasers and ElectroOptics, 2004.

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FRACTAL DIMENSION ANALYSIS OF FRACTURE TOUGHNESS USED HIGH STRENGTH CAST IRON S. Doi and M. Yasuoka 700 Dannoharu Oita, Japan [email protected] The rotating bending fatigue tests were done using ADI and PDI with ion carburizing. The plain specimen with ion carburizing about 30MPa than the virgin PDI, and the fatigue strength of the carburized ion notched specimen was given an equivalent to the virgin PDI. Especially, the ion carburized notched specimen is effective material they have a better effect than lower that the notched PDI. In the recapitulation, on the element parts demanded a shallow notch, the clear distinction appeared whether ion charge or not, respectively. An important point is that carburized PDI presented two bending S-N curve not clear in high cycle fatigue. If the hardness is constantly holed to an internal point, the shape of S-N curve is unclearly appeared. But, its phenomena appeared from ion boundary layer by observation of SEM photograph. The ion Carburizing can control the charged depth by the sputtering time. Consequently, this method warrants consideration as a non-polluting process and economical use of energy. 1

Pcn S-N curve by ion-carburized effect was controlled to affect on the crack propagating in our researched meso-scopic structure.

2

Typical of quasi-fish eye in the surface vicinity can be decided by a/b. Where, a: equivalent small defect radius, b: equivalent cleavage radius (yield area). Accordingly, it is expressed by life cycle of S-N curve.

3

The plastic zone of ADI is shorter than that of PDI at the fracture. The fracture toughness of PDI is larger than that ADI. In other words, there is not relation toughness and elongation too much.

Fig.1 Profile and dimensions

Fig.2 Fracture surface ADI,PDI

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S. Doi and M. Yasuoka

Fig.3 Fracture toughness and plastic zone

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INVESTIGATING GAP EFFECTS IN FATIGUE LIFE OF SPOT WELDED JOINTS M. Zehsaz and S. Hasanifard Faculty of Mechanical Engineering, University of Tabriz, Tabriz, Iran [email protected], [email protected] The use of aluminium alloys in vehicle bodies are ever increasing especially when the main manufacturing process of these components is spot welding. The gap effects in 3-D finite element analysis are generally neglected. This effect in spot welded joints is important in terms of the mechanical behaviour of them. In this research, the gap effects on the fatigue life of the joints has been studied using strain-based approach to obtain the fatigue life. The numbers of spots are two in a row, joining two sheets of 5182-0 aluminium alloy. To do so, the problem is physically modeled using ANSYS FEM based software. The three-dimensional mesh models, the gap effects and a non-linear analysis have been used for the joints of sheets with the gap of 0.06mm, 0.12mm, 0.18mm, as shown in Fig. 1. Because of symmetry, only one of the hot spot-welded joints is modelled.

FIGURE 1. 3-D meshes and the boundary conditions in two different views of a hot spot weld The elastic-plastic stresses at edges of spot welds were considered and Manson-Coffin formula has been applied to obtain fatigue life. The comparison between the experimental results and numerical approach shows that the existence of gap between sheets increases the amount of the stresses near the roots of nuggets. Therefore, the fatigue life of spot welded sheets decreases with increasing the gap distance. This is illustrated in Fig. 2.

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FIGURE 2. L-N curve for different sheet gaps

References 1.

Ni, K., Mahadevan, S., Strain-based probabilistic fatigue life prediction of spot-welded joints, International Journal of Fatigue 26(2004) 763-772.

2.

Adib, H., Gilgert, J., Pluvinage, G., Fatigue life duration prediction for welded spots by volumetric method, International Journal of Fatigue 26(2004) 81-94.

3.

Radaj, D., Sonsino, C.M., Fatigue Assessment of Welded Joints by Local Approaches, woodhead publishing Ltd.1998.

4.

SHARP, M.L., NORDMARK, G.E., MENZEMER, C.C., Fatigue design of aluminium components & structures, McGraw-Hill, 1996.

5.

GEAN, A., WESTGATE, S.A., KUSZA, J.C., EHRSTROM, J.C., Static and Fatigue Behaviour of Spot-Welded 5182-0 Aluminium Alloy Sheet, 1999.

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FATIGUE OF PMMA BONE CEMENT S. L. Evans School of Engineering, Cardiff University The Parade, Cardiff CF24 3AA, UK [email protected] The use of PMMA bone cement is the most successful way of fixing implants such as hip and knee replacements, and has many other uses in orthopaedic surgery. However, in the long term mechanical failure of the cement is common and may lead to clinical failure. Despite a large volume of published research, the fatigue of bone cements is not well understood and much more research is needed before fatigue failure can be reliably predicted and avoided. Most of the published studies of cement fatigue have used simple S-N tests on unnotched specimens. The presence of stress concentrations that act as sites for crack initiation has a critical effect on the fatigue life and so many of these studies have identified porosity as an important factor. However, it is not clear whether porosity is as important in the clinical setting where there are many other stress concentrations and perhaps cracks due to curing shrinkage. Here crack propagation may be more important, and there are many complications such as variable amplitude loading, slow crack growth and microstructural effects. PMMA has been widely used as a model for studies of fatigue and fracture in polymers, but there is still a limited understanding of the effects of factors such as variable amplitude loading. Bone cements have a more complicated structure, with previously polymerised beads in a softer matrix which cures on implantation, and other components such as particles of barium sulphate or zirconia to make the cement visible in radiographs. This microstructural complexity means that the cement may behave very differently from pure PMMA. In smooth specimens, cracks initiate from pores, at the stress concentrations formed between previously polymerised beads, and there is a correlation between porosity and fatigue life. The stress concentration Kt at a spherical pore depends only on the Poisson’s ratio and for cement it is about 2.06. The size of the pores does not affect Kt, unless the pores are large enough to significantly reduce the cross- section. This reduction in cross- sectional area can account for the observed reduction in fatigue life for specimens with greater porosity. Arguably the effect of porosity is therefore an artefact of the specimen design, rather than a change in the properties of the material. Apart from this effect, porosity may only be important when it increases the likelihood of interaction between pores, which can cause higher stress concentrations. There is evidence for crack initiation due to shrinkage stresses developed during curing, although this does not always occur. In the clinical setting, this may be more relevant than initiation from pores by fatigue processes. Crack propagation has not been widely studied, and there are several complications such as slow crack growth and microstructural differences in the crack path. Physiological loading varies widely in amplitude and frequency content and the effects of these variables have not been fully investigated. Cracks typically propagate through the beads, but in some cases it is found that the beads pull out of the matrix. It is not clear why this occurs. There does not appear to be poor adhesion between the beads and the matrix, and it may be that the presence of residual compressive stresses in the beads due to curing shrinkage of the surrounding matrix causes the crack to deviate. Since the residual stresses relax over periods of weeks or months, this may explain some of the inconsistencies between different studies, and the change at different 'K levels that has been observed. The crack deviation that is caused by this phenomenon leads to considerable

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disturbance of the crack front, with some shielding by intact ligaments that bridge the crack. This may account for much of the increased resistance to crack propagation in cements as compared to pure PMMA. Even when the crack propagates through the beads, the fracture surface is much rougher than in pure PMMA. Clinical failure of the cement occurs over long time periods, and this implies that the crack growth rate is very low, perhaps as low as 10-12 m/cycle. Many studies have assumed a threshold at a much higher growth rate, but when load shedding is correctly carried out it appears that there may not be a threshold and the Paris Law is obeyed to 10-11 m/cycle or below. However, crack arrest can occur at higher 'K, perhaps for microstructural reasons. Preliminary measurements of the effects of variable amplitude loading raise more questions than they answer. In pure PMMA, considerable retardation occurs, particularly at lower 'K. 30% overloads every 100 cycles resulted in crack growth rates as much as two orders of magnitude lower than constant amplitude loading. At higher 'K the effect was much less pronounced. In cement, however, little or no retardation occurred as a result of individual overloads. Single overloads applied at a crack growth rate of around 10-9 m/cycle produced an acceleration of subsequent crack growth by up to a factor of five, and in some cases the acceleration persisted for 25,000 cycles or more. Single overloads at this level produced no retardation whatsoever. The mechanisms by which these effects occur are unknown at present, but it is likely that plasticity induced crack closure may play a role. Other mechanisms such as extended crazing ahead of the crack tip or breakage of ligaments that bridge the crack may also be relevant; in pure PMMA in particular there can be extensive bridging at the sides by shear- yielded material in the plane stress region and this may be affected by overloading. Despite extensive research the fatigue behaviour of bone cements is not well understood. The effect of porosity has been highlighted in many studies, but it is not clear how relevant it is to clinical cement failure. Crack propagation behaviour is very different to that of pure PMMA due to the complex microstructure of cements. The effects of slow crack growth under constant load may be important, and there is evidence that variable amplitude loading may produce dramatic effects including both acceleration and retardation of subsequent crack growth. As yet the mechanisms involved are unknown and much further research is needed before it is possible to predict fatigue failure with any accuracy.

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INFLUENCE ON THERMAL BARRIER COATING DELAMINATION BEHAVIOUR OF EDGE GEOMETRY H. Brodin, X. H. Li1 and S. Sjoestroem1 Department of Mechanical Engieering, Linköping University, SE-581 83 LINKÖPING, Sweden 1SIEMENS Industrial Turbomachinery AB, SE-612 83 FINSPÅNG, Sweden [email protected], [email protected] Ceramic thermal barrier coatings are commonly used in gas turbine hot components (e.g., combustor liners/buckets and guide vane platforms). In components that are only partially coated or have cooling-air outlets, coating-end stress singularities may lead to the spallation of the coating. Depending on the geometry of the transition from coated to uncoated material, the severity of the stress singularity will vary. Basic references for the analysis of such stress singularities are, for instance, Bogy [1], Bogy [2], Bogy [3], and Dundurs [4], where it is shown that the severity of the stress singularity depends on the chamfer angle \ and that making this angle \ > 0 decreases the singularity order at the coating end, see Fig. 1.

FIGURE 1. Schematic drawing of a TBC system. A chamfer angle

\ is defined in the figure.

In the present study, a thin thermal barrier coating system has been studied. Bond- and top coats have been sprayed to a thickness of 150µm and 350µm, respectively. Vacuum-plasmaspraying technology was used, and the test specimens were rectangular (30x50x5mm) coupons of a nickel-based superalloy, Haynes 230. A NiCrAlSiY bond coat and an Y2O3 stabilised ZrO2 top coat were used. In order to achieve well-defined chamfers, sprayed components were ground on the edges with SiC grinding paper to desired geometry. By inspections of cross-sections that had not undergone thermal fatigue cycling, it was ensured that no damage was introduced into the system. Mechanical testing was done in a thermal cyclic test rig where specimens are heated in a furnace and cooled with compressed air. The thermal cycle data were: Tmin=100°C, Tmax=1100°C, dwell time at max temperature Tdwell=40 min and cycle time Tcyc=60 min. FE modelling of the system has been done aiming at supporting the findings from thermal fatigue tests. A parametric study including variation of the chamfer angle \has been done and the stress state near the chamfer evaluated.

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Evaluation of fatigue damage can be done visually for observation of coating failure (macroscopic observation on coating surface). 20% area with complete spallation was considered as thermal barrier coating failure. For evaluation of damage development, additional light microscopy investigations of cross-sections have been done. Results show that the fatigue life benefits from introduction of a chamfer angle at the coating end during thermal fatigue cycling. This is seen in Fig. 2, where fatigue life is plotted against chamfer angle \

FIGURE 2. Influence on fatigue life on chamfer angle \.

Reference 1.

Bogy D.B., J. Appl. Mech., vol. 35, 460-466, 1968

2.

Bogy D.B., Int. J. Solids Struct., vol. 6, 1287-1313, 1970

3.

Bogy D.B., J. Appl. Mech., vol. 38, 377-386, 1971

4.

Dundurs J., J. Appl. Mech., vol. 36, 650-652, 1969

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LOW CYCLE FATIGUE AND FRACTURE OF A COATED SUPERALLOY CMSX-4 S. Stekovic Division of Engineering Materials, Linköping University 58183 Linköping, Sweden [email protected] The single crystal CMSX-4 is the second-generation rhenium containing nickel-base superalloy developed by Cannon-Muskegon Corporation, Davis [1]. The alloy is widely used because of its good mechanical properties such as long-time strength and toughness at high temperatures, Simms et al. [2]. Alone, the alloy has limited oxidation and corrosion resistance and to solve this problem it is protected with coatings. The objective of this study is to examine and establish fatigue and fracture behaviour under low cycle fatigue test conditions of the coated single crystal superalloy CMSX-4. For this purpose three different coatings have been chosen, an overlay coating AMDRY997, an aluminide diffusion coating RT22 and an innovative coating called IC1. Cylindrical solid specimens were cyclically deformed with fully reversed tension-compression loading with total strain amplitude control at two temperatures, 500oC and 900oC. The tests were also done at the uncoated specimens taken from the same batch. The empirical relationship between plastic strain amplitude and the number of reversals to fatigue failure was determined by Coffin-Manson, Klesnil and Lukas [3], se eq. (1). The results will be given in the full paper. 'H 2

p

H '(2 N

f

)c

500oC

(1)

At the coatings had detrimental effects on the fatigue life of CMSX-4 relative to the uncoated specimens while at 900oC the coated specimens exhibited longer life than the uncoated specimens at the same temperature. AMDRY997 gave the longest life compared to RT22 and IC1. The coated superalloy exhibited hardening and higher stress level at higher applied strains and lower temperature. At 900oC softening occurred together with lower stress response level. The coatings lowered the stress response level from about 12% to 31% compared to the uncoated specimens under the same test conditions. Most of the observed cracks initiated at the coating surface, one example is shown in Fig. 1. Majority of the cracks was arrested at the interface between the coating and the superalloy. Surface roughness or rumpling was found in AMDRY997 with some cracks initiated from the rumples.

FIGURE 1. SEM micrograph showing surface crack initiation observed at the surface of AMDRY997 at 500oC

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The fatigue behaviour of CMSX-4 can be affected by precipitation of topologically close packed (TCP) phases such as round shaped P phase and acicular shaped V phase by two damage mechanisms, embrittlement damage mechanism related to the brittle nature of those phases and softening of J matrix by depletion of strengthening elements to form TCP phases, Simonetti and Caron [4]. The phases were observed under and in the interdiffusion zone, although no microcracks initiated from them were found. The cracks found in the coatings grew more or less perpendicular to the load axis. The initial crack path is flat along the plane with high tensile stress, normal to the stress axis. The cracks began to fluctuate then with visible fatigue striations.

References 1.

Davis, J.R., Heat-resistant materials, ASM specialty handbook, Materials Park, ASM International, The USA, 1997.

2.

Simms, C.T., Stoloff, N.F. and Hagel, W.C., Superalloys, Wiley, New York, 1987.

3.

Klesnil M. and Lukas P., Fatigue of Metallic Materials, Elsevier, Amsterdam, The Netherlands, 1992.

4.

Simonetti, M. and Caron, P., Materials Science and Engineering A, vol. A254, 1-12, 1998.

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THERMOMECHANICAL FATIGUE OF OPEN-CELL ALUMINIUM SPONGE T. Guillen, A. Ohrndorf, U. Krupp, H. J. Christ, S. Derimay1, J Hohe2 and W Becker1 Institut für Werkstofftechnik, Universität Siegen Paul-Bonatz-Str. 9-11, 57068 Siegen, Germany Phone +49 271 2184 Fax +49 271 2545 [email protected] 1Institut für Mechanik, TU Darmstadt 2Fraunhofer-Institut für Werkstoffmechanik, Freiburg While closed-cell metal foams have been intensively studied during the last ten years, only little attention has been put to the group of open-cell metal sponges. Due to their low density and good homogeneity metal sponges are promising candidates for structural and at the same time functional applications. For the successful design of new components using metal sponges a sound understanding of the behaviour under monotonic and cyclic loading conditions is required. The aim of the present study is to investigate the behaviour of the open-cell aluminium foam under this kind of loading conditions placing special attention to thermomechanical fatigue and creep characteristics. The studied metal sponge was precision-cast AlSi7Mg obtained by m-pore GmbH, Dresden, having a porosity of 8 ppi and a relative density of 5.1%. Figure 1 shows the macroscopic cell structure of the studied material which has similar mechanical properties than the PORMET material (AlSi9Cu sponge) that was studied in an earlier work [1].

FIGURE 1. Macrograph of the AlSi7Mg sponge. Rectangular specimens (25mmx25mmx70mm) were glued to a special specimen mount and subjected to monotonic loading and fatigue at room temperature. The tests were carried out by means of a servohydraulic testing machine (MTS 810). Since an induction heating system could not be used to heat the inhomogeneous sponge specimens, thermomechanical fatigue tests were carried out in a self-designed temperature chamber, where the specimens can be heated by a hot air fan and cooled by compressed air (see Fig. 2). For this tests the specimen’s ends were cast-infiltrated with Zn serving as specimen mounts in order to a allow the performance of tests at temperatures higher than 200°C.

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Results of monotonic tests revealed that the plateau stress in compression lies in a range of 0,7- 0,75 MPa. With respect to the tensile behaviour it was observed that the amount of plastic deformation at fracture is strongly influenced by the ductility of the cell strut material. This could be confirmed within the present study resulting in strain of fracture levels of 1,5%.

FIGURE 2. Temperature chamber for the realisation of TMF tests on open-cell aluminium sponge. Thermomechanical fatigue behaviour of the aluminium sponge has been compared to that under isothermal fatigue of room temperature and at elevated temperatures. The fatigue damage mechanisms for each loading condition was analysed by optical and scanning electron microscopy. The experimental results were compared with a micromechanical model that is based on the idealization of the Kelvin model foam and subsequent examination of the effective mechanical properties to be used within an energetic homogenisation scheme [2].

References 1.

A. Ohrndorf, U. Krupp, H.-J. Christ, Proc,. Fatigue 2002, A.F. Blohm (ed) pp.3093-3098,

2.

J. Hohe, W. Becker , Int. J. Mech. Sci., 45, 2003, 891-913.

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THE INFLUENCE OF ALTERNATE BLOCK LOADING ON THE FATIGUE LIFETIME M. Kohut and T. Lagoda Technical University of Opole ul. Mikoajczyka 5, 45-271 Opole, Poland [email protected] The paper presents the results of fatigue tests of cylinder specimens made of duralumin PA6 under alternate block loading for bending and torsion. Each block contains n and n cycles with sinusoidal course. Based on the fatigue curves amplitudes suitable for 105, 3˜105 and 106 number of cycles to failure were determined. The loading was applied in alternate two-amplitudes blocks by 104, 3˜104 or 105 each one (10% of the fatigue life for the given loading level) until failure of the specimen (fig.1).

Fig.1. Part of the stress course The obtained experimental results were described with the criterion of normal and shear energy density parameter in the critical plane [1] W eq (t)

ȕW Șs (t)  țW Ș (t)

(1)

where ȕ, ț – constant dependent on S-N description for bending and torsion of suitable material, W Șs

1 IJ Șs (t)İ 2

WȘ

1 ı Ș (t)İ Ș (t)sgn ı Ș (t), İ Ș (t) 2

Șs

>

(t)sgn IJ Șs (t), İ Șs (t)

>

@

@

(2)

(3)

The critical plane was determined with the fatigue damage accumulation method and the criterion of shear strain energy density parameter. The fatigue damages were accumulated in the critical plane according to the Palmgren-Miner hypothesis for strain energy density parameter

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j

S (N

block

¦

)

i 1

where Wai are according to (1).

the

§ ¨ ¨ 1 ¨ § W af ¨ ¨ N o ¨¨ W ai © ©

adequate

· ¸¸ ¹

m '

· ¸ ¸ ¸ ¸ ¸ ¹

for W ai t aW

amplitudes

of

(2)

af

strain

energy

density

parameter

After determination of the damage degree, the fatigue life (number of blocks) was calculated using the equation N

cal

N block S ( N block )

(3)

where N block is a single block described by equation N

blok

n

IJ

 nı

(4)

The obtained calculation results are similar to the experimental results (fig.2)

Fig.2. Comparison of the calculated and experimental results for duralumin AlCu4Mg The most results are included in scatter bands with the factor of three.

REFERENCES 1.

AGODA T., MACHA E., BDKOWSKI W.: A critical plane approach based on energy concepts: Application to biaxial random tension-compression high-cycle fatigue regime. Int.J.Fatigue, 1999, Vol.21, pp.431-443.

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FATIGUE DESIGN AND INSPECTION PLANNING OF WELDED JOINTS BASED ON REFINED PHYSICAL MODELLING T. Lassen and N. Recho Agder University College, Faculty of Engineering, Grimstad, Norway LaMI, Université Blaise Pascal - Clermont II – France [email protected] The fatigue behaviour of welded joints subjected to typical in-service stress levels is far more complex than conventional bi-linear S-N curves and pure fracture mechanics models predict. These models are based on tests carried out in accelerated laboratory conditions. When the stress range approaches the fatigue limit, the crack initiation period becomes a very important part of fatigue life. Based on this fact, a Two Phase Model (TPM) for the fatigue process is developed and calibrated. The model includes both the crack initiation and the crack propagation phase. The physical model is suggested as complementary tool to statistical based S-N curves. These curves are only valid for a given joint geometry and loading conditions. It is dangerous to extrapolate them outside the range of the data. The large amount of data pertain to accelerated laboratory condition whereas in service stresses usually are close to the fatigue limit stress region where very few tests actually are carried out. At this stress regime a reliable physical model is useful both for fatigue life predictions and to determine the damage process. The latter gives necessary information to scheduled inspection planning; we must know when and what to look for. The S-N curves which do not work with the notion of a crack cannot be of any help on this matter. Furthermore, the present model provides physical insight that statistical methods do not provide. The practical consequences of the model when it comes to design and inspection planning are illustrated and discussed. It is assumed that the total fatigue life consists of two major phases: N=NI + NP. The number of cycles to crack initiation NI is modeled by a local strain approach using the Manson Coffin equation, whereas the propagation phase is modeled by fracture mechanics adopting the simple version of the Paris law. The model is calibrated to fit the fatigue behaviour of fillet welded joints where cracks emanate from the weld toe, Fig 1. The model is fitted to both experimental crack growth histories at high stress ranges and to fatigue lives at any stress level. Emphasis is laid on how to determine the variable weld toe notch factor, the transition crack depth between the two phases and the material parameters. The model is valid for high quality joints where a thorough post fabrication inspection is carried out. The model is capable of taking into account the effect of the global geometry of the joint, the local weld toe geometry, applied stress ratio and the residual stress condition. The S-N curve obtained from the model coincides with the F-class S-N curve (British Standard 5400) at high stress levels, but becomes non-linear as the stress range approaches the fatigue limit. In this stress region the present model fits the experimental S-N data far better than the conventional bi-linear S-N curve.

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FIGURE1 – Typical joint configuration and definition of crack shape We have constructed an S-N curve which is nonlinear for a log-log scale and that predicts substantially longer lives at stress ranges below 100 MPa (14.5 ksi) than does the F-class linear curve. Furthermore, at these long fatigue lives (more than 5×106 cycles) the initiation life is at least 70% of the entire fatigue life. We will show by a simple example the practical consequences of these results with respect to: •

Predicting fatigue life for selecting dimensions of a joint

•

Predicting crack growth evolution for inspection planning

We compare our results with the results obtained by the median F-class curve and a pure Fracture Mechanics Model (FMM) calibrated to make life predictions made by F-class and by the FMM coincide. The fatigue behaviour of high quality welded joints is far more complex than conventional bilinear S-N curves and pure fracture mechanics model predict. At typically low in-service stress ranges the crack initiation period, defined as time to reach a crack depth of 0.1 mm, represents the dominating part of the fatigue life. To describe this behaviour a TPM is required. The non-linear S-N curves obtained from the TPM coincides with the conventional S-N curve predictions at high stress levels, but fits the experimental data near the fatigue limit far better. The abrupt knee-point of the bi-linear curve does not fit the facts in this stress region. The theoretical consequence of the model is that the fatigue limit is explained by an extremely long initiation period and not, as for the fracture mechanics model, by a threshold value in the stress intensity factor. The shallow surface breaking crack near the weld toe do not obey the threshold law, they tend to grow considerably faster. The first practical consequence of the model is that it predicts considerably longer fatigue lives at low stress levels than the conventional bi-linear curves in rules and regulations. This will results in higher permissible stresses and smaller dimensions of the joints. The second practical consequence is that a scheduled in-service inspection program should be more progressive with service time compared with programs based on a pure fracture mechanics model. This will result in a long initial inspection interval and short intervals at the end of service life.

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A MIXED MODE FATIGUE CRACK GROWTH MODEL INCLUDING THE RESIDUAL STRESS EFFECT DUE TO WELD S. Ma, X. B. Zhang, N. Recho and J. Li1 Blaise Pascal University of Clermont II, LaMI, France 1University of Paris XIII, Institute Galilée, LPMTM, France [email protected] When a crack is subjected to cyclic loading, the traditional studies of fatigue crack were concentrated on the mode I crack growth mechanism. A number of crack propagation laws were developed to evaluate the fatigue crack growth rate. However the effect of the loading angle on the propagation was not considered in these laws. In the other hand, when a crack exists in a metallic welded structure, the residual stress due to the weld may influence the crack growth. In this work, the experiments of a fatigue crack under mixed-mode loading are performed with CTS (Compact Tension Shear) specimen associated to a mixed mode loading device. The effect of loading angle on the crack growth rate and on crack bifurcation angle is analyzed. Also, the welded specimens are introduced in the experiments in order to investigate the influence of the filled weld. Furthermore, on the basis of the experimental results, a crack propagation model is proposed in order to evaluate numerically a fatigue crack growth rate, in which the effects of the loading mode and of the residual stresses due to weld are considered. Two different types of CTS specimens are used in the work, i.e. the non welded specimen and the welded specimen. In the welded specimen, the initial crack is parallel to the weld. Each type of specimens is made from two materials, aluminum alloy 7020 and steel S460. The fatigue tests are performed at room temperature. The CTS specimens are tested with two loading levels and three loading angles with respect to the crack axis. For each specimen, the relationship between the crack length a and the number of cycles N is obtained by marking method during the test. The stress intensity factor K is calculated by FEM. For a mixed-mode loading, the equivalent stress intensity factor Keq is used, which is the combination of KI (stress intensity factor in mode I) and KII (stress intensity factor in mode II). The crack growth rate da/dN is issued from the values of N and a. And then da/dN is presented as function of the equivalent stress intensity factor Keq. Effect of the loading angle on the crack propagation: The experimental results obtained on aluminum specimens and steel specimens show the same tendency. It can be found that for the same initial value of Keq, the crack grows faster in the case of 30° loading than in the other loading cases. This is for the reason that to obtain the same Keq, the loading level increases as the loading mode tends to pure mode II. Therefore, because of the lowest load, the crack growth rate is the lowest when the crack is subjected to pure mode I loading whatever the material is, whatever with or without weld. Effect of the weld on the crack propagation: The welded and non welded specimens are subjected to the same loading angle and to the same loading level. The experimental results show that for the same loading level, the crack growth rate is greater in non welded specimen than that in welded specimen. It means that the weld introduces compressive residual stresses near the weld toe. These residual stresses decrease the crack growth rate. When the specimens are subjected to pure mode I loading condition, this influence is more obvious than in the case of 60° and 30° loading because of the difference of the crack growth path. When loading angle is 60° and 30°, the crack grows obviously far from the weld. Therefore, there is only a little influence on the crack propagation.

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The same effect of weld is obtained from the steel specimen. Because the steel specimens are less thick than the aluminum ones, so the influence of the welded residual stresses is less important than that of in aluminum specimens. Numerical Model According to the experimental results, we have proposed a numerical model to study the crack growth. In this model, two parameters are considered: the mixity parameter and the residual stress due to weld. The Paris’ law is used with the equivalent stress intensity factor Keq. Effect of loading mode on the crack growth rate: The experimental results show that the exponent m which is the slope of the Paris’ law keeps constant when the crack grows under mixed mode loading. But the coefficient C changes as function of loading mode. Therefore, the influence of mixed mode on the crack growth rate can be introduced in the coefficient C. So we use a coefficient C* which is function of the mixity parameter Mp and an experimental coefficient which is equal to 3 for all the CTS specimens in this work. Mp is equal to elastic mixity parameter in this work because of the low stress level and can be written as the ratio between the stress intensity factors of mode I and mode II. In this model, the constants m and C may be measured in a pure mode I fatigue test. KI and KII are calculated by FEM. So Keq and Mp can be determined from the values of KI and KII. Effect of the welded residual stresses on the crack growth rate: The same experimental observation is obtained. Only the coefficient C changes as function of the residual stress level. So the coefficient C becomes CR which is written as function of different stress intensity factors and which is also equal to 3 for all the CTS specimens in this work. The verification of the proposed model on steel specimens has showed that the numerical results are in good agreement with the experimental results. More studies must be carried out in future to verify this model with different materials and different types of specimens. Conclusions From this work, we can draw out the following conclusions: 1

The crack growth rate is related to the loading mode. For the same initial Keq, the closer to pure mode II, the faster the crack growth rate is.

2

When a crack is parallel to the filled weld in the case of pure mode I loading, for the same loading level, the compressive residual stresses due to the weld decrease the crack growth rate. In the case of mixed mode loading condition, this effect is weak as the crack grows far from the weld.

3

The filled weld has low influence on the crack growth direction.

4

A numerical model is proposed in order to consider the effects of the loading mode and of the residual stress on the propagation and bifurcation of a crack under cyclic loading.

2T5. Fatigue and fracture

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EFFECTS OF SHOT PEENING ON FATIGUE PROPERTY IN SICP/AL-MMC Yasuo Ochi, Kiyotaka Masaki , Takashi Matsumura and Tatsuhiko Hamaguchi1 Department of mechanical Engineering & Intelligent Systems, University of Electro- Communications, Tokyo, Chofu, Tokyo 182-8585, Japan [email protected] 1Aluminum Development Division, Aisin Takaoka Co., Toyoda, Aichi, 473-0934, Japan SiC particle reinforced aluminum alloy matrix composite (SiCp/Al-MMC) has been expected for applications to components of aircrafts and automobiles because of high wear resistance, high temperature strength and light weight characteristics. Most of the components are subjected to fatigue loading. However, there have been little study for fatigue property of SiCp/Al-MMC. And also, it has been well known that shot peening is one of useful treatments for improvement of fatigue strength of machine components. In this study, two kinds of materials ; Al-Si-Mg cast aluminum alloy (JIS AC4CH) and SiC particle reinforced cast aluminum alloy (SiCp/AC4CH-MMC), were prepared. And also shot peening treatments were performed on two materials. Figure 1 shows microstructures of two materials, (a) is AC4CH and (b) is SiCp/AC4CH-MMC. In AC4CH, it shows typical dendrite structures with aluminum matrix and eutectoid silicon particles. In MMC, the volume fraction of SiC particle is about 10%, the average size of SiC particle is 9~14Pm, and SiC particles are

(a)AC4CH

(b) SiCp/AC4CH-MMC

FIGURE 1. Microstructures. TABLE 1. Mechanical properties.

distributed on boundaries of primary D(Al) crystals. Table 1 shows mechanical property of two materials. There were no clear difference of tensile strength and Young’s Modulus between two materials, but reduction of area of AC4CH is larger than that of SiCp/AC4CH-MMC. The shot peening were treated with steel shot (HRC53) with 0.6mm in diameter. The almen intensity was 0.135mmA and the coverage was 300%.

286

Y. Ochi et al.

High cycle fatigue tests of rotating bending loading were carried out with frequency of 2760rpm in air at room temperature. Effects of SiC particle reinforcement and shot peening treatment on fatigue properties were investigated. Observations of surface crack behaviors were using replication technique. And fracture surface were observed after fatigue tests by a fieldemission type scanning electron microscope (FE-SEM) in order to specify the crack initiation sites. Figure 2 shows S-N diagrams of all materials. Comparing with results of AC4CH and SiCp/ AC4CH-MMC without shot peening, the fatigue strength at 107 cycles of AC4CH is 100MPa and that of MMC is 110MPa. So, the improvement of fatigue strength by SiC particle reinforcement was small, and also, the fatigue lives before 106 cycles of MMC were less than those of AC4CH. As investigating the effects of shot peening treatment on the fatigue strength, the fatigue strength of entire regime of both materials were almost larger than those of non-peening materials, but the scatter of the fatigue life of peening materials were larger than those of the non-peening materials. And then, the fatigue strength at 107 cycles of AC4CH-SP was about 130MPa. On the other hands, the strength of SiCp/AC4CH-MMC-SP was about 110MPa. And also, from these results, it was shown that the fatigue lives before 107 cycles in SiCp/AC4CH-MMC were improved by shot peening treatment in spite of some scatter, but the effects for the fatigue strength at 107 cycles was not clear. From the observation of fracture surface, the crack initiation sites of all materials were casting defects, and there are no clear difference in these materials.

FIGURE 2. S-N diagrams.

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FATIGUE BEHAVIOUR OF FRICTION STIR WELDED 6061-T6 ALUMINIUM ALLOY Yoshihiko Uematsu, Keiro Tokaji, Yasunari Tozaki1 and Hideaki Shibata1 Gifu University, 1-1 Yanagido, Gifu City 501-1193, Japan, 1Gifu Prefectural Research Institute, 1288 Oze, Seki, Gifu 501-3265, Japan [email protected] Friction stir welding (FSW) is a recently developed solid state welding method, and now being used increasingly for joining aluminium alloys. However, the fatigue behaviour of FSW joints with relatively complicated microstructure is still unclear. In this study, fatigue behaviour of FSW joints of 6061-T6 aluminium alloy was investigated. The 6061-T6 plates were joined with welding speeds of 100 and 200 mm/min and the rotation speeds of tool of 1200 and 1800 rpm. Fatigue tests were conducted at stress ratio R = -1 under axial loading. The microstructure of the weld zone is usually classified into three regions, namely stir zone (SZ), thermo-mechanically affected zone (TMAZ) and heat affected zone (HAZ), Lomolino et al. [1]. Fig. 1 shows the typical microstructure of the longitudinal section around the pin of the FSW tool, where the microstructure is asymmetric between the top and bottom sides. In the SZ, fine equiaxed grains can be seen, resulting from dynamic recrystallization. It is clear that aluminium grains are severely deformed in the TMAZ that is the microstructural transition zone between SZ and HAZ. Vickers hardness profiles are shown in Fig. 2, revealing softening inside the weld zone. The low hardness plateau extends in the fine grained area, SZ, and hardness minima are located at the TMAZ. The softening can be attributed to the dissolution of precipitates due to the elevated temperature during FSW process, Su et al. [2]. It was found that the microstructures and hardness profiles were hardly affected by the welding condition.

FIGURE 1. Optical micrograph of longitudinal section in weld zone (1200rpm-200mm/min). The tensile strength, B, of the parent material was 308 MPa, while that of FSW joints was around 200 MPa regardless of the welding condition. All FSW joints fractured at the softened TMAZ. Fig. 3 shows the S-N diagram of FSW joints. The fatigue strength of FSW joints is lower than that of the parent material, especially in the high stress region. The welding condition has almost no influence on the fatigue strength as well as microstructure, hardness profile and tensile strength. It should be noted that the location of fatigue fracture is dependent on stress level as shown in Fig. 3, where the solid and open symbols indicate that the fracture at TMAZ and HAZ, respectively. In the high stress region, fracture occurred at the TMAZ, while in the low stress region, at the HAZ. Macroscopic observation using an optical microscope revealed that localized plastic deformation took place at the TMAZ due to the softening and asymmetric microstructure when high stress was

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applied. The stress concentration at the locally deformed TMAZ was responsible for the fatigue fracture at the TMAZ and the much lower fatigue strength than the parent material in the high stress region. On the other hand, such deformation at the TMAZ was not recognized when the applied stress was relatively low and fracture occurred at the HAZ. It implies that if the stress concentration at the TMAZ in not introduced, then the FSW joints of 6061-T6 aluminium alloy would fracture at the HAZ under fatigue condition. From the hardness measurements before and after fatigue tests, it is concluded that the fatigue fracture at the HAZ in FSW joints was attributed to both the grain refinement at the SZ and the dynamic aging at the SZ and TMAZ by cyclic loading.

FIGURE 2. Hardness profiles in friction stir welded joints.

FIGURE 3. S-N diagram.

References 1.

Lomolino, S., Tovo, R. and dos Santos, J., Int. J. of Fatigue, vol. 27, 305-316, 2005

2.

Su, J.-Q., Nelson, T.W., Mishra, R. and Mahoney, M., Acta Mat., vol. 51, 713-729, 2003

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TRANSFORMATION OF A NONPROPORTIONAL MULTIAXIAL LOADING TO AN EQUIVALENT PROPORTIONAL MULTIAXIAL LOADING A. Chamat, Z. Azari1, M. Abbadi and F. Cocheteux2 Laboratoire de Fiabilité Mécanique-Ecole National d’Ingénieur de Metz, Université de Metz, Ile du Saulcy, F-57045 Metz cedex 01, France 1Université de Picardie, 80039 Amiens, France 2Agence d’Essai Ferroviaire AEF-SI Vitry Sur Seine Paris, France [email protected] Fatigue fracture is a complex domain that manufacturers have always been intended to control in order to predict the life duration of structures. For this purpose, many criteria saw the day and each of them is based on a specific formulation. Palin Luc proposed an energetic criterion that takes into account the stress gradient, nature of applied load and triaxiality during a complete cycle of loading and over the whole cross section. Nevertheless, this approach is only valid for alternate proportional multiaxial loading, which is not compatible with the signal imposed in our investigation. Indeed, the applied loading (combined traction-torsion) corresponding to that undergone by a railway wheel, is a nonproportional multiaxial loading. To transform a nonproportional multiaxial loading to an equivalent proportional multiaxial loading, using Palin Luc’s criterion, four methods are possible: •

Case 1: the equivalent signal is sinusoidal (Figs. 1-2) and stress average values are chosen as: k

V W

trac  tor

6 . 1954

trac  tor

FIGURE 1. Applied signal •

FIGURE 2. Equivalent signal

Case 2: k factor is taken as the maximum stress ratio. Fig. 3 depicts the applied nonproportional multiaxial loading while Fig. 4 illustrates the equivalent proportional multiaxial loading whose stress ratio is: k

•

max V max W

trac

 tor

trac

 tor

3 . 18

Case 3: If all the points of the signal are taken into account (Fig. 6), k ratio varies during the cycle and its average is computed by integration. To apply Palin Luc’s approach, one

A. Chamat et al.

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compares the average strain energy density and the endurance limit of the strain energy density

. FIGURE. 3: Applied load •

FIGURE. 4: Equivalent load

Case 4: one compares the maximum strain energy density and the endurance limit of the maximum strain energy density.

FIGURE. 5: Applied signal

FIGURE. 6: Evolution of k

To preserve the effect of the whole points of the nonproportional multiaxial loading on the life duration, one took a load factor as a parameter to define the signal. Its value is equal to one for the real signal. Experimental results predict a load factor of 2.56 in the endurance domain. Table 1 summarizes Palin Luc’s model predictions for the different cases using the first (ellipse quarter) and second (energetic) criteria. TABLE 1: Predictions of Palin Luc’s model

Application of the nonproportional multiaxial loading to Palin Luc’s approach revealed that only propositions established in cases 2 and 4 predict a load factor close to the experimental value. In view of the previous results, the transformation of any nonproportional multiaxial loading to a proportional multiaxial loading, by implementing its extreme values in Palin Luc’s formulation, gives satisfactory results.

2T8. Polymers and composites

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ACOUSTIC EMISSION MONITORING OF DELAMINATION GROWTH IN FIBER-REINFORCED POLYMER-MATRIX COMPOSITES A. J. Brunner and M. Barbezat Laboratory of Materials and Engineering, Empa, Swiss Federal Laboratories for Materials Testing and Research Überlandstrasse 129, CH-8600 Dübendorf, Switzerland [email protected], [email protected] Acoustic Emission (AE) analysis can be applied to investigations of damage initiation and damage growth in fiber-reinforced polymer-matrix (FRP) composite materials and structures. The potential of AE as an aid in interpreting fracture mechanics tests of polymer-matrix composites has been shown, e.g., by Bohse et al. [1]. Contrary to other non-destructive techniques such as, e.g., ultrasonic C-scan, AE monitoring can be applied on-line during the tests. Results of the AE analysis are available virtually in real-time, even though a full analysis may require post-test data processing. Fig 1 shows an example of AE data obtained from a standardized Mode I opening load test on a unidrectionally carbon fiber-reinforced epoxy beam specimen. Delamination initiation, for example, can easily be identified by the steep increase in AE activity. More recently, Cartié et al. [2] have applied AE analysis to fracture mechanics tests on complex, three-dimensionally reinforced FRP specimens.

FIGURE 1. Acoustic Emission activity (number of hits per second, left) from a standard double cantilever beam test in Mode I (opening) loading of a carbon fiber reinforced epoxy beam specimen, the applied load is shown in green (in kN, right hand scale) Analysis of AE activity and AE intensity versus time or load can complement and even replace standard visual monitoring of delamination initiation and growth [1]. This eliminates the subjective, operator-dependent determination of crack or delamination length needed for fracture toughness calculations. Initiation is determined both, more consistently and conservatively with the use of AE analysis. Some limitations of the AE analysis of fracture mechanics tests will be discussed mainly by taking AE data from fracture mechanics tests in Mode I opening and Mode II shearing load. AE signal attenuation with distance from the source location is quite substantial in FRP composites. AE signal source location accuracy is limited by the anisotropy in FRP properties and also affected by large signal attenuation. This constitutes limiting factors in fracture mechanics testing of larger

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elements or structures. Separation of extraneous noise signals from those originating from damage accumulation is the main problem in fatigue tests. On the other hand, AE analysis can help in identifying whether a single mechanism (e.g., delamination growth) is dominating damage accumulation or whether several mechanisms are active at the same time or sequentially [3]. Combined with visual observation during and after testing, complex damage accumulation (initiation) and fracture mechanics processes can be investigated.

References 1.

Bohse, J., et al., In Proceedings of the Second ESIS TC4 Conference on Fracture of Polymers, Composites and Adhesives, edited by J.G. Williams, A. Pavan, ESIS Publication No. 27, Elsevier, Oxford, 2000, 15-26.

2.

Cartié D.D.R. et al., In Proceedings of the Third ESIS TC4 Conference on Fracture of Polymers, Composites and Adhesives, edited by B.R.K. Blackman, J.G. Williams, A. Pavan, ESIS Publication No. 23, Elsevier, Oxford, 2003, 503-514.

3.

A.J. Brunner et al., In Proceedings of the European Conference on Macromolecular Physics: Surfaces and Interfaces in Polymers and Composites, edited by R. Pick, Volume 21B, European Physical Society, 1997, 83-84.

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FRACTURE MECHANICS VERSUS STRENGTH CONCEPTS FOR EVALUATION OF ADHESION QUALITY B. Lauke Leibniz-Institut für Polymerforschung Dresden e.V. Hohe Str. 6, 01069 Dresden, Germany [email protected] The quality of adhesion between reinforcing components and matrix in composites, bonding between a substrate and adherent or the strength of a welding line in two component injection moulding is important for the mechanical properties of these materials. Consequently the determination of micromechanical adhesion parameters is decisive for the understanding and improvement of macromechanical properties of composites. The characterisation of adhesion between different materials generally follows two concepts: determination of adhesion strength or determination of fracture mechanics parameters. The application of the strength concept at the interface between two materials involves major principle problems. Because of the inhomogeneous stress distribution in most of the applied test methods the normalisation of the applied critical force with the cross section of the sample provides only a rough approximative measure of the composite quality but not a material property describing adhesion strength between the components. Another way to characterise adhesion is given by the consideration of a composite with a pre-crack, that leads to the fracture mechanical approach of bimaterial composites. In the following presentation some aspects of these two approaches are discussed for special experiments proposed in literature (Single fibre pull-out test) and own developed tests (Curved specimen particle test and Curved bimaterial test, see Fig. 1)

(a)

(b)

Figure 1. Determination of adhesion strength between particle and matrix (a), determination of adhesion strength between two polymers (b). Single fibre pull-out and microdroplet test These test have been the subject of numerous fundamental experimental and theoretical investigations during the last years. In these tests one of the most obvious problems is the very inhomogeneous stress state induced at the interface. Normal stresses at the entrance point and shear stresses more inside the matrix droplet are responsible for a changing stress state for a moving crack at the interface. Both test set-ups have been modelled by the finite element method / 1/ and the calculated stress state has been used to evaluate fracture mechanical parameters as:

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stress intensity factors and energy release rate. A very essential result of the analysis is the disclosure of the strong influence of the mixed-mode stress state on the debonding process. Single-particle in curved specimen test As a consequence of the disadvantages of the above test geometries for fibre/matix adhesion testing we have developed a test set-up that induces a rather uniform stress state normal to the fibre interface /2/. This basic idea was also applied to the particle-matrix bonding problem as shown in Fig. 1a, cf. /3/. Tensile axial loading of such a curved specimen concentrates stresses in the smallest cross section and causes a multiaxial loading situation in the centre, i. e. in the vicinity of the enclosed particle. By variation of sample curvature the distribution of normal tensile stresses at the interface between particle and coating can be changed. This enables the variation of the interface area which is under tensile stress. A finite-element analysis provides the stress field within the whole specimen and especially in the vicinity of the coated particle. The calculations provide the maximum radial stress at the particle surface as a function of applied load. Assuming that normal stresses at the interface are responsible for debonding, the adhesion strength can be obtained from the experimentally determined critical load at debonding initiation. Curved bimaterial test The determination of adhesion strength between compact materials is still an unsolved problem. There are various tests available to determine shear strength values, for example, from single and double shear lap tests or tensile adhesion strength from butt like tensile tests. However, the stress analysis of these testing arrangements reveals that the stress state is uniform only within the central regions of the sample whereas it is singular at the edges. Therefore the calculation of an adhesion strength by normalising the critical applied load by the whole interface area is questionable. The curved bimaterial test /4/ proposes an experimental arrangement that provides a uniform transverse tensile stress at the interface which does not have concentrations or singularities at the edges. The stress state at the interface is purely tensile and does not contain shear components. A special optimised sample geometry generates this stress state.

References 1.

Lauke, B., Schüller, T., Beckert, W., In The Application of Fracture mechanics to Polymers, Adhesives and Composites, edited by D.R. Moore, Elsevier Ltd. and ESIS, 2004, pp. 227232.

2.

Schüller, T., Beckert, W., Lauke, B., Friedrich, K., Composites Sci. and Technology, vol. 60, 2077-2082, 2000.

3.

Lauke, B, submitted to Composites Sci. and Technolog, 2005.

4.

Schüller, T., Lauke, B., Intern. J. of Adhesion & Adhesives, vol. 22, 169-174, 2002.

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ALTERNATIVE APPROACHES FOR THE EVALUATION OF THE SLOW CRACK GROWTH RESISTANCE OF POLYETHYLENE RESINS USED IN THE PRODUCTION OF EXTRUDED WATER PIPES F. M. Peres and C. G. Schon Dept. of Metall. and Mater. Engng., Escola Politecnica da Universidade de Sao Paulo Av. Prof. Mello Moraes 2463, CEP 05508-900 São Paulo-SP, Brazil [email protected], [email protected] Polyethylene (PE) pipes have been increasingly used in the water distribution industry in the last decades. Major advantages of this kind of material over its competitors (e.g. cast iron or PVC pipes) include flexibility, low costs and ease of installation. Despite of its popularity, PE pipes, which are expected to present service lives of about 50 years after installation [1,2], suffer from premature failures by fracture due to time-dependent deformation (creep). These failures lead to both environmental and economic (water loss and maintenance) costs. The search for improved materials leads the petrochemical industry to the continuous development of new resins. Strategies like the increase of mean molecular weight, copolimerization (chain branching) and molecular weight distribution engineering have been suggested to increase resistance to failure [2], which is nowadays accepted to occurs via slow crack growth (SCG) [3]. This resistance to in-service failure is usually measured in Long-Term Hydrostatic Strength (LTHS) tests, in which the tube is subject to different inner hydrostatic pressures, P, and different temperatures, T. The output of such tests is a bi-log graph of the highest principal stress (since the stress state of the tube is not uniaxial, this corresponds to the circumferential, or “hoop”, stress, Vh) versus time-to-fracture (tf) , known in the industrial praxis as the “regression curve” of the given resin. In a typical PE resin the Vh u tf curve is linear with negative slopes in such graphs (i.e. it is typical of a power-law behavior, with negative exponents), but two regimes can be identified: A high stress regime (Vh t Vc), in which the fracture is followed by extensive macroscopic plastic deformation (with the bulging or “ballooning” of the tube wall), denoted the “ductile”-mode, and a low stress regime (Vh < Vc), characterized by negligible macroscopic plastic deformation and a small through longitudinal fracture (slit fracture), denoted the “brittle-like” mode [1,2]. The “ductile-to-brittle” transition stress, Vc, is characteristic of a given formulation (i.e. resin + additives) and is not easily determined in tests conducted at ambient temperatures. In spite of its widespread acceptance in the industry, the LTHS test must be criticized. Due to the long duration of the tests (up to ~104 hours) LTHS tests are considerably expensive (which makes them an impracticable quality control tool) with most of the data being collected at high inner P (i.e. in the “ductile” region) to save time, while the tube is expected to operate in the “brittle-like” region. The LTHS philosophy, as used in the industry, also implies that tf is a material property, while extrinsic factors (e.g. damage introduced during the installation) may shorten the fracture nucleation time, leading to a premature failure (as observed in the practice). The aim of the present work is to present and to test two alternative approaches, which may be applied to the comparative evaluation of two or more resins without the need to proceed with a full scale LTHS test. For this purpose five different resins designed for pipe extrusion (for which the “regression curves” are known) and two resins designed for other purposes, obtained from four traditional PE resin suppliers, have been compared. The two approaches are the “ramp test”, proposed by Zhou et al.[4], and the Essential Work of Fracture (EWF) method [5].

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The “ramp test” method consists in the evaluation of the yield stress (Vy) and the drawing stress (Vd) of standard tensile test samples as a function of the strain rate. Both quantities, when plotted against the logarithm of the strain rate, follow straight lines with different slopes. The intersection of both lines, according to the original proposition, corresponds to the critical stress (Vc) for the ductile-to-brittle transition in the “regression curve” [4]. In spite of its minimalistic simplicity, this method is based on solid hypotheses about the micromechanics of fracture process (craze nucleation-and-growth and fibril rupture) in PE [6]. The procedure here proposed corresponds to combining a limited number of shorter LTHS tests at higher P, to determine the ductile wing of the “regression curve”, with the “ramp test”, to determine the lower limit of stress (Vc) at which an extrapolation of this wing would be safe. The EWF, on the other hand, allows a direct estimation of the essential part (we) of the specific work of fracture in standard (e.g. Double-edge notched tensile, DENT) samples. Since this quantity, in principle, is a material property [5], it would lead to better results in the evaluation of the resistance to slow crack growth of the resin, in contrast with the standard “regression curve” approach. The results show that the values of Vc determined via the “ramp test” are compatible with the ones estimated from the available “regression curves” for the resins and that the EWF measurements allow to order the resins consistently with their expected behaviors. There are also indications that the results obtained by the EWF method are richer in information compared with the standard LTHS approach.

References 1.

Janson, L.-E., Plastic pipes for water supply and sewage disposal, VBB/SWECO International, Stockholm, Sweden, 2003.

2.

Mills, M. J., Plastics: microstructure and engineering applications, 2nd ed., Edward Arnold, London, UK, 1993.

3.

Hamouda, H. B. H., Simoes-betbeder M., Grillon, F., Blouet, P., Billon, N., Piques, R., Polymer, vol. 42, 5425, 2001.

4.

Zhou, W., Chen, D., Shulkin, Y. Chudnowsky, A., Liraj, N., Sehanobish, K. and Wu, S., In Plastic failure – Analysis and Prevention, edited by Moalli, J., William Andrew Publishing/ Plastic Design Library, 2003.

5.

Clutton E. In Fracture Mechanics Testing Methods for Polymers, Adhesives and Composites, edited by Moore, D. G., Pavan, A. and Williams, J. G., Elsevier Science, Amsterdam, Holland, 2001.

6.

Chudnowsky, A. and Shulkin, Y. Int. J. Fracture, vol. 97, 83, 1999.

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A STEREOSCOPIC METHOD FOR FRACTOGRAPHIC INVESTIGATIONS OF ORDINARY CERAMICS C. Manhart and H. Harmuth Christian Doppler Laboratory for Building Materials with Optimised Properties, University of Leoben, 8700 Leoben, Austria [email protected], [email protected] Quantitative evaluation of fractographic investigations of ordinary ceramic materials with a maximum grain size of e.g. 4 mm is less common compared with investigations of fine ceramics and metals. For the investigations presented here fracture surfaces of a wedge splitting test described in [1] have been applied. The wedge splitting test already enabled a fracture mechanical characterization, and fracture mechanical parameters have been correlated with the investigations. Two of these fracture mechanical parameters where the notch tensile strength NT and a characteristic length lch (Eq. 1): l ch

G f ˜E

V

2 NT

(1)

In (1) Gf is the specific fracture energy and E Young’s modulus. The characteristic length is inverse proportional to a brittleness number, a decreasing brittleness of the material is shown by an increasing characteristic length. For stereoscopic investigations two images of each fracture surface with different tilt angle have been used. From these a digital surface profile was calculated on the basis of a three dimensional surface model, see Fig. 1.

FIGURE 1. Schematic drawing of a 3D-digital surface model This profile was evaluated in dfferent ways. One the hand, surface texture parameters according to [2] and the fractal dimension have been calculated. On the other hand, an autocorrelation function A(k), according to Eq. (2) has been calculated: 1 N k ˜ ¦ xi  x ˜ xi k  x N i 1 N 2 1 ˜ ¦ xi  x N i 1

>

A (k )







@ with x

1 N

N

¦

xi

(2)

i 1

In (2) xi is the ordinate of point i of the fracture surface pependieular to its base line, and N is the number of points evaluated.

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298

FIGURE 2. Dependence of the characteristic length lch and the nominal notch tensile strength

ıNT

on the average of the lateral correlation length of refractory specimen

A lateral correlation length  was determined according to [4]. As an example results for burnt refactory specimens with different brittleness are shown in Fig. 2. It is obvious that the characteristic length increases with the lateral correlation length , and the nominal notch tensile strength NT decreases with . Contrary to this no correlation of the fracture mechanical parameters determined in this investigation with the fractal dimension was observed. The results will be applied to establish stucture/property relationships and to investigate mechanisms of brittleness reduction for ordinary ceramic materials.

References 1.

Tschegg, E.K., New equipments for fracture tests on concrete, Materials Testing, 338-342, 1991.

2.

EN ISO 4287, Geometrical Product Specifications (GPS) - Surface texture: Profile method -Terms, definitions and surface texture parameters , Deutsches Institut für Normung, 1997.

3.

Ervin, E., Metals Handbook, Ninth Edition, Vol. 12, Fractography, ASM, Metals Park Ohio 44073, 193-210, 1987.

4.

Yang, H.-N., Wang, G.-C, Lu, T.-M. Diffraction from Rough Surfaces and Dynamic Growth Fronts, World Scientific, Singapore, p. 64, 1993.

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299

MODELINGS OF FIBER DEFORMATION DURING MACHINING ARAMID-FRP Eitoku Nakanishi, Masao Fukumori1, Yutaka Sawaki and Kiyoshi Isogimi Department of Mechanical Engineering, Faculty of Engineering, Mie University 1Department of Mechanical Engineering, Graduate school of Engineering, Mie University Kurima-machiya 1577, Tsu, Mie 514-8507, JAPAN [email protected], [email protected], [email protected], [email protected] Recently, composite materials are used in very widely. But the machining the composite materials is very difficult due to the difference of machinability and of mechanical properties between the fiber and matrix materials. Especially, machining the Aramid Fiber Reinforced Plastics (A-FRP) causes the poor machined surface by large fluffs of Aramid fiber[1] as shown in Fig.1(A). In this paper we tried to clarify the fracture phenomena of Aramid fiber during machining to suggest an optimum machining conditions. We observed the deformation of Aramid fiber bundle inside of the matrix in transparently during machining by using optical microscope. By this method, we can observe the deformation of Aramid fiber and delamination between fiber and matrix clearly as shown in Fig.1(B).

FIGURE 1. SEM and optical microscope observations. The machined surface appearances and delamination between fiber and matrix are much affected by fiber orientations of specimen. We expand the single fiber beam theory[2] to addressing the fiber bundle deformation[3]. In this theory, Aramid fiber is regarded as beams and the matrix is regarded as elastic foundation. And we can express the deformation of Aramid fiber bundle during machining as shown in Fig.2. Further, we consider that the fracture point of fiber may much affect the fluffs length and surface appearances. And we try to make a simple model that is based on elastic theory to evaluate the fracture point or higher stress filed of Aramid fiber bundle as shown in Fig.3.

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FIGURE 2. Deformation of Aramid fiber bundle.

FIGURE 3. Stress distribution.

References 1.

E. NAKANISHI, J. SUZUKI and K. ISOGIMI, Effect of Vibrations on Fracture Phenomena in Machining Aramid-Glass Hybrid Composites, Engng., Trans., 47, 2, 145-154, 1999.

2.

X. WANG, K. NAKAYAMA and M. ARAI, Investigation on the Cutting of Fiber Reinforced Composite Materials (2nd Report) -Mechanism of Surface Generation in Cutting FRP-(in Japanese), Journal of Japan Society of Precision Engineering, Vol.57, No.8, 1437-1442, 1991.

3.

E. NAKANISHI, Y. SAWAKI and K. ISOGIMI, Modeling of Deformation of Aramid Fiber Bundle During Machining Aramid FRP (in Japanese), Journal of Japan Society of Advanced Production Technology, Vol.22, No.1, 67-74, 2004.

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QUALITY CONTROL AND THE STRENGTH OF GLASS Fred Veer, Christiaan Louter and Ton Romein1 Faculty of Architecture , Delft University of Technology 1van Noordenne groep Po Box 5043, 2600 GA Delft [email protected] To determine the strength of glass is important to determine the dimensions of glass structures. Conventional materials have singular strength values that are quite reproducible and independent of size. The strength of glass is strongly dependent on the size of the glass and the quality of the edges. In earlier work, Veer [1], it was shown that the strength of small specimens of glass cannot be fully described by a simple Weibull function. Later research, Veer, [2], has shown that in larger pieces of annealed and also tempered float glass the data can still not be described by a single function. In addition significant differences are found when glass is tested flat or standing with the full edge stressed in 4P bending. Again these results can not be described adequatly with a Weibull function as is shown in figure 1.

Figure 1 : Weibull plot of fully tempered float glass 1000´125´10 mm One theory that explains the deviation was proposed. Namely that the glass specimens in the series were processed differently resulting in different flaw shapes and distributions. To investigate this several series of glass specimens were ordered with the following specifications. •

Final size of specimens should be 1000´125´10 mm.

•

All specimens in one serie should be processed on one grinding line with all specimens being done one after the other without interruption

•

All machines should be cleaned and the grinding heads checked and if necessary replaced before starting the processing

•

As many different grinding lines as possible should provide a series

All specimens are then tested under identical conditions. Each series is processed separately with Weibull coefficents being determined. The results of the series are then mixed and a seperate

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302

statistical analysis of the whole is made. The result show that each individual group has behaviour that can be described better than the collective results of all series. It is thus concluded that the differences between the individual processing lines contributes to the scatter. The strength of glass is thus also dependent on the quality of the machinery and the quality control in processing.

References 1.

F.A.Veer, J.Zuidema, The strength of glass, effect of edge quality, Proceedings Glass processing days conference 2003, Tampere, Finland, Tamglass ltd.Oy.

2.

F.A.Veer , F.P. Bos, J. Zuidema, T. Romein, Strength and fracture behaviour of annealed and tempered float glass, Proceedings ICF 11 conference 2005 , Turin, Italy, edited by A. Carpinteri

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303

EXPERIMENTAL STUDY OF CRACKED LAMINATE PLATES BY CAUSTICS G.A. Papadopoulos and E. Sideridis Section of Mechanics, The National Technical University of Athens, 5 Heroes of Polytechnion Avenue, GR-157 73, Zografou, Athens, Greece. [email protected] The strength of a composite material in form of laminate is obtained from the properties of the constituent laminae. The interface between different laminae is an important factor since it influences the stresses which are developed in the laminate and hence the strengths. In this study an experimental investigation of the strength of symmetrical and unsymmetrical cracked laminates made of isotropic layers [Lexan (PCBA) and Plexiglas (PMMA)] was attempted. An analysis based on the lamination theory was performed in order to determine the elastic constants of these laminates. Experimental measurements of the strength and the stress intensity factor KI in cracked specimens made of laminates with different stacking sequences were carried out. The material we deal is a laminate made of 2, 3 and 4 layers of isotropic material. In plane stress conditions in xyz axis system the stress-strain relationships are given as [9]

­V x ½ ° ° ®V y ¾ ° ° ¯W xy ¿

ª Q 11 Q 12 0 º ­ H x «Q Q 0 » °H « 12 22 » ® y ° ¬« 00 Q 66 ¼» ¯ J xy

½ ° ¾ ° ¿

(1)

The elements Qij of the stiffness matrix are related with the material properties as follows Q 11

E 1 Q

2

Q 22 ,

Q 12

QE 1 Q

2

,

Q 66

E 2 (1  Q )

Eq.(1) can be thought of a stress-strain relationship for the laminate. Thus, it can be written as

^V `k

kth

G

(2) layer of a multi-layered

>Q @k ^H `k

(3)

On the other hand the elastic constants in the laminate plane Ex, Ey, xy, Gxy can be determined by the classical theory of laminated plates by the aid of models which assume uniform stress through the thickness of the laminate. Thus: 1 Ex

where A ijc

A ij  1

A11c ,

and A ij

1 Ey

c , A 22

Q

xy

 A12c , A11c

1 G xy

1ª N º ( Q ij ) k t k » . ¦ « t ¬ k 1 ¼

Here tk is the thickness of kth layer and t the thickness of the whole laminate.

c A 66

(4)

G.A. Papadopoulos and E. Sideridis

304

Specimens were made of 2-4 layers in symmetrical or unsymmetrical combination of Lexan (PCBA) and Plexiglas (PMMA) layers having 1u103 m thickness each, thus providing the form of a symmetrical laminate [see Fig. 1a]. For the bonding of the layers special glue (trichloroethylene-dicloromethane 2/1) was used. In order to measure the strains longitudinal and transversal strain gauges (KYOWA type with gauge length 2 mm) and Huggenberger extensometer were used. Tensile experiments were carried out, to measure mechanical properties, using dogbone 3 specimens with total thickness varying from 2 u103 m to 4u10 m according to ASTM D638. 2 3 The width of the specimens was 30 u 10 m near the grips and 13 u 10 m at the mid – length

whereas the total length vas 180 u 10  3 m (see Fig. 1b). An edge crack of 5x10-3 m was cut in the specimens. The experimental obtained values of the Elastic modulus, E, Poisson ratio,

Q , and ultimate

stress V ult for PCBA and PMMA are given in Table 1. The elastic constants E, of the sandwich were used in caustics experiments caustic for the calculation of the stress intensity factor KI. The stress intensity factor was compared with those of the layers of the sandwich.

(a)

(b)

Figure 1. (a) The sandwich laminate, (b) Geometry of the dogbone spesimens.

TABLE 1: Elastic modulus, Poisson ratio and ultimate stress of Lexan and Plexiglass

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FRACTURE OF COMPOSITES IN MILITARY AIRCRAFT Robert Pell, Nick Athiniotis and Graham Clark Defence Science & Technology Organisation 506 Lorimer St. Fishermans Bend, Victoria, Australia, 3207 [email protected] The Defence Science and Technology Organisation (DSTO) provides failure analysis and accident investigation support to the Australian Defence Forces (ADF) and over 60 years has developed a strong capability as an impartial adviser on aviation failures. This paper provides a brief overview of military aviation accident investigation and failure analysis in Australia, an activity which draws upon a wide range of scientific and technical capability, including engineering analysis. In some specialised areas, notably composite materials, DSTO anticipated a requirement for a significant capability in failure analysis, on the basis that failure investigations in which the failure mode of the composite structure in an aircraft is not understood will always be open to doubt. As the use of composite materials in aircraft manufacture continues to increase the requirement to be able to analyse failures in composite materials also increases. Over some years, DSTO conducted research and participated in an international collaboration program to develop a functional capability in the failure analysis of composite materials. This effort was built upon a strong science foundation that already existed at DSTO in the design and manufacture of composite components, especially with respect to the repair and refurbishment of aging aircraft structures. This approach has resulted in a small, but expert capability in DSTO. In most instances composites failure analysis, by methodical examination of the fracture surfaces of broken fibres, can be used to determine whether fibre fracture has occurred under tension, shear or compression loading. Similarly, by detailed examination of the matrix material on the surface of a delamination, composites failure analysis can be used to determine whether the delamination was introduced as a defect during manufacture or if it occurred, in service, as a result of shear or transverse tension loading. The ability to identify failure modes in carbon-fibre, boron-fibre and glass-reinforced composites under a variety of loading conditions, and at a variety of scales, has been applied on an opportunity basis to failures experienced in the aircraft flown by the ADF, as well as a number of non-aviation cases. Citing one example, the ability to identify the features generated in carbon fibre fractures produced by compression loading (Fig. 1) made a significant contribution to an accident investigation conducted for the ADF. Part of the accident damage included the tail rotor blades of an ADF helicopter all of which were broken in an identical manner. This could have been caused by ground impact, however, it was possible that the blades may have been severed in flight. It was essential to determine the cause of failure and the identification of compression features in each of the tail rotor blade fractures confirmed that the failure had occurred under bending loads that would be consistent with ground impact.

306

R. Pell et al.

Figure 1. A schematic of the fracture process that occurs under compression loading and examples of the micro features used to identify compression fracture, The paper will present an overview of the variety of composite materials and structures, ranging from carbon fibre yacht masts to fibreglass reinforced automotive timing belts that have been successfully analysed at DSTO using composites failure analysis techniques. In the context of DSTO’s failure analysis and accident investigation activity as applied to military aircraft, the paper addresses, in some detail, a number of examples of failures in both carbon fibre and fibreglass composite components. These examples serve to illustrate the complex nature of the fracture/failure process in composite materials, and the contribution made by analysis of the fractures surfaces generated during failure. The paper also highlights the need to analyse fractures on both the macro and micro-scales with the need to reconcile these observations to achieve a valid conclusion.

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ANALYSIS OF 7005/AL2O3/10P MMC SHEETS JOINED BY FSW BY THERMOELASTICITY P. Cavaliere, G. L. Rossi1, R. Di Sante and M. Moretti1 Dept. of Ingegneria dell’Innovazione, Engineering Faculty, Univ. of Lecce, I-73100-Lecce, Italy 1Dept. of Industrial Engineering, Univ. of Perugia Friction Stir Welding represents a very attractive technology in reducing residual stresses and distortion in joints compared to conventional fusion welding ones. In particular, FSW of Aluminium based metal matrix composites is less affected by the inconveniences deriving from debonding and segregation of reinforcing particles. In this study, the metal matrix composite under investigation was a 7005 aluminium alloy reinforced with 10% of alumina particles Friction Stir Welded (T6 condition) by employing a threaded tool rotating speed of 600 RPM and a welding speed of 250 mm/min. The optical and scanning electron microscopy observations performed on the different zones of FSW joints cross section revealed the different structures of the nugget, the thermo-mechanical affected zone and the heat affected zones thanks to the difference in reinforcing particles dimensions as a consequence of friction process. Such phenomenon is accompanied with a strong grain refinement due to a dynamic recrystallization acting during the severe plastic deformation to which the material is subjected during the welding process. Only a few data are available in the literature on the fatigue behaviour of these materials. The aim of this work is also to apply thermoelastic stress analysis to the study of crack formation and propagation of friction stir welded MMC sheets, during cyclic fatigue tests. The room temperature tensile properties, previously measured in transverse direction respect to the welding one gave a response on the yield strength of 290 MPa, on UTS of 310 MPa with a measured strain to fracture of 1.5 %. Fatigue tests were carried out under the axial total stress-amplitude control mode with R=Vmin/Vmax = 0.1 using a resonant electro-mechanical testing machine (TESTRONICTM 50r 25 KN by RUMUL (SUI)). All the mechanical tests were performed up to failure which occurred at the interface with the welded area. The TSA measurement system allowed the crack evolution to be observed in real-time during fatigue cycles and stress fields to be derived on the specimens from the temperature variation measured. In the last stage of this work, the microstructure resulting from the FSW process was studied by employing optical and scanning electron microscopy, in order to correlate the microstructural evolution produced by the welded process with the fatigue properties previously determined. Keywords: FSW, MMC, TSA

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SURFACE MODIFICATION OF LIGHTWEIGHT AGGREGATE AND PROPERTIES OF THE LIGHTWEIGHT AGGREGATE CONCRETE T. Y. Lo and H. Z. Cui Department of Building & Construction City University of Hong Kong Hong Kong, P. R. China [email protected], [email protected] Structural lightweight aggregate concrete (LWAC) offers design flexibility and substantial cost savings by providing less dead load [1]. Because of higher water absorption of lightweight aggregate (LWA), process of mixing LWAC is more complex than that of normal weight concrete (NWC). Generally 1-hour water absorption of structural LWA is 6~15%, but that of normal weight aggregate (NWA) is lower than 1% [2]. Therefore pre-wetting LWA is typical method for LWA treatment for producing qualified LWAC, though the process of pre-wetting LWA is inconvenient [3]. In this paper, three aspects of LWA study have been carried out, i.e. a) LWA surface modification, b) mechanical properties and durability of LWAC made with the modified LWAs and, c) the study of interfacial zone of the LWACs. The effects of different concentration of surface modifier on water absorption of modified LWA were studied. Figure 1 shows the water absorption of unmodified and modified LWAs and displays the surface modification for LWA can reduce the water absorption obviously. For LWA modified with 1:5 concentration modifier, the water absorption only was 10.5% of unmodified LWA. Studies of mechanical properties and durability of LWACs [4] made with modified and unmodified LWA were carried out. The mechanical and durability properties of different LWAC series were determined by conducting cubic compressive, static modulus of elasticity, shrinkage and water permeability tests. 28 days LWAC compressive strength could be up to 46.1 MPa corresponding to the modified LWA used 1:20 concentration modifier. Based on the test results, it can be known that the surface modification can reduce water absorption of LWA effectively but without obvious disadvantageous effect on mechanical and durability of the LWAC.

FIGURE 1: Water absorption of unmodified and modified LWAs Scanning electron microscope (SEM) was used to study the interfacial zone of the LWACs. From the study of the microstructure of the interfacial zone it can be known that, for LWA

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modified with a lower concentration modifier, bonding strength between the hardened cement paste and modified LWA was better.

References 1.

Satish Chandra, Leif Berntsson, Lightweight aggregate concrete: Science, Technology and Applications, William Andrew Publishing, USA, 2002

2.

FIP Manual of Lightweight Aggregate Concrete, 2nd ed., Halsted Press, London, 1993.

3.

Y. Lo, et al, Microstructure of pre-wetted aggregate on lightweight concrete, Building and Environment, Volume 34, Issue 6, November 1999, Pages 759-764

4.

Joao A. Rossignolo and Marcos V.C. Agnesini, Durability of polymer-modified lightweight aggregate concrete, Cement & Concrete Composites 26 (2004) 375–380

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FINITE ELEMENT BASED PREDICTION OF FAILURE IN LAMINATED COMPOSITE PLATES H. Hosseini-Toudeshky, B. Hamidi1, B. Mohammadi2 and H. R. Ovesi3 Associate Professor, 1,2Post Graduate Student, 3Assistant Professor Aerospace Engineering Department, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran, Iran [email protected] Damage accumulation in laminated composite is a major concern in the design and use of composite structures. Accumulated damage can affect laminated response and ultimate strength, which are critical to design of load-carrying structural components. For the optimal design of composite structures, laminate response beyond the point of initial matrix cracking must be known, and subsequent damage and failure modes induced by accumulated matrix crack must be understood. Matrix cracking is often part of the failure process in fiber composites. It typically manifests itself as cracking in the off-axis plies of a laminate, for example, in the 90° plies of a laminate loaded in the 0° direction. The matrix cracks affect the stress distribution within the plies of the laminate by lowering the transverse stiffness of the plies. Matrix cracks also can serve as flaws for delamination initiation. Experimental results showed that matrix cracking commonly leads to subsequent forms of damage including micro-cracking and delamination [1, 2]. Tensile strength and response of composite laminates are commonly characterized through uniaxial tensile testing of finite-width laminate specimens. In order to predict accurately the tensile response of laminate, these damage mechanisms and their dependence on laminate configuration must be understood and accounted for through analysis. Certainly one tool to use in this design procedure is to calculate the interlaminar stresses and compare these with interlaminar allowable stress. Another point of view is to use the approach of fracture mechanics principles. O’Brien [3] developed a simple analytical method for evaluating the strain energy release rate associated with delamination growth from a matrix crack. McCartney considered the mechanics for predicting stress transfer in a general symmetric laminate, having a uniform distribution of ply cracks in single orientation, to combined general in-plane and through the thickness loading [4]. A two-part investigation was performed to study the stiffness response and strength of composite laminates subjected to uniaxial tension by Johnson et al.[1]. They performed extensive tests on specimens with specially tailored ply orientations to characterize damage initiation and propagation induced by matrix cracks. In second part of their investigation analytical models were developed to account for the damage modes observed in experimental investigation [2]. The focus of the experiments was to characterize the matrix crack-induced damage progression and failure modes in composite laminates under uniaxial tension loads. In this paper, initiation and propagation of matrix cracking and induced delamination between layers up to the final failure of the laminated composite plates are investigated using finite element method. The obtained results are compared with the available experimental results in the literatures [1]. Three dimensional finite element analyses of the laminated plates (graphite/epoxy, T300/508) are performed for various lay up configurations and thicknesses. A macro program using the capability of macro programming in ANSYS was developed to handle the full procedure of modeling including the mesh generation, matrix crack initiation and propagation, and induced delamination up to the final failure.

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The major steps in the developed macro program are; 1- Geometry definitions, mesh generation, constraints and material property definitions, 2- Applying an initial load, 3- Linear elastic analysis to find the stress and strain fields, 4- Calculation of matrix (eM) and delamination (edelam) criteria, 5- If eM>1 and edelam>1 then reduce the magnitude of the initial load and go to step 3. 6- If eM>1 and edelam2,3]. After heat treatment, photographs of microstructures of the starting conditions (prior to tempering) were taken. From the photos it is clearly seen that the specimens in the starting conditions had two different microstructures: •

by cooling down in oil the obtained microstructure was a hardened microstructure with visible plates of martensite common to the steel with this share of carbon, and its hardness was 850 HV1,

•

by austempering the obtained microstructure was a microstructure of lower bainite metal base, with probably lower share of residual austenite and with hardness of 440 HV1.

These investigations comprise two groups of experiments, namely the static tensile tests (2 specimens) and tests to investigate the fracture toughness of the material (3 specimens). A laboratory testing of fracture toughness of steel was carried out and diagrams of force relationships - CMOD, CTOD-'a and J-integral-'a were recorded. A standard three points bending test specimen (SENB) was investigated. All investigations of the fracture mechanics parameters were performed according to the British standard BS 7448: 1991 – Fracture mechanics toughness tests: Part 1. Method for determination of KIc , critical CTOD and critical J values of metallic materials. Crack mouth opening displacement (CMOD) in dependence of the load on the specimen (force F) is measured. The measured values are recorded in the form of a diagram FCMOD, Fig.1. Also, the diagrams CTOD-'a and J-integral-'a were recorded. After the critical value of notch opening displacement Vc has been determined, it is recalculated into the critical value of the CTOD parameter in the crack tip, i.e. in Gc. Elastic-plastic analysis of FE models is performed using the commercial FE package ABAQUS. For non-linear analysis, the Ramberg-Osgood type stress-strain relationship is used

H

V 0 where

D

E

V D V0

§ V ˜ ¨¨ ©V0

· ¸¸ ¹

n

and n are material constant and strain hardening exponent, respectively.

(1)

D. Pustai et al.

348

FIGURE 1. Dependence of crack mouth opening displacement CMOD on the force F, a) for hardened and tempered specimens, b) for austempered specimens, untempered and tempered Austempering without tempering gives significantly higher ductility in comparison to the most favourable case of hardened and tempered state. Austempering with a subsequent tempering at the temperature of -t = 480oC contributes to a more significant decrease in tensile strength Vm, for about 20%. The analysis of the critical value of the stress intensity factor KIc shows that with higher temperature of tempering -t, higher values of the parameter KIc in hardened and tempered specimens are obtained. For example, parameter KIc is approximately twice as high at the temperature of tempering -t = 480oC than the one at the temperature of tempering -t = 300oC. The best critical values of the stress intensity factor KIc are obtained by austempering without tempering and they are approximately 50% higher than the ones obtained by tempering at the temperature -t = 480oC, or even three times higher than the values obtained by hardening and tempering at the temperature -t = 300oC. By hardening and tempering at the temperature -t = 480oC, the obtained critical values of crack tip opening displacement Gc are approximately 3.5 to even eight times higher than those obtained by hardening and tempering at the temperature -t = 300oC. By austempering without tempering, the obtained critical value of crack tip opening displacement Gc is about seven times higher than the value obtained by hardening and tempering at the temperature -t = 300oC.

References 1.

Pustai, D. and Cajner, F., Inžynieria materialowa, vol. 5 (124), 733-736, 2001.

2.

Cajner, F., Strojarstvo, J. Theo. Apl. Mech. Engng., vol. 33 (5/6), 289-296, 1991.

3.

Cajner, F., Kovine, zlitine, tehnologije, vol. 28 (6), 533-538, 1994.

2T11. Fracture mechanics analysis

349

MODELLING THE EVOLUTION OF ELASTIC SYMMETRIES OF GROWING MIXED-MODE CRACKS H. Schutte and K. M. Abbasi Institute of Mechanics, Ruhr University of Bochum D-44780 Bochum, Germany [email protected] [email protected] A numerical study of growing elliptical cracks in a unit cube is undertaken with the help of an FEM simulation.

FIGURE 1. Growth of a crack in a unit cell. The propagation of the microcrack is governed by the principle of maximum driving force [1], which is a direct consequence of the variational principle of a body containing a crack. According to this criterion, a crack grows in the direction of maximal driving force

G*

m ax di

K D

FDE (I ) K E

I

1 Q E

2

[( K I ) 2  ( K I I ) 2 

1 ( K I I I ) 2 ] 1Q

where

and FDE is a matrix whose elements are universal functions of the kinking angle f [4] and K E are the stress intensity factors (SIFs) prior to the crack growth. The SIFs are computed with the help of an stress extrapolation method without the use of singular elements. For each propagation step the tensor of elasticity is calculated and analyzed with the help of its spectral decomposition and its eigenvalues [3]. For the original elliptical crack its is known that it results in a orthogonal symmetry with respect to the crack plane an the axes of the ellipse. After a considerable amount of growth the crack approaches a penny shape perpendicular to the axis of tension, which leads to transversally symmetry. For the other propagation steps the best orthogonal approximation of the elasticity is determined. Many damage mechanics models for quasi-brittle materials are based on the reduction of stiffness due to elliptical crack or penny-shaped microcracks in the material. To incorporate the results of the numerical analysis in a continuum damage model it is possible to avoid the computational expansive FEM simulation of crack growth in a unit cell, representing a continuum point, by using an replacement crack approach. For an elliptical crack there are analytical solutions

H. Schutte and K. M. Abbasi

350

available for the SIFs and so for the direction of growth and change of shape of the crack. Also the evolution of the additional (damaged) compliance can directly be computed from the dissipation of the crack as

S

d

* w2 ³ G a d s *

wı … wı

For the next growing steps there exists no analytical solution for the SIFs at multiply kinked crack fronts, so that in each step the grown crack is replaced by an elliptical crack, which has certain properties it in common. For thermodynamic consistency it is necessary that the dissipation of the kinking crack and the change of the potential of the growing crack are identical

³

*

G * a d s

C @ for the enriched crack tip elements. A finite element mesh for a plate, with an internal crack, subjected to step loading is depicted in Fig. 1. The geometry of this plate corresponds to a 2-D problem given by Chen [4] and solved using a finite difference algorithm. With the appropriate out-of-plane constraints, the results from the finite element formulation are essentially identical to those given in [4]. Figure 2 contains plots of the normalized mode I stress intensity factors and compares the 3-D result with the plane strain solution. The differences in the solutions are due to differences in the arrival time of the S, R and P waves along the crack front. The transient stress intensity factors also display a spatial variation along the crack front as shown in Fig. 2b. Interestingly, the location of the maximum stress intensity factor along the crack front does not always lie on the plane of symmetry, but changes as a function of time.

M. Saribay and H. F. Nied

396

(a)

(b)

FIGURE 1. a) Rectangular bar containing an internal crack, subjected to suddenly applied axial loads. b) Cubic crack tip element (32-noded hexahedron) showing orientation of local crack tip coordinate system with respect to global coordinates [3].

FIGURE 2. a) Normalized mode I stress intensity factors (K

I dyn

) for the central node on the crack

front as a function of time for the internally cracked rectangular plate. b) Stress intensity factors * along crack front at t = 0.685e-05 s. K 1

K 1 d ym

V

0

Sa.

References 1.

Saribay, M., Dynamic Stress Intensity Factors for Cracks Using The Enriched Finite Element Method, MS Thesis, Lehigh University, May 2005.

2.

Belytschko, T., Wing, K.L., Moran, B., Nonlinear Finite Elements for Continua and Structures, John Wiley & Sons, Ltd, England, 2000.

3.

Ayhan, A.O., and Nied, H.F., Int. J. Num. Meth. Eng., Vol. 54, Issue 6, 899–921, 2002.

4.

Chen Y.M, Eng. Fracture Mech., 7, 653-660, 1975.

2T14. Computational fracture mechanics

397

PARTLY CRACKED XFEM INTERFACE FOR INTERSECTING CRACKS J. L. Asferg, Ted Belytschko1, P. N. Poulsen and Leif Otto Nielsen Department of Civil Engineering, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark 1Department of Mechanical Engineering, Northwestern University, Evanston, IL, US. [email protected], [email protected], [email protected], [email protected] Throughout the last century intense research has been carried out regarding methods to determine the ultimate strength of reinforced concrete structures. Today well documented methods are available for estimating the ultimate strength of most reinforced concrete structures, however, most of these methods requires the use of empirical factors and do not consider phenomena such as size effects and reinforcement arrangement in detail. Regarding reinforced concrete structures in the serviceability limit state the predictive capability of existing methods of analysis is limited. Complex models dealing with the serviceability limit state requires prediction of the complex cracking which takes places in the concrete during loading. Modelling of cracks in plain concrete has been a focus area in the research community since the mid seventies where Hillerborg et al. [1] presented their fictitious crack model and Bažant [2] proposed the concept of a crack band. Today several FEM codes have interface elements suitable for discrete cracking and elements for smeared cracking. The use of interface elements however requires the crack path to be known beforehand, while crack modelling applying the smeared approach is not well-suited for modelling of localized crack growth. Among the methods that allow modelling of discrete crack growth without knowing the crack path beforehand is the extended finite element method - XFEM, Belytschko et. al. [4], Moes et. al. [3]. XFEM has been applied to a number of different problems within the area of fracture mechanics among which are cohesive cracking, Wells and Sluys [5], Zi and Belytschko [6]. Modelling of crack growth in plain concrete for benchmark tests such as three point bending and four point shear bending was also considered in Asferg et. al. [7], applying a simplified concept for the enrichment of the displacement field. Modelling of reinforced concrete beams applying the FEM was first carried out by Ngo and Scordelis [8]. Since then several approaches for modelling of the interaction between reinforcement and concrete has emerged. Today the most widely used concept for modelling the interaction between steel and concrete is the application of interface elements for the bond zone e.g. Lundgren [9] . The use of standard interface elements however poses some difficulties. Generation of more complex models with multidirectional reinforcement is cumbersome and special attention is required when ever two reinforcement bars are crossing each another. When the aim is to model crack growth without knowing the crack path beforehand applying e.g. the XFEM concept for the bulk concrete traditional interface elements are not applicable for the bond zone between reinforcement and concrete. The goal of the present research project is to develop a more feasible method for modelling of reinforced concrete structures and a super element may be the final goal of the project. However before such an element can be formulated an XFEM interface element for the bond zone has to be formulated. One of the requirements to the XFEM interface element is that it shall be able to handle intersecting cracks – longitudinal cracking along the reinforcement is initiated by cracks

J. L. Asferg et al.

398

crossing the reinforcement. Furthermore the interface element shall be formulated as an element that is able to partly crack. Bond between concrete and reinforcement is in nature a 3D problem and the confining pressure is one of the key effects for the stress transfer between concrete and reinforcement. However initially the XFEM interface is considered in a plane version. c.f. Fig 1.

FIGURE 1: Development of crack in interface between concrete and reinforcement. As initial test case for the XFEM interface a plane model of a concrete beam holding one reinforcement bar is considered. A constitutive bond model is chosen from literature and the results compared with results from the literature.

References 1.

Hillerborg, A, Modéer, M, Petterson P-E. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cem. Concr. Res., 1976; 6:773782.

2.

Bažant, Z P. Instabillity, ductility and size effect in strain-softening concrete, ASCE Journal of Engineering Mechanics; 1976 102: 331-344.

3.

Belytschko T, Black T. Elastic crack growth in finite elements with minimal remeshing. Int. J. Numer. Meth. Engng. 1999; 45(5):601-620.

4.

Moes, J. Dolbow and Belytschko, T., “A finite Element Method for Crack Growth without Remeshing”, Int. J. Numer. Meth. Engng., 1999; 46(1): 131-150

5.

Wells GN, Sluys LJ. A new method for modeling of cohesive cracks using finite elements. Int. J. Numer. Meth. Engng. 2001; 50(12):2667-2682.

6.

Zi G, Belytschko T, New crack-tip elements for XFEM and applications to cohesive cracks. Int. J. Numer. Meth. Engng. 2003; 57:221-2240.

7.

Asferg, J.L., Poulsen, P.N., Nielsen; L.O. “ Cohesive crack modeling applying XFEM – fully cracked element vs. partly cracked elements” Manuscript under preparation.

8.

Ngo. D., Scordelis C., “ Finite element analysis of reinforced concrete beams”, 1967, ACI J. Proc. 64, pp. 152-163.

9.

Lundgren, K, “Three-Dimensional Modelling of Bond in Reinforced Concrete” 1999, Ph.D. thesis, Publication 99:1, Div. of concrete, Chalmers University of Technology.

2T14. Computational fracture mechanics

399

ON THE EVALUATION OF ELASTIC COMPLIANCE TENSOR DUE TO GROWING MIXED-MODE MICROCRACKS K. M. Abbasi and H. Schutte Institute of Mechanics, Ruhr University of Bochum D-44780 Bochum, Germany [email protected], [email protected] Our aim is to determine the evolution of the elastic compliance tensor of a unit cell with a growing mixed-mode microcrack in it. To be able to validate certain damage evolution laws, we determine this so far missing evolution of the elastic compliance due to growing mixed-mode microcracks. The matrix of the unit cell is considered to be linearly elastic homogenous and isotropic and the crack is small compared to the unit cell, so the overall behaviour of the unit cell is linearly elastic. This enables us to use linear elastic fracture mechanics (LEFM) concepts for the propagation of the microcrack. Finite element simulations have been performed to simulate the quasi-static, elastic growth of microcracks. The models provide a general framework for mixed-mode linear elastic fracture mechanics analysis under small strain assumptions.

FIGURE 1. Growth of a microcrack in a unit cell. As the crack propagates, remeshing algorithms delete the mesh, extend the crack and mesh the cube according to the new crack configuration. The propagation of the microcrack is governed by the principle of maximum driving force [1], which is a direct consequence of the variational principle of a body containing a crack. According to this criterion, a crack grows in the direction of maximal driving force, and it reads 2

di

1 Q E

K D

FDE ( I ) K E

[( K I ) 2  ( K II ) 2 

1

( K III )2 ] 1 Q .

(1)

Where (2)

and FDE is a matrix whose elements are universal functions of f [4], f being the kinking angle, and K E are the so-called stress intensity factors (SIFs) prior to the crack growth[4].

K. M. Abbasi and H. Schutte

400

The initial crack is taken as an inclined elliptical or penny-shaped crack, for which analytical expressions for SIFs and the elastic compliance tensor are available. Rotation of the cracks around their centre points enables the simulation of possible modes of crack propagation. Many damage mechanics models for quasi-brittle materials are based on the reduction of stiffness due to elliptical crack or penny-shaped microcracks in the material. With our approach it becomes possible to validate the evaluation of damage and so the evolution of the compliance tensor resulting from different models.

FIGURE 2. Reduction of stiffness in the loading direction. Verification and validation studies are undertaken to compare the resulting SIFs and the components of the compliance tensor from the simulation with the available analytical results.

References: 1.

Le, K. C., Schütte H. and Stumpf H., Archive of Applied Mechanics, vol. 69(1), 337-344, 1999

2.

Mehrabadi, M. M. and Cowin, S. C., Mech. Appl. Math., vol. 43(1), 15-41, 1990

3.

Leblond, J. B., Int. J. Solids Structures, vol. 25(11), 1311-1325, 1989

4.

Amestoy, M, Leblond, J. B., Int. J. Solids Structures, vol. 29(4), 465-501, 1992

5.

Wu, C. H., Journal of Elasticity, vol. 8, 183-205, 1978

6.

Nemat-Nasser, S., Hori, M., Micromechanics: overall properties of heterogeneous materials, North-Holland, Amsterdam, Holland, 1993.

2T14. Computational fracture mechanics

401

ON THE PROBLEM OF DETERMINATION OF SAFETY FACTORS FOR MACHINE-BUILDING PARTS USING THE FINITE ELEMENT COMPUTATIONS L. B. Getsov, B. Z. Margolin and D. G. Fedorchenko SPbSPU (St. Petersburg), CRISM “Prometei” (St. Petersburg), SNTK (Samara) [email protected] The main principles of normalizing the safety factors on local static and low-cycle fatigue strength considered in this paper were substantiated experimentally (the report in preparation). The process of rupture at static loading may generally be of three types: a) caused by exhausting short-time plasticity of material; b) caused by creep; c) brittle. It is evident that the differentiation of safety factors depending on the type of rupture should be implemented in the normalization of local stresses. It is clear that the greatest safety factor value should be taken in the case of brittle fracture, with its strength values characterized by the maximum scatter of material parameters values. Static strength of plastic materials: The following approaches are expedient to apply for evaluation of safety factors on local stresses: 1. The application of a widespread model of kinematic hardening is completely justified for solving many practical problems. However, the optimum is SSS computation providing for the choice of a plasticity model depending on the material analyzed and ways of loading, in accordance with the multimodel approach concept. It should be also noted that in using deformation curves, strains will be related to a current full strain. 2. Static strength of plastic materials should be evaluated by exhaustion of the ultimate material plasticity *, which in its turn depends on the loading rate or time. Incidentally, one should discern the ultimate states under the conditions of intragranular and intergranular rupture. The intragranular rupture is characterized by the absence of the dependence of ultimate strains on loading rate; at the same time under the condition of intergranular rupture, ultimate strains diminish with the decrease of loading rate. 3. If local strength is evaluated under the condition of short-time plastic strain, the safety factor on strains */p (p – plastic strain) shall be not less than 2.0, * being defined with account of the stress state rigidity by the following formulas: İ * = İ p u l t 1 . 7 e x p ( - 1 . 5 V / V i ) (1a),

İ * = İ p u lt K eV

2 i

/ 3 ( V i V ) (1b),

which give a conservative estimation of plasticity. Here pult is the ultimate strain (deformability) at short time tension, and Ke, the characteristic of material state (Ke=1at the brittle state; Ke=1.2 at plastic state); V is the mean stress value. The value of p is defined using elasto-plastic computation, an appropriate plasticity model, and the lower strain envelop curve. In this case, the safety factor on stresses should not be lesser than 1.2-1.4. The evaluation of rupture situation of the parts operating in the creep condition is implemented with the use of the ultimate strain value, which depends on temperature, time and rigidity of stress state. Therefore, just as in the case of normalizing the safety factors on static strength of parts from plastic materials, the introduction of FEM computations and more exact knowledge of SSS in stress concentration locations does not provide the basis for correcting the values of safety factors in the condition of creep. There is no need to use the modern methods of stress computation in this case. The safety factors in the condition of creep should be defined by using the crack initiation criteria. Accounting for nonstationary situation by the application of computations with the formulas of linear summation of damages (in deformation or time interpretation), as has been shown by numerous researchers, allows us to obtain the conservative estimation, on the condition that the sum of damages is taken equal to 0.87.

L. B. Getsov et al.

402

At present, for evaluating the cyclic strength safety factors, various methods were suggested for determining the local strength safety factors that may be conditionally divided into five groups: computational for a rigid cycle; computational for a general situation; computational-experimental; based on the theory of adaptability; based on deformation criteria. For cyclic loading in general case, when unilateral accumulation of strains (characteristic for a mild cycle and generally called “ratchetting”) and stress variation (characterictic for a rigid cycle) take place, different approaches to the evaluation of cyclic strength safety factors may be applied. Among all known strength characteristics of material, life time under cyclic loading mostly depends on the constructional, technological, metallurgical and operational factors. Therefore, it is expedient to carry out the evaluation of the life time under cyclic loading for constructions basing on the results of testing specimens and construction components, with account of all abovementioned factors. The main operational factors affecting the life time of a part under cyclic loading are temperature, holding duration at maximum loads and temperatures, cyclic asymmetry, superposition of the highfrequency component upon the low-frequency variation of loads. The conducting of tests within the whole range of operational loads is rather laborious task. Therefore is most urgent to develop the methods based on conventional tests of specimens and allowing the evaluation of life time of the constructions subjected to complex loading in operation. In the general case of low-cyclic loading, the material damages may be computed with the use of deformation or energy criteria of rupture. Here, for computing the kinetics of stress-strain state both for complex noncyclic loading and for cyclic loading with altering loading parameters, instead of the number of cycles n (or the number of semicycles k), it is expedient to use the relations of Odquist’s type as parameters of state. These relations are expressed by the following formulas:

³ dH

Ȝ1=

p

 H

³ dp 

Ȝ2

p

p

dH

p

dp

(2 / 3d H

p ij

dH

p ij

(2 / 3 dp ij dp ij ) 0.5

) 0 .5

;

;

H

p

(2 / 3d H

p

p ij

dH

p ij

) 0 .5

( 2 / 3 p ij p ij ) 0 .5

(2) (3)

' Ȝ 1 = Ȝ (k ) - Ȝ (k -1 ) t 0 , where k – the ordinal number of a semicycle. The increment of nonelastic strains (dne) and the value of nonelastic strain intensity (ne) are defined by formulas : dijne=dpij+ dpij;

H

ne

( 2 / 3 d H inj e d H

ne

) 0 .5

(4)

In the case of creep, when stresses are known, the accumulated creep strains are defined by their separation from nonelastic strains. The methods of adaptability computation determine the cyclic strength safety factors for the general case: in the conditions of sign-variable flow and progressing deforming. Ultimate material characteristics for a signvariable flow are the following: The methods of adaptability computation determine the cyclic strength safety factors for the general case: in the conditions of sign-variable flow and progressing deforming. Ultimate material characteristics for a signvariable flow are the following: ı s – half-value of cyclic yield strength S0.4 in a stabilized cycle with the tolerance on plastic strain amplitude within a cycle equal to 0.4%. In the case of the presence of stress concentrators: ı s =

E H ( N )V

H (N )

where H ( 1 ) – semiamplitude of full strain corresponding to the

appearance of low-cycle fatigue macrocrack during N cycles;

V

H (N )

– complying with H ( 1 )

on the

isochronous cyclic strain curve. In the case of creep in one of the semicycles – ı s =S0.4 c - 0.5S0.4 , where S0.4

c

– cyclic yield strength on condition of the creep presence. For progressing deforming, as ultimate

characteristics are taken modes. Here

ı LT S

ı s = ı Ǻ – for transitional modes and ı s =

ı

LTS

( t , ¦ ' W ) for stationary

– long-time strength complying with the total duration of the mode, during all life time.

2T14. Computational fracture mechanics

403

DYNAMIC EXPLICIT CELL MODEL SIMULATIONS IN POROUS DUCTILE METALS L. Siad and M. O. Ouali Groupe de Mécanique, Matériaux et Structures (E.A. No 2617) Université de Reims Champagne Ardenne PHT du Moulin Le Blanc 7 boulevard Jean Delautre F-08000 Charleville-Mézières, France. [email protected] The problem of ductile fracture is a complex phenomenon due to various factors such as inelastic behaviour, large deformations, stress gradient … and has received considerable attention in recent years. For example, the occurrence of ductile fracture by hole growth and coalescence is the limiting factor in many metal-forming operations and consequently the ability to predict ductile fracture would allow modification of a production process and so to reduce the risk of failure occurring. Detailed micro-mechanical analysis for characteristic cell unit models with known porosity have been an important tool in the understanding of the influence of porosity in ductile materials. Indeed, cell models are usually considered as a structure in microscale within the material and the solutions obtained for the cell model can be used to rationally link microscopic properties and mesoscopic quantities. This approach allows to set up a general macroscale constitutive law for a damaged material in the frame of continuum mechanics. In this context, detailed cell model studies available in literature have ascertained that dilatant plasticity model particularly suitable to model porous ductile metals are the well-known micromechanically based model proposed by Gurson [1] and phenomenologically extended by Tvergaard and Needleman [2] [3]. On the other hand, in the last years, applications of dynamic explicit time integration schemes to problems involving high nonlinearity has increased, notably to those for which material failure occurs. This paper deals with the study of a quasi-static axymmetric cell behaviour by the finite element method using ABAQUS/Explicit code taking full account of finite deformation effects. The analyses are based on an axisymmetric unit cell model with special boundary conditions (Tvergaard [2] , Koplik and Needleman [4], Brocks et al. [5]), which allow for a relatively simple investigation of a full three dimensional array of voids, without having to solve the full 3D numerical problem. The influences of the initial porosity, the stress triaxiality ratio, and two void shapes (spherical and spheroidal) on the cell behaviour are investigated. The numerical quasi-static solutions are obtained by a full transient analysis of the equations of motion, in which the loading is applied so slowly that the quasi-static solution is well approximated. The aim of the analysis is to find the overall stress-strain behaviour of the cell model on the 'mesoscopic' level that represents the behaviour of a volume element on the macrospcopic level. The calculations have been carried out at constant overall stress triaxialities and a special technique has ben used to maintain the triaxiality constant. The deformations of the cell are monitored by means of the displacement of one of its corner to which a linear elastic truss is tied. The loading is strain controlled in such a way that the stress triaxiality ratio retains a constant prescribed value This requirement is ensured by adapting the displacement of one of the truss edges during the deformation process of the cell (Leblond and Siad [6]). For comparison purposes, the material parameters adopted are taken from literature (Koplik and Needleman [4], Pardoen and Hutchinson, [7] [8], Benzerga et al., [9]). To validate and check the accuracy of the method of analysis, a comparison of the obtained results using both quasi-static explicit and implicit finite element analysis along with available

L. Siad and M. O. Ouali

404

solutions in literature has been carried out. Results regarding the fracture initiation site, the evolution of the damage variable field are illustrated by contour plots from which it can be seen that damage starts developing either inside the cell or on its external surface, both on the ligament depending on the initial porosity and the stress triaxiality ratio. Particular attention is also devoted to the role of localized flow and to evolution of the void shape. Extension of the numerical model to cope with important situations where the coalescence parameters (more particularly the situation for which the matrix material is porous) and/or the nucleation of new voids have to be accounted for are possible but require considerable additional work. Furhermore, research towards the modelisation of the void shape effects based on the Gologanu-Leblond-Devaux model (Gologanu et al., [10] [11]) including dynamic effects is under progress.

References 1.

Gurson, A., J. Engng. Mater. Technol., vol. 99, 2-15, 1977.

2.

Tvergaard, V.., Int. J. Fracture., vol. 18, 237--252, 1982.

3.

Tvergaard, V. and Needleman, A., Acta Metall., vol. 32, 157-169, 1984

4.

Koplik, J. and Needleman, A., Int. J. Solids and Struct., vol. 24, 835-853, 1988

5.

Brocks, W. , Sun, D.-Z. and Hönig, A., Int. J. Plasticity, vol. 11, 971-989, 1995.

6.

Leblond, J.-B., and Siad, L., unpublished work, 2003.

7.

Pardoen, T. and Hutchinson, J.W., J. Mech. Phys. Solids, vol. 48, 2467-2512, 2000.

8.

Pardoen, T. and Hutchinson, J.W., Acta Materialia, vol. 51, 133-148, 2003.

9.

Benzerga, A., Besson, J. and Pineau, A., Acta Materialia vol. 52, Part I, 4623-4628, Part II, 4639-4650, 2004.

10. Gologanu, M. and Leblond, J.-B., J. Mech. Phys. Solids, vol. 48, 1723-1754, 1993. 11. Gologanu, M., Leblond, J.-B., and Devaux, J., J. Engng. Mater. Technol., vol. 116, 290-297, 1994.

2T14. Computational fracture mechanics

405

NUMERICAL EVALUATION OF ENERGY RELEASE RATES FOR BIMATERIALS INTERFACE CRACKS M.Belhouari, B.Bachir Bouiadjra, B.Boutabout and K.Kaddouri Department of Mechanical Engineering, University of Sidi Bel Abbes BP 89, Cité Ben M’hidi, Sidi Bel Abbes, 22000, Algeria [email protected] Bimaterials are extensively used in many engineered material systems, such as composite structures, electronic packaging, and thin film construction. Accurate stress intensity factor and strain energy release calculations are essential in the prediction of failure and the calculation of crack growth rates in these structures. The crack problems with interfaces in dissimilar materials are of paramount importance for many micromechanics and numerical fracture mechanics. The complexity of interfacial failure mechanism has caused researchers to devote a great deal of attention to study the selection of crack growth path. Generally, fracture along and adjacent to bimaterial interfaces has several morphological manifestations. In some cases the fracture defect into the interface, while in others fracture penetrate the interface into another material [1-6]. In present work the finite element methods is used to calculate the strain energy release rates at the interface crack. The effects of the crack length and the orientation of the interface were highlighted as well as the effects of the elastic properties of two bonded materials. In figure 1 are represented the variations of the energy release rate according to the Young moduli ratio E 1 / E 2 for different crack length. This figure shows that whatever the length of the crack, the fracture energy at crack tip decreases brutally from E 1 / E 2 < 10; beyond, this value, and the energy does not vary practically with the ratio. The increase of the crack length involves an increase in its fracture energy. Figure 2 illustrates the variation of the normalised energy release rate G / G 0 according to the of dephasing angle \ for a/w = 0,1. One can observe that the fracture energy of the interfacial crack strongly depends on the value of the parameter \ The values of this parameter lie between 0 and 90° showing that the crack propagation is in mixed mode (opening + shearing). For \ = 45° the energy release rate grows exponentially with the parameter \ whereas for values lower than 45°, this variation is weak. Figure 3 presents the variation of the fracture energy at the interfacial crack according to the ratio E 1 / E 2 for various angles of inclination of the interface. The fracture energy decreases gradually when the angle of inclination of the interface of the bimaterial increases.

M. Belhouari et al.

406

FIGURE 1. Variation of G / G0 vs E1 / E2. FIGURE 2. Variation of G / G0 vs \.

FIGURE 3. Variation of G / G0 vs E1 / E2.

References 1.

He, M.Y. and Hutchinson, J.W., Int J Solids Struc., vol. 25 ,1053-67, 1989

2.

He, M.Y. and Hutchinson, J.W., Journal of Applied Mechanics, vol. 56, 270-278, 1989

3.

Erdogan, F. and Biricikoglu, V., Int J Engrg Sci., vol. 11, 745-66, 1973

4.

Evans,A.G., Dalgleish,B.J., He,M.Y.and Hutchinson, J.W.,Acta Metall, vol.37,3249-54, 1989

5.

Evans, A.G. and Hutchinson, J.W., Acta, Mat., vol.37, 909, 1989

6.

Rice, J.R. and Sih, G.C. Journal of Applied Mechanics, vol.32, 418-423, 1965.

2T14. Computational fracture mechanics

407

INCLUSION EFFECT ON THE PLASTIC ZONE SIZE IN CONFINED PLASTICITY M. Benguediab, M. Elmegueni, M. Nait-Abdelaziz1 and A.Imad1 Department of Mechanical Engineering, University of Sidi Bel Abbes BP 89, Cité Ben M’hidi, Sidi Bel Abbes, 22000, Algeria 1Ecole Polytechnique Universitaire de Lille (France) [email protected] In understanding fatigue properties of metallic alloys, of outmost importance is the precise characterization of the plastic deformation of the material in the vicinity of the crack tip. The plastic behaviour near the tip of stationary growing fatigue crack in engineering materials has been intensively studied using classical plasticity theory based on the Von-mises yield criterion and the associative flow rules [1-2]. It is known that micro defects such inclusions are the possible zone of crack initiation. Several researches have been made in order to analyse the interaction effect between a crack and inclusion using the LEFM concepts [3-5]. The studies related to this effect of interaction for a elastic plastic behaviour are not very current in the literature. The aim of the study is to analyse the effect of presence of inclusions in metallic cracked plate on the plastic zone size at the crack tip using the finite element method. The study relates to the case of small scale plasticity. This case was selected because we estimate that an inclusion does not affect the plastic zone in large scale plasticity because of its low dimension. The model used consists of a plate in aluminium alloy 2024 subjected to tensile load. The plate contains an edge crack with length 30 mm and near the crack one supposes the existence of an inclusion in oxide of aluminium with circular shape having a radius of 200 µm. The material constituting the matrix has an elastic-plastic behaviour and that of inclusion is elastic linear. The ratio between the Young modulus of inclusion and the matrix is about 5. The geometrical model is idealised by quadrilateral elements with eight nodes. Special quarter node elements are implanted around the crack tips. As examples of the obtained results, figures 1, 2 and 3 presents the computed plastic zone contour for d/a = 1.25, 8 and 12,5 % compared with the case without presence of inclusion. The parameter d is the distance between the crack tip and the interface inclusion-matrix and a is the crack length. It can be seen that when the inclusion is very close to the crack tip (d/a =1.25 %), the radius of the plastic zone decreases. There is thus an effect of thinning of this zone. This behaviour can be explained by the fact that the presence of the inclusion, of which the materials is harder, causes the increase of the stresses in the vicinity of the crack, which will involve a reduction of the size of the plasticized zone. When inclusion is not in the plastic zone but it is located at a distance very close to this zone (d/a=8%). One can note that the radius of the plastic zone increases compared with the case without presence of inclusion (figure 2). That is due to the fact that inclusion being the seat of raised stress fields, the stresses in the part located upstream of inclusion cause plastic deformations in metal. This effect involves This effect involves the increase in the radius of the plastic zone. When inclusion is far from the plastic zone d/a=12.5%, the effect of interaction disappears and the plastic zone has a classical form which corresponds to the case without presence of micro defect.

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FIGURE 1. Contour of plastic

FIGURE 2. Contour of plastic

zone for d/a = 0,0125

zone for d/a = 0,05

FIGURE 3. Contour of plastic zone for d/a = 0,125

References 1.

Benguediab,M., Belhouari, M. and Ranganathan,N., Jour of Mater. Science and Techn., vol 9, 134-141., 2001

2.

Kuang , J. and Chen, Y., Engineering Fracture Mechanics, vol 55, 869–881,1996

3.

Lambert, D.J. and , Parks, D.M., Mech of Meterials, vol32,43-55, 2000

4.

Xiao, Z.M., Mech of Materials, vol 25, 263-272, 1997

5.

Murakami, Y., Proceeding of ICF 11, Editor J.Petit, 31-52, 1996

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MODIFIED KEY-CURVE-METHOD FOR DETERMINATION OF DYNAMIC CRACK RESISTANCE CURVES U. Muhlich, A. Emrich and M. Kuna TU Bergakademie Freiberg Institute of Mechanics and Fluid Dynamics Lampadiusstraße 4, Freiberg, 09599, Germany [email protected] Dynamic J-'a curves might be constructed by means of the results of various low-blow tests, where the experimental settings of the instrumented Charpy-V test are chosen in order to assure significant crack growth due to impact loading on the one hand and in order to avoid complete rupture on the other hand. While the final crack advance 'af can be measured for every low-blow test, the corresponding values for J have to be estimated in general from the load-deflection curve using standard concepts of conventional elastic plastic fracture mechanics. The experimental effort could be significantly reduced if a single specimen test method were used instead of this multi-specimen testing. The aim of the present work is to qualify the Key-Curve-Method (KCM), originally proposed by Ernst et al. [1] for quasi-static fracture tests, for this purpose. The idea of the KCM is to estimate the instantaneous crack length a as a function of the deflection s directly from the load-deflection record. Eberle et al. [2] have shown by means of numerical simulations that the corresponding value for J can be determined according to the estimation given in the ESIS-P2 standard [3]. Experimental data obtained from dynamic fracture tests with side-grooved specimens made of nodular cast iron GJS-400 are taken as reference. Finite element simulations of the fracture tests have been performed, where a continuum damage model (CDM) was employed in order to simulate crack growth numerically. The continuum damage model considered here was first proposed by Gurson [4] and modified among others by Tvergaard [5], Tvergaard and Needleman [6]. Here, an extension of this model was used which incorporates rate dependent yield and adiabatic softening. The numerical calculations were carried out with the aim to possess an equivalent numerical simulation for every considered experiment which offers the advantage that in contrast to the experiment the instantaneous crack length can be monitored. Furthermore, the corresponding value of J can be calculated directly according to its theoretical definition. Plane strain simulations were used here because they predict sufficiently well the behaviour of side-grooved Charpy specimens as shown in [2]. Furthermore, fully explicit analysis confirms that inertia effects can be neglected because the deflection rates considered here lie between 0.6 m/s and 1.2 m/s.

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410

FIGURE 1. Numerically obtained crack resistance curve versus estimation based on KCM Most of the material parameters of the CDM have been determined from static and dynamic tensile tests, whereas the critical void volume fraction and the height of the finite elements within the ligament were chosen in order to fit the load-deflection curve of one Charpy-V test with complete rupture. Then the low-blow tests have been simulated in order to validate the numerical calculations by means of the following criteria: the load-deflection curve and the final crack length predicted by the numerical simulation must fit the corresponding experimental results using a unique set of material parameters for all low-blow tests. Finally, the J-'a curves obtained directly by finite element simulations have been compared with their corresponding estimates based on KCM. One example is given in Figure 1. which indicates that for the considered material and the applied testing conditions the estimation of the crack resistance curve based on KCM is in good agreement with the direct computation.

References 1.

Ernst, H., Paris P.C. and Landes, J.D., Fracture Mechanics, ASTM STP 743, edited by R. Roberts, American Society for Testing and Materials, 1981

2.

Eberle, A., Klingbeil D. and Schicker, J., Nuc. Eng. Design, vol. 198, 75-87, 2000

3.

ESIS-P2, ESIS procedure for determining fracture behaviour of materials, 1992

4.

Gurson, A.L., J. Eng. Mat. Tech., Trans. ASME, vol. 99, 2-15, 1977

5.

Tvergaard , V., Int. J. Frac., vol. 17, 389-407, 1981

6.

Tvergaard, V., Needleman, A., Acta Metall, vol. 32, 157-169, 1984

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A COUPLED COMPUTATIONAL FRAMEWORK FOR DUCTILE DAMAGE AND FRACTURE Ron H. J. Peerlings, Jesus Mediavilla1 and Marc G. D. Geers Department of Mechanical Engineering, Eindhoven University of Technology PO Box 513, 5600 MB Eindhoven, The Netherlands 1Netherlands Institute for Metals Research PO Box 5008, 2600 GA Delft, The Netherlands [email protected], [email protected], [email protected] Metal forming processes generally introduce a certain amount of damage in the material being formed. Predictions of the damage formation and growth in a series of forming steps may assist in optimising the individual operations and their order. This is particularly true for operations such as cutting and blanking, which rely on the nucleation of damage and cracks in order to separate material. The precise moment and location of crack initiation and the trajectory followed by the crack(s) have an important influence on the quality of the products resulting from these processes. Since the nucleation and growth of cracks may be influenced by damage induced in previous forming steps, simulations require an integral approach towards damage and fracture. For this purpose we have developed a coupled damage–fracture framework, which uses a nonlocal continuum damage approach to model the evolution of material damage and full remeshing to trace the crack growth. In the continuum damage modelling, a scalar damage variable is used which models the influence of micro-defect evolution by degrading the elastic as well as the plastic response of the material in an isotropic fashion. The evolution of this damage variable depends on the plastic strain rate and the stress triaxiality; the latter influence models the well-known asymmetry of ductile damage growth in terms of tensile/compressive hydrostatic stress. As a result of the damage evolution, the local load-bearing capacity of the material at some stage starts to gradually decrease with plastic strain. In order to avoid pathological localisation and mesh-dependence issues due to this strain-softening, a nonlocal formulation of the damage growth is employed which is based on that proposed Geers [1]. This formulation uses an additional partial differential equation – next to the equilibrium equation – to guarantee that the damage process takes place in a finite volume and it thus dissipates a finite amount of energy. It can be shown to introduce a strong nonlocality, similar to the integral formulation used e.g. by Leblond et al. [2], but can be implemented in a more efficient manner using a two-field discretisation [1]. The length scale associated with the nonlocality must be related to the microstructure, e.g. to the average void spacing. Crack initiation is predicted when the continuum damage variable becomes critical somewhere in the domain and the local load-bearing capacity thus is completely exhausted. A transition to a discontinuous description is then made by inserting the crack in the geometry of the problem, fully remeshing the updated problem domain, transferring the relevant history data from the previous mesh, and continuing the analysis on the new mesh. These operations are repeated each time when the damage field becomes critical in front of the crack tip or elsewhere on the domain. The latter situation implies the initiation of a new crack, whereas the former results in the propagation of an existing crack. Crack propagation is thus driven by the growth of damage in a process zone in front of the crack tip and no separate fracture criteria are required (cf. the so-called local approach to fracture). A finite crack growth rate is ensured by the use of a nonlocal damage formulation as outlined above.

R. H. J. Peerlings et al.

412

Computationally, (locally) making the transition from a continuous damage description to a discontinuous, discrete crack is quite demanding. Migrating from one discretisation to the other is facilitated by an Updated Lagrange implementation of the coupled damage–plasticity modelling, cf. [1]. When crack initiation or propagation is predicted, the current problem geometry is extracted from the (updated) finite element discretisation and the new crack segment is inserted in it. A standard remesher is then used to discretise the new problem geometry. Remeshing is also used – even before crack initiation – in order to avoid element distortion and to accurately capture steep damage gradients; a damage-rate error indicator is used for this purpose. Crucial for the numerical stability of the simulations is the proper transfer of state variables from one discretisation to the next. If this transfer is not done carefully, inconsistencies between the different fields may arise, resulting in poor convergence or even divergence of subsequent loading increments. We have found this to be particularly true in the presence of damage and cracks. A dedicated transfer–crack opening algorithm has therefore been developed to ensure robustness of the simulations.

FIGURE 1. Evolution of the ductile damage variable Zp and the resulting crack propagation in a blanking simulation; shown is the zone between punch (top left) and die (bottom right). Fig. 1 shows an application of the coupled ductile damage–fracture framework to blanking of a sheet metal. The diagram shows the distribution of damage, Zp, in the shear zone between punch and die at four subsequent stages of the punch displacement. As the damage evolves, cracks are initiated at the punch and at the die, which subsequently propagate towards each other. Effects which are observed in practice, such as a smaller crack length for smaller clearances between punch and die, are properly captured by the modelling.

References 1.

Geers, M.G.D., Comp. Meth. Appl. Mech. Engng., vol. 193, 3377–3401, 2004.

2.

Leblond, J.-B., Perrin, G., Devaux, J., J. Appl. Mech, vol. 61, 236–242, 1994.

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MARBLE DISCS UNDER DISTRIBUTED LOADING: THEORETICAL, NUMERICAL AND EXPERIMENTAL STUDY Ch. Markides, E. Sarris1, D.N. Pazis, Z. Agioutantis1 and S. K. Kourkoulis Department of Mechanics, National Technical University of Athens, 5, Heroes of Polytechnion Avenue, 157 73 Zografou Campus, Athens, Greece 1Department of Mineral Resources Engineering, Technical University of Crete, 731 00, Hania, Crete [email protected], [email protected] The stress field developed in a cylindrical disc under the influence of a compressive load distributed uniformly along a predefined portion of its periphery, corresponding to an angle 20 (Fig.1), is studied in the present paper analytically, numerically and experimentally. For the theoretical solution of the problem it is assumed that the material of the disc behaves isotropically and linearly elastic. The stresses are calculated taking advantage of the solution introduced by Muskhelishvili for the 1st fundamental plane problem of linear elasticity. For this problem the complex potentials 1 and 1 are obtained through the following equations: f s

M 1 (s ) 

Z (s ) M 1c (s )  \ 1 (s ), Z c (s )

F "

"

i ³  X n  Y n d " 0

(1)

where (Xn+iYn) is the force applied per unit length and unit depth on the loaded portion of the cyclic boundary. For simplification the conformal mapping of the actual disc on the unit radius disc was used (z=()=R), as it is seen in Fig1. This disc represents a simply connected subset of the complex plane within which the complex potentials are holomorphic functions. Using the Cauchy type integrals with holomorphic weight functions together with the well known relations:

FIGURE 1. The geometry of the problem and the definition of symbols

V rr  V --

4 Re ) (z), V --  V rr  2i V r-

2 ª¬ z ) c  z  <  z º¼ e 2i-

(2)

one obtains the analytic expression for the stress tensor components in polar coordinates. As a second step the problem was solved numerically using the Finite Element Method and the MSC.Marc-Mentat code [2]. In order to simulate the tests in a more accurate manner both the specimen and the device used for the application of the load (Fig.2a) were modelled and contacttype elements were introduced for the description of the interface between the marble specimen

Ch. Markides et al.

414

and the metallic grips of the device. Coulomb type friction was assumed with a coefficient of friction which represents a friction angle of about 22 deg (no separation was included).

FIGURE 2: The model of the numerical analysis (a) and the experimental device (b). The experimental procedure included a series of experiments with cylindrical specimens made from Dionysos marble, which were subjected to compression with the aid of the device shown in Fig.2b. Dionysos marble is a white color stone, composed of 98% of calcite and 2% of quartz, muscovite, sericite and chlorite. During the tests the strain components were recorded with the aid of triple strain rosettes positioned at various strategic points of the specimens and using these values the respective stresses were obtained according to the generalized Hooke’s law. Comparing the results of the three approaches it was concluded that both the theoretically and numerically predicted stresses (which are found in excellent mutual agreement) are close enough to the ones of the experimental study. Some discrepancies detected are attributed to the slight nonlinearity which characterizes Dionysos marble.

References 1.

Muskhelishvili, N.I., Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen, The Netherlands, 1963.

2.

Sarris, E., Agioutantis, Z., Kaklis, K. and Kourkoulis, S.K., In Proceedings of the 7th International Workshop on Bifurcation, Instabilities and Degradation in Geomechanics, edited by G.E. Exadaktylos and I. Vardoulakis, Chania, Crete, Greece, 2005, p.84.

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SIMULATION OF THE MECHANICAL BEHAVIOUR OF THE LUMBAR INTERVERTEBRAL DISC M. Satraki, E. A. Magnissalis1, G. Ferentinos2 and S. K. Kourkoulis Department of Mechanics, National Technical University of Athens 5, Heroes of Polytechnion Avenue, 157 73 Zografou Campus, Athens, Greece 1First Orthopaedic Department of the University of Athens, Greece 2Kostas Liontos and associates-channel partner of Ansys-Greece [email protected] The aim of the present paper was the simulation of the mechanical behaviour of the human lumbar intervertebral disc under various types of static and time varying loads. The study is carried out with the aid of the finite element method. The model is built using the commercially distributed finite element program ANSYS 9.0, a powerful software package with great capabilities for simulating nonlinear materials and performing various types of analysis. Concerning the geometry and the mechanical properties of the disc, numerical values from the literature [1] were adopted after suitable elaboration [2,3]. The geometry and the structure of the disc according to the present simulation are shown in Fig.1. The endplates were assumed to behave as linear elastic bodies, the annulus was modeled as laminated composite material consisting of successive transversely isotropic layers while the nucleus was considered as viscoelastic material described by the curve-fitting model.

FIGURE 1. The discretization of the regions of the disc: (a) The cartilaginous vertebral endplates, (b) The annulus fibrosus and (c) The nucleus pulposus. All degrees of freedom were constrained at the lowest surface of the disc (the outer side of the lower endplate) whereas all the nodes of the uppermost surface were enslaved with respect to its central node (where the loading was applied) for the translational degrees of freedom. The final model consisted of 154386 elements, 172662 nodes and 697641 degrees of freedom. The model was subjected to static axial compression and bending as well as to a time varying loading program in an effort to simulate the daily activities of the human disc. Characteristic results are shown in Fig.2, where the deformed shape of the disc is shown in case of bending (Fig.2a) together with the variation of the stress components along a characteristic line (Fig.2b).

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FIGURE 2. The deformed shape of the disc under bending (a) and the distribution of the stress components along the central horizontal line at the mid-height(b). The time-dependent loading programme started with a linearly increasing compressive force for the first hour up to a maximum level of 850 N. The load was kept constant for 16 hours, it was removed gradually (linearly) during the 17th hour and the model was kept load-free for 7 hours. The results of the analysis are shown in Fig.3 together with the respective ones given by Natarajan [4]. The qualitative agreement is good, even for the present relatively simplified model. Preliminary results of sophisticated models, which are under development, support the present analysis.

FIGURE 3. Results of the experimental and numerical study by Natarajan et al. [4] (a) and the respective predictions of the present model for the vertical displacement vs. time (b).

References 1.

Chen C.-S., Cheng C.-K., Liu C.-L., Lo W.-H., Medical Engineering and Physics, vol 23, 483-491, 2001.

2.

Lekhnitskii S. G., Theory of Elasticity of an Anisotropic Elastic Body, Holden-Day Inc, San Francisco, 1963.

3.

Whitney J. M., Riley M. B., “Elastic Properties of Fiber Reinforced Composite Materials, AIAA Journal, vol 4, No 9, 1966.

4.

Natarajan R.N., Williams J.R., Anderson G.J., Computers and structures, vol 81, 835-842, 2003.

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THE PULL-OUT STRENGTH OF TRANSPEDICULAR SCREWS IN POSTERIOR SPINAL FUSION P. Chazistergos, G. Ferentinos2, E. A. Magnissalis1 and S. K. Kourkoulis Department of Mathematics, National Technical University of Athens 5, Heroes of Polytechnion Avenue, 157 73 Zografou Campus, Athens, Greece 1First Orthopaedic Department of university of Athens-Greece. 2Kostas Liantos and associates-channel partner of Ansys-Greece. [email protected] Finite element methods are widely used for the analysis of the failure mechanisms of spinal fixation systems and the stress distribution patterns within vertebral bodies as an important part in clinical evaluation of spinal injuries. For the purpose of fixation and stabilization of the spine using pedicle screws the pull-out strength of the screw is one of the most important factors to be considered. In this study the influence of various factors, related to the contact interface of the bone-screw system, and the geometry of the screw, on the pull-out strength of the fixation screws are explored. Towards this direction a finite element model (FEM) of the human lumbar vertebral bone and transpedicular fixation screw was designed simulating the main characteristics of commercially available fixation pedicle screws. The material of the screw was assumed to be a Ti alloy, which was modeled as linear elastic material with modulus of elasticity E=117 GPa and Poison’s ratio Q =0.3. The respective values for the cancelous bone were E=100 MPa, Q =0.2 while for the cancelous shell were E=780 MPa, Q =0.3 [1-3]. Both the bone and the shell were assumed isotropic and linearly elastic. The analysis was performed using the commercially available software ANSYS8 and the finite model is shown in Fig1.

Fig. 1: Detailed view of the FEM indicating the screw (green) the cancelous bone (purple) and the cortical shell (red). Special attention was paid to the optimum simulation of the bone-screw interface, which defines the load transfer mechanism between the bone and the screw [1]. This FE study included two different scenarios, the first one for the bone-screw interface of the first postoperative weeks, where screw and bone are in simple contact (contact model) and the second one for the fully bonded bone-screw interface, which simulates the long term conditions (bonded model).

P. Chazistergos et al.

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Fig.2: The equivalent stress into the bone plotted along a line that passes from every thread edge for the two cases. During the first part of the study both the contact and the bonded model were tested under constant displacements of 0.005mm at the pull-out direction and the stress distribution patterns on the screw and bone were studied. For the displacement applied of the stresses developed into the bone were mainly below the yield stress, on the contrary, for displacement 0.006mm the yield stress was exceeded. The analysis revealed the different stress distribution mechanisms of the contact and the bonded model. At the bonded model the stress into the bone was distributed along the threads in such a way that no of strong stress concentration appeared. On the contrary for the contact model areas of strong stress concentration into the bone were developed at the edges of the threads. For both models the results of the FE analysis indicated that major role in the process of load bearing is played by the cortical shell. The maximum stresses developed into the vertebral bone are on the interface between the cortical shell and the screw. As one moves deeper the stresses tend to be uniformly distributed in the areas between the threads of the screw. Such an observation leads to the conclusion that the fracture of the bone will first appear on the cortex-screw interface and the deeper surfaces will follow. The pull-out strength required to produce the same displacement to the screws of the two models is of course significantly higher for the bonded model. The second part of the analysis included the parametric study of the dependence of the pull-out force on the geometric characteristics of the screw. The parameters studied were the depth and the angle of the thread. The analysis revealed increase of the pull-out force with the depth and the inclination angle of the threads. The pattern of the stress distribution was considered also, revealing that, higher thread angles result to a more uniform distribution of the stresses relaxing the strain field developed in the bone.

References: 1.

Chen S.-I,. Lin R-M and Chang C-H., Medical engineering & physics, vol (25) 275-282. 2003.

2.

Zhang Q.H, Tan S.H.,. Chou S.M, Journal of biomechanics vol (37),479-485 2004.

3.

Michael A. K. Liebschner,Phd,D.L. kopperdahl,Phd,W.S. Rosenberg,MD,T M. Keaveny, Finite Element Modeling of the Human Thoracolumbar Spine Spine vol(28),number 6,pp 559-565. 2003.

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MECHANICAL BEHAVIOR SIMULATION OF HIP PROSTHESES STRESS DISTRIBUTIONS ANALYSIS M. Kadi, R. Boulahia, K. Azouaoui, N. Ouali, A. Ahmed-benyahia and T. Boukharouba Laboratoire de Mécanique Avancée (LMA), Faculté Génie Mécanique & Génie des Procédés USTHB, Bab-Ezzouar BP. 32, El-Alia, 16111 Alger (Algeria) [email protected] Numerical simulation by finite elements, of in-vitro mechanical behavior of human femur and hip total prosthesis is carried out. Three models are considered: right human femur, femur + cement + prosthesis (pre-clinical model) and prosthesis + cement (laboratory model). The obtained results show that in presence of an implant, the orthopedic cement thickness and the distally from femoral head of the constrained stem in an embedding medium, notably modify the stress fields and the extent of the compressed zones and those in tension in cement. In this work we are interested to the mechanical behavior of a femoral implant. To describe this type of behavior, we choose a simulation based on finite element method. The analysis of the invitro behavior of this type of implant requires: •

determination of the stress distributions generated along the femoral stem, in the cement and along the femur,

•

localization of the hot-point and evaluation of the tensile stress amplitude on the femoral stem; stress responsible of the failure and even sometimes of the rupture,

•

dentification of the compressed zones and those in tension in the orthopedic cement.

The results obtained enabled us to analyze the stress distributions by comparing the localization of the maximum tensile stress designated hereafter by hot-point and the stress amplitudes for the various analyzed cases. Figure (1) gives the stress distributions along the femur (models: a and b) and along the femoral stem (model: b). We observe that the hot-point localization moves from 37mm (Figure 1.b1) to 30mm (Figure 1.b2) along the (z) axis. Therefore, we note a change of the magnitude and distribution of the stresses according to the two models. This can be explained by the fact that for right human femur the load is applied and directly transferred from the head towards the remainder of the femur. On the other hand, in presence of an artificial implant, the load transfer towards the femur is effectuated by deformation of the implant stem, which is in direct contact with the femur; it is the case of an implant cemented in the femur.

Figure 1: Von Mises equivalent stress(b1): right human femur and (b2): femur + cement + implant

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From the stress distributions relating to models (b and c), we noticed that laboratory model (model c) does not reflect reality at different levels (Figure 2): - the stress peaks present very high values, - the stress value decrease rapidly from the constrained section located at 80mm from the loading point, until reaching zero at mid-height of constrained stem. On the other hand, in the case of the pre-clinical model (model b) the stress decreases gradually from a distance equivalent to that of constrain (model c) to change sign from 150mm of load application point (model b), - the laboratory model (model c) over-estimates the real loading.

Figure 2: Variation of tensile stress along the femoral stem for 5 cement thickness (model (c): cement + implant) We can conclude that the presence of a standard cemented hip total prosthesis (model (b): femur + cement + implant) influences notably the distribution of the stresses and the localization of the hot-point especially. The latter moves towards the outside of at least 7mm accompanied by a sensible growth of maximum stress value. This is mainly due to the mode of load transfer. Moreover, the distribution of the stresses in the case of a right human femur (model a) is much more uniform than that generated in the femoral stem, case of the model (b): femur + cement + implant. The latter increases rapidly to reach the peak (maximum value). We note also that the orthopedic cement thickness used to constrain the stem in an embedding medium influences: •

less the stress distribution and the amplitude of these stresses, generated in the femoral stem,

•

the extent of the compressed zones and those in tension at the cross-sections of orthopedic cement.

We can conclude that ISO7206 standard concerns a very large range of hip total prostheses (various forms, various cross sections, various sizes, etc.), which explains the differences in the found results for the models (b and c) and this, although the results given by model (c) which overestimates the real loading. This requires to develop new laboratory models which takes into account the different aspects of pre-clinical loading.

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DBEM ANALYSIS OF AXISYMMETRIC CRACK GROWTH IN A PISTON CROWN T. Lucht Department of Mechanical Engineering, Solid Mechanics Technical University of Denmark 2800 Lyngby, Denmark [email protected] An engineering problem is considered in which an axisymmetric crack initiates from the inside of a piston crown due to both thermal and mechanical load from the combustion as shown in Fig.1. To study the crack propagation the boundary element method is well suited because discretization only occurs at the boundary. Portela et al. [1] developed an analysis for mixed mode crack growth in two dimensions using a single region boundary element method. This method also known as the Dual Boundary Element Method (DBEM) avoids the singularity in the final system of equations by using displacement equations on one surface and traction equations on the other. Two dimensional problems, which include thermal load besides the mechanical load, have been analyzed by Prasad et al. [2]. The DBEM uses displacement and temperature equations on one crack surface and traction and flux equations on the other crack surface. The thermal load is treated as a body force term which normally requires domain integrals. By a Galerkin technique the domain integrals are transformed to boundary integrals, so that all the advantages of the DBEM remain. The stress intensity factors (SIFs) for [1], [2] are computed by the use of the J-integral. Another approach for the evaluation of SIFs for thermoelastic problems by BEM is presented by Mukhopadhyay et al. [3], who use a formulation based on the modified crack closure integral (MCCI). Lacerda L.A. and Wrobel L.C [4] present a DBEM for axisymmetric crack analysis. The SIFs are evaluated by employing the MCCI and very accurate results were obtained, as compared to numerical and analytical results. The method for predicting the direction of the crack growth is adopted from [1], as direction of the crack growth is assumed to be perpendicular to the maximum principal stress.

FIGURE 1. Piston crown loaded with the maximum combustion pressure and steady state temperature field

T. Lucht

422

References 1.

Portela A., Aliabadi M.H. and Rooke D.P., International Journal for Numerical Methods in Engineering, vol. 33, 1269 -1287, 1992

2.

Prasad N.N.V., Aliabadi M.H. and Rooke D.P., International Journal of Fracture, vol. 66, 255-272, 1994

3.

Mukhopadhyay N.K., Maiti S.K., Kakodkar A., Nuclear Engineering and Design, vol. 187, 277–290, 1999

4.

De Lacerda L.A. and Wrobel L.C., International Journal of Fracture, vol. 113, 267-284, 2002

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RESIDUAL SHEAR STRESSES AND KII COMPUTATION W. Cheng and I. Finnie BEAR, Inc. 2216 5th Street Berkeley, CA 74710-2217, USA Department of Mechanical Engineering University of California, Berkeley, CA 94720 USA When calculating stress intensity factors due to residual stresses, the stresses must satisfy equilibrium conditions and boundary conditions. In this case Legendre polynomials of orders 2 and higher are often used for residual normal stresses. For mode II loading it is desirable to have a similar polynomial series for residual shear stresses. Consider a plate of thickness t subjected to shear stress Wxy along the x-direction with origin located at the centerline of the plate and distance x normalized by t/2. Since the shear stress must vanish at free surface, x = r1, Wxy(x) may be expressed as

(1  x) (1  x) J(x)

IJ xy (x)

(1)

where J(x) is a function to be determined, and it must satisfy the force equilibrium

³

1

1

IJ xy (x) dx

³

1

1

(1  x) (1  x) J(x) dx

0

(2)

Clearly, J(x) can be constructed by a set of orthogonal functions with a weight function equal to (1-x)(1+x). In fact, J(x) belongs to the family of Jacobi polynomials, which also include the Legendre polynomials,

J n (x)

wn (  1) n (1  x 2 )  1 (1  x 2 )1  n n wx 2 n!

>

@

(3)

In practice, the nth order polynomial Jn is more conveniently computed by using the recurrence relation J n (2  n)n

(2n  1)(n  1) x J n  1  n(n  1) J n  2

with

J0

1,

J 1 (x)

2x

(4)

It is seen that for J0 = 1, the shear stress corresponds to a parabolic distribution. For Ji with i > 0, the resultant force over the thickness is always zero. It is noticed that Ji consist of a complete set of polynomials. Thus, an arbitrary shear stress may be expressed as n

IJ xy (x)

(1  x)(1  x) ¦ ȕ i J i (x) i 0

(5)

where Ei are amplitude coefficients. From eqn (5) a residual shear stress can be constructed when the first term (i = 0) is omitted. Next, a method based on FEM for KI [1] is extended to compute KII. The displacement, u(a,S), due to a crack of size a in the x-direction at a location S is obtained by introducing a virtual force Q at point S in the direction of u(a,S). Following the approach for KI, we find

W. Cheng and I. Finnie

424

K II (a)

ª w u(a, S) « wa ¬

q º ª w u (a, S) º » »/« wa ¼ ¬ ¼

(6)

uq(a,S)

in which is the displacement in x-direction produced by the virtual force Q. The formulation of eqn (6) not only simplifies the computation of stress intensity factor but also eliminates the need of a crack element near the crack tip. To validate the solution given by eqn (6), KII is obtained for a uniform shear stress and a parabolic shear stress acting on the faces of an edgecracked plate using 108 elements along the crack plane. Very good agreement is found between the computed results and those given in Refs. [2] and [3]. Using the same element mesh, KII for shear stresses i = 1, 2 and 3 given in eqn (5) are obtained and plotted in Fig. 1.

FIGURE 1. Computed KII for shear stresses.

References 1.

Cheng, W. and Finnie, I., Computation of Stress Intensity Factors for a 2-D body from Displacements at an Arbitrary Location, Int. J. of Fracture, vol. 81, 259-267, 1996.

2.

Tada, H., Paris, P. and Irwin, G., The Stress Analysis of Cracks Handbook. Del Research Corp., Hellertown, PA, 1972.

3.

M. Ichikawa and T. Takamatsu, Fracture toughness test for the thin plate under mode II loading. Trans. Japan Soc. Mech. Engrs, vol. 51, 1115-1121, 1985.

2T15. Experimental fracture mechanics

425

QUANTITATIVE INTERPRETATION OF CRACK TIP STRAIN FIELD MEASUREMENTS A. M. Korsunsky Department of Engineering Science University of Oxford, Parks Road, Oxford OX1 3PJ, United Kingdom [email protected] Recent years have witnessed greatly improved availability of experimental measurements of twoand three-dimensional strain and stress distributions, notably through the development of diffraction techniques utilising penetrating radiation, such as high energy X-ray or neutrons (Korsunsky and James, [1]). These methods now provide unprecedented level of detail that brings with it challenges for interpretation. Of particular interest is the question whether conventional fracture mechanics parameters, such as the stress intensity factor, can be extracted from such measurements with confidence. The present paper describes a rational interpretation procedure that can be applied to a set of measurements in order to answer the question posed above.

FIGURE 1. (a) Crack opening strain measured from the Al matrix 311 peak in an Al-SiC cracked bar. (b) LEFM K-field predicition, K=28 MPam. The experimental configuration used to collect strain maps from engineering samples is described, with particular attention being paid to the efficiency of data collection in the energydispersive mode, and the evaluation of macroscopic engineering strain values from the pointwise data. Using these techniques, the characteristic strain variation in the vicinity of the crack front was studied in a nominally single-phase aluminium alloy and in a composite reinforced with SiC particles. The transition was studied between the surface and the bulk of a specimen containing a crack, demonstrating the capability of the technique to extract plane strain information often required for LEFM analysis. The experimental map of matrix strain in a composite was matched to the LEFM prediction to determine the value of the stress intensity factor. The methodology used is related to the variational eigenstrain procedure introduced in the context of residual elastic strain interpretation (Korsunsky et al. [2]). A variational problem was formulated about minimising the sum-of-squares mismatch between the prediction and the measurements, and determining the unknown parameter (SIF) from the resulting linear system of equations. The implications and applications of the newly proposed technique are discussed.

A. M. Korsunsky

426

References 1.

Korsunsky, A.M. and James K.E., In Proceedings of the Third International Conference on Experimental Mechanics, edited by C. Quan, F.S. Chau, A. Asundi, B.S. Wong, C.T. Lim, SPIE Publications, Singapore, 2005, 487-493.

2.

Korsunsky, A.M., Regino G. and Nowell D., In Proceedings of the Sixth European Conference on Residual Stresses, edited by A.M. Dias, J. Pina, A.C. Batista, E. Diogo, TransTech Publications, Coimbra, 2002, 329-334.

2T15. Experimental fracture mechanics

427

MIXED MODE (I+II) STRESS INTENSITY FACTOR MEASUREMENT USING IMAGE CORRELATION A. Shterenlikht, P. López-Crespo1, P. J. Withers, J. R. Yates1 and E. A. Patterson2 Materials Science Centre, Manchester University, Grosvenor Street, Manchester, M1 7HS, UK 1Mechanical Engineering Department, Sheffield University, Mappin Street, Sheffield, S1 3JD, UK 2Mechanical Engineering, Michigan State University, 2555 Engineering Building, East Lansing, MI 48824-1226, USA [email protected] Image correlation is becoming a popular full field optical experimental technique in wide range of applications because it is cheap, fast and easy. It performs equally well at the micro and the macro scales and requires minimal surface preparation. In this work the 2D image correlation technique was used to measure the in-plane displacement fields near the crack tip. Commercial image correlation software DaVis 6.0 by LaVision was employed. This work is a logical continuation of Shterenlikht et al. [1] where the stress intensity factors were calculated from the strain fields, or more precisely, from the first strain invariant. However, the strains calculated using numerical differentiation of the noisy experimental displacement data proved to be of such poor quality, that reliable stress intensity values were not achievable. Accordingly, in this work the stress intensity factors are calculated directly from the experimentally obtained displacement fields without further differentiation. Muskhelishvili’s [2] approach was used to represent the displacements and the stress intensity factors as complex Fourier series of the two analytical functions. The expression for the stress intensity factors was taken from Sih et al. [3]. This leads to a system of equations for the unknown Fourier coefficients. If the number of terms in the series expansion for the analytical functions is smaller than the number of experimental points, then the system is over-determined. If, in addition, the crack tip location is added as another two unknowns, then the system becomes non-linear and can be solved using a genetic algorithm. This method was applied to a centre cracked sample proposed by Otsuka et al. [4]. This sample can be loaded under 7 combinations of mixed mode (I+II) from pure mode I to pure mode II. Fig. 7 shows the sample loaded at 45o to the crack plane. Several samples were machined from 7010 Al alloy with the gauge section thickness varied from 2 to 4 mm and the crack length varied from 20 to 40 mm. The samples were subjected to several combinations of mixed mode (I+II) loading. A combination of the CCD resolution and the image correlation parameters resulted in the displacement resolution of 3.7 Pm/pixel. Results to date indicate that the solution is very sensitive to the crack tip location. If the crack tip is is assumed to be where it appears in the initial image of the specimen surface, then the least squares solution produces the stress intensity factors within 50% of the nominal applied values. If, however, the best fit crack tip position is sought as a part of the solution, the accuracy of the calculated stress intensity factors can be increased significantly. The best results are obtained when the number of the data points is 5-10 times greater than the number of terms in the Fourier series.

A. Shterenlikht et al.

428

At present the data points for the analysis are chosen manually. The efforts are made to automate this process as this would greatly speed up the analysis and make it possible to move to the real time crack monitoring.

FIGURE 1. Experimental setup showing: the specimen clamped by two pairs of loading plates pulled through a pair of loading holes such that the notch is at 45o with the loading axis; the testing machine; and the optical system consisting of a ring light, lenses and a CCD camera.

References 1.

Shterenlikht, A., Días Garrido, F.A., López-Crespo, P., Withers, P.J. and Patterson, E.A., Applied Mechanics and Materials, vol. 1-2, 107-112, 2004.

2.

Muskhelishvili, N.I., Some Basic Problems of the Mathematical Theory of Elasticity, 4 edn, Noordhoff International, Leyden, The Netherlands, 1977.

3.

Sih, G.C., Paris, P.C. and Erdogan, F., Journal of Applied Mechanics, vol. 29, 306-312, 1962.

4.

Otsuka, A., Tohgo, K. and Matsuyama, H., Engineering Fracture Mechanics, vol. 28, 721732, 1987.

2T15. Experimental fracture mechanics

429

FRACTURE OF TURBINE BLADES UNDER SELF-EXCITING MODES C.A. Sciammarella, C. Casavola, L. Lamberti and C. Pappalettere Politecnico di Bari, Dipartimento di Ingegneria Meccanica e Gestionale Viale Japigia 182 – Bari, ITALY [email protected]; [email protected]; [email protected]; [email protected] Failure of blades of a turbo-compressor occurred during operation. Three different typical failure geometries were observed repeatedly. One mode was clearly identifiable as the first bending mode. The other two (Figs. 1-2) could not be directly identified. Experimental mechanics was utilized to identify the frequencies causing the blade fracture. Stroboscopic holographic interferometry analysis of the blades was performed. A quantitative evaluation of the recorded vibration amplitudes was made. An initial image of the blade at rest was recorded. The blade was excited and the image was subtracted continuously from the initial image and the result of the subtraction was observed on a monitor. The illumination was synchronized with the vibrations and four images taken with phase changes of 0o, 90o , 180o, 270o, were recorded. The recorded images were processed with the Holo Moiré Strain AnalyzerTM. The strains were computed and transformed to the local coordinates of the curved blade surface. Using Hooke’s law, stresses were determined. The stress trajectories of the blade surface were utilized to obtain the stress-trajectories (isostatics). The stress trajectories were found to match with the initial crack surface trajectory. With this process it was possible to identify the excitations that caused the blade fracture. This analysis reveals that the initial crack trajectories follow the isostatics thus failing in a similar mode to the maximum-tensile-strain law. This law states that when the larger principal strain reaches a critical value, then cracks perpendicular to the direction of the principal strain will appear. This experimental observation has very important implications from the point of view of multi-axial fatigue behavior. One possible way to understand this behavior is to consider the damage theory of fracture. During the alternating loading caused by the self-induced vibrations the material experiences an accumulative damage patterned by the prevailing stress field. As the cycles accumulate the material initial homogeneity and isotropy cease to exist and weaker regions where defects accumulate are created thus providing a natural path to the crack propagation at a distance long enough before the dynamics of the problem changes due to the crack propagation. The authors believe that any attempt to explain this behavior by arguments based on continuum mechanics of homogeneous and isotropic bodies will not be able to provide an explanation for the documented behavior of the blade. Therefore, this paper presents an analysis of failure mechanisms justifying the experimental evidence. The observed failure appears to be a form of the principal normal stress fracture criterion. In the present case, it provides not the actual applied stress causing failure but gives the geometry of the minimum resistance of the crack path. Hence, an argument based on damage accumulation must be introduced to explain the observed behavior.

430

C.A. Sciammarella et al.

FIGURE 1. Picture of the broken blade in a compound mode. a) Picture of the blade; b) Isostatics showing the actual crack trajectory as measured from broken blade.

FIGURE 2. Picture of the broken blade in a compound mode. a) Picture of the blade; b) Isostatics showing the actual crack trajectory as measured from broken blade.

2T15. Experimental fracture mechanics

431

PREDICTING CRACK ARREST BEHAVIOUR OF STRUCTURAL STEELS USING NEW PROCEDURES C. Gallo, J. A. Alvarez, F. Gutierrez-Solana and J. A. Polanco Department of Materials Science and Engineering. University of Cantabria E. T. S. de Ingenieros de Caminos, C. y P. Av/ Los Castros s/n, 39005, Santander, Spain [email protected], [email protected] The crack arrest philosophy, based on the concept that a brittle crack can be arrested when it emerges from a critical region, is especially useful for such situations where additional safety against unforeseen circumstances is needed. This criterion is included in the R6 procedure [1] as a complementary method against fracture toughness criterion for the assessment of the structural integrity of components containing defects. It is well known that structurally representative crack arrest tests, such as double tension test (DTT) or compact crack arrest (CCA) test, incorporate important limitations that motivates the use of alternative methods [2]. Different types of equations and estimations from small – scale tests (Pellini, Charpy, etc.) are continuously used in order to predict the main properties of crack arrest, which are the crack arrest temperature (CAT) and the crack arrest fracture toughness (KIa). However, not always these results have the required precision or the needed conservative estimation [3]. Various steel grades covering a wide range of strength, toughness levels and industrial applications [4], have been used to investigate alternative methods for obtaining better results and predictions of crack arrest properties. Two different methods have been developed. On the one hand, an intermediate scale crack arrest (ISCA) test has been performed as an additional testing method based upon the existing double tension test [5]. The proposed method provides an alternative approach avoiding the difficult testing procedure and associated high cost. On the other hand, a modified instrumented Charpy test has been developed to obtain a better reproduction of the propagation process using a specimen that presents a modification in the area of initiation by means of a brittle weld metal and electro-discharged machined notch instead of the conventional one, thus minimising the energy required for crack initiation. CAT and KIa results obtained from ISCA, DTT and CCA tests are in agreement, as can be seen in Fig. 1 that represents KIa results obtained as a function of working temperatures for AH32 structural steel [5]. In addition, crack arrest predictions based on Pellini or conventional Charpy tests, sometimes non-conservative, are improved when results from modified Charpy tests are considered, showing closer values to the direct experimental results and maintaining always conservative characteristics, as can be also seen in Fig. 1.

C. Gallo et al.

432

FIGURE 1. KIa results and predictions for AH32 structural steel.

References 1.

“Assessment of the Integrity of Structures Containing Defects”. R6, Revision 4, British Energy. 2001.

2.

Wiesner C. S. and Hayes B., “A Review of Crack Arrest Tests, Models and Applications”, Crack Arrest Concepts for Failure Prevention and Life Extension. Abington publishing. 1996.

3.

Gallo C., Álvarez J. A., Gutiérrez-Solana F. and Polanco J. A., “Predicting Crack Arrest Behaviour of Structural Steels Using Small-Scale Material Characterisation Tests”, From Charpy to Present Impact Testing, ESIS publication 30, Elsevier, pp. 271-278. 2002.

4.

“An Energy Balance Approach For Crack Arrest”. ECSC Sponsored Research Project. Final Report. Contract No. 7210/PR/182. 2003.

5.

Slater S., Gallo C. Álvarez J. A. and Gutiérrez-Solana F., “Development of a New Intermediate Scale Crack Arrest (ISCA) Test”. Engineering Fracture Mechanics, to be published. 2005.

2T15. Experimental fracture mechanics

433

MECHANICAL PROPERTIES OF LARGE PLASTIC-MOLD STEEL BLOOMS. M. Chiarbonello, D. Firrao, R. Gerosa1, A. Ghidini2, M.G. Ienco3, P. Matteis, G. Mortarino, A.Parodi3, M.R. Pinasco3, B. Rivolta1, G. Scavino, G. Silva1, E. Stagno3 and G. Ubertalli Dip. SMIC, Politecnico di Torino, Corso duca degli Abruzzi 24, 10129, Torino, Italy 1Dip. Meccanica, Politecnico di Milano 2Lucchini Sidermeccanica S.p.A. 3Dip. DCCI, Università di Genova Tel. +390115644663, Fax. +390115644699 [email protected]. Molds for plastic automotive components such as bumpers and dashboards are usually machined from large pre-hardened steel blocks. Due to the large size, the blooms undergo a slack quench, so that mixed microstructures occur throughout, both after quench and after the tempering stages. Mechanical properties that are both not homogeneous in the section and everywhere lower (particularly in fracture toughness) than those of correctly quenched and tempered alloy steel specimens are obtained. Successive machining to form molds may be so deep that any of the microstructure occurring at different positions in the original bloom can be found at the mold face, where notch effects are commonly present. Welding, for local shape alterations, may yield further defects. The examined and most commonly used steel grade is 1.2738 (or 40CrMnNiMo8-6-4, ISO 4957 standard), a heat-treatable, 0.4% C, high-hardenability, low-alloy steel. Previous studies have assessed the deleterious influence of the mixed microstructures due to a slack quench upon the toughness of quenched and tempered low alloy steels (Sachs, Sangdahl, and Brown [Sachs, G., Sangdahl, G.S., Brown, W.F., Iron Age, Nov.23, p 59 and Nov. 30, p 76, 1950.], Zhang and Knott [Zhang, X.Z., Knott, J.F., Acta Mater., Vol. 47, No. 12, p 3483, 1999.]); nevertheless, whereas the fracture toughness properties of other tool steels have been known since many years (Baus et. al. [Baus, A., Charbonnier, J.C., Lieurade, H.P., Marandet, B., Roesch, L., Sanz, G., Rev. Met, 72, p 891, 1975.], Mosca, Partendo, and Zocchi [Mosca, E., Partendo, R., Zocchi, R., Met. It., 67, 1975, p 562.], Okorafor [Okorafor, O.E., Mat. Sci. Tecn., 1987, vol. 3, p 118.]), the same property has been analyzed in the present mold steel only recently by Firrao et. al. [Firrao, D., Matteis, P., Scavino, G., Ubertalli, G., Ienco, M.G., Parodi, A., Pinasco, M.R., Stagno, E., Gerosa, R., Rivolta, B., Silva G., Ghidini A., In 2nd Int. Conf. Heat treatment and surface engineering in automotive applications, Riva del Garda (Italy), 2005, paper n. 64, to be published.], who considered the microstructure as obtained in large blooms, and by Firrao, Matteis and Vassallo [D. Firrao, P.Matteis, M. Vassallo, In Proc. 11th Int. Conf. on Fracture, Turin, Italy, 2005, paper n. 5590.], who presented some preliminary results upon re-heat treated specimens. In the present work, fracture toughness and resilience tests have been performed upon 1.2738 steel specimens that were cut from different positions inside a commercial bloom and individually re-heat-treated. The specimens were re-austenitized, gas-quenched at a cooling rate sufficient to achieve a full quench and tempered in two stages at the usual temperatures. Results have been compared with a previously reported [Firrao, D., Matteis, P., Scavino, G., Ubertalli, G., Ienco, M.G., Parodi, A., Pinasco, M.R., Stagno, E., Gerosa, R., Rivolta, B., Silva G., Ghidini A., In 2nd Int. Conf. Heat treatment and surface engineering in automotive applications, Riva del Garda (Italy), 2005, paper n. 64, to be published.] pointwise survey of the as-received microstructures and mechanical properties of the same bloom and of another one (both blooms were actually used to

M. Chiarbonello et al.

434

machine bumper molds); the results of such a survey have been completed in the present work by further Charpy KV and tensile measures performed upon the as-received material. The re-heat treated specimens, despite achieving a higher strength than specimens cut from asreceived blocks, resulted in a significantly higher fracture toughness, albeit with a large dispersion, and in a proportionally improved, albeit not yet satisfying, RT impact energy. The relationship between the mechanical properties, the morphology of the fracture surfaces and the microstructure is discussed, particularly by comparing the as-received and the re-heattreated specimens. The following technological conclusions are proposed: •

the commonly employed production cycle, by performing the heat treatment before the gross machining and upon blooms whose section exceeds the steel hardenability, does not yield the steel’s maximum capabilities in terms of toughness and (to a minor extent) strength;

•

the fracture toughness of the large blooms should be considered a critical characteristic and fracture mechanics verifications, already usual in other fields of industry, should dutifully be applied to the molds' design;

•

alternative classes of steels, whose properties may be less affected by the molds’ dimensions, should be considered for future research and application.

References 1.

Sachs, G., Sangdahl, G.S., Brown, W.F., Iron Age, Nov.23, p 59 and Nov. 30, p 76, 1950.

2.

Zhang, X.Z., Knott, J.F., Acta Mater., Vol. 47, No. 12, p 3483, 1999.

3.

Baus, A., Charbonnier, J.C., Lieurade, H.P., Marandet, B., Roesch, L., Sanz, G., Rev. Met, 72, p 891, 1975.

4.

Mosca, E., Partendo, R., Zocchi, R., Met. It., 67, 1975, p 562.

5.

Okorafor, O.E., Mat. Sci. Tecn., 1987, vol. 3, p 118.

6.

Firrao, D., Matteis, P., Scavino, G., Ubertalli, G., Ienco, M.G., Parodi, A., Pinasco, M.R., Stagno, E., Gerosa, R., Rivolta, B., Silva G., Ghidini A., In 2nd Int. Conf. Heat treatment and surface engineering in automotive applications, Riva del Garda (Italy), 2005, paper n. 64, to be published.

7.

D. Firrao, P.Matteis, M. Vassallo, In Proc. 11th Int. Conf. on Fracture, Turin, Italy, 2005, paper n. 5590.

2T15. Experimental fracture mechanics

435

NON-LINEAR PHOTOELASTIC METHOD FOR STUDY FRACTURE PROBLEMS G. Albaut Novosibirsk State University of Architecture and Civil Engineering (Sibstrin) 113 Leningradskaya st., t. Novosibirsk, 630008, Russia [email protected] In this report the problems of fracture mechanics with geometrical and physical nonlinearity were investigated by non-linear photoelastic methods [1, 2, 3]. The strain changed from -50% till +250% of relative lengthening. Changes in geometry and in thickness of the specimens were taken into consideration. Non-compressible optical-sensitive polyurethane rubber was used for model producing. Main directions of studies 1

Developing of some theoretical aspects of non-linear photoelastic methods.

2

Analysis of rubber models with crack or side notches under tension.

3

The investigation of plastic problems in fracture mechanics by photoelastic coating method.

4

Determination of stresses in plate steel necking under tension by different means.

•

Nonlinear photoelasticity method has been developed to study large elastic and plastic strains changing from -50% till +300% of relative lengthening. Optical-mechanics dependences of the nonlinear photoelasticity were obtained and methods of stress-strain division were elaborated.

•

The investigation of rubber plates and strips with cracks and cuts was executed. Under loading the cracks transformed into ellipse or circle. The stress fields and their concentration coefficients near cracks were obtained.

•

Progressive method of photoelastic coating was developed for the study of problems of technological plasticity under strains till 100% of relative lengthening and more.

•

Some problems of plastic strains were solved for steel and aluminum specimens with catches under large strains. These were the problems of determination of plastic strain kinetics, stress fields near sharp notch tip and other.

•

Important plastic problem of fracture was solved experimental. This was stress-strain distribution in localized necking in thin tensile bar. For example, in Figure 1 and 2, the pictures of interference fringe patterns in coating and epures of principal stresses 1 and 2 in cross section of necking are given. They were obtained different means.

It is noted necessary that non-linear photoelastic method is a basic experimental method for creation of non-linear fracture mechanics.

G. Albaut

436

FIGURE 1. The fringe pictures in the samples with the different kinds of necking.

FIGURE 2 Epures

ı1

and

ı2

in cross section of necking obtained by the five different methods.

Reference 1.

M. Akhmezyanov, G. Albaut, Internatinal Journal of Fracture. vol. 128 (1), 223-231, 2004.

2.

Albaut G.N., In Proceedings of 21st Symposium on experimental mechanics of solids. Jachranca, Poland, 2004, 23-128.

3.

Albaut G.N., Nonlinear photoelasticity in application to problems of fracture mechanics, Novosibirsk: NGASU, Russia, 2002 (in Russian).

2T15. Experimental fracture mechanics

437

FATIGUE CRACK LENGTH MEASUREMENT METHOD WITH AN ION SPUTTERED FILM Gang Deng, Koutarou Nasu1, Tilahun Daniel Redda1 and Tsutomu Nakanishi Faculty of Engineering, University of Miyazaki, Miyazaki, 889-2192, JAPAN 1Graduated School, University of Miyazaki, Miyazaki, 889-2192, JAPAN [email protected] The purpose of this research is to show a simple and high precision method to measure the length of a crack as well as a micro crack using an extremely thin ion sputtered film. An ion sputtered grid film was proposed to measure the crack length for a bending test specimen. Based on the comparisons between the measurement results and that by an optical microscope, the ion sputtered gird film has a very high measurement precision. This method is considered convenient and practicable for the crack length measurement of insulating materials such as ceramics. Meanwhile, an one-piece ion sputtered film was used on a metal bending specimen, the possibility to apply the ion sputtered film in the crack length measurement of a metal machine element was confirmed by the change of the electric resistance of the film with crack growth. Crack length measurement method with a thin grid film One of the simple and practical methods measuring a fatigue crack length is the crack gauge similar to a strain gauge. The electric resistance of the crack gauge will change when the crack grows and snaps the grids of the crack gauge, The crack length can be known by counting the number of the snapped grids. However, the precision of the crack gauge is not so satisfied because of the existence of a plastic film between the grids and crack surface and the thickness of the grid. The snapping position is always behind the crack tip, the measurement error is about 0.1-0.2mm. The effective method to increase the precision of the crack gauge method is removing the plastic film and reducing the thickness of the film and grids. An ion sputtered metal film, the thickness of which is only several tens of nanometer, was formed directly on an acryl surface. And the film was scribed as a grid pattern. Since the length l of a grid is exceedingly larger than its width w, the electric resistance R of a cracked grid can be expressed as following,

R

­ cons tan t ® ¯ f

(a z w) (a w)

(1)

where a is the length of crack in the grid. So, it can be understood that the resistance of a cracked grid changes only at the instant when the crack snaps off the grid. Crack length measurement results A very simple system was used to measure the resistance of the ion sputtered grid film in this research. Figure 1 shows the output voltage corresponding to the resistance of the film during a three-point bend fatigue experiment, in which the snapping instant of grids are identified very clearly. The precision was checked by an optical microscope. Table 1 gives crack length comparisons measured by the film and a optical microscope. From table 1 it can be concluded that the ion sputtered grid film has a very high measurement precision.

438

G. Deng et al.

FIGURE 1. Voltage of a grid pattern film

FIGURE 2. Electric resistance of an one-piece ion sputtered film For the applications of the ion sputtered film on a metal surface, an insulating film between the ion sputtered film and metal surface is necessary. And making the grids without damaging the insulating film is so difficult that an one-piece (no grids) ion sputtered film is desirable. An investigation for the possibility to use an ion sputtered film on a metal surface was performed on a steel three-point bend specimen. Silicon was used as an insulating material. The silicon film was formed by vacuum evaporation, the thickness of which was only one micrometer. The ion sputtered film was made on the silicon film. Figure 2 shows the change of the resistance of the onepiece ion sputtered film during crack propagation in a fatigue test. Although the relationship between the resistance of the film and crack length is waiting for clarified and the researches are planed further into the techniques to make insulating film as well as the details of the measurement method, the possibility to use the ion sputtered film on a metal surface is confirmed.

2T15. Experimental fracture mechanics

439

INDIVIDUAL FRACTURE EVENTS IN CELLULAR FOODS Hannemieke Luyten, Eva M. Castro-Prada, Eefjan Timmerman, Wim Lichtendonk and Ton van Vliet WCFS c/o A&F, PO Box 17, 6700 AA Wageningen, the Netherlands [email protected] Crispy foods like biscuits and breads crusts are cellular solids with relatively large pores of a wide size distribution. Important for the crispy character of such products are both the fracture behaviour and the acoustic emission (Luyten et al. [1]). With aging under deteriorating conditions, these products become less crispy. This is often ascribed to an increase in water activity of the crusts resulting in a change in the mobility of the different molecules, and thus a change in the solid material properties. However, it is difficult to relate directly the change in molecular properties to changes in crispy behaviour. One of the reasons for this is the product morphology, dry crispy foods are irregular built cellular solids. An example is given in Fig. 1.

FIGURE 1. Macro-photography picture of the cellular structure of a Cracotte. Picture by H. Tromp, WCFS. We will present a method to measure the fracture properties and accompanying acoustic emission of the individual fracture events in a crispy cellular solid food. This method allows measuring simultaneously mechanical and acoustical behaviour on deformation at a sample speed of 65 kHz (Luyten et al. 2004 [2]). The number of fracture events was found to be related to the morphology of the crispy food, or more precisely to the number of beams and struts in the cellular solid that fractures. This method enables us to study the solid material behaviour of the crispy foods independently from their morphology. Also it is now possible to relate the molecular behaviour and changes therein to the mechanical behaviour of the whole crust and the perception of crispness. The method makes it also possible to study if the behaviour of crispy foods as perceived with biting and eating is just the sum of a series of single fracture events, or if interference between single fracture events is important for the fracture properties of the whole material. This applies especially to the acoustic emission. Results for the effect of deformation speed and the morphology of the cellular solid food will be presented and discussed. Not only the amount of events (an example of results is given in Fig. 2) is important for the perception of crispness, but also the size

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440

of the peaks, and possible effects of interference on the frequency of the emitted sound in the audible region.

FIGURE 2. The effect of the cutting speed on the number of fracture events in rusk rolls. Results are given for the sound emission (red), force (blue) and the number of cell walls per unit length (green line) that could be distinguished in a picture like Fig. 1.

References 1.

H. Luyten, H., Plijter, J.J. and van Vliet, T., J. Texture Studies, vol. 35, 445-492, 2004.

2.

Luyten, H., Lichtendonk, W., Castro, E.M., Visser, J., and van Vliet, T., In Food Colloids Interactions, Microstructure and Processing, edited by E. Dickinson, Royal Society of Chemistry, Cambridge, 2004, 380-392.

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EXFOLIATION FRACTURE MODE IN HEAVILY DRAWN PEARLITIC STEELS J. Toribio and F. J. Ayaso Department of Materials Engineering, University of Salamanca E.P.S., Campus Viriato, Avda. Requejo 33, 49022 Zamora, Spain Tel: (34-980) 54 50 00, Fax: (34-980) 54 50 02 [email protected] Cold drawing is used to produce prestressing steel wires for prestressed concrete employed in civil engineering construction. Such a manufacturing technique affects the steel microstructure [1-3], thus leading to crack deflection and anisotropic fracture behavior in air atmosphere and aggressive environments [4-6]. This report deals with the strength anisotropy of cold drawn steels and studies, by means of computer-assisted image analysis techniques, a special mode of fracture (called exfoliation fracture throughout this paper) in notched samples of heavily drawn steels supplied from commercial stock. Samples from a real industrial process were used. The manufacturing chain was stopped, and samples of five intermediate stages were extracted, apart from the original material or base product (hot rolled bar: not cold drawn at all) and the final commercial product (prestressing steel wire: heavily cold drawn). Fracture tests under tension loading were performed on axisymmetric notched specimens with a circumferentially-shaped notch. Four notch geometries (cf. Fig. 1) were used with each material, in order to achieve very different stress states in the vicinity of the notch tip and thus very distinct constraint situations.

FIGURE 1. Notched specimens used in the experiments. A significant result related to the notched samples of heavily drawn steels was the anisotropic fracture behavior exhibiting a propagation step oriented quasi-parallel to the wire axis or cold drawing direction (exfoliation fracture) whose aspect is given in Fig. 2 for specimen 5B. The fractographic appearance of the step shown in Fig. 2 resembles cleavage-like fracture. However, it is not conventional cleavage, but a sort of oriented and enlarged cleavage, its orientation being parallel to the wire axis or cold drawing direction, and with river patterns which are detectable in such a direction. In the case of conventional cleavage taking place in pearlitic eutectoid steel, the cleavage facet size is a strong function of the prior austenite grain size, although it is always somewhat less [7]. This size is the zone in which the adjoining pearlite colonies of the grain share a common crystallographic orientation of ferrite. It represents the critical fracture unit and determines the intrinsic toughness in an isotropic pearlitic material. For anisotropic materials such as the cold drawn steels analyzed in this paper, there is a orientation of all microstructural units (and particularly of the pearlitic colonies) in the direction of cold drawing and therefore ferrite lamellae

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change their orientation during cold drawing (as a part of a colony and a set of ferrite/cementite plates which do orientate in the cold drawing direction). Then the new critical fracture unit in the drawn material would be the pearlite colony more than the prior austenite grain, because different pearlite colonies in the same grain follow distinct orientations paths along the manufacturing route. Thus the slender pearlitic colonies become the new microstructural fracture units and determine the size of the enlarged cleavage facets characteristic of the exfoliation fracture in notched samples of heavily drawn steels.

FIGURE 2. Fractographic appearance in specimen 5B.

References 1.

Langford, G., Metall. Trans., vol. 1, 465, 1970.

2.

Embury, J.D. and Fisher, R.M., Acta. Metall., vol. 14, 147, 1966.

3.

Toribio, J. and Ovejero, E., J. Mater. Engng. Perform., vol. 9, 272, 2000.

4.

Toribio, J. and Lancha, A.M., J. Mater. Sci., vol. 31, 6015, 1996.

5.

Cherry, B.W. and Price, S.M., Corros. Sci., vol. 20, 1163, 1980.

6.

Sarafianos, N., J. Mater. Sci. Lett., vol. 8, 1486, 1989.

7.

Park, Y.J. and Bernstein, I.M., Metall. Trans., vol. 10A, 1653, 1979.

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INVESTIGATION OF CRACK CLOSURE BY USING THERMOEASTIC STRESS ANALYSIS L. Marsavina, R. A. Tomlinson1, E. A. Patterson1 and J. R. Yates1 University POLITEHNICA Timisoara, Blvd. M. Viteazul, Nr. 1, Timisoara 300222, RO 1University of Sheffield, Department of Mechanical Engineering, Mappin Street, Sheffield S1 3JD, UK [email protected] A comparison between the effective stress intensity factors obtained using the replicas method and the experimental value of stress intensity factors determined by thermoelastic stress analysis is presented. The investigation was performed on mixed-mode propagated cracks in a biaxial fatigue testing machine using cruciform specimens with 45q cracks. A successive load cycle was used to grow the cracks in order to prevent crack branching during propagation. Thermoelastic data was recorded for a crack half length of 9 mm with an applied mixed-mode ratio 'KI/'KII = 0.45, and the stress intensity factor and closure ratio determined for a range of R ratios. The thermoelastic measurements were performed at lower applied cyclic loads than those used to propagate the crack in order to prevent crack growth and branching during the data acquisition. Surface replicas were used to measure the opening displacements, but not the sliding displacements due to the very small amount of sliding displacement produced by the predominantly mode I applied loads. Three R ratios of R = 0, 0.2 and 0.5 were considered. The measured maximum and minimum opening displacements from the replicas were found to be higher than the theoretical ones. This can be explained by the plastic deformation left by the successive loading cycle used for crack propagation. The comparison between the theoretical, the experimental (obtained by thermoelasticity) and the effective values (obtained from replicas method) of the stress intensity factor 'KI highlights that the experimental results obtained by thermoelasticity represents the driving force for crack propagation, as shown in Fig.1. However, the experimental values of the stress intensity factors obtained by thermoelasticity are below the theoretical ones but above the effective values obtained taking into account the closure using the replicas.

FIGURE 1. Theoretical, experimental and effective variation of the stress intensity factor 'KI against R – ratio, for an applied 'KII/'KI=0.45

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References 1.

Tomlinson R.A., Yates J.R. – An investigation of crack closure uing thermoelasticity, In Proceedings of the 2000 SEM IX International Congress on Experimental Mechanics, Orlando, USA, 2000.

2.

Dulieu – Barton J.M., Fulton M.C., Stanley P. – The analysis of thermoelastic isopahic data from crack tip stress fields, Fatigue Fract. Engng. Mater. Struct., 23, 301 – 313, 2000.

3.

Tomlinson R.A., Marsavina L. - Thermoelastic investigation for fatgue life assessment, Experimental Mechanics, vol. 44, 487 - 494, 2004.

4.

Diaz F.A., Patterson E.A., Tomlinson R.A., Yates J.R. - Measuring stress intensity fctors during fatigue crack growth using thermoelasticity, Fatigue Fract. Engng. Mater. Struct., 27, 571 – 583, 2004.

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FRACTURE TOUGHNESS INVESTIGATIONS OF SEVERE PLASTIC DEFORMED TUNGSTEN ALLOYS M. Faleschini, W. Knabl1 and R. Pippan Erich Schmid Institute for Materials Science, Leoben, Austria 1Plansee AG., Reutte, Austria [email protected] Tungsten and several W-alloys are widely used in high temperature applications. They offer high melting points, low vapour pressures, good thermal conductivity, high erosion resistance and good thermoshock properties. These properties are necessary and essential in future applications like fusion reactors. Like other bcc materials tungsten shows a DBTT (ductile-to-brittle transition temperature) which is very dependent on its processing and impurities. This complicates the machining (turning etc.) of complex parts. Thus a low brittleness is essential and desired. In contrast to usual widely used deforming techniques (rolling, drawing etc.) Severe Plastic Deformation (SPD) is not only capable of increasing the tensile strength and hardness of a material, it also can increase its ductility. HPT is a well-known method to produce fine-grained structures with different degrees of deformation within a single specimen [1, 2]. This procedure was therefore used to deform three different rolled tungsten alloys, pure tungsten (W), a lanthanum-oxide dispersion strengthened tungsten alloy ('WL10', W 1La2O3) and a potassium doped tungsten alloy ('WVM', W 0.005K). These deformed specimens were subjected to fracture toughness tests at room temperature. The HPT specimens were also heat treated in a vacuum furnace to determine its influence on microstructural properties. The High Pressure Torsion straining is performed at 400°C with an inductive heating unit. The pill-shaped specimen (6mm diameter) is inserted in between two hardmetal-anvils which are pressed together. One of the anvils is rotated under a high hydrostatic pressure of several GPa. This leads to a continuous straining of the specimen. The microstructure of the material is strongly influenced by this process, resulting in a high dislocation density and grain sizes in the region of 200-400 nm. EBSD-scans reveal information of orientation relations of grains, proving that the misorientation is increased by HPT. The thermal stability of high pressure strained tungsten alloys is also investigated. This is done by a heat treatment in a vacuum furnace (p~10-6 mbar) at 800, 1000 and 1200°C for one hour. Pure tungsten is nearly fully recrystallized after one hour at 1200°C, also losing its increased material properties after SPD. In contrast to that, the potassium doped WVM still has a grain size of approximately 500nm and remarkable microhardness. This is due to the fact that the potassium bubbles impede grain boundary movement at high temperatures [3] and thus increase thermal/ creep stability. The recrystallization behaviour of severe plastic deformed materials thus is another important property which has been investigated, especially because the generated high angle grain boundaries have high mobilities and low activation energies [4]. Fracture toughness tests have been performed at room temperature. Therefor small SENBspecimens were prepared from HPT-deformed tungsten alloys. Fig.1 shows the measured values vs. applied true strain.

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Fig. 1: Facture toughness vs. applied true strain for three different tungsten alloys.

References 1.

R. Z. Valiev, R. K. Islamgaliev, I. V. Alexandrov, Progress in Mat. Science 45, 103-189, 2000

2.

A. Vorhauer, R. Pippan, Scripta Materialia 51, 921-925, 2004

3.

E. Pink, L. Bartha, The metallurgy of doped non-sag tungsten, Elsevier Appl. Sci. (1989)

4.

F. J. Humphreys, M. Hatherly, Recrystallization and Related Annealing Phenomena, Pergamon 2002.

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PHOTOELASTIC ANALYSIS OF MODE I STRESS INTENSITY FACTOR IN BEAMS WITH ANGULAR NOTCHES M. Tabanyukhova and V. Pangaev Novosibirsk State University of Architecture and Civil Engineering (Sibstrin) 630008, h. 113, st. Leningradskaja, t. Novosibirsk, Russia [email protected] The values of Mode I of stress intensity factors (SIF) were analyzed in the case of normal crack opening depending on angle parameter in the elements having angle notches. The data were obtained both from numerical and polarization-optical experiments with the use of the simplified procedure of the determination of Mode I SIF for angle notches considering the symmetry of investigated models. Result compared with work [1]. 1. Basic dependences The generalized Mode I SIF KI in that case may be determined from a dependence obtained on the basis of Williams’ asymptotic solution [2]. K

V x (0, y ) I

y O1  1

2S

,

(1)

where x(0,y) - stress on a symmetry axis, y - coordinate of a considered point, (1-1) - the degree of a singularity. Procedure of its determination was explained in work [3]. Too Mode I SIF was determined by formular of classical fracture mechanics (constant value of a singularity degree -0.5) as

KI

V

2S r .

(2)

2. Beams with the angle notch The determination of the generalized Mode I SIF was executed under three-dot bending of the beams loosened by an angle notch in the tension zone with considering of the modified singularity degree (1-1) (1) and with halp of dependence for classical crack (2). Angle parameters varied from 00 up to 1500. The model geometry and the loading scheme were given in Figure 1. At first the field of dimensionless stresses was found by the finite element method. Then two complete sets of beam models were studied by polarization-optical method by step-by-step loading. The depth of the notch angle in the first batch was made l=0,5b (as in case of numerical experiment), in the second it was l=0,25b. Photos of interference fringe patterns were obtained. The fragments from some of them were shown in Figure 1. In result the stress values were obtained near notches’ tops by two means - numeerical and experimental. Mode I SIF were calculated on the basis of these stresses with halp of dependence (1) and (2). It is possible to note that all values Mode I SIF practically coincided at the notch angles from 00 up to 600, but further they were different.

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FIGURE 1. Fragments of interference fringe pattens in beam under thee-got bending

Reference 1.

Srinivasa Murthy N., Ragnavendra Rao P, Photoelastic parametric studies of mode I stress intensity factors, Experimental Fracture Mechanics,Pergamon Press Ltd. V.22, 3, 527-532, 1985.

2.

Williams M. L., Stress singularities resulting from various boundary conditions in angular corners of plates in extension, J. Appl. Mech. V.74, 526-528, 1952.

3.

Albaut G.N., Kurguzov V.D., Kurbanov . B., Tabanyukhova M.V., Kharinova N.V., J.Higher Educational establishments. Building, Novosibirsk, Russia, 9, 92-98, 2004.

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FULL-SCALE EXPERIMENTAL INVESTIGATIONS ON PRESSURE TUBES RUPTURE OF RBMK Natalya Yu. Medvedeva, Andrey V. Andreev, Sergey V. Timkin, Igor A. Peshkov, Vladislav N. Zhilko, Dmitri Ye. Martsiniouk and Olga A. Poshtovaya Federal State Unitary Enterprise “Electrogorsk Research and Engineering Center on Nuclear Power Plants Safety” Bezymyannaya St. 6, 142530, Moscow region, Electrogorsk, Russia [email protected], [email protected], [email protected] The investigation is concerned with the processes occurring in the RBMK reactor space in the course of a fuel channel (FC) rupture. Experimental approach to evaluate the risk of multiple FCs rupture as a result of escaping coolant effect is presented. Now three incidents related to fuel channel rupture occurred at different NPP units. The most severe scenario of this accident is a sequential breaking of several FCs (i.e. multiple pressure tube rupture, or MPTR) as a chain reaction following a single channel rupture. Since the problem is complex and interdisciplinary (mechanical, thermo-hydraulic, and fluidstructure interaction processes), the analysis of MPTR requires performing of a series of theoretical and experimental studies of separate physical processes running in the RBMK reactor. The experimental rigs concerned the MPTR have been designed and constructed at Electrogorsk Research & Engineering Center, Russia. Full-scale TKR test facility was designed and constructed as a main part of the investigation project. The TKR tested core – a module of the reactor stack (MRS), is a full-scale fragment of the RBMK-100 reactor space from the support plate of upper metal structure to the safety plate of the bottom metal structure with a graphite stack with FC tubes of 5u5 cells (25 graphite columns with FC). The fragment is surrounded with a series of graphite columns with reflector cooling channels (RCC). General view of the TKR test facility is represented in Fig. 1. The TKR test facility is intended for the study of an emergency single fuel channel rupture and its consequences, in particular: - measurement of pressure and temperatures in the graphite stack; - measurement of bending of the graphite columns; - measurement of strains of the channel tubes; - assessment of parameters of fracture of the graphite blocks and channel tube (see Fig. 2). Since the TKR test facility contains only 45 of 2488 channels of the RBMK reactor, experimental solution of the MPTR was based on experimental simulation of the worst case scenario as the most dangerous accident progression from point of view of sequential FC rupture. The wide range of experimental tests performed in the small-scale test facilities, theoretical investigations, and the preparatory tests in the TKR test facility made it possible to define and realize worst case scenario in the TKR test facility.

450

N. Y. Medvedeva et al.

FIGURE 1. Module of the reactor stack of the full-scale TKR test facility.

FIGURE 2. View of the fracture center after the full-scale test at the TKR test facility.

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STUDY OF FRACTURE MECHANISM OF COMPOSITE MATERIAL BUILDINGS BY PHOTOELASTICITY AND PHOTOELASITC COATING METHODS Olga Ivanova, Galina Albaut, Valerij Mitasov, Vladimir Nikiforovskij and Marina Tabanyukhova Novosibirsk State University of Architecture and Civil Engineering (Sibstrin) 113 Leningradskaya st., t. Novosibirsk, 630008, Russia [email protected] Two types of problems have been solved in the present investigations. The influence of cracks on the stress under loading in tensile zone of reinforced beam models has been investigated by photoelasticity. The stress fields and their concentration coefficients have been obtained in this case. Another of solved problems is a study of fracture mechanisms in composite material elements by photoelastic coating method. First problem Beam with one or two naturally developing cracks were investigated to their destruction. Some results of the problems solved were given in figure 1 here. The models of beams were made from optical sensitive materials. This was an epoxy resin or plexiglass. The models were reinforced by the wire with the reinforcement coefficient equal to 0.01. During the process of the model manufacture thin notches were filled with epoxy glue. The beam models were loaded by pure bend and the cracks in the places of a glued notch appeared. In figure 1 the isochromatic fringe patterns were given. They represent the curves with principal stress differences of equal level. Epures of the normal stress x, y and the shear stress xy were obtained by means of numerical integrating of the equilibrium equation for the plane problem. While analyzing these distributions one may note that the engineering hypotheses of bending theory are not correct near the cracks. Second problem The fracture mechanism of elements from natural materials was studied with the help of photoelastic coating method. Several results of the investigation were given in figure 2. Here fracture schemes were calculated by the finite element method numerically. The first scheme was obtained from the fracture by the shear stress and the second one was obtained by the compression stresses. The calculation was checked by the photoelastic coating method experimentally. Several photos were given in figure 2. The comparison of results showed that the fracture of the studied element was executed by the shear stress but not the compression stress.

452

O. Ivanova et al.

FIGURE 1. Isochromatic fringe patterns and stress epures in reinforced beam models with one or two cracks

FIGURE 2. Fracture schemes of concrete cube obtained by numerical method and isochromatic fringe patterns in photoelastic coating

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FRACTURE ENERGY IN MODE I AND MODE II OF TEXTILE REINFORCED WOOD R. Putzger and P. Haller Institute for Steel- and Wood Construction, Technische Universität Dresden Eisenstuckstraße 33 NB, 01069 Dresden, Germany [email protected] Textile reinforcement in timber constructions enables substantial improvement of load bearing behaviour. Failures in wood due to insufficient strength perpendicular to grain caused by anisotropy are reduced. Durability of especially unprotected outdoor applications is increased, too. The laminate used for reinforcement consists of a textile which is embedded in a matrix and connected to the wood by an interface according to figure 1. These constituent parts are exposed to several physical and chemical factors. Only a good compound allow to efficiently use high strengths of synthetical fibres or heavy textiles. We aim at guaranteeing high bond strength for a long period of time. Two methods are used for assessment of wood-textile compound, see figure 1 – right. First, peel force is determined according to ASTM D 3167 and serves for comparison of the influence of the environmental factors mainly among each other. Secondly, fracture mechanics deliver a characteristic bond value independent of specimen geometry. The fracture energy Gf as a measure for the quality of bond strength can be used in analysis and design later. Two different specimens were tested in the laboratory by means of fracture mechanics. The DCB-cleavage specimen is used in a tensile test and fails in mode I because of delamination. Unlike this, the TENF-specimen is examined in a three point bending test and fails in mode II shear failure. Results of all fracture tests published in this paper follow the recommendation of RILEM TC133. The tests confirmed stable crack growth also in glued joints for intermediate textile layers.

FIGURE 1. Factors of influence on bond strength and test methods used.

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TABLE 1. Experimental results of fracture tests (COV in %) and load vs. deflection curve.

The results of fracture mechanics tests are summarised in table 1. By means of textile reinforcement it was possible to increase fracture energy by approximately 40 % in mode I and by 25 % in mode II respectively. An exception is the laminate of epoxy resin and aramid fabric. In this case fracture energy in mode II was lower in comparison to specimens made of solid wood. Tests series with polyester resin matrix resulted in higher fracture energy than the one where an epoxy matrix was used. This general tendency was confirmed also by evaluation of peel tests, Haller [1]. An influence of textile with respect to textile weight or structure could not be observed. Further on, table 1 contains mean values of ultimate load of each test series. The fracture energies were based on a small average sample number with a partially high coefficient of variation. This has to be considered in the interpretation of the results. The fracture mechanics investigations have confirmed a stable crack growth as well for intermediate textile layers. But for successful testing a suitable wood selection is of great importance. The tests provided a basis for using fracture energy Gf as a measure for the quality of compound. Based on peel tests, the expectations of good bond strength of textile reinforced wood were met and confirmed by high values of fracture energy. As result of strengthening the fracture energy could significantly be improved compared as to solid wood.

References 1.

Haller, P.; Putzger, R.; Curbach, M. (Editor). In: Proceedings of the 2nd Colloquium on Textile Reinforced Structures (CTRS2), Technische Universität Dresden: Eigenverlag, 2003, S. 247-258

2.

Aicher, S.; Boström, L.; Gierl, M.; Kretschmann, D.; Valentin, G. In: RILEM TC 133 Report, SP Swedish National Testing and Research Institute, Building Technology, SPReport 1997: 13. Boras, 1997

3.

Aicher, S.; Gustafsson, P. J. (Editor); Haller, P.; Petersson, H. In: A report of RILEM TC-133. Structural Mechanics, Lund University, Sweden, 2002

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MEASUREMENT BASED PERFORMANCE PREDICTION OF THE EUROPABRUCKE AGAINST TRAFFIC LOADING R. Veit and H. Wenzel Vienna Consulting Engineers Hadikgasse 60, A-1140 Vienna, Austria [email protected], [email protected] Bridges are ageing and traffic is growing, which creates a demand for accurate fatigue life assessment. The Europabrücke – a well known Austrian steel bridge near Innsbruck, opened in 1963 - is one of the main alpine north-south routes for urban and freight traffic. A long-term preoccupation of VCE with BRIMOS£ (BRIdge MOnitoring System) on the Europabrücke (since 1997) and the assessed prevailing vibration intensities with regard to fatigue problems and possible damage led to the installation of a permanent measuring system in 2003. Today’s monitoring abilities enable us to measure performance precisely. High-precision sensor data of accelerations and displacements in dependence of separately registered wind and temperature data and their implementation into analytical calculation provide the possibility to realize lifetime considerations, which are of eminent importance for bridge operators. The superior goal, which is to be shown in this paper, is to determine the relation between the randomly induced traffic loading (vehicles per day) and the fatigue-relevant, dynamic response of the structure, exclusively caused by freight traffic. As life-time predictions in modern standards depend on lots of assumptions, the emphasis is to replace those premises – referring to loading - by measurements. In that context the present work is focused on three levels: •

Global behaviour in dependence of all relevant loading cases (Based on laser-displacement measurement)

•

Cross-sectional behaviour under special consideration of the cantilever regions (Based on laser-calibrated acceleration measurement – Fig.1)

•

Local systems analysing the interaction between tyres and the beam-slab connections (Based on inductive displacement transducers)

In each of these levels of analysis the consumption of the structure’s overall-capacity per year is to be determined. An indispensable requirement is to reduce the permanent monitoring system’s data by Rainflow-Counting, describing the remaining fatigue-relevant recurring response-cycles in different categories of intensity and occurrence. As the present lifetime calculations are performed in terms of stresses by means of damage-accumulation, global and local Finite Element Analysis is necessary for the transition of measurment data (Nominal & Structural Stresses). The detailed knowledge about the progression of the prevailing traffic from the very beginning up to these days and the implementation of published future trend studies can be used for an extrapolation of the measured impact for the whole lifetime. As this research work tries to encourage in-situ measurements instead of “design situations”, it is also aspired to analyse the consequence of statistical scatter in each level of impact as well as on fatigue resistance.

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FIGURE 1. Reproduced cantilever displacements (blue) vs. directly measured ones (red).

References 1.

Veit R., Wenzel H., Fink J.: Measurement data based lifetime-estimation of the Europabrücke due to traffic loading - a three level approach, In Proceedings of the 58th International Conference of International Institute of Welding, Prague, July 2005

2.

Haibach E.: Betriebsfestigkeit – Verfahren und Daten zur Bauteilberechnung, VDI-Verlag, Düsseldorf, 2002.

3.

Niemi E.: Structural Stress Approach to Fatigue Analysis of Welded Components Designer’s Guide, IIW doc. XIII-1819-00/XV1090-01

4.

ESDEP - European Steel Design Education Program: WG12 Fatigue, Lecture Notes, Katholieke Universiteit Leuven

5.

Wenzel H., Pichler D.: Ambient Vibration Monitoring, J. Wiley and Sons Ltd, Chichester England, 2005, ISBN 0470024305

6.

Spaethe G.: Die Sicherheit tragender Baukonstruktionen, 2nd Edition, Springer-Verlag, Wien, New York, 1992

7.

Bronstein I., Semendjajew K.A.: Taschenbuch der Mathematik, 5th Edition, Harri DeutschVerlag, Frankfurt am Main, 2001

8.

Dreßler K., Gründer B., Hack M., Köttgen V.B.: Extrapolation of Rainflow Matrices, SAE Technical Paper No. 960569 (1996)

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THE EFFECT OF THE LABORATORY SPECIMEN ON FATIGUE CRACK GROWTH RATE S. C. Forth, W. M. Johnston and B. R. Seshadri NASA Langley Research Center Lockheed Martin Corporation, West Reid Street, MS 188E, Hampton, VA 23681 USA National Institute of Aerospace [email protected] One of the responses of a material to extreme forces, such as stress, temperature, etc., is to crack. A crack appears when the material reaches a limit in its capability to absorb damage and fails. Sometimes, a crack will grow under a periodically applied condition, such as cyclic loading, that are well below the stresses required to fail the material, denoted fatigue crack growth. Over the past thirty years, laboratory experiments have been devised to develop fatigue crack growth rate data that is representative of the material response. The crack growth rate data generated in the laboratory is then used to predict the safe operating envelope of a structure. The ability to interrelate laboratory data and structural response is called similitude. In essence, a nondimensional term, called the stress intensity factor, was developed that includes the applied stresses, crack size and geometric configuration. The stress intensity factor is then directly related to the rate at which cracks propagate in a material, resulting in the material property of fatigue crack growth response. Standardized specimen configurations have been developed for laboratory testing to generate crack growth rate data that supports similitude of the stress intensity factor solution. Recent research into the fatigue crack growth threshold has exposed some limitations in the standards [1, 2]. The typical approach to generate the threshold at a specific stress-ratio is accomplished by reducing both the maximum and minimum applied load at a specific rate until the crack arrests. Pippan, et al. [3], Smith and Piascik [4 ] and Forth, et al. [5] have all postulated that this method may produce results that are not representative of the material behaviour. Furthermore, Liknes and Stephens [6] and Garr and Hresko [7] have suggested that specimen configurations contained within the standards can have an effect on threshold. The middle crack tension, compact tension and eccentrically loaded edge-crack tension specimen configurations are widely used for generating fatigue crack growth rate data [8]. In this proposed paper, the authors present: (1) laboratory fatigue crack growth rate test data of a high strength steel alloy that shows specimen configuration, width and thickness effects (Fig. 1); (2) three-dimensional finite element analyses of each of the specimens identifying the differences on stress intensity solution; and (3) propose modifications to the laboratory testing standards to support similitude of the stress intensity factor solution.

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Figure 1. Crack growth rate versus stress intensity factor range data for different specimen configurations.

References 1.

Tabernig, B., Powell, P. and Pippan, R., Fatigue Crack Growth Thresholds, Endurance Limits, and Design, ASTM STP 1372, ASTM, 96-108, 2000.

2.

Newman, J.C., Jr., Fatigue Crack Growth Thresholds, Endurance Limits, and Design, ASTM STP 1372, ASTM, 227-251, 2000.

3.

Pippan, R., Stuwe, H.P. and Golos, K., International Journal of Fatigue, 16, 579-582, 1994.

4.

Smith, S.W. and R.S. Piascik, Fatigue Crack Growth Thresholds, Endurance Limits, and Design, ASTM STP 1372, ASTM, 109-122, 2000.

5.

Forth, S.C., Newman, Jr., J.C. and Forman, R.G., International Journal of Fatigue, 25, 1, 9-15, 2003.

6.

Liknes, H.O. and Stephens, R.R., Fatigue Crack Growth Thresholds, Endurance Limits, and Design, ASTM STP 1372, ASTM, 175-191, 2000.

7.

Garr, K.R. and Hresko, G.C., Fatigue Crack Growth Thresholds, Endurance Limits, and Design, ASTM STP 1372, ASTM, 155-174, 2000.

8.

Liaw, P.K., Peck, M.G. and Rudd, G.E., Engineering Fracture Mechanics, 43, 379-400, 1992.

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VALIDITY OF THE CAUSTICS METHOD FOR PLATES WITH CIRCULAR HOLE P. Tsirigas, G. Kontos1, D. N. Pazis, S. K. Kourkoulis and Z. Agioutantis1 Department of Mechanics, National Technical University of Athens 5, Heroes of Polytechnion Avenue, 157 73 Zografou Campus, Athens, Greece 1Department of Mineral Resources Engineering, Technical University of Crete, 731 00, Hania, Crete [email protected], [email protected] The method of caustics introduced by Manogg [1] and developed further by Theocaris [2] is nowadays considered as a very useful and flexible tool for the investigation of the stress concentration and the stress intensity factors for the case of structures with geometrical discontinuities. However, a number of questions regarding the range of validity of the method remain unanswered, in spite of the intensive research carried out. The most crucial points are related to the influence of the plastic zones developed in the immediate vicinity of the singular points [3], to the triaxiality [4,5] and to the size of the discontinuities especially in the case of holes [6]. In the present paper the range of validity of the method is studied for the case of a plate of finite dimensions with a central circular hole. The study was carried out experimentally. In addition the Finite Elements Method was employed for the determination of the stress and strain distributions within the plate. The specimens used for the experimental part of the study were made from PMMA. They were rectangular plates with dimensions Height x Width x Thickness equal to 300 x 120 x 2 mm3. A central hole was drilled adopting a novel procedure, in order to avoid the development of residual stresses. The diameter of the hole varied between 2mm and 12mm. The specimens were subjected to monotonic, quasi-static tensile load up to their final failure. The typical optical arrangement described by Kalthoff [7] was adopted for the realization of caustics. During the loading process the caustics developed from the light beams reflected at the front and rear sides of the specimens as well as those developed from the light beams transmitted through the specimens were photographed at predefined load steps. Then measuring the maximum diameter Dmax of the caustics (using suitable software for the minimization of the experimental errors) it was possible to determine the stress applied by the well-known formula:

p

1

1

12 O 3m H z 0 c r ,t ,f

§ D m ax 2 ¨ R d ¨© 2, 67

· ¸¸ ¹

4

(1)

where p is the stress applied at infinity, is a constant equal to 1 for the front reflection and equal to 2 for the rear reflection and the transmission case, R is the diameter of the hole, d is the thickness of the plate and cr,t,f denote the stress-optical constants for rear reflection, transmission and front reflection, respectively. In the above equation m is the magnification factor of the optical arrangement equal to (z0-zi)/zi, where zo is the distance between the specimen and the screen and zi is the distance between the focal point of the convergent light beam and the specimen. Using the above equation and the load recorded from the loading frame it was possible to ( V c a u s tic / V a c tu a l ) , i.e. the ratio of the stress determine for each load step the ratio e predicted by the caustics over the actually applied stress. The variation of e versus the load level is

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plotted in Fig.1 for a characteristic test. It is clearly seen that the results obtained from the method of caustics approximate the value of the actual load in a satisfactory manner for a well-defined interval of the load range, marked with two red vertical lines. The agreement becomes poor outside this interval and for loads approaching the fracture load the discrepancies increase dramatically.

FIGURE 1. The ratio of the theoretical over the experimental stress versus the applied load Taking advantage of the experimentally determined yield stress of the material used and the stress variation in the specimens as obtained from the numerical analysis it was concluded that the upper limit is dictated by the development of the plastic zones around the hole. Concerning the lower limit of the validity interval it was concluded that it is dictated by the size of the initial curve of the caustic. Indeed for specific combinations of the diameter of the hole and the load level it is possible that the initial curve of the caustic falls within the hole of the specimen rendering the results obtained from the study of the respective caustics erroneous.

References 1.

Manogg, P., Anwendung der Schattenoptik zur Untersuchungs des Zerreissvongangs von Platten, Dissertation, Freiburg, Germany, 1964.

2.

Theocaris, P.S., J. Appl. Mechanics, vol. 37, 409-415, 1970.

3.

Konsta-Gdoutos, M. and Gdoutos, E.E., Engng. Fract. Mechanics, vol. 42, 251-263, 1992.

4.

Meletis E.I., Huang W. and Gdoutos E.E., Engng. Fract. Mechanics, vol. 39, 875-885, 1991.

5.

Rosakis, A.J. and Ravi-Chandar, K., Int. J. Solids Structures, vol. 22, 121-134, 1986.

6.

Tsirigas, P., Stress concentration around a hole in a plate of finite dimensions: Numerical and experimental study, Master Thesis, Nat. Techn. Univ. Athens, Greece, 2005 (In Greek).

7.

Kalthoff, J.F., Handbook on Experimental Mechanics, edited by A.S. Kobayashi, VCH, 1993, 407-476.

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AN ENHANCED NORMALIZATION METHOD FOR DYNAMIC FRACTURE TOUGHNESS TESTING S. M. Graham and D. J. Stiles Assistant Professor United States Naval Academy, 590 Holloway Rd, Annapolis, MD 21402 Naval Surface Warfare Center, Carderock Division, 9500 MacArthur Blvd, West Bethesda, MD 20817 [email protected], [email protected] Fracture toughness testing of ductile materials can be difficult in situations where it is not possible to measure crack extension during the test, such as under high rate loading or in aggressive environments. In these situations, an alternative method of inferring crack extension must be used to generate the tearing resistance curve, and thereby determine ductile crack initiation. ASTM test method E1820-01 uses the Normalization method to generate the plasticity function for the specimen, which can then be used to calculate crack extension. This method relies heavily on accurate measurement of the load, displacement and crack length at the end of test. These measurements are used to generate a point on the normalized load-displacement plot, known as the “anchor point”. If a test ends with unstable crack extension, the anchor point cannot be determined and the method cannot be applied. If there is a large amount of crack extension in a test, the uncertainty in the derived plasticity function increases, which can lead to non-conservative J-R curves. An alternative approach that can be used to reduce the dependency on the anchor point is the Compliance Ratio (CR) method. This method uses a quasi-static test with unloading compliance to generate a load-displacement record with no crack extension, or “key curve”. Once this key curve is obtained, it can be scaled to account for the effect of loading rate. The specimen compliance at any point in a dynamic test record is determined by comparing the key curve with the actual load at the same displacement, and from this the crack extension can be determined. There are problems with this approach when the quasi-static key curve does not match the dynamic test record early in the test where blunting transitions to ductile tearing. Fortunately, there is a way to overcome the problems associated with each of these methods and draw from the advantages of each. The basic premise behind the proposed Enhanced Normalization (EN) method is that the CR method key curve is reasonably accurate beyond the “knee” of the curve where the specimen is undergoing stable ductile crack extension, which is precisely where the Normalization method provides the least information about the plasticity function. By using a quasi-static test to generate the plasticity function beyond initiation, and then scaling it to account for rate effects, the region beyond the tangency point can be filled in and the dependence on the anchor point can be removed. The proposed Enhanced Normalization method is used to analyze a series of dynamic fracture toughness tests of ASTM A336, Grade F22, forged steel. This test program included 3 quasi-static tests and 6 dynamic tests, all conducted at -2 °C (28 °F). The dynamic tests were conducted in a drop tower with an impact velocity of 3.5 m/s and impact energy of 2175 J. The measured compliances from the quasi-static test of specimen S1 were used to calculate crack lengths and to generate the normalized load-displacement curve. Next, the dynamic data from specimen D4 was normalized using the initial crack length with estimated blunting. The ratio of the maximum loads in the dynamic and quasi-static tests was used as an initial estimate of the scaling ratio for the quasi-static plasticity curve. The actual scale value was varied to obtain a good visual match between the dynamic and quasi-static curves in the vicinity of the “knee”. The two normalized curves are plotted together in Figure 1. The anchor point is shown for comparison with the quasi-

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S. M. Graham and D. J. Stiles

static plasticity curve, however, it is not used in the subsequent analysis. The point of divergence between the two curves was estimated and used to establish the dividing line. All points on the dynamic plasticity curve to the right of this line, and all quasi-static points to the left were eliminated, thereby leaving the combined plasticity curve. This curve was then used to calculate crack lengths for the dynamic test by determining the crack length that would bring a data point onto an interpolated spline curve. The resulting J-R curve is shown in Figure 2. There is very little scatter in crack extensions along the blunting line and the initiation of ductile tearing is clearly visible. This J-R curve is a big improvement over what was obtained using the CR method, and is more conservative than what was obtained with straight Normalization.

Figure 1. Dynamic and Quasi-static plasticity curves.

Figure 2. J-R curve obtained from Enhanced Normalization Method

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THE POTENTIAL DROP TECHNIQUE FOR MEASURING CRACK GROWTH IN SHEAR V. Spitas and P. Michelis Laboratory of Applied Mechanics, Technical University of Crete University Campus, 74100 Chania, GREECE Institute of Mechanics of Materials and Geostructures S. A. 22 Askiton Str., 15236 Penteli, GREECE [email protected] The classical potential drop technique [1] is used to measure a growing crack in a conductive material and has been a standard methodology for measuring “open” cracks, i.e. those propagating in predominantly mode I (tension). In tension the electrical modeling is rather straightforward since a known electrical current passes through the body of the tensile specimen and the developed voltage due to the constantly changing resistance as the crack propagates is measured at two electrodes fixed at both sides of the developing crack. In mode II (in-plane shear) however there is little data available in the existing literature as the issue of generating a pure and uniform in-plane shear stress field on a specimen (i.e. without the existence of bending or any other normal stresses) is still open and under discussion. A solution to this problem comes from a specially designed shear specimen which can develop a uniform and pure in-plane shear stress field at its central region (Spitas et al. [2]) if loaded as illustrated in Fig. 1. The geometry of the specimen is patented [3] and resembles the Iosipescu specimen [4] but its main difference lies both in the shape of the grooves (U grooves instead of V grooves) for minimizing stress concentration and in the way of exerting the loading onto the specimen. For this latter reason a specially developed servo-hydraulic shear-testing machine has been developed in the last 15 years through EU funded industrial research projects.

FIGURE 1. The shear specimen and its loading conditions. The modified potential drop technique on the shear specimen uses the same concept of the change of the electrical resistance with the advancement of the crack tip but differs from the classical one since the electrical current density varies widely within the specimen therefore the potential drop it is not only indicative of the length but of the direction of the crack as well. The current passes through two thin electrodes welded on the surface of the specimen and the resulting potential difference between two other similar thin electrodes is measured as the crack tip advances. In this way the length of the crack can be estimated from the measured change in electrical potential drop.

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A rigorous F.E. Analysis using FRANC2D and MAXWELL for the mechanical and electrical field respectively was performed and it illustrated that the stress intensity factor in Mode II (KII) can be linked with the length of the crack and hence with the potential drop between the measuring electrodes welded onto the specimen. From this analysis a relationship between the change in relative electrical resistance and crack length can be established and therefore any set of experimental results which include change in electrical resistance versus the number of fatigue cycles can be translated into da / dN versus ' K II plots. The modified potential drop method for the shear specimen was successfully applied on single crystal nickel based superalloy CMSX4 tested in fatigue at 950qC. The accuracy of the numerical predictions of the F.E. Analysis for the electrical field was experimentally verified both by measuring artificial cuts of known length and by optical crack length measurements of the actual cracks using a robotic travelling long-distance optical microscope. For small crack lengths the numerical predictions coincided with the actual measurements within 2%, which corresponds to an error of roughly 20m.

Reference 1.

ASM Handbook Vol. 8, Mechanical Testing and Evaluation, ASM, Ohio, U.S.A., 2000.

2.

Spitas, V., Besterci, M., Michelis, P., Spitas, C., Sulleiova, K. and Balokova, B., Powder Metallurgy Progress, vol. 4 (4), 233-242, 2005.

3.

Michelis, P., European Patent EP 0687899.

4.

Iosipescu, N., J. of Materials, vol. 2 (3), 537-566, 1967.

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A MODIFIED DCB GEOMETRY FOR CTOA MEASUREMENT IN THIN SHEET 2024-T3 ALUMINIUM ALLOY Y. H. Tai, S. H. Hashemi, R. Gay, I. C. Howard and J. R. Yates The University of Sheffield, Department of Mechanical Engineering Mappin Street, Sheffield, S1 3JD, UK [email protected] Failure analysis carried out by various researchers has shown that fracture models based on the Crack Tip Opening Angle (CTOA) criterion which have been calibrated based on data from large C(T) and M(T) specimens can be transferred successfully to cracked aircraft fuselage structures and other low constraint structures for residual strength predictions [1,2,3]. One major difficulty with this method is the experimental measurement of CTOA [4] either in real structures or in a laboratory scale test. This could be the limiting factor that prevents the more extensive use of this promising fracture parameter. There are a number of ways to obtain CTOA data but the most appropriate and reliable method has yet to be agreed. The paper describes the use of a modified double cantilever beam specimen (Fig. 1) for the direct measurement of the critical CTOA data for thin sheet 2024-T3 aluminium alloy commonly used in aerospace applications. It highlights the features of ductile growth in low constraint configurations and the experimental technique used to reproduce these features in a laboratory scale experiment. This includes the specimen design geometry, loading configurations used, specimen preparation, and CTOA measurement technique. The experimental technique used is a development from the previous work of Shterenlikht et al [5].

FIGURE 1. Modified double cantilever beam specimen geometry. Using the developed technique, CTOA resistance curves for test samples of 2.3mm ligament thickness were generated for fractures with the crack propagating in the axial (TL) and in the transverse (LT) direction of the rolled aluminium alloy sheet. The specimen geometry and loading configuration allowed for extensive crack growth and managed to achieve a fairly straight crack path throughout the test (Fig. 2) which is desirable. Results showed that the technique was capable of producing large amounts of highly consistent CTOA data even from one single specimen. The tests produced a steady state mean value of CTOA of 4.2° with a standard deviation of 0.5°. This technique is promising as it provides a precise and easy experimental technique for direct CTOA measurement using relatively small scale laboratory specimens. A comparison of the test results from the current work with similar data from literature will be included in the paper.

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FIGURE 2. Fractured specimen with scribed mesh.

References 1.

Dawicke, D. S., and Newman Jr, J. C., Residual Strength Predictions for Multiple Site Damage Cracking Using a Three Dimensional FEA and a CTOA Criterion, Fatigue and Fracture Mechanics, Vol 29 ASTM STP 1332, 1998.

2.

Hsu, C., Tom, J. J., and Anderson, B. L., Residual Strength Analysis Using CTOA Criteria for Fuselage Structures Containing Multiple Site Damage, In Proceedings of ICF 16, Turin, March 2005.

3.

Newman Jr, J. C., James, M. A., and Zerbst, U., Engineering Fracture Mechanics, Vol 70, 371-385, 2003.

4.

Schwalbe, K. H., Newman Jr, J. C., and Shannon Jr, Engineering Fracture Mechanics, Vol 72, 557-576, 2005.

5.

Shterenlikht, A., Hashemi, S. H., Howard, I. C., Yates, J. R., and Andrews, R. M., Engineering Fracture Mechanics, Vol 71, 1997-2013, 2004.

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COULD COD SERVE AS FRACTURE CRITERION IN CASE OF MARBLE? A. Marinelli, S. K. Kourkoulis1 and I. Vayas Faculty of Civil Engineering, National Technical University of Athens 9, Heroes of Polytechnion Avenue, 157 80 Zografou Campus, Athens, Greece [email protected] 1Department of Mechanics, National Technical University of Athens 5, Heroes of Polytechnion Avenue, 157 73 Zografou Campus, Athens, Greece [email protected] An experimental study is presented here related to the behaviour of U-notched prismatic Dionysos marble specimens subjected to either three- or four-point bending or to direct tension, in an effort to investigate the variation of the Crack Opening Displacement (COD) versus the externally applied load. The purpose of the study is the determination of an-easy-to-use and reliable tool that could serve as fracture criterion in the hands of engineers working for the restoration projects of various ancient monuments as well as in every day’s practical applications.

The specimens were either of the form of Single Edge Notched (SEN) prismatic beams of rectangular cross section (bending tests) or Double Edge Notched Tensile (DENT) dog-bone shaped plates (tension tests). Series of experiments were carried out for each loading type with specimens of various sizes and various crack lengths in an effort to quantify the dependence of the mechanical constants and COD on the size and the shape of the specimens. Such an investigation is necessary since it is known that the results of laboratory tests with Dionysos marble (like most geomaterials) are shadowed by the extremely pronounced size and shape effects, as it is seen in Figure 1, where the tensile strength is plotted versus the diameter of the specimen [1]. The tests were carried out by controlling the (vertically) induced displacements. The strain components at some strategic points were measured using a system of triple strain gauge rosettes. The COD was measured as Crack Mouth Opening Displacement (CMOD) with the aid of suitable clip gauges mounted by pairs of machined knife edges.

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FIGURE 2. CMOD vs. the applied load for characteristic tests with DENT (a) and 3PB specimens (b). Characteristic results concerning the variation of the CMOD versus the applied load are plotted in Fig.2 for both types of tests. It is interesting to observe the non-linearity exhibited by the CMOD especially in the case of DENT specimens at the notch from which the fracture started. Such behaviour should be expected since the constitutive behaviour of Dionysos marble is relatively non-linear [2] for loads approaching the fracture load. The results of the experiments indicated that the values of the critical COD vary depending strongly on the orientation of the specimens with respect to the bedding planes of the marble. It is thus indicated that COD could be used as a fracture criterion only in the form of a surface in a three dimensional space (, , COD) where and are the inclination angles of the crack and the axis of the load with respect to the principal anisotropy directions of the material. Acknowledgements The present study is part of the scientific project “PROHITECH: Earthquake Protection of Historical Buildings by Reversible Mixed Technologies”, Contract number: INCO-CT-2004509119 supported financially by EU. The support is gratefully acknowledged.

References 1.

Vardoulakis, I. and Kourkoulis, S. K., Monuments under seismic action, Final Report EV5VCT93-0300, Nat. Techn. Univ. of Athens, 1997.

2.

Kourkoulis, S.K., Exadaktylos, G.E., Vardoulakis, I. In Proc. 14th European Conference on Fracture, Vol. II, pp. 243-250, Krakow, Poland, A. Neimitz, I.V. Rokach, D. Kocanda, K. Golos (Eds.), EMAS Publishing, United Kingdom, (2002).

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CREEP RUPTURE OF A LEAD-FREE Sn-Ag-Cu SOLDER C.-K. Lin and D.-Y. Chu Department of Mechanical Engineering, National Central University Chung-Li 32054, TAIWAN [email protected] Due to environmental and healthy concern, the allowable usage of lead will be decreased. The search of new lead-free solders with equivalent mechanical properties and microstructural stability to eutectic tin-lead (Sn-Pb) solder is an ongoing task. Solder joints in electronic products play not only a role to interconnect the electronic components but also to ensure the structural reliability of the electronic packages. As service temperatures for electronic assemblies are usually located in the high homologous temperature ranges (> 0.5Tm) of solder alloys, creep damage may take place. Therefore, a thorough understanding of the creep behavior of the newly developed lead-free solders is of extreme importance to the designers of electronic assemblies. Although there have been a few creep studies on Sn-Ag-Cu alloys in the literature [1-5], studies related to temperature effects on the creep behavior and lifetime prediction methodology in such lead-free solders were quite limited. Hence, the purpose of this study was to investigate and quantify the creep properties of a promising lead-free Sn-3.5Ag-0.5Cu solder at various environmental temperatures so as to provide important and helpful information for design of reliable electronic packages. The creep tests were performed under constant load at room temperature (RT), 60oC, and 90oC under a tensile stress range of V/E = 10-4 to 10-3. These testing temperatures correspond to a range of about 0.6-0.74 Tm for the given lead-free solder. Experimental results indicated that at a given temperature, the given Sn-3.5Ag-0.5Cu alloy showed much better tensile and creep strength than the conventional Sn-37Pb solder due to a dispersion-strengthening mechanism. The ultimate tensile strength (UTS) and creep resistance were found to be decreased with increasing temperature for the given lead-free solder. The stress exponents (n) of minimum strain rate (H min) were decreased from 9 at RT to 6 at 60oC and 90oC, suggesting the controlling creep mechanism for the given conditions was a lattice-controlled dislocation climb coupled with a dispersion-strengthening mechanism and the part of dispersion strengthening was more effective at a lower temperature. As Monkman-Grant expressions for each set of data at a given temperature are quite comparable, all the data from various temperatures can be fitted very well by a single MonkmanGrant relationship, as shown in Fig. 1. A model, using a term of applied stress normalized by Young’s modulus, was proposed in this study to correlate the rupture times at various temperatures and could explain the rupture time data reasonably well for the given lead-free solder, as shown in Fig. 2. Apparently, Monkman-Grant relationship and the proposed model each individually showed very good results in estimating the creep rupture time of the given ternary Sn-Ag-Cu solder subjected to various combinations of stress and temperature by a unified, single expression.

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FIGURE 1. Monkman-Grant plot of all data for Sn-3.5Ag-0.5Cu alloy.

FIGURE 2. Normalized stress vs. rupture time for Sn-3.5Ag-0.5Cu alloy.

References 1.

Plumbridge, W.J., Gagg, C.R. and Peters, S., J. Electron. Mater., vol. 30, 1178-1183, 2001.

2.

Guo, F., Lucas, J.P. and Subramanian, K.N., J. Mater. Sci., vol. 12, 27-35, 2001.

3.

Yu, J., Joo, D.K. and Shin, S.W., Acta Mater., vol. 50, 4315-4324, 2002.

4.

Joo, D.K., Yu, J. and Shin, S.W., J. Electron. Mater., vol. 32, 541-547, 2003.

5.

Guo, F., Choi, S., Subramanian, K.N., Bieler, T.R., Lucas, J.P., Achari, A. and Paruchuri, M., Mater. Sci. Eng. A, vol. 351, 190-199, 2003.

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QUANTITATIVE EVALUATION OF ACCELERATION CREEP IN MAGNESIUM-ALUMINUM ALLOYS AT 0.65TM H. Sato Department of Machines and System Engineering, Faculty of Science and Technology, Hirosaki University, Bunkyo-3, Hirosaki, Aomori, 036-8561 JAPAN [email protected] In creep failure, ternary stage is important portion of creep deformation. Although accelaretion creep is important to understand whole creep behavior, creep characteristics are evaluated mainly based on minimum or steady state creep rate and time to failure. In this report, creep characteristics in accerelation creep of magnesium-aluminum alloys are quantatively evaluated. It is well recognized that the steady state or minimum creep rate of solution-strengthened alloys can be reasonably described by following Dorn-type equation (1) in power-law stress range.

H

A©

Gb N kT

n

m

§V · § Q · ¨ ¸ exp ¨  c ¸ ©G ¹ © RT ¹

(1)

Here, A’, G, b, k and R are the constants, and others show regular meaning. The values T, N and ? are the absolute temperature, the solute concentration and the applied stress. The value m, n and Qc characterize the creep behavior and are the concentration exponent, the stress exponent and the apparent activation energy of creep, respectively. In magnesium-aluminum solid solutions, creep characteristics depend on deformation conditions in complex manners. At the temperatures below 0.7Tm, the power-law creep characteristics are attributed to Alloy-type and Metal-type at lower and higher stresses, respectively (1,2). In Mg-3mol%Al alloys, the change of creep characteristics appears at 30MPa at 600K. In compression creep of magnesium-aluminum binary alloys, simple relationship between creep rate and creep strain appears in ternary creep regime(1). The relationship is similar to that of Omega-method(3), but in magnesium-aluminum alloys, the primary stage is not igoreble. In this report, stress dependence of acceralation creep characteristics of magnesium-aluminum solution strengthened alloys are quantitatively evaluated based on similar relationship of the Omega method. In ternary stage of constant stress creep of the alloys, logarithmic of creep rates are proportional to creep strain, and show relationship described by equation (2).

ln H Here, k and

k H  ln H 0

(2)

H 0 are constants determined experimentally, which shows magnitude of acceleration

of strain rate in ternary stage and initial creep rate, respectivily. This equation is similar to that proposed in the Omega method(3), but in magnesium-aluminum alloys, the relation is satisfiled in ternary stage even though true stresses are kept constant, and primary creep is observed. Equation (2) derives strain-time relationship as equation (3).

H

H init 

1 § t · ln ¨ 1  ¸¸ k ¨© tr ¹

(3)

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472

Here, H init and t r are constants that shows magnitude of primary creep and time to infinite strain, respectively. In equation (3), three parameters detarmine shape of creep curve under paticular stress and temperature. Figure 1 shows example of strain rate-strain relationship of magnesium-3mol% aluminum solution strengthened alloys. The relations described by equation (1) are shown strain above 0.1 in various stress levels. Figure 2 shows an expample of stress dependence of the k-value, one of three paramters which determin creep curve, i.e. equation (3). The stress dependence of the k changes at around 30MPa that correspounds to the change of creep characteristics which is detarmined by minimum creep rates(1). These stress dependences are also observed in other parameters. As conclusion, creep characteristics of magnesium-aluminum solid solution alloys in compression are reasonably described Omega like concept. Stress dependence of creep parameters changes at the stress that corresponds to the change of deformation mechanisms. Quantitative evaluation of ternary acceleration creep suggests possibility of reasonable prediction of time to failure. Change of microstructure during acceleration creep will also be presented.

Figure1.Example of strain rate-strain curve

Figure2.Stress dependance of the k-value

References 1.

Hiroyuki Sato, et al., In The Fourth Pacific Rim International Conference on Advanced Materials and Processing (PRICM4), Edited by S. Hanada, et al., The Japan Institute of Metals, 2001, 1155-1158.

2.

H. Oikawa, In Hot deformation of Aluminum Alloys, edited By T.G. Langdon, et al., TMS, Warrendale, (1991), 153

3.

M. Prager, In Strength of Materials, edited by H. Oikawa, et al., The Japan Institute of Metals, 1994, 571-574

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LONG-TERM CREEP RUPTURE PREDICTION IN UNIDIRECTIONAL COMPOSITES Jun Koyanagi, Fumio Ogawa1 and Hiroyuki Kawada Department of Mechanical Engineering, Waseda University 3-4-1 Okubo, Shinjuku-ku, Tokyo, Japan 1Graduate of Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo, Japan [email protected] In many articles, analyses about creep behavior and creep rupture in unidirectional composites have been done in the past two decades. McLean [1] formulates the creep behavior in unidirectional composite with a simple constitutive equation in matrix. Curtin establish the GLS theory that can determine a rupture strain in unidirectional composites. By combining these two models, Du and McMeeking et al. [3,4] and Ohno and Miyake [5,6] predict the creep rupture in unidirectional composites. However, several problems are pointed out: an interfacial debonding is not considered, McLean model can not express the exact creep behavior. On the other hands, the previous author’s works [7] and Okabe et al. [8] show that micro damages such as an interfacial debonding causes the composite rupture strain to decrease. That is to say, the rupture strain in unidirectional composite has time-dependency on an assumption that the interfacial debonding propagates or the stress recovery length increases with time. However, the decrease of the rupture strain has not been formulated on a consideration of history dependent accumulation of micro damages. The fact results in that the predicted creep rupture time is overestimated. This is because despite of there is an interaction between stress recovery length and fiber breaks probability, the formulation has not been done. In this study, the matrix constitutive equation is applied the compliance component as a function of time, power low, and its deformation behavior can be expressed by a convolution integral equation. Hence, to formulate the specimen strain as a function of time, Laplace transformation is used on way to the equation derivation, and the Shapery approximation is applied as the inverse Laplace transformation. (Eq. 1)

H t

J t V 1  V f  J  t V f E f

(1)

Also, for the long-term creep, the time-dependnet rupture strain as a funciton of the average stress recovery length is formulated in Eq. 2. 1

H rup

V0 §

L0 ¨ E f ¨©  m  1 Lr

·m ¸¸ ¹

(2)

Fiber breaks probability that dominates rupture strain and that is dominated the stresss recovery lengh is formulated on a consideration of that each stress recovery length depends on when the fiber breaks as shown in Eq. 3. q t

t d q t 2 § E fH · 1 L r  t  t cc d t cc ¨ ¸ ³ 0 L0 © V 0 ¹ q t d t cc

(3)

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By solving this equation, the decrease of the rupture strain in unidirectional composite can be formulated on a consideration of the history dependent micro damage growth for the long-term creep rupture. That is to say, if the stress recovery length increase function regarding one fiber break is obtained, the long-term time-dependednt rupture strain can be calculated. By using glass fiber reinforced polymer unidirectional composite specimen, the creep rupture tests were performed. The results are compared with the analytical prediction involving follows assumptions.

L r t

N ˜ t  Lr  0

(4)

Parameters used in this analysis are as follows: Ef=72000MPa, Vf=0.02, J0=0.000294 1/MPa,

D=0.27, Tc=2.0E+05 sec, Js=0.577, V0=2500 MPa, L0=25 mm, and Lr(0)=500 Pm. The rate of stress recovery length increase, N, is assumed 5.0E-09, 5.0E-10 and 5.0E-11. The results of the creep rupture prediction involving the above assumption is shown in Figure

Figure Prediction of creep rupture time and experimental results

References 1.

McLean M. Creep deformation of metal-matrix composites. Compos Sci Technol 1985; 23: 37-52.

2.

Curtin WA. Theory of mechanical properties of ceramic-matrix composites. J Am Ceram Soc 1991; 74: 2837-2845.

3.

Du ZZ, McMeeking RM. Creep Models for Metal Matrix Composites with Long Brittle Fibers. J Mech Phys Solids 1995; 43: 701—726.

4.

Sofronis P, McMeeking RM. The effect of interface diffusion and slip on the creep resistance of particulate composite materials. Mech Mater 1994; 18: 55-68.

5.

Ohno N, et al. A model for shear stress relaxation around fiber break in unidirectional composites and creep rupture analysis. J Soc Mater Sci Japan 1998; 47: 184-191.

6.

Ohno N, Miyake T. Stress relaxation in broken fibers in unidirectional composites: modeling and application to creep rupture analysis. I J Plasticity 1999; 15: 167-189.

7.

Koyanagi J, et al. Prediction of Creep Rupture in Unidirectional Composite :Creep Rupture Model with Interfacial Debonding and its Propagation. Adv Compos Mater 2004; Vol 13 No. 3-4: 199-213.

8.

Okabe T, et al. A 3D shear-lag model considering micro-damage and statistical strength prediction of unidirectional fiber-reinforced composites. Compos Sci Technol 2001; 61: 17731787.

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A COMPUTATIONAL MODEL FOR CARDBOARD CREEP FRACTURE Julia Schonwalder, Gideon P. A. G. van Zijl1 and Jan G. Rots Delft University of Technology, 1University of Stellenbosch Faculty of Architecture, Berlageweg 1, 2628 CR Delft, The Netherlands [email protected] Recently paper and cardboard is emerging as a construction material. This involves further research into the mechanical response of cardboard and cardboard structures concerning structural safety and long-term stability. The behaviour of paper and cardboard is highly time- and ratedependent. The time-dependent crack growth can cause delayed structural collapse. In a computational model, which aims to predict structural response of a material, the time-dependent crack growth can be considered by the incorporation of the time scale. In this paper an interactive experimental and a computational research effort is reported, through which the tensile creep fracture phenomenon is characterised and a computational prediction tool developed. The focus is on tensile creep in machine direction of a solid board. In an extensive test series the response of the board under sustained and strain-rate loading was determined. A finite element model which was developed for creep fracture of masonry and cementitious materials e.g. by De Borst [1], Van Zijl [2] and Lourenço et al. [3] was modified. The model is based on linear visco-elasticity, combined with computational plasticity to capture the limited tensile resistance. With the modified parameters the tensile responses of cardboard at the same rates employed in the experiments were obtained by FE analyses. The results are summarised in Table 1. It is seen that the maximum tensile strength of the experiments and the modelling match very well. TABLE 1. Experimental and numerical results of tensile peak strength of different constant strain rate loading Peak strength (N/mm2) Rate (mm/min)

Numerical

0.001

Experimental (nr tests, CoV) 16.0 (1, -)

0.5

25.0 (10, 10%)

24.0

5

26.0 (10, 10%)

26.0

50

28.2 (10, 10%)

28.0

16.5

Also the creep tests were modelled with the FE analyses, at the same load levels where failure occurred in the experiments. Fig. 1 shows that the analysed time to failure coincides with the experimental values fairly well.

J. Schonwalder et al.

476

FIGURE 1. Experimental and numerical time to failure under sustained load. Even though cardboard is known as a non-linear viscoelastic material, see e.g. [4], the model based on a linear viscoelastic assumption, showed evidence of predicting the time to failure under creep loading considerably well. Also the creep model is confined to primary and secondary creep. An integration of tertiary creep would further improve the results.

References 1.

De Borst, R., Smeared cracking, plasticity, creep and thermal loading – a unified approach. Computer Methods in Applied Mechanics and Engineering, vol. 62, 89-110, 1986.

2.

Van Zijl, G.P.A.G., Computational Modelling of masonry creep and shrinkage, Dissertation, Delft University of Technology, The Netherlands, 1999.

3.

Lourenço, P.B., Rots, J.G. and Blaauwendraad, J., Continuum model for Masonry: Parameter estimation and validation, ASCE Journal of Structural Engineering, vol. 124, 642-652, 1998.

4.

Haslach, H.W. JR., The moisture and rate-dependent mechanical properties of paper: a review, Mechanics of Time-Dependent Materials, vol. 4, 169-210, 2000.

2T16. Creep fracture

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CREEP FRACTURE OF BINARY AND TERNARY COMMERCIAL ALUMINUM ALLOYS K. Ishikawa Department of Mechanical Engineering, Toyo University 2100 Kujirai, Kawagoe, Saitama, Japan 350-8585 [email protected] Binary and ternary commercial aluminum alloys were crept to the rupture under a condition of constant applied stress. The applied stress was guaranteed within 0.5% of the expected value. The commercial aluminum alloys have medium and high strength at the ambient temperatures. The binary alloy was A5083, the main alloy element of which was ca. 5% magnesium. Two kinds of ternary alloys were A6061 and A7075. The former contains 3% magnesium and 1% silicon. The latter consists of 3% magnesium and 7% zinc. The test temperatures were kept in the region of the solid solution of the alloys. The temperatures were guaranteed within 2K. The whole creep tests were carried out until the rupture of the specimens at the constant applied stress and temperature. The elongation was measured with the laser extensometer with the accuracy of 50 Pm. The creep curves were converted into the true strain of the plastic elongation. The steady state creep was not observed for the whole alloys. The minimum strain rate was described by the following equation [1].

H min v V

m

exp  Q min

kT



(1)

Where m depends upon the test temperature, and Qmin depends upon the applied stress. The experimental values of m were showed in Table 1. TABLE 1 Stress exponent, m of minimum strain rate for the respective alloys

The creep life was also expressed by the following equation [2].

t life f V

n

exp Q life kT



(2)

Where n depends upon the test temperature, and Qlife depends upon the applied stress. The experimental values of n were showed in Table 2.

K. Ishikawa

478

TABLE 2 Stress exponent, n of creep life for the respective alloys

For A5083, Q min | Q life

210  0 . 13 V kJ mol

for A6061, Q min | Q life

352  1 . 08 V kJ

mol

,

439  3 . 52 V kJ mol . V is the applied stress. The activation and for A7075, Q min | Q life energy for creep fracture was determined by the atomic interaction between the defects at high temperatures. Furthermore, there was found the simple relationship between the minimum strain rate and creep life given by the following equation [3].

H min u t life

K

(2)

The constant, K does not depend on the test temperature and the applied stress. For A5083, K = 0.11, for A6061, K = 0.12 and for A7075, K = 0.1. The experimental results would suggest that the creep behaviour and fracture was intensively associated with the interaction between the defects in the alloys. The strength could be due to the difference in the interaction between the defects. The diffusion process was dominant, since the final fracture pattern was dimple [4].

References 1.

Skrzypek, J. and Ganczarski, A., Modeling of Materials Damage and Failure of Structures, Springer, Berlin, Germany, 1999

2.

Altenbach, H. and Skrzypek, J. J., Creep and Damage in Materials and Structures, SpringerVerlag, Wien, Austria, 1999

3.

Barsoum, M., Fundamentals of Ceramics, McGraw-Hill, New York, USA, 1997

4.

4. Weertman, J. and Weertman, J. R. Elementary Dislocation Theory, Macmillan, New York. USA, 1964

2T16. Creep fracture

479

ANALYSIS OF CREEP CRACK INITIATION AND GROWTH IN LABORATORY SPECIMENS K. Wasmer Swiss Federal Laboratories for Materials Testing and Research (EMPA) Feuerwerkerstrasse 39, 3602 Thun, Switzerland [email protected] In the power generation, petro-chemical and nuclear industries, predicting the life of aging equipment has become both a safety issue and an economic necessity. In order to perform such assessments, a number of in-house procedures, as well as national standards (e.g. BS7910 and R5) have been developed. These procedures use a deterministic approach based on certain assumptions and material properties. Depending on the procedures, methods and material properties used, significant variability in predictions can be observed. In such circumstances there is a need to develop statistical and probabilistic approaches in order to increase confidence in the application of the methods. However, it has been observed that statistical and probabilistic methods may over or under predict by factor over 100 creep crack initiation and growth (CCI and CCG, respectively). This is due to two main facts. Firstly, often data from laboratory specimens such as Compact Tension (CT) or C-Shape (C) is used to predict CCI and CCG in order to reduce the costs. Secondly, although the procedures adopt the same basic principles, often different formulae are employed to make an assessment. The main parameters that are used are reference stress,

ıref

,

stress intensity factor, K, and the creep strain rate, İ˙ , which are required to estimate the creep fracture mechanics term C*. Hence, first, it is necessary to select the best parameters in order to characterise as well as possible the creep crack initiation and growth behaviour in laboratory specimens as well as real components. This has already been done for some real components such as pipes and bent pipes subjected to internal pressure as well as plate subjected to bending stress for different materials [1-3]. In contrast, very little studies has been carried out to find the origin and the reasons as well as the parameters which makes that one set of parameters predicts well, for example, the CCI and/or CCG for one specific CT test and under or over estimates significantly another identical test apart from the applied load and this is the focus of this study. In this paper, sensitivity analysis of CCI and CCG in pre-cracked CT and C specimens of a 2¼Cr1Mo ferritic steel and a 9%Cr-steel designated as P22 and P91, respectively, is performed. The test temperature was at 565 and 650ºC for P22 and P91, respectively. The results have been interpreted in terms of the creep fracture mechanics parameter C*. The experimental C* for CT and C specimens were obtained according to the recommendations of ASTM E 1457-00 [4]. In contrast, in making the calculation, the reference stress method based on Eq. (1) has been used to determine C* for the laboratory specimens [5]. Several formulae can be employed for calculating reference stress depending on whether it is based on a plane strain (P) or plane stress (P). Additional parameters such as the yield criterion (Von Mises and Tresca) and the choice of strain rate (secondary or average, C

* ref

İ˙s and İ˙Ave , respectively) also influence the calculation of C*.

V ref ˜ H ref

§ K ˜¨ ¨V © ref

· ¸ ¸ ¹

2 n 1 A ˜ V ref ˜ K 2 , assuming the Norton law

(1)

It has been found that, based on the different assumption mentioned above, the discrepancy between the extreme solutions is greater than 600 in calculating C* from Eq. (1). The parameter responsible for a most this disparity is the reference stress. In fact, depending on ref chosen, a factor

K. Wasmer

480

ranging between 200 and 300 is obtained. Much less influential is the choice of the strain rate which is found to vary between 3 and 7 depending on the material, material condition and temperature.

* for all CCG tests from the same * By plotting C Pred (calculated from one solution) vs. C Exp batch, a ratio between 600 and 2000 is measured between the upper and lower bounds. This demonstrates that, for laboratory specimens, the selection of the best set of parameters for one specific test is by far not enough to be certain that this solution will work for all other tests performed from the same batch of material under the same condition except the applied load. To establish the origin of this problem, a comparison between Eqs (1) and (2) has been carried out. The results show that using the Norton low to characterise the strain rate in Eq. (1) is the main problem. In fact, the difference computed varies from 50 to 700 times. C * Exp

P ˜ ' c n ˜ ˜ K pl , from ASTM E – 1457 [4] B ˜ W  a n  1

(2)

References 1.

Wasmer, K., Nikbin, K. M. and Webster, G. A., in Proceeding of the ASME Pressure Vessels and Piping, Vol. 438, Nº 1191: New and Emerging Computational Methods: Applications to Fracture, Damage, and Reliability, Vancouver, pp: 17-24, 2002.

2.

Wasmer, K., Nikbin, K. M. and Webster, G. A., Int. J. of Pressure Vessels and Piping, vol. 80, Issues 7-8, pp: 489-498, 2003.

3.

Nikbin, K. M., Yatomi, M., Wasmer, K. and Webster, G. A., Int. J. of Pressure Vessels and Piping, vol. 80, Issues 7-8, pp: 585-595, 2003.

4.

ASTM E 1457-00, Annual Book of ASTM Standards, vol. 3, Issue 1, pp: 936-950, 2001.

5.

Ainsworth, R.A. Some Observations on Creep Crack Growth, Int Jnl of Fracture, vol. 20, pp: 147-159, 1982.

2T16. Creep fracture

481

TEMPERATURE GRADIENT EFFECTS ON THE CREEP BEHAVIOUR OF STRUCTURES F. Vakili-Tahami and S. Hasanifard Faculty of Mechanical Engineering, University of Tabriz, Tabriz, Iran [email protected], [email protected]

$ Increasing the operating temperature level beyond 400 C required systematic investigations on the influence of temperature upon the behaviour of highly stressed components.

Limited creep deformation and longer creep lifetime are the major criteria for the evolving science of high-temperature component design. To satisfy the safety and economic requirements for competitive design of engineering components, two major research fields have been identified. In one field, metallurgists try to understand the microstructural mechanisms of creep in order to develop new creep resistant alloys. Parallel to this, in the other field, scientists and engineers try to describe the evolution of creep deformation and damage for different materials using the empirical or physics-based constitutive models. The latter field is the frame work of this research study. To provide a ‘right first time’ design, it is essential to predict the creep behaviour of components at the design stage using accurate computer modelling techniques. The modelling procedures can also help to determine the inspection procedures and intervals. In this paper the effect of temperature gradient on the thermal stress distribution and creep stress-strain redistribution has been studied over selected structures using uncoupled Finite Element based numerical analysis. For this purpose, the steady state temperature gradient has been obtained over a super-heater pipe-line support using the FE based numerical method. The temperature profiles for the pipe and the support have been used as input data to obtain thermal stress distribution and creep stress-strain redistribution over the plate. In contrast to the low temperature creep, the minimum creep strain rate,

H min,

at high-

temperatures is a function of stress and temperature: H min

f (V , T )

(1)

In this paper the stress dependency of the minimum creep strain rate,H min, has been expressed using a power-law equation, whereas the temperature dependency has been expressed using two different models. It has been shown that the structural behaviour is severely affected by the existing temperature gradient. This is due to the exponential relationship between temperature and creep strain rate. It has also been shown that the creep lifetime can be estimated more accurately using this method.

F. Vakili-Tahami and S. Hasanifard

482

References 1.

Vakili-Tahami, F., Hayhurst, D. R., growth of damage and subsequent creep crack growth due to Reheat Cracking of A 316H stainless steel welded pressure vessel at 550oC, Internal Research Report DMM.01.05, Third issue, 19th October 2001, Mech. Aerospace and Manufacturing Engineering, UMIST.

2.

Hall, F.R., Hayhurst, D.R., Continuum damage mechanics modelling of high-temperature deformation and failure in a pipe weldment, 1991.

3.

Perrin, I. J., Hayhurst, D. R., Ainsworth, R. A., Approximate creep rupture lifetimes for butt and welded ferritic steel pressurised pipes, European Journal of Mechanics, 2000, A/Solids, 19, 223-258.

4.

British Energy Generation Ltd., An assessment procedure for the high-temperature response of structures, R5, Issue 2, Revision 2, 2001.

2T17. Environment assisted fracture

483

A SURGICAL IMPLANT CREVICE-ASSISTED CORROSION FATIGUE INBODY FAILURE Hossein Amel-Farzad, Mohammad-Taghi Peivandi1 and S. Mohammad-Reza Yosof-Sani Department of Materials and Metallurgy Engineering, Engineering Faculty, Ferdowsi University of Mashhad, Mashhad, Iran 1Department of Orthopaedics, Medical Faculty, Mashhad University of Medical Sciences, Mashhad, Iran [email protected], [email protected], [email protected] An orthopaedic stainless steel implant, called “DCS Barrel Plate”, was received which had fractured inside the patient's body. It had been in his leg for almost two years and it is guessed that it has been fractured during the first few months, when the bone has been recovering itself, but had not completed this step; and it had has been forbidden for the patient to walk freely, not to deform the redonstructing bone. Different investigations containing visual assessments, stereoscopy, SEM fractography, EDX chemical analysis, metallography, hardness testing and quantometry was performed to analyze the mechanism of failure and its cause(s). These plates are under cyclic tensile loading and relaxing during the patient’s walking. They have a bended zone which lets them fit with the bone better. It is obvious that the plate is mostly stressed in the part in-contact with the fractured zone of the bone, which is exactly this bended zone in our case, because there is no bone structure to divide the applied stress, there. It is also necessary to note that, the implant has a distinct contact with the bone all over its length, containing this bended and frequently tensile stressed zone. The fracture had occurred exactly from this frequently tensile stressed region. It must be noted that the alloy was not the standard 316L, but an attentively different austenitic steel containing 0.115%wt C, and 5.45%wt Mn, 9.995wt Cr and 1.44%wt Ni; which, as follows, has enough corrosion resistance even in the presence of crevices, but low when static or dynamic stress applied. A great number of “Crevice Corrosion pits” was observed exactly in this zone and side, which were sometimes a few millimeters deep. But, none of these dangerous pits had led to the final fracture. The main fracture has a mechanism of crack growth, initiated from the frequently tensile stressed region and some other severe crevice corrosion pits formed inside the hole. Although this place had not been in-contact with bone, but the best sealed location for the concentration of the Cl- ions, and had been in contact with the screw too. SEM fractography and EDX chemical analysis was performed from the main fracture surface, some of secondary cracks’ and also pits’ surfaces, which were both opened carefully. The EDX analysis showed the presence of Cl atoms in the deposits formed inside both cracks and pits; and so supported the guess of the effect of Cl- ions on both the cracks growth and pits formation. The SEM fractography showed the fatigue mechanisms, even though there were lots of corrosion deposits all over the fracture surface, even after severe ultrasonic cleaning. It also showed fretting in some points of the fracture surface, caused by the frequent loading after the definite fracture. No sign of general classic grain boundary sensitization was observed. But, severe intergranular cracks were observed in the in-contact zone and frequently stressed zone, but no other place, during the SEM fractography and also metallography. Also, the hardness values were about 25 HRC and had no significant change along the sample. Finally, the main failure mechanism was determined as “crevice effect assisted corrosion fatigue”. Although the formation of these crevice corrosion pits were assisted by the applied stress themselves.

484

H. Amel-Farzad et al.

Fig 1. Microstructure of the plate along the plate near the fracture point, containing its in-contact side, showing crevice corrosion pits, and a continuous net of intergranular cracks near the incontact surface leading to deeper crack similar to IGSCC cracks too (a). The plate and its fracture zone are shown from two different views (b and c). Crevice corrosion pits and the cracks initiated from these pits are evident in (c). No crevice corrosion pit or crack nor independent or initiated from the pits, can be seen far from the fracture point. Pay attention that after the nearest holes to the fracture point, the applied stress is divided between the bone and the plate, and so the applied stress is much lower, even though both the crevice and the Cl- exist.

Fig 2. The severely rusted fracture surface of the plate, in which the top side is the in-contact one is evident. As it can be seen the fracture surface is typical of fatigue fractures. White arrows indicate the initiation points, from which fatigue cracks have initiated inside the hole, in contact with the screw (a). Photograph of the surface of the biggest crevice corrosion pit in the plate, in which the rusted brown surface, which contains a long crack too, is the inner side of the hole; and the rusted and cracked surface in right hand side is the in–contact side whose pre-existing crack has been opened more during the overloading. The extremely rusted and cracked surface in the center belongs to the pit, which continues some millimeters till it passes even all over the thickness of the sample. This extremely deep pit can be seen in the figure 1-c in the vicinity of the fracture surface of the left hand side part of the plate, at the bottom of the hole. The blue-like fully dimpled surface is made during the ductile fracture by overloading intentionally in the lab.

2T17. Environment assisted fracture

485

ASYMPTOTICALLY STABLE GROWTH OF DELAMINATIONS UNDER HYDROGEN EMBRITTLEMENT CONDITIONS A. V. Balueva Spelman College, Department of Mathematics 350 Spelman Lane SW, Atlanta, GA 30314, USA [email protected] Delamination, defined here as separation of the surface layer from the solid body, is observed in many engineering processes and natural phenomena, ranging from surface buckling of layered composites to surface fracturing caused by hydrogen embrittlement in metals. For example, in the case of pipelines for hydrocarbon transport, anti-corrosion, polymer coating sometimes results in more frequent appearance of small scale delaminations. In time, these delaminations spread under molecular hydrogen accumulated in a cavity, damaging the coating and allowing the moisture access to the metal; the result being the external corrosive fracture of the pipeline and its premature replacement. Understanding the mechanism of protective coating delamination may improve estimates of the pipeline longevity, thereby creating an essential industrial potential. We consider delamination crack growth controlled by gas diffusion into the crack. If the gas is accumulated inside the delamination, after some incubation period, it starts growing under the pressure of the accumulated gas. An important example is given by hydrogen induced delamination. Hydrogen absorbed by a metal is typically dissolved in the proton form within the lattice. Some of the protons reach the surface of pre-existing or freshly created cracks or delaminations where they recombine with electrons and form molecular hydrogen in the crack cavity. Because usually the molecular form of hydrogen is thermodynamically more stable, this process leads to accumulation of hydrogen gas inside the delamination crack. Then, the fracture often takes place even in the absence of any external loading, that is, only under the excessive hydrogen pressure.

FIGURE 1. Kinetic dependence of the fracture toughness, KIc, on crack velocity, v. Since the fracture toughness, KIc, and, therefore, fracture energy, J, in most cases cannot be assumed crack velocity independent in conditions of hydrogen embrittlement, we use the actual kinetic dependencies, KIc(v) (e.g. in Fig. 1). As numerically shown in the author’s earlier work for the internal crack growth, the crack velocity first increases in accordance with the kinetic

486

A. V. Balueva

dependence until reaching some value of vs and remains at the same level afterwards. Since, as has been obtained in the previous paper by the author, kinetic equations for internal and delamination cracks are essentially identical, the same conclusion can be derived for the latter. In this paper the stability and asymptotic approach to the constant velocity of delamination growth is proved analytically. If vs is known, the corresponding value of fracture toughness, Ks, is obtained by substituting vs into the full kinetic function, KIc(v), resulting in K s= KIc(vs).

2T17. Environment assisted fracture

487

CORROSION AND MECHANICAL STRENGTH OF RUSSIAN LIGHT WATER REACTORS B. T. Timofeev CRISM “Prometey”, 49 Shpalernaya street, 193015, St. Petersburg, Russia [email protected] The Russian light water reactors of types WWER-440 and WWER-1000 made of heat irradiation resistant steels is usually protected from coolant effect by anticorrosive austenitic cladding. Only ten reactors type WWER-440 of the first generation were manufacturing without protection of inner surface. Now only four such reactors are operated in Novo-Voronezh and Kola NPPs. Effect of boric acid on corrosion rate of CrMoV steel was presented in Fig.1. The other type of operating reactor pressure vessels has anticorrosive protection of inner surface. The thickness of austenitic clad metal in inner surface of reactor is not more than 9 mm. Not long ago, by the selection of main reactor dimensions and strength analysis the thickness of this austenitic clad metal was not taken into account and cladding cracking was not considered at service life assessment. Later this problem was paid greater attention and some investigations in our country and abroad were carried out. In these works were studied low-cycle fatigue, fatigue crack growth rate and brittle fracture resistance of 15Cr2MoVA steel and austenitic-ferritic clad metal. The coolant influence on low cycle fatigue was investigated for base metal - 15Cr2MoVA steel. The tests were carried out by biaxial stress state (tension-reduction) in water medium (pressure – 6 MPa, temperature – 270°C) by various loading frequencies. By this it was established that the medium effect on fatigue strength of materials is absent even by the frequency of loading by 20 times from 0,0085 to 0,167 Hz (Fig.2). This may be explained by the formation of protective magnetic film at the surface of investigated specimens. By small amplitudes of strain this film is practically not damaged by cyclic loading.

Fig.1 Effect of boric acid on corrosion rate of 15Cr2MoVA steel ( out by SAW using Sv-10CrMoVTi wire (

) and weld metal carried ) at 300°

488

B. T. Timofeev

The report presents summarized results on corrosion and mechanical strength of materials for Russian light water reactors including experience of long-term operation. The comparison of initial properties of these materials with the analogous characteristics after 100000 and 200000 hours of operation showed that in most cases the variations were insignificant and the values specified by the requirements of normative documentation according to PNAE G-7-002-86 for the used types of steel and according to PNAE G-7-010-89 – for weld metal.

2T17. Environment assisted fracture

489

CORROSION FATIGUE CHARACTERISTICS OF CF8A STEEL DEGRADED AT HIGH TEMPERATURE Seong-Cheol Jang, Dong-Ho Bae1, Gyou-Young Lee, and Seong-Yeb Baek Student, Graduate School, Mechanical Engineering Department, Sungkyunkwan University, 300 Chunchun-dong, Jangan-gu, Suwon, Kyunggi-do 440-746, Korea. [email protected] 1Professor, School of Mechanical Engineering, Sungkyunkwan University, 300 Chunchun-dong, Jangan-gu, Suwon, Kyunggi-do 440-746, Korea. [email protected] Even though nuclear power showed remarkable increase as an industrial energy source, recently, its demand has been slowed down by conservatism of nuclear power industry and market stagnation. Therefore, many researchers have so far investigated on improving and developing technologies to maximize the economical efficiency as well as safety maintenance of nuclear power plant using the destructive and nondestructive approaches. In particular, evaluation of mechanical characteristics of materials by aging degradation due to corrosion, creep, and fatigue is actively investigated. In this paper, as a fundamental study to evaluate fracture characteristics and material degradation by corrosion, evaluated electrochemical corrosion and corrosion fatigue characteristics of CF8A steel using as a material of the piping system in nuclear power plant. CF8A steel was artificially aged at 400qC for 3 months. The environmental test condition is 3.5wt.% NaCl solution of room temperature. Summarized conclusions are as follows, 1

Corrosion rate of CF8A steel in NaCl solution of room temperature increases with concentration of NaCl solution increase. However, concentration of NaCl solution will be more than 4.0wt.%, it showed decreasing tendency. Corrosion rate in 3.5wt.% NaCl solution was assessed as 4.927mpy that is 2.7 times of one in distilled water (1.846 mpy).

2

Corrosion rate of aged CF8A steel in NaCl solution of room temperature increases with concentration of NaCl solution increase. However, concentration of NaCl solution will be more than 4.0wt.%, it shows decreasing tendency. Corrosion rate in 3.5wt.% NaCl solution was assessed as 11.889 mpy that is 4 times of one in distilled water (2.930 mpy) and 2.4 times of unaged material in the same environmental condition.

3

Crack growth rates of aged and unaged CF8A steel in air condition do not show remarkable difference. However, in 3.5wt.% NaCl solution, crack growth rates of them showed higher than ones in air. Particularly, crack growth rate of aged material remarkably increases compare to one of unaged material. TABLE 1 Chemical compositions of CF8A (wt.%) C 0.05

Mn 0.626

Si 1.18

Cr 19.88

Ni 8.74

S 0.014

S.-C. Jang et al.

490

Figure 1. Comparison of corrosion rates between aged and unaged CF8A steel in NaCl solution

Figure 2. Comparison of da/dN-'K curves of CF8A steel

References 1.

ASTM, G5, 73-76, 1987

2.

Bandy, R. and Jones, D. A., J. Corrosion, vol. 32, 126, 1976

3.

ASTM, E647-00, 578-614, 2000.

4.

Marsh, K. J., Smith, R. A., and Ritchie, R. O., EMAS, 11-37, 1990.

5.

Wei, R. P. and Brazill, R. L., ASTM, STP 738, 103-119, 1979.

2T17. Environment assisted fracture

491

MODELING ENVIRONMENT-ASSISTED FATIGUE CRACK PROPAGATION J.-A. Ruiz-Sabariego and S. Pommier Lab. of Mechanics and Technology (LMT), 61 av. du Président Wilson, 94235 Cachan, France [email protected] Predicting fatigue crack growth in metals under random loadings remains difficult since fatigue crack growth is very sensitive to load history. Load history effect in fatigue is known for decades to stem from plastic deformation in the vicinity of the crack tip. Moreover, history effects in fatigue are closely related to the elastic-plastic behaviour of the material [1]. The thermodynamics of dissipative processes made possible to establish a model of crack propagation in mode I, where the variables are namely, the position of the crack tip “a”, the stress intensity factor “KIf” and the intensity of crack tip blunting “U”. This model contents: •

one elastic-plastic constitutive equation for the cracked structure, established through the FEM and using an elastic-plastic constitutive behavior of the material

dU dt •

§ g ¨I ©

J · ,... ¸ 2 ¹

(1)

one cracking law with one fitting parameter D

da dt

D

dU dt

(2)

In this model, the crack growth rate is a time derivative equation (da/dt) instead of a cyclederivative equation (da/dN). It has the advantage to avoid explicitly any cycle counting in random fatigue. The model has already been implemented and tested to predict fatigue crack growth under random load. This latter would also be a good way to model environment-assisted fatigue crack propagation, as diffusion of chemical species, creep or oxidation are time dependent phenomena. The idea is to transcribe some of the known mechanisms that are responsible of the deterioration of the resistance against crack propagation of most of the metallic alloys ( “blunting model”, hydrogen-assisted cracking … [2] ). For example, in the case of a “blunting model”, adsorbed gas molecules coming from gaseous atmosphere are responsible for slip irreversibility in the crack tip and thus localize the plastic strain by favoring the activation of new slip planes. This irreversibility can be model considering D parameter as a “S” curve, which represents the saturation of the mechanism, function of the blunting rate. This parameter rather represents oxidation on the crack tip surface [3].

FIGURE 1. Frequency effect with D function of blunting rate.

J.-A. Ruiz-Sabariego and S. Pommier

492

Diffusion mechanism involved in the hydrogen-assisted cracking needs to introduce in the model a new kinematics variable that would represent the flux of chemical species through the crack tip. It’s then possible to enrich the model with a E parameter, function of the stress intensity factor and/or others of the variables representing the load.

da dt

D

dU dt

 E K (3)

FIGURE 2. Effect of a E constant parameter modeling diffusion mechanism.

References 1.

Pommier S et Risbet M, “Partial-derivative equations for fatigue crack growth in metal”, Int Jal of Fracture. Vol 131. Num 1. Pages 79-106. 2005.

2.

J. Petit, G. Hénaff, C. Sarrazin-Baudoux, 1997, Gaseous atmosphere influence on fatigue crack propagation. In: R.A. Smith Editor, Reliability assessment of cyclically loaded engineering structures Kluwer Academic Publishers, Dordrecht, pp. 301–342

3.

V. V. Bolotin, A. A. Shipkov, J. Appl. Maths Mechs, Vol 65, No. 6, pp. 1001-1010, 2001

2T18. Dynamic, high strain rate, or impact fracture

493

MEASURING THE FRACTURE RESISTANCE OF COMPOSITES AND ADHESIVELY BONDED JOINTS AT HIGH TEST RATES. B. R. K. Blackman, D. D. R. Cartie1, A. J. Kinloch, F. S. Rodriquez-Sanchez and W. S. Teo Department of Mechanical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK. 1Advanced Materials Department, Cranfield University, SIMS bldg 42A, Cranfield, MK43 0AL, UK. [email protected] Research into the mode I delamination resistance of uni-directionally reinforced composites and the fracture resistance of adhesively bonded joints led to the publication of two test standards in 2001 [1, 2]. The ESIS TC4 technical committee contributed significantly to the development of both of these test standards via pre-standardisation round-robin testing, and protocol development. Since then, the committee has focussed its attention on other important technical issues including delamination in multi-directional and cross-ply laminates, mode II fracture in both laminates and adhesive joints, and most recently delamination fatigue and high rate loading. In the present work, we will describe the strategy and progress made towards developing a protocol for high rate loading at 1m/s. Various workers have reported results from performing mode I DCB tests at high rates [3-6] and at least one review has been published [7]. However, no standards exist, and a number of technical issues remain to be resolved. Perhaps the first of these is the issue of whether the DCB test specimen is suitable for high speed testing. The recommended dimensions for the DCB in [1] specify a minimum beam thickness of 3mm for carbon-fibre reinforced composites and 5mm for glass-fibre reinforced composites. This permits the manufacture of rather compliant specimens which tend to suffer from severe flexural wave effects at the higher test rates. These in turn lead to problems with measuring load, and even high frequency response load-cells can resonate at loading rates of 1m/s. A second issue is the potential loss of symmetry at high rates, as the standard quasi-static test applies displacement to one half of the specimen only. This has been noted to be quite a pronounced effect at loading rates of 10m/s [3]. A third issue is crack stability, as frequently a transition from stable to unstable, stick-slip crack growth is observed with increasing test rate. From an experimental perspective, performing high rate DCB tests requires specialist equipment. High-speed servo-hydraulic test machines have been available now since the late 1980s and these represent an efficient way to load the samples. Also, various workers have used drop weight towers to impact and load one half of the specimen. An additional requirement is the need for high speed recording of the test parameters, e.g. crack length, crack opening displacement and/or applied load. From an analytical perspective, determining the resistance to crack growth at high rates requires consideration of the kinetic energy effects in the fracture mechanics energy balance and also of the transient phenomena that are observed. It is against this background that the ESIS TC4 group has commenced work to develop a high rate DCB test protocol for composite laminates and bonded joints. Details of the protocol and of the first experimental results will be presented.

B. R. K. Blackman et al.

494

References 1.

ISO, Standard test method for mode I interlaminar fracture toughness, GIC, of unidirectional fibre-reinforced polymer matrix composites. 2001. ISO 15024.

2.

BSI, Determination of the mode I adhesive fracture energy, GIC, of structural adhesives using the double cantilever beam (DCB) and tapered double cantilever beam (TDCB) specimens. 2001. BS 7991.

3.

Blackman, B.R.K., Dear, J.P., Kinloch, A.J., MacGillivray, H., Wang, Y., Williams, J.G. and Yayla, P., The failure of fibre-composites and adhesively-bonded fibre-composites under high rates of test. Part I: Mode I Loading-Experimental studies. Journal of Materials Science, 1995. 30: p. 5885-5900.

4.

Blackman, B.R.K., Kinloch, A.J., Wang, Y.and Williams, J.G., The failure of fibrecomposites and adhesively bonded fibre-composites under high rates of test. Part II: Mode I Loading-dynamic effects. Journal of Materials Science, 1996. 31: p. 4451-4466.

5.

Gillespie Jr, J.W., L.A. Carlsson, and A.J. Smiley, Rate-dependent mode I interlaminar crack growth mechanisms in graphite/epoxy and graphite/peek. Composites Science and Technology, 1987. 28: p. 1-15.

6.

Smiley, A.J. and R.B. Pipes, Rate effects on mode I interlaminar fracture toughness in composite materials. Journal of Composite Materials, 1987. 21(7): p. 670-687.

7.

Cantwell, W.J. and M. Blyton, Influence of loading rate on the interlaminar fracture properties of high performance composites- A review. Appl Mech Rev, 1999. 52(6): p. 199212.

2T18. Dynamic, high strain rate, or impact fracture

495

QUASISTATIC AND DYNAMIC FRACTURE OF PEARLITIC STEEL B. Strnadel, P. Hausild1 and M. Karlik1 Technical University of Ostrava, Department of Materials Engineering, 17. listopadu 15, 708 33 Ostrava, Czech Republic [email protected] 1Czech Technical University, Faculty of Nuclear Sciences and Physical Engineering, Department of Materials, Trojanova 13, 120 00 Praha 2, Czech Republic [email protected], [email protected], The processes of cleavage crack initiation and characteristic features of fracture surfaces in pearlitic hypo-eutectoid steel (the chemical composition is given in Table 1) have been investigated using Charpy impact specimens and CT specimens for fracture toughness KIc assessment. The results demonstrated that initial cracking in both dynamically and quasistatically loaded specimens was mainly shear cracking of pearlite, e.g. localized slip bands in ferrite promoted cracking of the cementite plates, which was then followed by tearing of the adjacent ferrite laths (Fig. 1). Inclusion triggering cleavage exhibiting as facet where cleavage river lines extended from the particle in its centre was observed as a second fracture micro-mechanism. In CT specimens cleavage occurred by multi-initiation due to the sharp stress peak ahead of the crack tip throughout the whole specimen thickness. In Charpy specimens, the cleavage initiation has been preceded by the ductile tearing changing the stress distribution at the notch root. In consequence of the ductile crack tunneling, the single cleavage triggering site situated in the centerline of Charpy specimens was found.

FIGURE 1. Cleavage initiation by shear cracking of pearlite (CT specimen).

TABLE 1. Chemical composition (wt. %)

The results of fracture toughness tests were statistically treated using the following formula (1):

B. Strnadel et al.

496

PF

ª B §K K m ¨¨ Ic 1  exp «  Ku «¬ B o ©

4 º · ¸¸ ln 2 » »¼ ¹

(1)

where KIc is the fracture toughness, PF is the probability of fracture, B is the specimen thickness, and Bo, Km, and Ku are the parameters.

FIGURE 2. Distribution of the brittle fracture probability. Graphically the distribution function of fracture toughness is given in Fig. 2. The similar statistical analysis was carried out on the set of Charpy notch toughness results. The relationship between both statistical distributions has been established using the results of the fractographic analysis.

2T18. Dynamic, high strain rate, or impact fracture

497

FRAGMENTATION IN THE EXPANDING RING EXPERIMENT H. Zhang and K. Ravi-Chandar The University of Texas at Austin 1 University Station, C0600 Austin, TX 78712-0235 [email protected] Ever since the inspiring work of Mott [1] on the explosive fragmentation of shells, the expanding ring test has been used as an effective tool for evaluating the dynamic constitutive and failure behavior of materials at strain rates of about 104 s-1. Due to the complexity of the experimental configuration used in the expanding ring test, very few experimental results are available in the literature. A large database collected by Grady and Benson [2], which shows that the ring fails by generating a large number of localized necking deformation and a number of fractures at the neck points, has served as the main benchmark for analytical and numerical investigators. Two different points of view are prevalent in the literature, one is based on a statistical approach following on Mott and the other based on the growth of perturbations that localize deformation into necks (see for example, Guduru and Freund, [3]). Both approaches provide realistic predictions of the statistics of the fragmentation and its dependence on the rate of loading; hence additional experimental investigations that are instrumented to identify the appropriate necking and fragmentation mechanisms at these strain rates to are essential. In this paper, we report on electromagnetically driven high-strain-rate expanding ring tests conducted on aluminum rings; this experiment is a recreation of the pioneering work of Niordsen [4]. A large capacitor is discharged through a copper coil. The coil is held firmly in place to prevent expansion; the current passing through the coil – on the order of 10 to 20 kA – is measured with a Rogowski coil. The ring specimen is placed outside this coil with a very small gap filled with an insulator. A large current is induced in the ring specimen which then interacts with the field in the coil and propels the ring specimen radially outward at high speeds. With our experimental setup, copper and aluminum rings can be accelerated to 200 m/s expanding velocity within about 20 microseconds, corresponding to a strain rate of 104 s-1. Under this loading condition, the specimen initially develops large plastic strains uniformly around the ring, but at strains above 35 percent, multiple necks are initiated and growen further into fractures. The main innovation in our experiments is the use of high-speed and high-resolution photography to study the dynamic necking and failure behaviors of the rings. A high speed camera capapble of obtaining pictures at roughly 10 microsecond intervals with spatial resolution of better than 1000 lines per inch is used to image the process of expansion, necking and final fracture. A selected frame from the expansion experiment is shown in Figure 1. The effects of expanding velocity, ring radius, and on the fragmentation of the ring were examined based on image analysis of high speed photographs and statistical analysis of ring fragments. Our results show that for the aluminum rings, almost all necks occur nearly simultaneously without much communication between each other during the ring expansion; the fragmentation process – from the onset of the first fracture to the total fragmentation of the ring – is complete within about 10 Ps. Since the complete time sequence of the strain evolution in the ring, the sequence of appearance of necks and fracture points is identified in the experiment, numerical simulations of any particular experiment, with the appropriate comparison to the measured kinematic quantities, can be performed to infer the constitutive and failure properties of the ring material. A comparison of the experimental results with numerical examinations based on an assumed elastic-plastic constitutive response for the material will be presented.

H. Zhang and K. Ravi-Chandar

498

Figure 1. Fragmentation inan expanding ring experiment; annealed Al 6061 alloy with an initial ring diameter of 30 mm.

References 1.

N.F. Mott, Fragmentation of shell cases, Proc of the Royal Soc London, Series A, Mathematical and Physical Sciences, 189, 300-308, 1947

2.

D.E. Grady and D.A.Benson, Fragmentation of metal rings by electromagnetic loading, Exp Mech, 12, 393-400, 1983.

3.

P.R. Gududru and L.B. Freund, The dynamics of multiple neck formation and fragmentation in high rate extension of ductile materials, Int J of Solids and Struct, 39, 5615-5632, 2002.

4.

F.I. Niordson, A unit for testing materials at high strain rates, Exp Mech, 1965, 5, 23-32.

2T18. Dynamic, high strain rate, or impact fracture

499

INFLUENCE OF FRICTION ON RESULTS OF AN INSTRUMENTED IMPACT TEST I. V. Rokach Kielce University of Technology Al. 1000-lecia PP 7, 25-314 Kielce, Poland [email protected] Contrary to the quasi-static case, where adjustable rollers used as supports reduce effect of friction significantly, the fixed supports are usually used in dynamic tests. Thus, there is always some friction in the specimen/support contact zones during an impact test. In the literature related to the numerical modelling of an impact fracture test, the problem of friction between a specimen and anvil has not attracted much attention. From the very beginning of the impact test modelling it was clear that friction affects results of a test considerably (see Saxon et al. [1]). However, detailed quantitative analysis of friction caused changes in time variation of contact forces and dynamic stress intensity factor (DSIF) is still unavailable. In this work, some results of the finite element (FE) modelling of an impact test for a wide range of specimen configurations and values of coefficient of friction are presented.

FIGURE. 1. Impact specimen model. Let us consider an impact specimen loaded by the striker force F(t) and normal and tangential anvil forces Rn(t) and Rt(t), respectively (Fig. 1). In this study, the simplest form of the friction law (Coulomb law with constant sliding coefficient of friction (CoF) f) has been considered. This law assumes that |Rt(t)| = f Rn(t) if there is sliding in the specimen/support contact zone and |Rt(t)|< f Rn(t) otherwise. In quasi-static case, both elementary beam theory analysis and FE computations show that monotonic growth of the bending force (i) always causes sliding of the specimen in the specimen/ support contact zone in the outside direction with respect to crack tip and (ii) corresponding friction forces act as a compressive load for the crack tip zone. The opposite is true for the decreasing load case. Thus, quasi-static stress intensity factor (SIF) KIqs(t,f) can be calculated as

K Iqs ( t , f )

K Iqs ( t , 0 )(1  sign( F ) fg ( O ))

(1)

where KIqs(t,0) is the SIF for the same loading in the frictionless case, =a/W, the dot means derivative with respect to time. Using the results of Bakker [2] and Kaya and Erdogan [3], it was

I. V. Rokach

500

found that for = 0.01-0.8 function g() can be approximated by 0.157 + 0.353 with accuracy of about 1%. For the preliminary stage of specimen deformation during an impact test, high oscillations of both tup and anvil forces are observed. During this stage, each friction force can either change its sign along with the sliding direction of the specimen with respect to the support or its absolute value can be lower than |fRn(t)| when the specimen is stick with the support. Due to these reasons, predictions of quasi-static theory and results of dynamic analysis could be different. Dynamic calculations for the plane stress model of the impact specimen have been performed using commercial FE program ADINA 8.0.2 for the following sets of parameters: L/ W=4.5(0.5)6.0, =0.3(0.1)0.6, f=0(0.1)0.8, rt/W=0.2, ra/W=0.25. All calculations have been performed for: •

Poisson’s ratio of the specimen material equal to 0.3

•

Constant impact velocity vi = 7 .5 u 1 0  4 (E/U)1/2 (that corresponds to about 4 m/s for steels), where E and U are the Young’s modulus and density of the specimen material, respectively

•

Perfectly stiff striker and supports.

The following conclusions have been made from the results of calculations: 1

Friction between the specimen and the supports considerably affects contact forces and DSIF during a dynamic fracture test and should be taken into account especially for high CoF values.

2

Contrary to the quasi-static case, the relative movements of the specimen in the specimen/ support contact zone are quite complex and include movement in the reverse direction and temporal stick conditions. Due to this reason friction force is not always equal to the normal contact force multiplied by sliding CoF.

3

In general, friction causes increasing of the amplitude of DSIF oscillation and reduction of the mean value of the DSIF. A simple formula for prediction of amount of this reduction has been proposed.

References 1.

Saxon, H.J., Jones, A.T., West, A.J. and Mamaros T.C. In Instrumented Impact Testing, ASTM STP 563, American Society for Testing and Materials, Philadelphia, 1974, 30-49.

2.

Bakker, A., Fat. & Fract. Engng Mat. & Struct., vol. 13, 145÷154, 1990.

3.

Kaya, A.C., Erdogan, F.: Int. J. Fract., vol. 16, 171÷190, 1980.

2T18. Dynamic, high strain rate, or impact fracture

501

INFLUENCE OF MOISTURE CONTENT ON THE DYNAMIC BEHAVIOUR OF CONCRETE I. Vegt and J. Weerheijm Delft University of Technology, Faculty of Civil Engineering and Geosciences P.O. Box 5048, 2600 GA Delft, The Netherlands [email protected] Terrorist attacks, explosion scenarios in tunnels and the potential hazards from storage of high energetic materials have become important safety issues. Knowledge about the response of concrete structures to impact and explosive loading is required for reliable safety assessment and the design of protective structures. A complicating factor is the fact that concrete is a ratedependent material, which means that the mechanical properties of concrete depend on the applied loading rate. The mechanical response of structures exposed to explosive loading can only be predicted properly with material models that include this rate effect.

FIGURE 1. Experimental results on rate effect in concrete The rate dependency of concrete can be divided into two regimes; the regime with moderate rate effects for loading rates in the range from 10-9 s-1 (static loading rate) up to 1 s-1, and the regime with extensive rate effects for loading rates beyond 1 s-1, see Fig. 1. The moisture content, Rossi [1], and the change in geometry of the fracture planes, Körmeling et al [2], are the main causes of the increase of the material parameters of concrete for the moderate regime. It is assumed that the free water in the micro-pores exhibit the so-called “Stéfan effect” causing a strengthening effect in concrete with increasing loading rate. This is the phenomenon that occurs when a viscous liquid is trapped between two plates that are separated quickly, causing a reaction force on the plates that is proportional to the velocity of separation. The second explanation of the ratedependency is based on the alteration of the fracture planes when the loading rate increases. The cracks are forced to develop along a shorter path of higher resistance, which results in a higher strength. The micro-inertia effects in the fracture process zone mainly cause the rate dependency of concrete in the high regime, Weerheijm [3]. The contribution of moisture content in this regime is still unknown. This study aims to combine experimental research on the material properties of concrete, numerical models and microscopic research to describe and understand the basic mechanisms that cause the rate effect in concrete at moderate and high loading rates. To determine the dynamic tensile properties of concrete under moderate strain rates (1 s-1) the gravity driven Split Hopkinson Bar (SHB) at the Stevin laboratory of the Delft University of

I. Vegt and J. Weerheijm

502

Technology is used. The specimens have a length of 100 mm and a diameter of 74 mm. The moisture content of the specimens is varied (normal, wet and dry). The tensile strength as well as the fracture energy are determined. As a reference deformation controlled static tests with a strain rate of 10-9 s-1 have been conducted. After the impact tests, the specimens are impregnated with epoxy and studied with an optical microscope to study the width of the fracture zone and the crack patterns at the different moisture levels. The material properties of concrete at moderate loading rate and the dynamic/static ratio of the strength and fracture energy are determined. Preliminary results show an increase in tensile strength for all three moisture contents. The high moisture level (wet) shows a larger dynamic/static strength ratio than the normal and low moisture level (dry). A similar trend is observed in the results of the fracture energy. The results of the SHB-tests, the static tests and the post-test examination of the fracture planes will be presented and discussed in this paper. The influence of moisture on the rate effect and the changes in the fracture zone are also discussed. The rate dependent tensile material properties emerging from the experimental research are not the true material properties since inevitably the combined material and structural response is recorded. To eliminate the effect of structural behaviour from the results inverse computational modelling is applied. The strength, fracture energy, time to failure and the characteristics of the fracture zone resulting from the experiments are used as input parameters for the numerical model. In literature various rate dependent material models are proposed. Most of these models reproduce the strength rate dependency quite well. Data and knowledge of the rate effect on the failure process, the softening branch, is very scarce and consequently the modelling has been quite speculative hitherto. In the computational study of the SHB tests a visco-elastic visco-plastic damage model [4] was used. An attempt to deduct the true material behaviour is covered in this paper.

References 1.

Rossi, P., Materials and Structures, Supplement March 1997, 54-62

2.

Körmeling, H.A., Zielinsky, A.J. and Reinhardt, H.W., Experiments on concrete under single and repeated uniaxial impact tensile loading, Delft University of Technology, Report No. 580-3, 1980

3.

Weerheijm, J., Concrete under impact tensile loading and lateral compression, Dissertation, Delft University of Technology, 1992

4.

Pedersen, R.R., Sluys, L.J., Vegt, I., Weerheijm, J. and Simone, A., Modelling of impact behaviour of concrete – a computational approach, Submitted to ECF16

2T18. Dynamic, high strain rate, or impact fracture

503

STRENGTH AND TOUGHNESS PROPERTIES OF STEELS UNDER DYNAMIC LOADING J. Fang Technical Center, Baoshan Iron & Steel Co., Ltd. Kedong Road, Fujin Road, Shanghai 201900, China. [email protected] It is feasible and convenient to prepare miniature round bar and Charpy V notch specimens simultaneously from structural steels for conventional tensile, Charpy impact and impact tensile testing, which provides the relative testing rate high up to 102 /s for uniaxial loading and 5×105 MPa·m1/2·s-1 for impact in this study, achieving the possibility of acquiring the dynamic response properties of HSLA combined with its quasi static performance all together.

FIGURE 1. Illustration of the impact equipment and specimens. As a result, the strength property of X80 pipeline steel is proved to be dependent of the loading rate. The four order of magnitude does rate increase by, its yield stress and tensile strength rise by 100MPa. As to remove the noise signals due to the vibration and inertia effect on the impact tensile stress-strain curves, dynamic flow yield stress is nominally calculated as the average of first two peak and valley stress values on the curve, see Fig.2. The validation of the Server equation (1) for the estimation of dynamic yield stress by means of general yield force, i.e. Fgy by instrumented impact was also studied by performing correlated testing between impact tensile and Charpy impact. The linear relationship of Vyd with Fgy is authenticated satisfactorily, whereas the coincidence of dynamic tensile strength, i.e. Vbd with Fm is void. Moreover, crack extension resistance curve J-'a was established for monitoring the energy absorbed by crack initiation and propagation, which implicates the toughness property of HSLA under dynamic loadings, as Fig. 3. V

yd

2 . 99 F gy

S 4 B (W  a 0 ) 2

(1)

J. Fang

504

FIGURE 2. Stress-Strain curves obtained by tensile under dynamic and static loading.

FIGURE 3. Dynamic crack extension resistance curves. As above, quasi static tensile, impact tensile and instrumented Charpy impact testing are integrated into the unique experimental platform, on which the all-round assessment of material strength, plasticity and toughness properties could be accomplished with the strain loading rate from 10-2-102 /s and various simulated loading conditions such as tensile or impact.

References 1.

Server W.L., J. Engng. Mat. Technol., Trans. ASME, vol. 100, 183-188, 1978.

2.

Kobayashi T., Yamamoto I., Niinomi M., J. of Testing and Evaluation, JTEVA, vol. 21, 145153, 1993.

3.

Bohme W. In Evaluating Material Properties by Dynamic Testing, edited by E. van. Walle, Mechanical Engineering Publication, London, 1996, 1-23.

4.

Fang J., Ding F.L., Wang C.Z., J. Phys. IV France, vol. 110, 551-557, 2003.

2T18. Dynamic, high strain rate, or impact fracture

505

RUBBER PARTICLE SIZE EFFECT ON IMPACT CHARACTERISTICS OF PC/ ABS (50/50) BLENDS M. Nizar Machmud, Masaki Omiya, Hirotsugu Inoue and Kikuo Kishimoto Department of Mechanical and Control Engineering, Tokyo Institute of Technology, 2-12-1 O-okayama, Meguro-ku, 152-8552, Tokyo, Japan [email protected], [email protected], [email protected], [email protected] Impact charateristics of simply-supported circular thin plates made of PC/ABS (50/50) blends having 10 wt% content of rubber with a rubber particle diameter of 270 nm called PA-1 and of 150-170 nm called PA-2 tested at room temperature by use of a drop weight impact apparatus under different speeds: 2, 3, and 4 m/sec has been studied. Features of the target were viewed to describe definite alteration of the plates induced by a hemispherical tip-ended cylindrical striker due to effect of rubber particle size distributed in the blends. It was found that the blends with a rubber particle diameter of 150-170 nm were not in shattering and exhibited a multiaxial crack shape at the speed of 3 m/sec. Equivalent ABS materials of the blends were then examined at the similar speeds. The results of this study showed that brittle ABS materials produced tough PC/ABS blends. It was apparent that distribution of bimodal type with smaller rubber particle toughened the PC/ABS blends at room temperature. Examination by use of scanning electron microscope (SEM) on fracture surface of the failed specimens was also carried out. The brittleness and toughness of the PC/ABS blends at the speed of 3 m/sec were then analyzed using an optical microscope and a transmission electron microscope (TEM) for observation on global and local deformation, respectively. Drop weight impact test The drop weight impact test has been carried out on our laboratory apparatus at room temperature under a range of impact speeds: 2, 3 and 4 m/sec. Behavior of the blends was induced by a hemispherical tip-ended cylindrical striker made of stainless steel (SS55) with diameter of 20 mm that struck perpendicularly the center of the simply-supported circular thin plate with an initial thickness of 2 mm and diameter of 99.3 mm. The body of the impactor attached to guiding rods was designed to give a total impactor mass of 2.4 kg. Description of the test is presented in Fig. 1. The range of impact speeds v was calculated from

v

2gh d

(1)

where g is the acceleration due to gravity, and hd is drop height measured during the impact tests. Although the impactor speed is presumed to be accurately predicted by this formula, the actual speed may be lower than the calculated speed due to friction caused by the guiding rods. However, other researchers have verified that the friction has a negligible effect on the accuracy of speed prediction using the formula [9].

M. N. Machmud et al.

506

a)

b)

c)

Fig. 1 Drop weight impact test: (a) test apparatus, (b) specimen, (c) striker Materials Table 1. Properties of PC/ABS blends with monomodal and bimodal types

References 1.

R.A. Kudva, H. Keskkula and D.R. Paul, Polymer, vol. 41, 225-237, 2000

2.

Th. Seelig and E. van der Giessen, Int. J. Solids and Structures, vol. 39, 3505-3522, 2002

3.

J.P.F. Inberg and R.J. Gaymans, Polymer, vol. 43, 2425- 2434, 2002

4.

J.P.F. Inberg, A. Takens and R.J. Gaymans, Polymer, vol. 43, 2795-2802, 2002

5.

J.P.F. Inberg and R.J. Gaymans, Polymer, vol. 43, 3767-3777, 2002

6.

W. Jiang, H. Liang, J. Zhang, D. He and B. Jiang, J. Appl. Polym. Sci., vol. 58, 537-539, 1995

7.

C.M. Tai, R.K.Y. Li and C.N. Ng, Polymer Testing, vol. 19, 143-154, 2000

8.

W.G. Perkins, Polymer Engineering and Science, vol. 39, 2445-2460, 1999

9.

L.S. Kistler and A.M. Waas, Int. J. Impact Engng, vol. 21, 711-736, 1998

10. B.C. Simonsen and L.P. Lauridsen, Int. J. Impact Engng, vol. 24, 1017-1039, 2000

2T18. Dynamic, high strain rate, or impact fracture

507

EFFECT OF STRAIN RATE ON MECHANICAL PROPERTIES OF REINFORCED POLYOLEFINS Marcus Schossig, Christian Bieroegel, Wolfgang Grellmann, Reinhard Bardenheier1 and Thomas Mecklenburg2 Institute of Materials Science, Martin-Luther University Halle-Wittenberg, D-06099 Halle/Saale, Germany 1Instron Limited, HP12 3SY High Wycombe, UK 2Basell Polyolefine GmbH, D-65926 Frankfurt, Germany [email protected] This paper deals with results of high-speed tensile tests on glass-fibre reinforced thermoplastic materials. Starting point of the investigations is the fact, that requirements for a modern material have been steadily increased. One reason here is the increasing use of computer-aided design over the past years. Especially for the automotive industry, not only the mechanical properties as results of quasi-static tests are of interest. According to EuroNCAP crash tests, strain rates up to 200 s-1 can be observed in the region of crash boxes at 64 km/h initial speed (Fig. 1a) [1, 2]. Therefore, it is necessary to perform dynamic tests with strain rates up to maximum values of 104–106 s-1 [3, 4]. For example, with commercially available servo-hydraulic testing machines strain rates between 10-3 to 103 s-1 can be realized (Fig. 1b).

a)

b)

FIGURE 1. a) Schema of strain rates in crash tests [2] and b) spectrum of strain rates [3] At the moment, there is no standard for the execution of high-speed tensile tests. A tentative draft of the High Strain Rate Experts Group from the International Iron and Steel Institute for metals was presented in March 2004 [5]. However, a corresponding draft for polymeric materials does not exist. Furthermore, in the literature high-speed tensile tests of polymers are hardly described. This is due to experimental difficulties during performance of high-speed tensile tests and high costs. The results shown in this paper will contribute to a better understanding of deformation behaviour of polymeric materials under high strain rates. Aim of the investigations was to assess the influence of strain rate on stress–strain behaviour of glass-fibre reinforced materials. For this reason, polypropylene and polybutene materials with glass-fibre contents of 0, 20, 30 and 40 wt.-% were examined. Polybutene has a wide application potential. Presently it is used mainly as unreinforced pipe material and new application fields can be opened by the addition of glass fibres. The high-speed tensile tests were performed with specimen type 1A according to ISO 527-2; a clamping of 115 mm was used for a better comparability with the results from quasi-static tests.

M. Schossig et al.

508

The tests were carried out with an Instron servo-hydraulic testing machine. The load was measured with the help of a piezoquarz load cell and the displacement was measured by Linear Variable Differential Transducer (LVDT). The following test speeds were realized: 1/120, 1/2, 1, 2, 5, 10 and 20 m/s. The corresponding strain rates, at a clamping length of 115 mm, are in the range of 0.0725 to 174 s-1. With increasing the strain rate, an increase of the strength and a decrease of the deformation ability can be detected for the investigated materials (Fig. 2a). This behaviour is described in the literature as positive strain rate dependence [3, 6]. A change of the fracture behaviour with increasing content of glass fibres at a constant strain rate can be observed. The fracture behaviour of the polypropylene materials changes from single break over multiple breaks to multiple splinter break (Fig. 2b).The polybutene material system shows a transition from single break to multiple break at higher glass fibre contents.

a)

b)

FIGURE 2: a) Schematic stress–strain curves and b) fracture appearance for various glass-fibre reinforced polypropylene materials at a strain rate of 87s-1

References 1.

Frontal Impact Testing Protocol, European New Car Assessment Programme (EuroNCAP), March 2004.

2.

Werner, H. and Gese, H., Importance of strain rate dependent material paramters for crash simulations, DVM-Tagung "Werkstoffprüfung 2002 – Kennwertermittlung für die Praxis", Bad Nauheim, December 5–6, 2002.

3.

Bardenheier, R. and Rogers, G., Dynamic Impact Testing, Instron Ltd., 2003.

4.

Bleck, W. and Larour, P., Effect of Strain Rate and Temperature on the Mechanical Properties of LC and IF Steels, RWTH Aachen,

5.

Borsutzki, M., et al., Recommendations for Dynamic Tensile Testing of Sheet Steels, High Strain Rate Experts Group, International Iron and Steel Institute, March 2004.

6.

Guden, M. and Hall, I. W., High strain-rate compression testing of a short-fiber reinforced aluminum composite, vol. A232, 1–10, 1997

2T18. Dynamic, high strain rate, or impact fracture

509

FRACTURE RELATED MECHANICAL PROPERTIES OF AIRCRAFT CAST ALUMINUM ALLOY A357 N. D. Alexopoulos Laboratory of Technology and Strength of Materials Department of Mechanical and Aeronautical Engineering University of Patras Panepistimioupolis Rion, 26500 Patras, Greece [email protected] Precision casting is currently attracting considerable attention as a reliable manufacturing process for producing aeronautical and automotive aluminum components of complex shape geometries cost efficiently. Inferior mechanical properties, specifically in terms of ductility and toughness, and increased scatter compared to the respective wrought aluminum alloys, represent serious drawbacks for their increased exploitation in aeronautical applications. The tighter controls currently applied during the casting process, as well as the advancements on the casting processes and the better understanding of the physical metallurgy background of the age-hardened aluminum alloys led to an improvement of the material quality and, hence, to an appreciable increase of the competitiveness of aluminum casting products. The most widely used alloy for the above applications is the precision-hardened Al-Si-Mg A357 cast alloy. Alloy A357 with minor modifications in chemical composition has been extensively investigated in recent research projects, e.g. ADVACAST [Anon., Advanced Aluminum Precision Casting For Integrally Stiffened Net - Shape Components (ADVACAST). Final Technical Report of the BRITE Project 4084, Brussels, Belgium, 1996.], YPER [Alexopoulos, N.D., Development of new near net shape cast aluminum alloys with improved mechanical properties. Final Technical Report of the Project YPER 94/274, Greek General Secreriat of Research and Technology, Patra, Greece, (in Greek) 2002.] and PABE [Anon., Production and development of cast aluminum components for aeronautical applications, Final Technical Report of the Project PABE 96BE/219, Greek General Secreriat of Research and Technology, Bolos, Greece, (in Greek) 2000.]. The characterization of the quality of a cast alloy involves non-destructive inspection, quantitative metallography and mechanical testing, e.g. Alexopoulos [Alexopoulos, N.D., Int. Journal of Cast Metals Research, submitted for publication, 2005.]. Hardness, tensile and impact tests are the tests currently used to characterize the quality of a cast aluminum alloy in terms of mechanical performance. The demands for increased damage tolerance abilities of cast aluminum alloys have made fracture and tensile toughness important properties. Notice that in aircraft and automotive industry, certain minimum values in tensile strength, ductility and fracture toughness are prerequisite for considering a material as a candidate for structural applications. e.g. [Anon., Advanced Aluminum Precision Casting For Integrally Stiffened Net - Shape Components (ADVACAST). Final Technical Report of the BRITE Project 4084, Brussels, Belgium, 1996.]. Hardness measurements and tensile mechanical properties of the aircraft cast aluminum alloy A357 have been evaluated in Alexopoulos and Pantelakis [Alexopoulos, N.D. and Pantelakis, Sp.G., Materials & Design, Vol. 25, 419-430, 2004.] for 25 different artificial aging heat treatment conditions. Yield strength, tensile strength, elongation to fracture and strain energy density W were evaluated from all tensile tests. Strain energy density W was evaluated as the area below the stressstrain curve, accounts for both, ductility and toughness and is actually the energy given per material volume for the material fracture. In Alexopoulos and Pantelakis [Alexopoulos, N.D. and Pantelakis, Sp.G., Metallurgical and Materials Transactions A, Vol. 35A, 3079-3089, 2004.], impact Charpy V-notch tests were performed for the same heat treatment conditions of the A357

N. D. Alexopoulos

510

alloy. Impact resistance RCVN was evaluated from the impact tests as the fraction of the material’s energy to fracture to the specimen’s cross-section. In the early 70’s the empirical equation (1) was proposed by Barson and Rolfe [Barson, J. and Rolfe, S., In Impact Testing of Metals, ASTM STP 466, Ohaio, 1970, 281-302.], for both, lowalloyed and austenitic steels to calculate the alloy’s plane strain fracture toughness KIc for known Charpy V-notch impact energy WCVN and yield strength values Rp. The m and n coefficients are both, empirical and material dependant constants. However, the correlation of the material’s fracture toughness and impact energy has not been reported on the open literature for aluminum alloys.

§ K Ic ¨ ¨ R © p

· ¸ ¸ ¹

2

§W m ˜ ¨ CVN ¨ R p ©

2

· ¸ n ¸ ¹

(1)

In the present work, the material property impact resistance RCVN has been empirically related to the material’s strain energy density W. To this end, the strain energy density W has been involved in equation (1) instead of the plane strain fracture toughness KIc, for the case of cast aluminum alloys. According to Yeong et al. [Yeong, D., Orringen, O. and Sih, G., Journal of Theoretical and Applied Fracture Mechanics, Vol. 22, 127-137, 1995.], strain energy density W is proportional to KIc2, thus providing a background for this assessment. Different empirical correlations are proposed to establish useful relationship between RCVN and W. Performed fractographic analyses by using a scanning electron microscope are supporting the physically arbitrary correlation of tensile strain energy density and impact resistance. The above correlations can be used to estimate the ductility and toughness of the under-consideration A357 material, from a Charpy impact test.

References 1.

Anon., Advanced Aluminum Precision Casting For Integrally Stiffened Net - Shape Components (ADVACAST). Final Technical Report of the BRITE Project 4084, Brussels, Belgium, 1996.

2.

Alexopoulos, N.D., Development of new near net shape cast aluminum alloys with improved mechanical properties. Final Technical Report of the Project YPER 94/274, Greek General Secreriat of Research and Technology, Patra, Greece, (in Greek) 2002.

3.

Anon., Production and development of cast aluminum components for aeronautical applications, Final Technical Report of the Project PABE 96BE/219, Greek General Secreriat of Research and Technology, Bolos, Greece, (in Greek) 2000.

4.

Alexopoulos, N.D., Int. Journal of Cast Metals Research, submitted for publication, 2005.

5.

Alexopoulos, N.D. and Pantelakis, Sp.G., Materials & Design, Vol. 25, 419-430, 2004.

6.

Alexopoulos, N.D. and Pantelakis, Sp.G., Metallurgical and Materials Transactions A, Vol. 35A, 3079-3089, 2004.

7.

Barson, J. and Rolfe, S., In Impact Testing of Metals, ASTM STP 466, Ohaio, 1970, 281-302.

8.

Yeong, D., Orringen, O. and Sih, G., Journal of Theoretical and Applied Fracture Mechanics, Vol. 22, 127-137, 1995.

2T18. Dynamic, high strain rate, or impact fracture

511

SHEAR FAILURE OF TI-6AL-4V BY DIRECT IMPACT AND ANALYSE OF THE PROCESS OF ELASTIC AND PLASTIC WAVE PROPAGATION P. Chwalik, A. Rusinek and J. R. Klepaczko Laboratory of Physics and Mechanics of Materials, UMR 7554 University Paul Verlaine, Ile du Saulcy, 57045 Metz Cedex 01, France [email protected], [email protected], [email protected] An Adiabatic Shear Banding (ASB) in Ti–6Al–4V alloy is studied in this work by application of the finite element technique. Two approaches of impact shearing have been considered for a wide range of impact velocities, that is an infinite layer and a finite band. The Critical Impact Velocity (CIV) in shear was estimated. A special experimental technique developed at LPMM-Metz has permitted shear tests at the strain rates up to 105 s-1. After analysis of experimental data available in the open literature for Ti6Al-4V alloy and the results obtained with the MDS technique, the following explicit form of the constitutive relation has been implemented in LPMM-Metz [1-3]

W

P (T ) ª § T «B¨ P 0 « ¨© T 0 ¬

· ¸¸ ¹

Q

*  * 

P (T )

P 0 1  AT  CT

n (T )

§ T · ¸¸ n 0 ¨¨ 1  T m ¹ ©

n T

p

2





1/ m § * · º T  ¨¨ 1  log 0 ¸¸ » * ¹ » D © ¼

(1) (2)

(3)

B, µ0, Q, n, m are respectively, the modulus of plasticity, the shear modulus at T=0K, the temperature index, the strain hardening exponent and the logarithmic rate sensitivity, T0, *p, *0 and D are normalization constants, also T, Tm, A, C respectively, the absolute temperature, melting point temperature, material constants. The constitutive relation accounts for strain hardening, rate sensitivity and thermal coupling. In this way a complete dynamic approach with elastic-plastic wave propagation, ASB development and failure could be considered. After identification of all material constants for Ti-6Al-4V, the relations (1)-(3) have been introduced into the finite element code ABAQUS Explicit. Many aspects in FE analysis were optimized in [1], for example the meshes density, boundary and initial conditions, contacts etc. All 2D simulation was assumed with plane stress elements CPS4R (four nodes, reduced integration). An innite-length layer with 1% geometrical imperfection defined in the layer thickness was submitted to shear [1]. The apparition of CIV was observed for impact velocity 94 m/s. The CIV occurs due to trapping of plastic deformation triggered by plastic waves. Different risetimes were chosen and different constitutive relations (for example Johnson-Cook [4]) were also studied. In this way the results obtained for shear by application of constitutive relation (1-3) are very close to the localisation phenomena observed by Klepaczko and Rezaig [5], and by Rusinek et al. [6] in the case of tension. The wave reflection leads to different strain localisation.

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FIGURE 1. Impact shearing: layer at 20m/s (a), layer at 100m/s (b), ASB formation in shearing specimen at 20m/s (c), and 100m/s (d). As the second task, the development and evolution of ASB and failure in double shear specimens used in LPMM was analysed. In order to calculate numerically an evolution of the plastic zones and failure, it is necessary to introduce a local failure criterion defined by (5). Value of the critical strain *f can be determined as proportional to the instability strain defined by (wW/ w*)A=0 in the adiabatic conditions of deformation with the proportionality coefficient D. * f ( * )

D * i ( * )

(5)

At lower impact velocities, for example 20m/s, Fig 1a and c, the localization of shear band is situated in the middle of the sheared zone. When the impact velocity increases approximately to 100 m/s, Fig 1b and d, the shift of the band is observed in the direction of the impact side of specimen. The value of CIV is similar to these estimated for an infinite layer. The constitutive relation developed in LPMM offers a good possibility of implantation in finite element codes like ABAQUS Explicit. It has permitted to study the ASB formation, elastic and plastic wave propagation and to estimate the CIV for Ti-6Al-4V.

References 1.

Klepaczko, J.R., Klosak, M., Eur. J. Mech. A/ Solids, vol. 18, 93-113, 1999.

2.

Rusinek, A., Klepaczko, J.R., Int. J. of Plasticity, vol. 17, 87-115, 2001.

3.

Chwalik, P., Ph.D Thesis, University of Metz, 2005

4.

Seo, S., Min, O., Yang, B., Journal of Impact Engineering, vol. 31, 735–754, 2005.

5.

Klepaczko, J.R., Rezaig, B., Mechanics of Materials, vol. 24, 125-139, 1996

6.

Rusinek, A., Zaera R., Klepaczko J.R., Cheriguene R., Acta Materialia, submitted 2005.

2T18. Dynamic, high strain rate, or impact fracture

513

EVALUATING OF FRACTURE MECHANICS PROPERTIES AT INTERMEDIATE STRAIN RATES, TRANSFERABLE TO COMPONENTS Peter Trubitz, Annette Ludwig, Gerhard Pusch and Hans-Peter Winkler1 TU Bergakademie Freiberg Institute of Materials Engineering Gustav-Zeuner-Str. 5, Freiberg, 09599, Germany [email protected] 1GNS Gesellschaft für Nuklear-Service mbH Hollestraße 7 A, 45127, Essen, Germany The evaluation of fracture mechanics properties at intermediate strain rates can be carried out on the basis of different standards. The starting point of the lecture is a comparative evaluation of the relevant standards and test procedures [1–4]. The aim of the fracture mechanics test at intermediate strain rates are not only generally materials characterizations but often the portability of the determined parameters on bigger sizes in case of evaluation of real components. In this situation the definition of component transferable material parameters is an important problem. In this context the crack initiation point gets an all-dominant importance [5, 6]. In case of multiple specimens testing typically the definition of the crack initiation point based on the results of stretch-zone measurements. With the scope of a bigger research program for the evaluation of the behaviour of bulk containers made of spheroidal graphite cast iron (ductile cast iron DCI) grad GJS-400 [7] one task is the determination of component transferable fracture mechanic values at intermediate strain rates at different temperatures. This group of materials shows damage behaviour at intermediate strain rates without typical stretching, located at the crack tip. Therefore the crack initiation value can not by determined by stretch-zone measurements. By static loading crack growth was detected as a process of dissociation of the graphite particles and crack growth between the particles (“graphite-particle-blunting”). Based on this scanning electron fractography of the DCI a characteristic structure parameter – the mean distance of the graphite particles O Fig. 1 – was submitted for the definition of the crack initiation point. Starting from a generally materials characterization including determination of the most important structural parameters the first results of the instrumented pre-cracked Charpy impact tests (multiple-specimen technique applied as low-blow-procedure) at room temperature and at 40 °C will be presented. The estimated dynamical crack-resistance curves (dynamic R-curves) and the dynamical crack-initiation-values will be discussed taking into account the different testing standards and test procedures as well as our own proposal for the definition of the crack initialization point (Fig. 2).

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FIGURE 1. Definition of OFIGURE 2. dynamic R-curve of DCI (schematic)

References 1.

ISO 12135:2002: Metallic material – Unified method of test fort he determination of quasistatic fracture toughness. First Edition. 2002-12-01

2.

ASTM E 1820-01: Standard Test Method for Measurement of Fracture Toughnes. ASTM International, 2001

3.

ESIS P2-92: ESIS Procedure for Determination the Fracture Behaviour of Materials. European Structural Integrity Society – ESIS, Technical Committee I: Elastic-Plastic Fracture. Subcommittee I.4: Fracture Mechanics Testing Standards. ESIS Office, c/o Materials Laboratory, Delft University of Technology, Delft, The Netherlands. January 1992

4.

Charpy fracture test methods. Proposed standard methods for instrumented pre-cracked Charpy impact testing of steels. Draft 19. European Structural Integrity Society [ESIS], Technical Sub-Committee on Dynamic Testing at Intermediate Strain Rates. April 2005

5.

Roos, E.: Grundlagen und notwendige Voraussetzungen zur Anwendung der Risswiderstandskurve in der Sicherheitsanalyse angerissener Bauteile. Habilitationsschrift Universität Stuttgart 1992. VDI-Fortschr.-Bericht Reihe 18, Nr. 122. VDI-Verlag GmbH, Düsseldorf 1993

6.

Holland, D.: Einfluß des Spannungszustandes auf die Vorgänge beim Gleitbruch von Baustählen. Dissertation RWTH Aachen, 1992

7.

Winkler, H.-P.; Trubitz, P.; Pusch, G.; Warnke, E.P.; Beute, K. and Novotny, V.: Dynamic Fracture Toughness Data for CASTOR Casks. Vortrag auf der Tagung Patram 2004. 20. - 24. September 2004, Berlin

2T18. Dynamic, high strain rate, or impact fracture

515

CRACK RESISTANCE DETERMINATION FROM THE CHARPY IMPACT TEST R. Chaouadi SCK-CEN Boeretang 200, 2400 Mol, Belgium [email protected] Many engineers and scientists investigated the possibility to correlate Charpy impact energy with the fracture toughness. As a result, many empirical correlations can be found in literature [1-2]. However, most of these correlations had a limited application range due primarily to their empirical basis. Recently, a simple procedure was provided to determine crack length from the load-displacement test record [3]. The basic idea is that crack length is proportional to the absorbed energy, namely: § Ei  E0 ' ai v ¨ ¨E © final  E 0

· ¸ ¸ ¹

2

(1)

where "Ei" is the absorbed energy at time "i", E0 is a threshold energy corresponding to onset of crack extension and Efinal is the final energy corresponding to a measured crack extension 'afinal. This procedure was validated on a large number of materials using various cracked geometries. The main objective of this paper is to investigate the possibility to apply a similar procedure to a V-notched geometry, namely the Charpy specimen. Such an evaluation would lead to determine the crack resistance from the Charpy-V impact test. Two low alloyed steels used in the reactor pressure vessel industry were selected. Tests were performed on Charpy-V notched specimen loaded statically as well as dynamically. Precracked Charpy specimens with the crack length-to-width ratio of 0.5 and 0.2 were also tested at both loading rates. It is found that this procedure is applicable to the notched geometry (see Figure 1). The experimental results obtained on the notched and cracked geometries at both loading rates can be rationalized by taking into account the notch and loading rate effects.

R. Chaouadi

516

FIGURE 1. Crack resistance behavior from the Charpy-V notched geometry in static loading: multiple specimen versus single specimen method.

References 1.

Rolfe S.T. and Barsom, J.M., Fracture and Fatigue Control in Structure – Application of Fracture Mechanics, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1977.

2.

Schindler, H.J., In Pendulum Impact Testing: A Century of Progress, edited by T.A. Sievert and M.P. Manahan, ASTM STP 1380, 2000, 337-353.

3.

Chaouadi, R., J. Testing and Evaluation, Vol. 32, No. 6, 469-475, 2004.

2T18. Dynamic, high strain rate, or impact fracture

517

A STOCHASTIC INTERFACE MODEL FOR THE FRACTURE OF BARS S. Nagy and F. Kun Department of Theoretical Physics, University of Debrecen, Debrecen, Hungary H-4032 Debrecen, Poroszlay u. 6/c, Hungary [email protected] The fracture of heterogeneous materials is an important scientific and technological problem which has attracted an intensive research during the past years. The interaction of the heterogeneous stress field with the disordered microstructure of the material makes the fracture process difficult to handle theoretically, hence, most of the theoretical approaches rely on computer simulations of discrete models. Recently, it was found experimentally that the cracking of a bar under three point bending proceeds in bursts which are characterized by power law distributions. Motivated by these experimental findings, in this work we study the damage process of an elastic bar under three point bending focusing on the bursts of microscopic breaking events and on the spatial distribution of the damage. We model the bars as two rigid blocks which are glued together by an elastic interface. It is assumed that the interface region can deform while the two rigid blocks remain intact under the deflection of the specimen. The rigidity implies that the deformation of the specimen can be characterized simply by the deflection of the middle of the bar d. The interface region is discretized by elastic fibers of number N which are placed equidistantly between the two blocks. If the local deformation ei of a fiber exceeds a threshold value eic it breaks and a microcrack nucleates in the interface. The disordered properties of the material are represented by the randomness of the breaking thresholds eic which are independent identically distributed random variables. During the deformation process those fibers which exceed their threshold value break, i.e. they are removed from the interface. The amount of disorder of the failure thresholds eic has a substantial effect on the macroscopic response of the specimen. In case of zero disorder the failure of the interface is completely brittle, i.e. fiber breaking starts at the bottom and continues upwards as d is increased and the consitutive curve is sharply peaked. As the strength of the disorder is increased the constitutive curve gets more and more rounded and develops into a quadratic maximum. On the microlevel it means that that the neighbouring fibers do not simply break one after the other. To characterize the damage process of the loaded bar under stress controlled conditions we determined the distribution of the burst sizes s of fiber breaks for the disorder distribution varying the width of the distribution d. Simulations revealed that the avalanche size distribution D(s) shows a power law behaviour and the exponent t is universal, i.e. it is insensitive to the strength of the disorder, see FIG. 1. It turned out that t coincides with the exponent of the classical parallel bundle of fibers with equal load sharing t»2.5. Furthermore, we showed that ahead the crack tip a fracture process zone is formed where the local failure mechanism is percolation in a gradient field. The process zone proved to shrink with increasing deformation making the crack tip sharper as the crack advances The largest burst has a power law dependence on the strength of the disorder.

S. Nagy and F. Kun

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FIG. 1 Based on our simple model we also studied the energetics of the impact process during three point bending induced dynamically by impact. Depending on the energy E of the hit on the specimen the impact process can be classified into two states. Calculations revealed that there exists a critical value of the impact energy below which partial failure of the interface occurs (damaged phase), while above it the crack passes through the entire specimen resulting in global failure (fractured phase). The critical energy separates the two phases of the system and a continous phase transition occurs between them. Identifying the number of intact fibers Nint by the order parameter it was analytically proven that Nint has a power law dependence on the distance from Ec with exponent b=1/2 in case of zero disorder. Numerical results showed that the exponent grows with growing strength of disorder up to the value b=2/3.

References 1.

F. Kun et. al Phys. Rev. Letters 93, 227204 (2004)

2T18. Dynamic, high strain rate, or impact fracture

519

THE ANTI-PENETRATION PROPERTIES OF SPACE ARMOR Tso-Liang Teng, Cho-Chung Liang and Cheng-Chung Lu Department of Mechanical and Automation Engineering, Da-Yeh University 112. Shan-Jeau Rd., Dah-Tsuen, Chang-Hua, Taiwan, R. O. C. [email protected], [email protected] New types of armor, including space armor, multiple-layered armor, composite armor and modular armor have been successfully developed and installed on the armored vehicles of several nations. The protective capability of armor against penetration is established. Of developed composite armor, space armor has a simple structure and is easy to produce and can be produced at low cost. This study uses the finite element package DYTRAN and the pre and post processor PNTRAN to elucidate the ballistic resistance and penetration of space armor. Factors such as armor thickness, space of armor and projectile profile are considered. A tool for simulating the protection afforded by armor and supporting the design of space armor is developed. Figure 1 presents the deformation plot of the steel ball as it penetrates the space armor. The total thickness of the space armor is 6.35 mm. Each layer is assumed to be 3.175 mm in thick and 62.8 mm in long and wide. The armor incline at 60 degree to the vertical, and the space between the two layers is 10 mm.

(t=0sec)

(t=24sec)

(t=64sec)

(t=96sec)

(t=144sec)

(t=240sec)

Figure 1 the deformation plot of the steel ball and plate( t1 = t2 = 3.175 mm, d=10 mm ) The first layer is completely penetrated and the steel ball is deformed. The steel ball rebounded from the second layer. The surface of the second layer has only a bowl-shaped contour, indicating that the steel ball was stopped. The figure thus shows the anti-penetration capacity of space armor. The improved capability of space armor is inferred to be related to the following causes.(1) The penetration of the first layer will deteriorate the projectile and thus reduces the energy with which it collides with the second layer. (2) The fall in speed of the projectile upon penetration into the first layer also reduces the energy of collision with the second layer.(3) The deviation of the

520

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direction of projectile from its original direction also increases the angle of incidence of the projectile, causing it to be rebounded after it has penetrated through the first layer. Figure 2 plots the residual velocity of the steel ball after it has penetrated the space armor. The plot implies that the ballistic resistance increase with the gap width. Figure 3 plots the relationships between the residual velocity of projectile and the ratio of thicknesses of the two layers (t1/t2). The magnitude of the residual velocity is proportional to the ratio of thicknesses. Figure 4 plots the change in residual velocity versus the L/D ratio. In only the L/D=1 case, the residual velocity is less than that of a steel ball projectile of the same mass, given the same gap width. In the other cases, the residual velocity exceeded that of the ball projectile, increasing with the L/D ratio. The space armor has a poor ballistic resistance to slender projectiles.

Fig.2 the residual velocity of the steel ball with various distance of space armor

Fig.3 the relationships between the residual velocity of projectileand the ratio of thicknesses

Figure 4 the residual velocity of a cylindrical projectile versus the L/D ratio

2T18. Dynamic, high strain rate, or impact fracture

521

KEY CURVE METHODS FOR DYNAMIC FRACTURE MECHANICS OF CAST IRON W. Baer Federal Institute for Materials Research and Testing (BAM) Unter den Eichen 87, D-12200 Berlin, Germany [email protected] Today, ductile cast iron materials (DCI) are used for safety relevant components such as for instance transport and storage casks for radioactive materials. The corresponding methods and codes for safety assessment take into account fracture mechanics concepts more and more. Nevertheless, some necessary prerequisites for the practical application of these codes like the quantification and availability of both the loading as well as the materials resistance in terms of fracture mechanics quantities have not been fulfilled sufficiently up to date. The focus of the present paper is laid on the material side only. The experimental fracture mechanical material characterization of DCI at quasi-static loading conditions is practised by means of crack resistance curves. These can be determined with respect to accepted test standards using efficient single specimen methods for the measurement of crack growth. Nevertheless, it is of special importance to assess the safety at accidental conditions too where fast changes of the stress and strain state in the material and the component prevail due to dynamic (high rate) loading. At present, there are only multiple specimen techniques available for the determination of crack resistance curves of DCI at these loading conditions, like the low blow method. However, significant disadvantages of these methods are their high demand of material and time what makes them expensive. Furthermore, they integrate over a larger area of the material why it is not possible to identify and map local gradients of microstructure and properties. That is the reason why the further development of the fracture mechanics test methods for DCI materials at dynamic loading is absolutely necessary. Therefore, BAM has started a research project recently that is financed by the German Science Foundation and whose goal is to solve the above mentioned task by development and qualification of an appropriate single specimen method for the determination of dynamic crack resistance curves and characteristics of DCI. From the experimental as well as the economical point of view major advantages of this approach are a low demand of material and high efficiency of time. Furthermore, there is also the possibility to integrate a single specimen method into the manufacturing quality control system where only small amounts of material can be taken out of the component without destroying it. The well-known efficient single specimen methods for crack growth measurement at quasistatic loading, like the compliance method or the DC potential drop technique, can not be used in dynamic testing successfully. Whereas the key curve method basically offers the possibility for crack growth measurement even at high loading rates, higher temperatures or corrosive environment. Therefore, it is first of all reported in the present paper on the review and systematization of published key curve methods that have nearly exclusively been applied to steels in the last 25 years with different success. Based on that, an assessment of their applicability to dynamic testing of DCI is made. It is basically distinguished between the experimental, analytical and numerical determination of key curves. An analytical approach and a numerical method were then chosen as

522

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advanced key curve methods promising success also with dynamic DCI testing. Further research work will now be done to investigate these methods in comparison and with respect to qualification of one method and application to DCI. The final goal of the project will be to provide an efficient single specimen method which is as simple as possible and allows determining dynamic crack resistance curves of DCI as well as deduced material characteristics for component safety analysis reproducibly and reliably.

2T18. Dynamic, high strain rate, or impact fracture

523

DYNAMIC TENSILE BEHAVIOR OF ARAMID FRP USING SPLIT HOPKINSON BAR METHOD Yutaka Sawaki, Jun Watanabe1, Eitoku Nakanishi2 and Kiyoshi Isogimi3 Department of Mechanical Engineering, Faculty of Engineering, Mie University Kurima-machiyacho 1577, Tsu 514-8507, Japan [email protected] 1Department of Mechanical Engineering, Graduate School of Engineering, Mie University Kurima-machiyacho 1577, Tsu 514-8507, Japan [email protected] 2Department of Mechanical Engineering, Faculty of Engineering, Mie University Kurima-machiyacho 1577, Tsu 514-8507, Japan [email protected] 3Department of Mechanical Engineering, Faculty of Engineering, Mie University Kurima-machiyacho 1577, Tsu 514-8507, Japan [email protected] It is well known that fiber reinforced composite materials are new industrial materials replaced with metal, wood or concrete, etc. and are equipped with high intensity and high elasticity. An aramid fiber has relatively high impact intensity compared with carbon fiber or glass fiber. When an aramid fiber was made into a composite material (Aramid Fiber Reinforced Plastic: AFRP), it has the feature which shows the metallic ductility which was similar to aluminium. From the above-mentioned reason, AFRP attracts attention as reinforced composite polymer material. Several recent works on various FRP(s) subject to tensile impact loading are performed [1], [2], [3]. In this paper, dynamic tensile behaviour of Aramid Fiber Reinforced Plastic (AFRP) at relatively high strain rates of approximately 70 to 230 s-1 is investigated by using one bar method, which is a variation of sprit Hopkinson bar method. In this experiment, the specimen is created using unsaturated polyester resin as a matrix material and contains an Aramid fiber bundle (Kevlar 49: Du Pont-Toray Co., LTD.) in an axial direction in order to obtain fundamental properties of fiber reinforcement as shown in Fig. 1.

FIGURE 1. Dimensions of specimen. Experimental results on the stress-strain relationships of AFRP at several strain rate are compared with those of GFRP and matrix material (Polyester). Static tensile test is also carried out for comparison of dynamic test results. An example of the stress-strain curve obtained by dynamic

Y. Sawaki et al.

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tensile test at strain-rate 230 s-1 is shown in Fig. 2. From this figure, it turns out that the value of maximum stress of the present AFRP specimen is about 9 times compared with one of only unsaturated polyester specimen and the value of maximum strain is also about 2.5times. It is thought that there is reinforcement of the matrix material by the aramid fiber.

FIGURE 2. Stress-strain curve at strain rate of 230 s-1. As the result, it is recognized that the value of maximum stress and strain of AFRP increased with increasing strain rate.

References 1.

Gilat, A., Goldberg R.K. and Roberts, G.D., Composites Sci. Tech., vol. 62, 1469-1476, 2002.

2.

Rio, T.G., Barbero E., Zaera R. and Novarro, C., Composites Sci. Tech., vol. 65, 61-71, 2005.

3.

Sun, B., Liu F. and Gu, B., Composites :Part A , in press, 2005.

2T19. Damage mechanics

525

DETECTION OF LOW-VELOCITY IMPACT DAMAGE IN CARBON-EPOXY PLATES USING NDT A. M. Amaro, M. F. M. S. de Moura1 and P. N. B. Reis2 CEMUC – Centro de Engenharia Mecânica da Universidade de Coimbra, Polo II, 3030 Coimbra, Portugal 1Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal 2Departamento de Engenharia Electromecânica, Universidade da Beira Interior - UBI, 6200 Covilhã, Portugal [email protected], [email protected], [email protected] Composite materials are excellent for aeronautical applications due to their high specific strength and stiffness. However, these materials may absorb limited amounts of energy through localized damage mechanisms without extensive plastic deformation. Different types of damage may be encountered in the impacted region, including matrix cracking, delaminations and broken fibbers. The presence of this damage is detrimental to the material performance and structural integrity of the composite structure. For example, impact damage is considered as the primary cause of in service delamination in composites giving rise to reductions of the compressive residual strength up to 60%, de Moura and Marques [1]. Therefore considerable research have been developed on impact response of composite materials, particularly to study the relationships between the composite constituent properties, the damage mechanisms and the degradation of mechanical properties due to impact, Cantwell and Morton [2]. A major problem with composite materials is the detection of low-velocity impact damage. In addition to the conventional destructive, nondestructive evaluation techniques have been receiving much attention for detection and monitoring of damage evolution within the composite structure. In order to realize the full potential of fibber reinforced composites in critical load bearing applications, reliable and cost effective non-destructive test (NDT) methods must be developed, Adams and Cawley [3]. However, many of the NDT techniques used for metallic structures are unsuitable for composite structures. The objective of this work is to evaluate features and capabilities of four different methods used to detect and quantify impact damages on carbon-fibber-reinforced epoxy composite. Composite laminates were prepared from high strength unidirectional carbon pre-preg “TEXIPREG HS 160 REM” and processed in agreement with recommendations of the manufacturer. Two stacking sequences were considered for carbon fibber laminates: [0,90,0,90]2s and [904,04]S. The overall dimensions of the plates were 300x300x2.4 mm. Quality control of the plates was performed by C-Scan, to evaluate the eventual presence of defects resulting from manufacturing process. The impact energy used in the tests, was 3 J, which correspond to a load around of 3000 N. Finally, the damages in the laminates were analysed by Electronic Speckle Pattern Interferometry (ESPI), Shearography, Ultrasonic Testing and X – rays radiography. It was concluded that the four techniques studied are able to detect almost of the defects. However, the interferometric methods showed some limitations. For example, the ESPI can require an experient operator capable of recognizing and interpreting the presence of defects inside all the fringe patterns provide by the method. The application of this technique can be more difficult when small damages are produced. On the other hand Shearography has an easier interpretation. However, there are also difficulties on the visualization and quantification of defects

A. M. Amaro et al.

526

since damage evaluation is based on anomalies in the displacement gradient fields. X – rays radiography method is a good alternative technique, but it does not allow to define the position of defects along thickness. The X – rays radiography method was compared with the Deply Technique (destructive technique), which confirmed that superposition of different delaminations correspond to x-rays image. The Ultrasonic methods, A-Scan and C-Scan, showed to be the best solution to inspect the laminates. According to the experimental results, these techniques are able to detect and measure the defect extension with great precision. Another important conclusion is that these techniques are complementary in the detection of position of defects and quantification of their variation along thickness.

References 1.

de Moura, M. F. S. F. and Marques, A. T., Composites: Part A, vol. 33, 361-368, 2002.

2.

Cantwell, W. J. and Morton, J., Composites, vol. 22, 347-362, 1991.

3.

Adams, R.D. and Cawley, P.D., NDT International, vol. 21, 208-222, 1998.

2T19. Damage mechanics

527

DAMAGE ACCUMULATION AT HIGH TEMPERATURE CREEP OF A SINGLE-CRYSTAL SUPERALLOY A. Staroselsky and B. Cassenti Pratt and Whitney 400 Main Street MS 165-16 East Hartford, CT 06108, USA [email protected] [email protected] The micromechanics of the high temperature creep and damage acumulation in single crystal nickel base superalloy is the subject of this study. These alloys are used in turbine blade and vane applications in advanced commercial and military gas turbines and in turbopumps for the space shuttle main engines. The objective of this program was to develop a robust predictive tool to relate single crystal structure macroscopic behavior and fracture crack initiation to micromechanical events. We have developed the crystallographic–based model for non-isothermal high temperature cyclic deformation and coupled it with damage kinetics. The approach used in simulations of deformation process of L12 single crystal alloys gives us a tool to obtain the deformation behavior of the structure. Although the quantitative description of plastic flow by crystallographic slip may be traced back to early works of Taylor, Elam, and Sachs (1923, 1925, 1928), there have been considerable recent advances in the understanding of anisotropic elasto-viscoplastic deformation behavior, damage kinetics and thermal mechanical fatigue of single-crystal materials, allowing improvements the prediction of the deformation and failure behavior of the high temperature turbine components. We have developed a unified materials constitutive model including thermally-dependent creep activation mechanisms for different crystallographic orientations. The model extends existing approaches [1, 2] to increase the accuracy of material deformation response predictions on cyclic and thermal-cyclic loading. Historically, only secondary creep effects were considered (e.g., Larson-Miller, etc.) in engineering calculations. However, during the thermal-mechanical loading of high temperature single crystal turbine parts, all three creep stages: primary, secondary and tertiary, manifest themselves and none of them can be neglected. Account must be taken of all creep mechanisms, and is especially important in the case of non-homogeneous thermal loading of components with extensive stress redistribution and relaxation. We have experimentally observed and simulated, with our unified microstructure-based model, loading cases with only primary and tertiary creep regimes as well as creep without any noticeable primary creep. Having developed the constitutive model and implemented it in the comercial finite element software, ANSYS, as a material user routine, we predicted yield/creep anisotropy and yield – thermal dependence. The general form of the governing relation for the plastic shearing rate may be written as follows: D

D

D

D

pe

cb

se

s (W ,W ,W , T ), Z D D , s (T ), Z D , d D , T ) ,

D

, d D ,T ) ,

octahedral

slip

cube

systems

slip

systems

(1)

A. Staroselsky and B. Cassenti

528

where is the deformation resistance and Z D

D

D

is a kinematic hardening of D-th slip system; W

D

D

is

D

resolved shear stress, and W pe ,W cb ,W se - “non-Schmidt” shear stresses, and d is the amount of damage assosiated with plastic shear. These constitutive equations are fully coupled with evolution equations for the state variables listed above. The process for damage nucleation/accommodation is a Poissonian stochastic process, with the evolution (probability rate) described by a Boltzmann formula. Damage accomodation causes tertiary creep and shear localization around local concentrators. Shear bands are one of the major causes of single crystal cracking and the model prediction of the initial shear localization was used as a criteria for crack initiation. Small deformation analysis usually does not provide enough information to distinguish and calibrate different mechanisms of inelastic deformation and damage accumulation. We extended the analysis to finite deformations (Asaro [3]), and coupled it with crystallographic texture analysis (Bronkhorst et al [4]). The change of the local crystal lattice is strongly dependent on each slip system activity and hardening mechanisms. We calibrated the model strain-stress and crystallographic texture predictions with test data for small and moderate deformations. This allows us to numerically predict the position and orientation of shear localization. The developed non-isothermal, crystal –viscoplastic, damage mechanics model is used for cyclic ratcheting and thermomechanical fatigue (TMF) analysis. The model results will be used for developing reduced order models efficiently reflecting long term thermal cyclic behavior and crack nucleation in high temperature single crystal components of gas turbines.

References 1.

Nissley, D., Meyer, T., and Walker, K. Life Predictions and Constitutive Models for Engine Hot Section Anisotropic Materials, Pratt & Whitney, Report NAS3-23939, 1991

2.

Hesebeck, O., Int. J. Damage Mech., vol. 10, 325-346, 2001

3.

Asaro, R.J. Advanced Applied Mechanics, vol. 23, 1983.

4.

Bronkhorst, C.A., Kalidindi, S.R., and Anand, L., Phil. Trans. R. Soc. Lond. A, vol. 341, 443477, 1992

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ASYMPTOTIC HOMOGENISATION FOR HETEROGENEOUS MEDIA WITH EVOLVING MICROCRACKS E. K. Agiasofitou, C. Dascalu and J. L. Auriault University Joseph Fourier, Laboratoire Sols Solides Structures Domaine Universitaire B.P. 53, 38041 Grenoble Cedex 9 FRANCE [email protected], [email protected], [email protected] In this work, an asymptotic expansion homogenization is used to study the overall behaviour of a damaged elastic body with a locally periodic distribution of growing microcracks. The microstructure evolution is represented, at the macroscopic level, by a local internal variable related to the microcracks lengths. An evolution damage law is deduced, through asymptotic homogenisation, by assuming a microscopic fracture criterion of Griffith type. Finite element solutions, in elasticity, are presented in order to illustrate this new approach. Many articles have been devoted to the overall behaviour of micro-fractured solids (see for instance Nemat-Nasser and Hori [1] for a review). Almost all these works are confined to the case of stationary cracks. Exceptions are Prat and Bazant [2] and Caiazzo and Constanzo [3], which take into account the fracture evolution. Their approach of scale change is not the asymptotic homogenization. On the other hand, asymptotic homogenization techniques have been used for stationary microcracks in Leguillon and Sanchez-Palencia [4] and Telega [5]. Our aim is to use this rigorous link between microstructure and the overall behaviour in the case of propagating microcracks. The elastic medium is locally periodic with the period microcracks *

of effective length l

wV

S ij

wx ª¬ V

U

j

S ij

º¼ N

j

w 2 u Si , wt2 0

V

l(x , t).

S ij

:

chosen so as to contain a set of

In the solid part : S the equation of motion is

a ijk h e x k h ( u

S

)

in :

S

,

on *,

(1)

where ı S and u S are the stress and the displacement fields, U is the mass density and a is the elastic tensor, which verifies the classical symmetries and the ellipticity condition. We assume that the crack faces are traction free. Following the method of asymptotic homogenisation (e.g. Bensousssan et al [6], Bakhvalov et al [7], Auriault [8]), we assume that the period size of the elastic medium is characterized by a small parameter H

uS (i )

and we look for u S in the form

u ( 0 ) ( x , y , t )  H u (1) ( x , y , t )  H 2 u ( 2 ) ( x , y , t )  

(2)

where the u are y-periodic functions with y x H , y is the microscopic (fast) variable and x is the macroscopic (slow) variable. The macroscopic equation of motion, at the first order of approximation, is obtained as

E. K. Agiasofitou et al.

530



w 2 u i( 0 ) w C ijkh e xkh ( u ( 0 ) )  U  wx j wt 2

0, (3)

kh kh where C ( l ) ¢ a ijk h  a ijlm e ylm ( ȟ ( l ))² is the effective elastic tensor and ȟ are the characteristic functions [6], [7] which depend on the crack evolution.

A propagation criterion of Griffith type (see Freund [9]) is assumed for microcracks. The equation of energy written in a cell concludes in the following result after applying the asymptotic expansion

· w § : C ijk h ( l ) e x kh ( u ( 0 ) ) e x ij ( u ( 0 ) ) ¸  2 G c r ¨ wt © 2 ¹

0 (4)

where Gcr is the critical value of the energy release rate and it is a material constant and : is the measure of : . Combining the macroscopic equation of motion (3) and the equation (4), we obtain an equation for the damage variable l

l ( x , t ) in the form

w C ijkh w l 1 w C i jkh  le x k h ( u ( 0 ) ) e x ij ( u ( 0 ) )  e x kh ( u ( 0 ) ) u i( 0 )  2 wl wl wx j  C ijk h

w  e xk h ( u ( 0 ) ) u i( 0 )  2 G: c r  wwt §¨© 12 U ( u i( 0 ) ) 2 ·¸¹ wx j

0.

(5)

Finite element solutions for the coupled problem (3) and (5) are obtained for particular, twodimensional, geometries of the micro-fractured cells. The influence of the cracks evolution on the homogenized mechanical response is analyzed through the obtained numerical solutions.

References 1.

Nemat_Nasser, S. and Hori M., Micromechanics: overall properties of heterogeneous materials, Elsevier, Amsterdam-Lausann-New York, 1999.

2.

Prat, P.C. and Bazant, Z.P., J. Mech. Phys. Solids, vol. 45, 611-636, 1997.

3.

Caiazzo, A.A . and Constanzo, F., Int. J. Solids Struct., vol. 37, 3375-3398, 2000.

4.

Leguillon, D. and Sanchez-Palencia E., J. Méc. Théor. et Appl., vol. 1, 195-209, 1982.

5.

Telega, J.L., Comput. Mech., vol. 6, 109-127, 1990.

6.

Bensounssan, A., Lions, J.L. and Papanicolaou G., Asymptotic analysis for periodic Structures, North_Holland, Amsterdam, 1978.

7.

Bakhvalov, N. and Panasenko, G. Homogenisation: averaging processes in periodic media, Kluwer Academic Publishers Group, Dordrecht, 1989.

8.

Auriault, J-L., Int. J. Engng. Sci., vol. 29, 785-795, 1991.

9.

Freund, L.B., Dynamic Fracture Mechanics, Cambridge University Press, 1998.

2T19. Damage mechanics

531

ON THE ANALYSIS OF DAMAGE LOCALIZATION AS PRECURSOR OF MACRO-CRACKS H. Stumpf and K. Hackl Lehrstuhl für Allgemeine Mechanik, Ruhr-Universität Bochum D-44780 Bochum, Germany [email protected] In damage mechanics it is well-known that localization zones are often precursors of macrocracks. Correspondingly, in fracture mechanics extended experimental investigations (e.g. Klemm and Kalthoff, 1984; Bertram and Kalthoff, 2003) have shown that at the tip of a crack there is no stress singularity, instead, in front of the crack a small process zone can be observed caused by intensive dislocation motion in the case of ductile materials as metals or by intensive microcracking in the case of brittle materials as limestone or granite. At the same time high temperatures develop in the process zone. The size of the process zone depends strongly on the material properties. For glass the process zone is very small, but a very high temperature can be measured there. Another essential feature is the fact that the process zone evolves with high speed, if the crack moves with high speed. In this paper we present a framework for the analysis of dissipative processes with narrow zones of plastification and/or intensive micro-cracking and heat production taking into account also the inertia effects of moving micro-defects (for nonlocal brittle damage see Stumpf and Hackl, 2003 and for ductile damage Stumpf et al. 2004). To describe fields of dislocations and micro-cracks we choose as independent kinematical variables of physical and material space F, Fd , Fp and their gradients,

e

^F , F d , F p , ’ F d , ’ F p ` ,

where F is the physical deformation gradient, deformation tensor.

(1)

Fd a damage tensor and Fp the plastic

Power-conjugate to (1) is a set of physical and material forces and stresses, s

^T , T d , T p , H d , H p ` ,

(2)

where T is the physical first Piola-Kirchhoff stress tensor and the others are material stress tensors representing forces and stresses acting on defects. As additional variables we include temperature

ș

and

’ș .

Formulating the classical dynamical balance laws of physical forces and nonlocal dynamical balance laws of material forces, furthermore first and second law of thermodynamics, we have as many equations as unknowns. From the second law of thermodynamics it follows that the free energy are of the form ȥ

ȥˆ ( e , ș ) ,

s

w e ȥˆ ( e , ș )  sˆ * ( e , ș , e , ’ ș ) ,

ȥ

and the stresses (2)

(2)

H. Stumpf and K. Hackl

532

where the dissipative driving forces sˆ * ( e , ș , e , ’ ș ) are given in terms of a dissipation potential ij

ijˆ ( e , ș , e , ș ) by

sˆ * ( e , ș, e , ’ ș)

w e ijˆ ( e , ș, e , ’ ș ) .

(3)

The dissipative driving forces determine also the evolution of the macro-crack.

References 1.

Stumpf, H. and Hackl, K., Int. J. Solids Structures, vol. 40, 1567-1584, 2003.

2.

Stumpf, H., Makowski, J., Gorski, J. and Hackl, K., Mech. Res. Comm., vol. 31, 355-363, 2004.

3.

Klemm, W. and Kalthoff, J.F., Entwicklung eines thermomechanischen Messverfahrens zur Charakterisierung des Werkstoffverhaltens bei schneller duktiler Rissausbreitung in Rohrfernleitungsstählen, DVM, Berlin, 1984.

4.

Bertram, A. and Kalthoff, J.F., Crack propagation toughness of rock for the range from low to very high crack speeds, Key Engineering materials, vols 251-252, 23-430.

2T19. Damage mechanics

533

FATIGUE ASSESSMENT BASED ON STATISTICAL ANALYSIS OF THEORETICAL PARAMETERS J. Cacko Slovak Academy of Sciences Institute of Materials and Machine Mechanics, Raianska 75, SK-831 02 Bratislava [email protected] The basic problem in material research is to predict lifetime behaviour of structures [1]. That is not only a material problem, but also loading conditions, technology design and environmental properties are very significant [2]. A service loading has usually a random character. Traditional experimental investigation methods are very expensive and time-consuming in this case. Therefore, a computer-simulation method seems to be a very suitable way to this purpose. In order to evaluate fatigue damage under dynamic loading, the cumulative representation of a damage increase over a closed cycle is accepted [3]. Under a harmonic loading with constant both amplitudes and mean values of cycles, stress-life (V-N) and/or strain-life (H-N) curves can be experimentally obtained. Then it is possible to specify a relative damage over a closed loading cycle according to some hypothesis (e.g. Miner, Corten-Dolan, etc.) [4]. The difficulties arise under varying mean value of cycles because the relative damage accumulated over individual cycles cannot be simply added. The complete loading history must be respected, and it is a big problem especially under random loading. The serious difficulty is that we must know the complete time loading history until the actual loading cycle. Therefore, a new approach to suitably interpret the loading history has been created. Knowledge of a fatigue damaging process is a necessary condition for an optimum structure design and for effective production with respect to material and energy saving. Especially, CAD, CAM and CAE technologies are very successful because they are by far quicker and less expensive in comparison with traditional theoretical and experimental methods. Moreover, an analytical solution is usually not possible regarding to a stochastic nature of a service loading. For the optimum structure design, it is very important to estimate an elapsed time and/or number of cycles to failure. Because there is no deterministic principle to describe a cumulative damage mechanics in a material unambiguously, especially under stochastic loading, we must use some of cumulative hypotheses and failure criteria. The hypotheses should follow a physical nature of the cumulative mechanics in a material but they are usually originated according to experimental experience and practice. Nevertheless, non-homogeneity of material properties makes some risk of estimation [5]. Therefore, the calculation must be completed by guaranteed reliability of estimated characteristics. The number of closed hysteresis cycles to fracture Nf can be estimated as

N

f

ª « N 0 «k « ¬

where

Rm – ultimate strength

R

m

VC

³[ 0

*q

º » d[ *» » ¼



f [*

1

, (1)

J. Cacko

534

VC – endurance limit N0 – corresponding number of cycles to fracture for VC q

q – slope exponent of Wöhler´s curve ( V a N

const )

f

k – parameter (for Miner´s rule k=1)

[*

V a* * V C , where V a is equivalent cycle amplitude (equivalent cycle = cycle with zero

mean value). Because the parameters in (1), especially VC and q cannot be considered as deterministic values, they must be determined using some probabilistic method, e.g. Monte Carlo one. Then we can use a Weibull´s model

g N

f



md N

m 1 f

e

d N

m f

; N

f

t 0,

(2)

where m and d are parameters of the model. According to this model, the most reliable number of cycles to failure can be assessed. In the paper, a theoretical basis of the procedure is described, as well as a practical experience is presented, too.

References 1.

Cacko, J. Structural Safety, vol. 12, No 2, 151-158, 1993.

2.

Cacko, J. Int. J. Fatigue, 14 No 3, 183-188, 1992.

3.

Cacko, J. Engineering Against Fatigue, edited by J.H. Beynon, Balkema, Rotterdam, 1999, 357-364.

4.

Cacko, J. Fracture From Defects, edited by K.J. Miller, EMAS, Sheffield, 1998, 235-240.

5.

Cacko, J. ECF 13, edited by M. Fuentes, Elsevier, Amsterdam, 2000, CD-R.

2T19. Damage mechanics

535

DETERMINATION OF DUCTILE DAMAGE PARAMETERS BY LOCAL DEFORMATION FIELDS M. Kuna and M. Springmann Technische Universität Bergakademie Freiberg, Institute of Mechanics and Fluid Dynamics, Lampadiusstr. 4, 09596 Freiberg, Germany [email protected] Modern continuum damage models have been successfully developed to describe the non-linear deformation process, damage and fracture of ductile metals. Most prominent models are due to Gurson-Tvergaard-Needleman (GTN) [1] and Rousselier (R) [2]. However, the determination of the unknown material parameters involved in such models is still a challenging issue. Usually, smooth or notched tensile specimens are used to determine the damage parameters from global test data as forces and displacements, whereby numerical simulations are somehow fitted to the experimental point of specimen failure, see the round robin [3]. In fact, the large number of unknown material parameters and the intrinsically coupling between matrix hardening and damage require more comprehensive information from the experiment, which can be gained from measured inhomogeneous deformation fields. The present work comprises the development and application of methods for the parameter identification of damage laws by means of locally measured displacement fields and measured force-displacement curves. Both damage models (GTN) and (R) have been implemented into an own finite element system SPC-PMHP [5, 6]. The classical Rousselier model was complemented by accelerated void growth and void nucleation according to [4]. Thus, both models cover the same features: power law hardening of matrix material, strain controlled void nucleation, void growth and void coalescence (failure). Each model contains 12 material parameters (i=1,2,…,12), including 3 for hardening and 9 for damage [5, 6].

p

^ pi `

Experiments are performed at notched flat bar tensile specimens made of steel StE690, see Fig. 1. The spatial displacement fields are recorded by means of optical field measuring technique in the region of the notch by the object grating method [8], in order to observe directly the local damage development. The corresponding finite element mesh is shown in Fig. 1. The deviation between measured displacements values

u k and the numerical results u k (p ) from a finite

element analysis is quantified by the objective function ) ( p ) , summed up over all measuring points nM and load steps nL. The material parameters p must be iteratively improved until the objective function achieves the global minimum. For this purpose, a gradient based method is used, whereby the gradients with respect to p are computed by a sensitivity analysis.

) (p )

1 2

nL

nM

3

ª º ¦ ¦ ¦ «  u k ( p ) i j -  u k i j »¼ i 1 j 1 k 1 ¬

2

o

m in

(1)

A successful strategy to identify the material parameters was found by careful numerical studies [7]. The efficiency of the proposed solution method for the inverse problem was demonstrated by various applications for different notch geometries. The obtained parameters are in agreement with data from the literature.

M. Kuna and M. Springmann

536

FIGURE 1. Notched tensile specimen and FEM-discretization of one eighths.

References 1.

Tvergaard, V., Needleman, A., Acta Metallurgica vol. 32, 157–169, 1984.

2.

Rousselier, G., Nuclear Engineering and Design vol. 105, 97-111, 1987.

3.

Bernauer, G., Brocks, W., Numerical round robin on micromechanical models, Phase II, Task B1, Technical report, ESIS European Structural Integrity Society, 1999.

4.

Chu, C.C., Needleman, A., J. Engineering Materials in Technology, vol. 102, 249-256, 1980.

5.

Springmann, M., Kuna, M., Computational Materials Science vol. 26, 202-209, 2003

6.

Springmann, M., Kuna, M., Computational Materials Science, vol. 32, 544-552, 2005

7.

Springmann, M., Identifikation von Materialparametern schädigungsmechanischer Gesetze unter Einbeziehung der Dehnungslokalisierung. Dissertation, TU Freiberg, 2005.

8.

Benutzerhandbuch ARAMIS: Verformungsmessung nach dem Rasterverfahren. Gesellschaft für optische Messtechnik mbH, Braunschweig, 2000.

2T19. Damage mechanics

537

FRACTURE OF CONCRETE DUE TO CORROSION N. Thanh, A. Millard1, Y. Berthaud, S. Care and V. L’Hostis2 LMT Cachan ; 61 Av Pt Wilson F-94235 Cachan ; [email protected] 1CEA/DEN CEN Saclay 2CEA/DEN/DPC/SCCME/LECBA, 91191 Gif sur Yvette Cedex, France Cracking of concrete due to corrosion is a very common pathology that can be observed on various structures. Corrosion is initiated by the penetration of chlorides or by the reactive transport of carbon dioxide in most cases. The consequences of corrosions are (i) the reduction of the resistive section of reinforcements (ii) the creation of expansive products (commonly denoted rust) (iii) the fragilization of steel and finally (iv) the cracking of concrete [1-4]. Three stages are distinguished: (1) the incubation that corresponds to diffusion processes of chemical species (chloride or carbon dioxide) inside concrete from the free surface to the steel concrete interface; (2) the initiation stage starts when the passivation film of rebars is broken ; (3) the cracking stage corresponds to the expansive growth of corrosion products leading to the lack of carrying capacity of the structure. We have decided to study this stage in Laboratory. The first stage takes decades for real cases. In our study it has been accelerated by the use of accelerated corrosion under the effect of electrical current or potential. We decide to impose the electrical current density that allow to predict (using the Faraday’s law) the production of iron oxides. The imposed values range between 1 and 5 A/m2. Two types of specimen have been designed for plane strain and plane stress analyses: a 100*150*300 mm3 one and a 100*150*20 one mm3. Figure 1 shows the reinforcement either at the corner (P1) or in the middle (P2) and the typical cracking pattern for case P2.

FIGURE 1. Specimen for accelerated corrosion on the plates (20 mm thick) and typical cracking patter for case P2.

FIGURE 2. Evolution of the strains on the lateral face (gauge B) for two different specimens (case P1).

N. Thanh et al.

538

The evolution of the strain given by gauges glued at the upper surface (case P1) for two different specimens (not shown in this abstract) and on the lateral surface (case P1) show that in a first regime no deformation is measured due to corrosion: the oxide fill up the porosity. Then pressure rises up to the rupture of concrete which explains the diminution of the lateral strain (Fig. 2) Figure 1 shows the typical cracking pattern obtained within few days under a low intensity current (1A / m2). For case P2 it is interesting to notice that the first crack to appear is the one above the steel bar (it starts from the free surface). The inclined cracks do not appear at the free surface. Using a CCD camera it has been possible to record the overall evolution of cracking. A FEM modeling [7] has been developed based on a classical damage model for concrete, on the identified properties of iron oxides (very low stiffness). It gives for case P2 a typical result (Fig. 3) for the damage field, which corresponds to the experimental data.

FIGURE 3: Damage field for case P2

References 1.

Castel A., François R., Arliguie G., Mat. & Struct., vol. 33, 539-544, 2000

2.

Almusallam A. A., Al-Gahtani A. S., Aziz A. R., and Rasheeduzzafart, Const. and Build. Mat., vol. 10, 123-129, 1995

3.

Andrade C., Alonso C., Molina F. J., Mat. and Struc., vol. 26, 453-464, 1993

4.

Petre – Lazar I., Evaluation du comportement en service des ouvrages en béton armé soumis à la corrosion des aciers, PhD thesis, Université de Laval, Québec, 2000

5.

Rodriguez J., Ortega L. M., Casal J., Cons. and Build. Mater., 239-248, 1997

6.

Samsonov G.V., The oxide handbook », IFI/PLENUP, 1973

7.

A. Millard, V. L’Hostis, K. Beddiar, Y. Berthaud, S. CARE, Modelling the cracking of a reinforced concrete structure submitted to corrosion of steels – first validation of a damage model based on experimental tests, Proceedings of the OECD/NEA/CSNI-RILEM Workshop on use and performance of concrete in NPP fuel cycle facilities, Madrid, Espagne (15-16 mars 2004).

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539

EXPERIMENTAL STUDY OF SPRAYED CONCRETE STRENGTH USING MARBLE AGGREGATES A. Sotiropoulou and Z. G. Pandermarakis Department of Civil and Structural Engineering Technology Teachers School of Pedagogical and Technological Education “Irene” Train Station, Athens - Greece [email protected], [email protected] Sprayed concrete provides today the combined features of high productivity, increased quality and low cost in work which concerns repairs, preservations, and general work which requires support. Cement usually mixed with fine aggregate (up to 8mm) is forced with pressure to walls with appropriate and controlled addition of water into the pump at mixture stage (wet process) or just before the exit by nozzle (dry method). Even if with enough advantages –included the increased bonding strength– this particular process and hence whole the final product (sprayed concrete) is infected by many uncontrolled factors [1]. Multivaried parameters as substrate morphology, aggregate character and also of cement type and aggregates, the non-constant flow of water and material, the unavoidable rebound of aggregates and mainly the human factor through pump and nozzle handling leads to a varied water to cement ratio (w/c) and also of bulk properties of sprayed concrete. In such a situation the final product will be hardly controlled and investigated [2]. So experimental work in this specific area is internationally limited. In present study we try to describe the influence of aggregate type, modifying the traditional composition replacing the limestone aggregates with marble particles. Marble grains are a sub product of marble extraction industry and efforts for satisfactory uses has also an environmental meaning besides the special modifications of final product. The cement was of type I55 and as aggregate was used a group with common limestone grains and a second group by marble grains. They were prepared specific panels with dimensions 100x100x14cm into which we sprayed by dry process and suitable pump the concrete. From these panels we extracted sprayed cement cores and shaped cylinder specimens with dimensions of length to diameter: 10cm/5cm. From each group we manufactured also as cast specimens by analogous dimensions in order to use them as reference index. For these specimens we checked their strength to unidirectional compression stresses and to an indirect tension stress condition through splitting test at 3, 7, 14, 28 and 56 days after their construction by sprayed process or casting [3,4].Part of results they are presented at figs.1-4. The loading rate was approximated at 1kN/s. From the corresponding diagrams we could directly see that specimens with limestone aggregates gave in general higher strengths than these with marble aggragates, mainly at as cast specimens. This could be attributed to lower mechanical characteristics of marble which compose from remains of its extraction process, or even to an increased portion of clay’s constituents. Important differentiations in the morphology of aggregates though analysis of corresponding micrographs were not observed. Besides, we identify an inter-granular fracture of aggregates and an perfect bonding to cement paste. This leads us to say that the appearing coincidence of sprayed and as cast specimens could attribute to special effects that they introduce to concrete and modifying it highly eliminating other special features. Perhaps, here, the developing inhomogeneousness and the intrinsic special appearance due to way of manufacture and the significant losses of aggregate through rebound effect, could depress the initial differences.

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The present work –which constitutes one of the first research programs supported financially by government in Technological Institutions in our country- is continued at this moment trying to improve the properties of sprayed concrete with marble aggregates modifying its composition and strengthening it using suitable reinforcing fibers

References 1.

“Shotcrete: Engineering Developments” ed. E.S. Bernard, A.A.Balkema publ., Lisse, 2001

2.

“Sprayed Concrete Conference” by TEE and EBEA, Athens - Greece, Sept. 2001

3.

European Standard: EN 12390-6: “Testing hardened concrete-Part6: Tensile splitting strength of test specimens”, Oct. 2000

4.

European Standard: EN 12390.03: “Testing hardened concrete-Part3: Compressive strength of test specimens”, Dec. 2001

5.

Austin S.A. and Robins P.J. “Sprayed Concrete: Properties, Design and Application”, Whittles Publ. 1995

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ANALYSIS OF THE BEHAVIOUR OF INTERFACE CRACKS IN GRAVITY DAM B.Bachir Bouiadjra, A.Bachir Bouiadjra, M.Belhouari and B.Serier Department of Mechanical Engineering, University of Sidi Bel Abbes BP 89, Cité Ben M’hidi, Sidi Bel Abbes, 22000, Algeria [email protected] The interface between concrete dam and rock foundation is one of the most important regions governing the strength and stability of gravity dams [1]. The fundamental understanding of the fracture behaviour at the Rock-Concrete interface requires evaluation of fracture criteria such as stress intensity factor, energy release rate etc. Fracture mechanics concepts and theories have been successfully applied to study the cracking phenomena in dams [2-6]. However, not much work is reported regarding the crack at the interface of concrete dam/rock foundation, witch is one of potential sites of cracks initiation and propagation. The determination of the stress intensity factor at the crack tip is one the possible means to analyse the behaviour of interface cracks in gravity dam. It is known that the finite element method gives, with a great accuracy, the stress intensity factors at the crack tip. In this study, the finite element method is used to analyse the behaviour of interface cracks between concrete and rock in gravity dam by the plot of the mode I and II stresses intensity factors as a function of the crack length. The effect of crack inclination according to the interface is highlighted. The effects of hydrostatic pressure in all studied cases were highlighted. The dam used for the analysis is a gravity dam type. It is 80 m high and 60 m width. The crest of the dam is 5 m width. The geometrical model is idealised by a mesh having 2125 eight nodded elements. The crack tip is modelled with the standard quarter-point elements. A linear elastic material model coupled to a linear elastic discrete fracture model was used in the analysis. As an example of the obtained results, figure 1 presents the variation of the mode I stress intensity factor (KI) as a function of the normalised crack length a/w (where w is the width of dam) for different applied pressures ( h= 40, 60 and 80 m). It can be noted that whatever the size of the crack, an increase of the high h leads to an elevation of the stresses intensity factor at the crack tip. The opening of the crack is thus highly affected by the applied hydrostatic pressure. One can see that the Mode I stress intensity factor increases slightly according to the normalised crack length when this last is lower than 40%. Beyond this value, the rate of increase of KI is more accentuated, what allow us to confirm that the opening of the crack becomes dangerous when its length exceeds 40% of the dam width. Figure 2 illustrates the variation of the mode II stress intensity factor (KII) according to the normalised crack length a/w. It is shown that KII practically does not vary with the crack length when this last is lower than 70% of the dam width. From this length, the absolute value of KII, increases with a great rate. According to figure 2, It can be seen that the effect of the water pressure on the KII variation is negligible when the ratio a/w is lower than 0.7.

B. Bachir Bouiadjra et al.

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FIGURE 1. Variation of KI according to the crack length FGURE 2. Variation of KII according to the crack length

References 1.

Bruhwiler, E. and Wittmann, F.H., Engng Fract Mech, vol 35, 565-571, 1990

2.

Ingraffea, A.R, Linsbauer, H.N. and Rossamanith, H.P., In Shah SP, Swartz SE, editors. SEM/ RILEM International Conference on Fracture of Concrete Rock. Houston, Texas, 1987,31133.

3.

Saouma,V.E, Ayari, M.L. and Boggs, H., In Shah SP, Swartz SE, editors. SEM/RILEM International Conference on Fracture of Concrete Rock. Houston, Texas, 1987, 334

4.

Widmann, R., Engng Fract Mech, vol. 35, 1-3, 1990

5.

Chandra JM, Singh KD, , Engng Fract Mech 2001;68;201-19. Ingraffea, A. R., Engng Fract Mech, vol. 35, 553-564, 1990

6. .

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APPLICATION OF COMPOSITE MECHANICS TO COMPOSITES ENHANCED CONCRETE STRUCTURES C. C. Chamis and P. K. Gotsis NASA Glenn Research Center, Technological Education Institute Cleveland, OH 44135, 62125 Serres, Greece [email protected], [email protected] Reinforced concrete is widely used in the construction industry. Concrete tends to crack, chip and be damaged as a result of inadvertent loads or overloads which may not have been accounted for in the initial design. The damage in concrete structures may extend to a state where the safety of that structure becomes a major concern. Recently, a considerable effort is being expended on repairing damaged or upgrading concrete structures by using fiber reinforced composites. The use of composites is natural since the repairing composites tend to be thin laminates which are easily bonded to damaged concrete structures which are of cylindrical and flat surfaces in general. Composite jacketed concrete is the most effective repair and upgrade method for concrete structural members such as columns that are accessible for all sides. The method is commercially available. Concrete surfaces need be cleaned and prepared for bonding. Unidirectional fiber composite prepreg tape is wrapped around columns helically with sufficient number of layers to provide the necessary confinement of concrete. The composite tape is usually glass/epoxy for small to medium size columns. More expensive graphite/epoxy tapes may be needed for upgrading larger columns that require greater stiffness composite reinforcement. Graphite/epoxy composites that have greater stiffness and are more expensive are also not as ductile as glass/epoxy composites. After sufficiently wrapping the structural member with the required type of prepreg tape, it needs to be heated to the necessary curing temperature to cure the thermosetting epoxy binder. The curing temperature is generally in the range of 121-177°C (250-350°F). Commercial companies provide the necessary tools that automate the fiber composite tape wrapping and curing processes. This method is very economical and effective for upgrading columns of existing older structures that, according to present code, do not have sufficient lateral reinforcement for concrete confinement. Composite protective covers are for environmentally exposed concrete infrastructure subjected to chronic degradation due to exposure to hygral, thermal, and mechanical cycling, deicing agents, and loading effects. The maintenance of structures at a good service condition requires constant vigilance for inspection and repair of degraded components. Inspection and repair of transportation structures is costly and requires the disruption of traffic for significant internals. In many cases transportation structures are neglected until they degrade beyond repair and a very costly removal and replacement process becomes necessary. When degraded concrete structural components such as bridge girders and decks are repaired or replaced, their future durability may be significantly enhanced by protecting the concrete from environmental factors by providing a resilient fiber composite cover. The most significant protection is from the surface water and deicing salts. Similarly, when pavements on bridges are replaced, a fiber composite membrane layer may be added above the structural deck to protect the deck and girders. Transportation structures are subject to adverse environmental factors as well as mechanical loading. The selection of a particular design must take into account all significant factors affecting durability. Infrastructure elements can be designed with more general and adaptable fiber and mat reinforcement architectures than currently available. The potential to design structures with braided/woven composites to satisfy long term durability and safety requirements is excellent. For

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the very same multiplicity of design options that promise great potential, the realization of that potential will depend on the availability of evaluation tools that take into account all aspects of structural durability. The fundamental premise in the implementation of a structural durability model is that interaction among the various factors affecting durability is of utmost importance and must always be taken into account. The methodology used to enable hybrid structural durability assessment could be a generalization of the proven and demonstrated computational capability for the progressive damage and fracture evaluation of laminated composite structures. Extensive experience gained in the development of computational capabilities on laminated composites will be highly beneficial for the success of the assessment of fiber composite infrastructure applications. Different methods for designing and analyzing thin laminates have been developed and are available in many computer codes. Though this area of research is receiving considerable attention lately, the application of composite mechanics, in order to simultaneously simulate the reinforced concrete section with the thin composite layer, has not been recognized as yet. Recent research at Glenn Research Center demonstrated that damaged concrete structures and their repairing composites can be simulated simultaneously by composite laminate analogy which is available in some of those computer codes. By using composite laminate analogy, we can represent any concrete structural section by assuming that it consists of several layers through its thickness. By so doing, we take advantage of all the features available in computer codes for composite mechanics – for example ICAN (Integrated Composite Analyzer). The code that is used in the simulation described herein is the ICAN [1]. The objective of the proposed paper is to describe those composite mechanics and attendant computer codes, and illustrate their application to select reinforced concrete structural sections and structures. The appropriate composite mechanics is described briefly. Then, it is applied to select structural sections and to select structures (special arch and a dome). Note that results presented herein are computational. ICAN is designed to carry out a comprehensive analysis including the hygral, thermal and mechanical properties/response of multilayered continuous fiber reinforced polymer matrix composites.

Reference: 1.

Murthy, P.L.N. and Chamis, C.C., Integrated Composite Analyzer (ICAN), Users and Programmers Manual. NASA TP 2515, March 1986.

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INITIATION AND COALESCENCE OF LOCALS DAMAGES ON BLANCO DE MACAEL MARBLE Kais Mehiri, Pascal Vieville1, Paul Lipinski2, Albert Tidu3 and Valentin Tijeras4 Ecole Nationale d’Ingénieurs de Metz (ENIM) LFM1 / LPMM2 / LETAM3 Centro Tecnico de la Piedra, Spain4 [email protected], [email protected], [email protected], [email protected], [email protected] In the context of a project of characterisation of Spain marble and its integration in the construction domain like a building support material, an analysis of the different Macael’s marbles is in progress. The final purpose is the conception of a simulation tool able to transform the material from a safe status to a ruin one. The damage description software tool is based on the Incremental Self Consistent method which permits to realise the transition between the mesoscopic and the macroscopic scales [1]. This method takes into account the void inclusions (pores), which represent one of the principal sources of the local-failure mechanisms initiation. A first study concerning observations at various scales of three Macael marbles (Blanco de Macael, Travertino Rojo and Crema Real) has been done [2]. This study permitted us to define the internal architecture of the three studied marbles, and to determine the various chemical compositions and the different structural heterogeneities. To succeed in defining the design of the simulation tool, the second step is the identification and the characterisation of the local failure mechanisms. In fact, considering the various heterogeneities, the analysis of their propagation and their coalescence makes possible the anticipation of the critical status of the material for a given morphology and a typical load [3]. That is why we concentrate in this article on the study of various local damage mechanisms of Blanco de Macael. The precedent observation’s study permits us to conclude that the Blanco de Macael is a marble with a polycrystalline structure and a fine grain (Fig. 1a) and such that the average grain size is about 100µm (1425µm for largest one and 56µm for smallest observed). This size is comparable to the building white marbles like Carrara marble 188µm and Dionysos 30µm [4].

FIGURE 1 : a-Optical (Polorasid Light) microscope picture of the Blanco de Macael, b-SEM (BSEI) pictures of mineral inclusion on the Blanco de Macael This marble presents a very marked homogeneous composition (Table. 1). In fact, the observation under the SEM, with the BSEI to highlight the contrast of density, reveals that the mineral inclusions are more dense then the calcite and the average size are about some micrometers (Fig. 1b).

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TABLE 1. Some physical and chemical propreties of the Blanco de Macael marble.

According to the imperfection observations at various scales, we note that the defect coalescence in the white marble is intergranular (Fig . 2a) and the damage induces the crush of the grain into a microcrystals of a distinguishable rhomboedral crystal structure recognisable thanks to its three edges (Fig. 2c) . This paper aims to characterise and understand the various damage mechanisms on the Blanco de Macael marble. The principal results deduced from the compressions tests and the observations on samples at various damage levels are exposed. We also study the acoustics activities during the compression tests in order to establish a correlation between the saved acoustic activities and the damage level.

FIGURE 2 : a-Optical (PL) microscope picture of damaged Blanco de Macael sample b,c- SEM (BSEI) pictures

References 1.

Berveiller M., Zaoui A., Modelisation du comportement mécanique des solides microhétérogènes. Learning documentations CNRS, 1998.

2.

K .Mehiri, P.Viéville, P.Lipinski, A.Tidu , V.Tijeras, Fifth international conference on fatigue and fracture, Politecnico di Bari, Italy, paper 15, 2005.

3.

Broohm A.,Lipinski P., Zattarin P., Prediction of mechanical behaviour of inhomogeneous and anisotropic materials using an incremental scheme, Arch. Mech., 52, 6, pp 947-967, 2000.

4.

Cardani.G., Meda.A., Flexural strength and notch senitivity in natural building stones: Carrara and Dionysos marble. Construction and Building Materials 13, 393-403 ,1999.

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INFLUENCE OF CONCRETE´S MINERALOGICAL COMPONENTS ON FRACTURE COMPRESSIVE AND TRACTIVE M.P. Morales Alfaro and F.A.I. Darwish Universidade Federal Fluminense RJ,Rua Passo da Pátria 156-3 andar – Sala 365 - bloco “D” São Domingos – Niterói - RJ Brazil – CEP 24210-020 [email protected] or [email protected] Intoduction Diverse specialties as Geology, Chemistry, and Civil Engineering, are responsible for the selection of materials utilized to produce and prepare construction materials. The isolated knowledge between who manufactures and who constructs, leads, in general, to control its quality for its mechanical behavior without knowledge of external properties of the mineralogical components of the matrix that conforms them. History of the problem Few researches about the mineralogical influence of concrete components on the mechanical properties, could not explain many mechanical behaviors. Said researches have generated a controversy since 1964 in relation to the reason for the effect of water/cement in the tenacity of the fracture of concrete. According to Dos Santos (1998, p.16) [1]: •

"As well as Petersson (1980), one concludes that the value of the relation water/cement influences inversely in proportional form the tenacity of the concrete’s fracture. When the relation water/cement is increased, the tenacity of the fracture diminishes. This conclusion opposes the position of LOTT and KESLER (1964)".

Objective The objective of this research is to determine if the mineralogy of the components of concrete influences significantly in the formation of the surfaces of fracture when submitting it in compression, traction for compression, and specially, to the direct traction for the item above displayed. Materials and experimental techniques This Study used Cement Portland V-ARI-RS for high initial resistance, course aggregate had been triturated and were from three geologic origins with Tnom. max. ½ inch, m.f 7.6 and the same granulometry. Fine aggregate had m.f 2.43. The tests were done in cylindrical concretes of 6x12 inches except the high strength concrete, which was done in 4x8 inches. The test in tenacity used “short rod” cylindrical specimen. The study was conducted in: TABLE 1: Characteristic Compressive Strength’s Concretes and slump

Results and analise

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TABLE 2 – Summarized Properties mechanics of the concretes

The results in this study of the reason for the influence water-cement in the tenacity of the fracture in the concrete standard revealed essentially the independent type of course aggregate and the reason water-cement in virtue of the predominance of the effect of pores, humidity, and the low cement content of the mixture. For the concrete of medium resistance, the tenacity increases with the increase of the reason water-cement. Being kept invariable the cement contents increase the tenacity of the concrete. The increase of the reason water-cement can be attributed to the performance of the pores as energy spendthrifts during the process of consistent fracture observed in the concrete standard. The superiority of the tenacity of the concrete of medium resistance in relation to the concrete standard is attributed to the biggest cement content. In relation to the tenacity of the concrete of high performance a value of around 2 MPa—m resulted as minimum limit with a relation water-cement of 0,36. Comparing with the results of the tenacity for concrete, and the standard of average resistance, this high value resulted from a reduction of the reason water-cement; even with similar cement content of this last one, a comparison is not possible. The study with high performance concrete, used microsilica and additive superfluidificante; the effect of these additives tends to eliminate the porosity and transition zones are filled in almost its totality so make the interface aggregate-mortar very resistant, and the rupture mechanism in general goes to be given by breaking of aggregates different of the mechanism of rupture of the concrete standard and medium resistance. It is a probably explication for the high value of the high strength concrete.

References 1.

Santos,A.C; Sousa, J.L.A.O.; Bittencourt, T.N. “Determinação Experimental da Tenacidade ao Fraturamento do Concreto com Corpos de Prova do tipo “short rod”, BT/PEF/9807, Boletim Técnico da Escola Politécnica da Universidade da São Paulo, (1998, p16).

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CONSTITUTIVE MODEL FOR DESCRIPTION OF HIGH-STRAIN RATE BEHAVIOR OF CONCRETE I. R. Ionescu and O. Cazacu Laboaratoire de Mathematiques, Universite de Savoie, Le Bourget-du-Lac, France [email protected] Department of Mechanical and Aerospace Engineering, GERC, University of Florida, Shalimar, FL 32579, USA [email protected] Kinetic energy penetration phenomena are of interest in a variety of applications ranging from terminal ballistics to protection of spacecraft due to meteoroid impact, containment of high mass or high velocity debris due to accidents or high rate energy release, design of hardened protective facilities, erosion and fracture of solids due to impact, etc. The occurrence of multiple phenomena in the target such as localization, plasticity, anisotropic damage, fragmentation pushes the limits of existing modeling and computational capabilities for description of the target response. Since the deformation rates are very large an eulerian description coupled with a fluid-like model are suitable to describe the target. Fluid-type constitutive equations have been used to describe the high-strain rate behavior of metallic materials (e.g. Batra [1]). Implicit in these models is the hypothesis of incompressibility, hence those models cannot describe the irreversible volumetric changes observed in porous materials (e.g. geologic or cementitious materials). In this paper, an extension of the Bingham fluid model that captures the combined effects of plasticity, damage and viscous effects on the behavior of porous media when subjected to large deformations and high strain rates is presented. In contrast with a classical fluid, which cannot sustain a shear stress, we suppose that at rest the Cauchy stress tensor V must belong to an admissible convex set K. Conversely, if the stress is in K, then the rate of deformation tensor D

D (v)

( ’ v  ’ T v ) / 2 (v denotes the Eulerian velocity field) vanishes. If the stress

tensor is not in K then there is flow, the rate of deformation tensor D being subject to certain kinamtic conditions, i.e. ­° V = f ( D , h ) D (v)  C , ® °¯ V  K

if D (v ) z 0 , if D (v )

0.

(1)

where h is a set of internal variables. At difference with a classic fluid, the function f involved in (1) is not defined and cannot be prolonged by continuity in D =0. The convex K is defined by a continuous scalar function that describes the flow-no flow condition. To capture the combined effects of plasticity and damage, we propose the following specific form of (1): ­ ª k(P , U ) º ° V c = « 2K + » D c if D c z 0 , Dc ® ¬ ¼ ° c V k ( P , U ) if D c 0. d ¯

d iv ( v ) d 0 ,

­ tr (V ) / 3 =  p c ( P )  ( O  2K / 3) div ( v ) if div (v )  0, ® if div (v ) 0. ¯ tr (V ) / 3 t  p c ( P )

(2)

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with two internal variables: the volumetric strain P and a damage parameter G associated to the loss of cohesive strength due to air pore collapse. The model is further applied to the description of the steady-state flow of a cementitious material over a penetrator. A mixed finiteelement and finite-volume strategy was developed. Fig. 1 shows the distribution of D . Note that a zone of intense inelastic deformation develops around the penetrator and it extends outward to about 3 projectile radii from the centerline. Outside this zone, the material is rigid. To capture sharply the boundary between the rigid domain and the domain of inelastic, a mesh adaptation strategy and an anisotropic mesh generator was used.

FIGURE 1. The distribution of D for a concrete material. We have found that damage occurs ahead of the projectile and along planes which are not symmetric with respect to the penetrator centreline. This damage induced anisotropy may be responsible for observed trajectory instabilities.

References 1.

Batra, R.C., Int. J. Engng.Sci, vol. 25, 1131-1141, 1987.

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HYDRAYLIC FRACTURING IN WEAK ROCKS P. Papanastasiou Department of Civil and Environmental Engineering, University of Cyprus, 1678 Nicosia, Cyprus [email protected] Hydraulic fracturing (HF) is a technique used to stimulate oil and gas reservoirs by inducing fractures in the formation and then propagating them by the injection of a high viscosity fluid [1]. HF is also used in Environmental engineering for waste disposal in shallow formations, for cleaning up contaminated sites and in Geotechnical projects such as injection of grout, permeability testing, deep well injection and dam construction. A correct prediction of hydraulic pressure needed to initiate and propagate the fractures and the created fracture geometry is vital for safely designing such a process. The fracturing fluid-pressure is the only parameter measured in the field that is available for controlling and evaluating the HF treatment. The currently-used hydraulic fracture propagation simulators are based on linear elasticity and often underestimate the down-hole pressure that is measured in the field operations [2]. A particular task of this research was to investigate the effect on non-linear rock behaviour on the pressure needed for propagation and on the dimensions of the created fractures. The physical and mathematical modelling of hydraulic fracturing leads to strong non-linearity characterized by full coupling between the viscous flow of the fracturing fluid, the rock deformation and the fracture propagation processes. Fluid-flow in the fracture is modelled by lubrication theory. Rock deformation is modelled by the Mohr-Coulomb flow theory of plasticity. The propagation criterion was based on the softening behaviour of rocks and it was incorporated in a non-linear cohesive type model with interface elements. Such a criterion is often used in the modelling of the cracking process in concrete. We solved the problem numerically by developing a fully coupled elastoplastic HF FEM code. In the FE code we incorporated a meshing/ remeshing scheme and a special continuation method (arc-length type) based on the volume of the injected fluid for controlling the solution during fracture propagation and closure [3]. We found that plastic yielding provides a shielding mechanism near the tip resulting in an increase of the effective fracture toughness which was determined, independently from the propagation criterion, using the J-integral [4]. Higher pressure is needed to propagate an elastoplastic fracture and the created fracture is shorter and wider than an elastic fracture [5]. We demonstrated that the standard HF simulators, which are all based on elasticity, will yield better results if the unloading modulus is used as the Young's modulus. This is explained by the fact that in along fracture propagation the material unloading behind the advancing fracture dominates in the rock deformation process. We have also modelled fracture closure in an elastoplastic formation. In practice, the measured pressure vs time is analyzed during closure of a mini hydraulic fracture for determining the insitu stresses and permeability, parameters that are subsequently used for calibrating the long propagation modelling [6]. We found that the closure pattern of a fracture which has first been propagated is completely different from the closure pattern of a pressurized stationary fracture. A pressurized stationary elastoplastic fracture closes uniformly bur remains open after the applied load is released. An elastoplastic fracture which has first been propagated makes surface contact initially near the fracture tip and subsequently towards the mouth of the fracture [7]. Therefore, the assumption made that the fracture closes completely once the fluid-pressure in the fracture drops to the value of the far-field stress, is not valid. These results are in agreement with the observations in

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experiments carried out on fracture propagation and closure on large blocks of soft rocks [8]. In addition we showed that the formation will be more stable after it is fractured due to the redistribution of the stresses [9]. Therefore, rock failure causing sanding during production of hydrocarbon is minimized after hydraulic fracturing.

Acknowledgement This research was supported by Schlumberger Cambridge Research.

References 1.

Economides M.J. and Nolte, K.G., Reservoir Stimulation, Prentice Hall, Englewood, N.J., USA, 1989.

2.

Palmer, I.D. and Veatch Jr R.W.. In Proceedings of the 62nd Annual Technical Conference and exhibition of the Society of Petroleum Engineers, Dallas, Texas, 1987, SPE 16902,

3.

Papanastasiou, P. , J. Comp. Mech.s, Vol. 24, 258-267, 1999.

4.

Rice J.R., J. Appl. Mech., Vol. 35, 379-386, 1968

5.

Papanastasiou, P., Int. J. Fracture, Vol. 96, 127-147, 1999

6.

Nolte, K.G., In proceedings of the SPE Annual Technical Conference and Exhibition, New Orleans, LA, 1990, SPE 20704

7.

Papanastasiou, P. Int. J. Fracture, Vol. 103, 149-161, 2000.

8.

Dam, D.B.: "Influence of inelastic rock deformation on hydraulic fracture geometry", Ph.D. Thesis, Delft University of Technology (1999).

9.

Papanastasiou, P. Int. J. Num. Anal. Meth. Geomech., Vol. 23, 1927-1944,1999.

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APPLICATION OF FRACTURE MECHANICS ON UNREINFORCED CONCRETE WALLS Thomas Eck, Bong-Gu Kang and Wolfgang Brameshuber Institute of Building Materials Research, RWTH Aachen University Schinkelstr. 3, 52064 Aachen, Germany [email protected] In this contribution investigations on the size effect of unreinforced concrete walls which are funded by the Deutsche Forschungsgemeinschaft (German Research Foundation) are described. Inducement of this project was the subordinated meaning of unreinforced concrete walls for residential buildings caused by not available design models, although these walls have buildpractically and economically substantial advantages. The major reason for the absence of relations according to plain concrete, which could be consulted for design, are the missing experimental investigations on the load configuration of vertical force and bending acting together. In order to cover all possible load cases at altogether 5 different concrete mixtures, investigations on the bending and simultaneous acting longitudinal force demand as well as pure bending (to determine the mechanical and fracture-mechanical properties of the concrete) without longitudinal force and pure excentric longitudinal force (with an excentricity up to d/3) at three specimen sizes were carried out. With the results of accompanying investigations determining concrete-technological parameter the experiments could be reconstructed on the basis of numerical simulations and material laws for the respective concrete mixtures have been evaluated. After the final evaluation of the bending test the determined scale influences are arranged and on the basis of these results FE-models are set up for the simulation of the one-dimensional experiments up to first computation of a wall including the boundary conditions. In the next step the boundary conditions of the wall are varied in the context of the FE simulation, in order to activate the system load-carrying capacity apart from the concrete tensile strength. Vibrated concrete C25/30 with a maximum particle size of 8 and 32 mm, C50/60 with a maximum particle size of 32 mm and C80/95 with a maximum particle size of 16 mm were examined also like self-consolidating concrete C50/60 with likewise 16 mm maximum particle size. Due to the investigation of notched and not notched samples, the variation of excentricity and loading level as well as the execution of at least three similar tests, a total number of approx. 300 test results. Beams of three different sizes have been tested, the smallest with a height of d = 100 mm and a span of l = 500 mm, the medium with dimensions d/l = 200/1000 mm and the largest with d/l = 400/2000 mm. The specimen thickness of all sizes was kept constant 100 mm. In the next figures some results of the different experiments and simulations are shown. In figure 1 the FE-Model used for the simulation of the three point bending test (only one half of the beam was simulated) and the material law of vibrated concrete C25/30 is given.

554

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FIGURE 1. FE-Model of the three point bending test and resulting material law. The next figure shows the experimental setup for the excentric longitudinal force tests by the example of a small beam and the fracture pattern on the right hand site.

FIGURE 2. Excentric longitudinal force (setup and fracture pattern). With the results of the experiments based on the three load cases it is possible to simulate the fracture behaviour of a wall including the effects of different boundary conditions. The last step to verify the fracture process and examine the results of the FE-analysis is the investigation of unreinforced concrete walls in full scale.

2T21. Concrete and rock

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SUBCRITICAL CRACK GROWTH IN ROCKS UNDER WATER ENVIRONMENT Yoshitaka Nara, Hirofumi Kurata and Katsuhiko Kaneko Graduate School of Engineering, Hokkaido University Kita 13 Nishi 8, Kita-ku, Sapporo 060-8628, JAPAN [email protected] Classical fracture mechanics postulates that the crack propagates dynamically when the stress intensity factor reaches a critical level, that is, fracture toughness [1]. However, the crack can propagate slowly even when the stress intensity factor is less than the critical level. This phenomenon is called subcritical crack growth, and the main mechanism of subcritical crack growth is stress corrosion [2]. Subcritical crack growth is one of the main causes of timedependent behavior in rocks. It has been shown that subcritical crack growth in rocks under air condition is facilitated by water vapour pressure [3]. In this study, subcritical crack growth in rocks under water environment is investigated.

In this study, the Double Torsion (DT) test [4] was used as a testing method. In Fig. 1, a schematic illustration of a DT specimen and the loading configuration are shown. In Fig. 1, P is the applied load. In this testing method, the stress intensity factor is independent of the crack length. The experimental result obtained for rock is shown in Fig. 2. Rock studied was Kumamoto andesite [5]. It is shown that subcritical crack growth is facilitated when the temperature is high from Fig. 2. In Fig. 3, the experimental result obtained in air [2] and in water at the same temperature (284 K) is shown. It is clear that subcritical crack growth is facilitated in water. It can be concluded that subcritial crack growth in rock is facilitated by water and temperature.

Y. Nara et al.

556

References 1.

Griffith, A.A., Phil. Trans. Roy. Soc., vol. 221, 163-198, 1920.

2.

Atkinson, B.K. and Meredith, P.G., in Fracture Mechanics of Rock, Academic Press, London, U.K., 111-166, 1987.

3.

Nara, Y. and Kaneko, K., Int. J. Rock Mech. Min. Sci., 2005 (in press).

4.

Evans, A.G., J. Mater. Sci., vol.7, 1137-1146, 1972.

5.

Jeong, H.S., Nara, Y., Obara, Y. and Kaneko, K., In Proceedings of the International Symposium on the Fusion Technology of Geosystem Engineering, Rock Engineering and Geophysical Exploration, Seoul, Korea, 2003, 221-228.

2T22. Sandwich structures

557

STRESS ANALYSIS AND PREDICTION OF FAILURE IN STRUCTURALLY GRADED SANDWICH PANELS Anders Lyckegaard, Elena Bozhevolnaya and Ole Thybo Thomsen Institute of Mechanical Engineering, Aalborg University Pontoppidanstræde 101, 9220 Aalborg East, Denmark [email protected] Structural sandwich panels can be considered as a special type of composite laminate where thick, lightweight and compliant core material separates two thin, stiff and strong face sheets. Sandwich panels transfer bending and shearing load very effectively, but at the same time they offer limited resistance towards application of transverse loads, see e.g. Zenkert [1] or Allen [2]. A commonly used method of overcoming the problems associated with concentrated transverse loading is to introduce core inserts of higher strength and stiffness. This usually solves the problem of local reinforcement, but it also introduces new interfaces between materials of very different elastic properties. Bozhevolnaya and Thomsen [3-4] investigated the static strength and fatigue strength of the core junctions experimentally for a number of different designs that were originally proposed by Bozhevolnaya et al. [5], see Fig 1. The beams tested in [3-4] were comprised of aluminium face sheets and core materials made from cross-linked PVC foam. It was found that the static strength and the fatigue strength in particular could be improved by redesign in the form of a change of shape of the core junction (referred to as structural grading of the core). In the present investigation the sandwich structures that were evaluated experimentally by Bozhevolnaya and Thomsen [3-4] will be the subject of a detailed stress analysis. The stress distribution near the tri-material wedge at the core junction is known to exhibit stress singularities within the frame work of linear elasticity theory, see e.g. Pagaeu [6]. Hence, it is assumed that crack initiation will start here, which the aforementioned experimental results generally supported. For the purpose of comparing various designs of core junctions, the stress fields at the junctions will be evaluated based on a point stress criterion for crack initiation, which was previously used successfully for cross linked PVC foams by Ribeiry-Ayeh and Hallström [7]. If the application of a point stress criterion proves successful, then it may be used as a future basis for optimisation of core junctions in sandwich structures.

A. Lyckegaard et al.

558

FIGURE 1. The geometry and loading of the studied sandwich beams, a) conventional butt junction, b) scarf junctions with obtuse angles of the main core at the lower side; c) scarf junction with sharp angles of the softer core at the lower beam side; d) butt junctions with reinforcing patches.

References 1.

Zenkert, D., An Introduction to Sandwich Construction, EMACS, 1995

2.

Allen, H. G. Analysis and Design of Structural Sandwich Panels, Franklin Book Co, 1969

3.

Bozhevolnaya, E and Thomsen, O.T., Composite Structures, Vol. 70, pp 517-527, 2005.

4.

Bozhevolnaya, E and Thomsen, O.T., Composite Structures, Vol. 70, pp 528-533, 2005.

5.

Bozhevolnaya, E., Lyckegaard, A., Jakobsen, L. and Thomsen, O.T. “Sandwich Panel and a Method of Producing a Sandwich Panel” Application No./Patent No. 03027020.1- (Danish Patent P14477DK00), 2003

6.

Pageau, S. S., Joseph, P. F., Biggers, Jr., S. B., International Journal Solids and Structures, Vol. 31, No. 21, pp. 2979-2997, 1994

7.

Ribeiro-Ayeh, S, Hallström , S., Engineering Fracture Mechanics, Vol. 70, pp 1491-1507, 2003.

2T22. Sandwich structures

559

DEBONDING AND KINKING IN FOAM-CORE SANDWICH BEAMS D. A. Zacharopoulos, V. D. Balopoulos, Z. S. Metaxa, P. A. Kalaitzidis and E. E. Gdoutos Department of Civil Engineering, Democritus University of Thrace 12 Vassilissis Sofias St., Xanthi, 67100, Greece [email protected], [email protected], [email protected], [email protected], [email protected] In this work we consider the effects of debonding in a double cantilever beam (DCB) specimen of aluminum faces and PVC-foam core (Divinycel H, see [DIAB International AB, Divinycell Grade H Technical Manual, Sweden, 2003.]), as shown in Figure 1 below. The configuration follows the one proposed by Prasad and Carlsson [5], which is similar to the standard ASTM D5528 94a peel test [ASTM Standard D5528-94a. “Standard Test Method for Mode-I Interlaminar Fracture Toughness of Unidirectional Fiber-Reinforced Polymer Matrix Composites,” ASTM Annual Book of ASTM Standard 15.03, 283–292, American Society for Testing and Materials, 1999.]. All materials are linear elastic, and four cases of core density are considered (H 60, H 80, H 100, and H 250), which have been the subject of other investigations [e.g., Shivakumar, K., Chen, H., and Smith, A. S., Journal of Sandwich Structures and Materials vol. 7, 77–90, 2005.] too. All cases are typical of foam-core sandwich structures, where the core is much more flexible than the adhesive and faces. In each case debonding is introduced between the core and adhesive at the loaded end.

FIGURE 1. Sandwich peel-test specimen. (a) DCB specimen. (b) DCB specimen geometry.

Debonding is a common manufacturing defect of sandwich beams and panels that may severely hamper their load bearing capacity. It is akin to pre-cracking between either the face and adhesive or the adhesive and core. Face debonding is usually ignored, since face and adhesive materials are commonly much tougher than core materials. Pre-cracking between adhesive and core may grow either interfacially or into the core (kinking), as decided by energy release criteria. Under loadcontrol conditions, initiation of crack growth of either kind may leads to immediate (brittle) structural failure. Stability considerations aside, the rational analysis and design of sandwich sections requires at least some qualitative understanding of how the energy release rates and stress intensity factors (SIFs) depend on the loading conditions, the length of debonding, and the properties and dimensions of the surrounding materials. Cracks in sandwich constructions have characteristic lengths (e.g., initial debonding length) that are very large compared either to material characteristic lengths (e.g., bubble size in PVC foam cores) or to possible process zones. Therefore, the assumptions and machinery of linear elastic fracture mechanics (LEFM) may be employed in the study of sandwich debonding, and all analytical and numerical results presented forthwith depend explicitly or implicitly on LEFM.

D. A. Zacharopoulos et al.

560

Thus, we concentrate our investigation on obtaining the stress intensity factors (SIFs) and total energy release rates under unit loadings. Failure loads and type of crack propagation (interfacial or kinked) follow immediately by comparison with the corresponding toughness measures for the interface and the core. Step-by-step crack propagation under plane-strain conditions is simulated in FRANC 2D (see [Ingraffea, A. and Wawrzynek, P., User’s guide for FRANC 2D Version 3.1, www.cfg.cornell.edu, 1993.] for an introduction), and we obtain the total energy release rates ( G ) and the stress intensity factors ( K I , K II ) for increasing lengths of interfacial and volume cracks. The computational results in all cases considered are characterized by immediate kinking, followed by rapid curving of the sub-interfacial crack and eventual propagation parallel to the interface. These results are discussed with respect to their qualitative and quantitative features, with emphasis on their theoretical and experimental ramifications.

References 1.

Daniel, I, M., Gdoutos, E. E., Wang, K.-A., and Abot, J. L., International Journal of Damage Mechanics, vol. 11, 309-334, 2002.

2.

Zenkert, D., An Introduction to Sandwich Construction, Engineering Materials Advisory Service, Sheffield, UK, 1995.

3.

Prasad, S. and Carlsson, A.L., Engineering Fracture Mechanics, vol. 47, 813–824, 1994.

4.

Prasad, S. and Carlsson, A.L., Engineering Fracture Mechanics, vol. 47, 825–841, 1994.

5.

Sukumar, N., Huang, Y.Z., Prevost, H.J., and Suo, Z, International Journal for Numerical Methods in Engineering, vol. 59, 1075–1102, 2004.

6.

Oh, Hae-Soo, Journal of Computational Physics, vol. 193, 86–114, 2003.

7.

Shivakumar, K., Chen, H., and Smith, A. S., Journal of Sandwich Structures and Materials vol. 7, 77–90, 2005.

8.

Ingraffea, A. and Wawrzynek, P., User’s guide for FRANC 2D Version 3.1, www.cfg.cornell.edu, 1993.

9.

ASTM Standard D5528-94a. “Standard Test Method for Mode-I Interlaminar Fracture Toughness of Unidirectional Fiber-Reinforced Polymer Matrix Composites,” ASTM Annual Book of ASTM Standard 15.03, 283–292, American Society for Testing and Materials, 1999.

10. DIAB International AB, Divinycell Grade H Technical Manual, Sweden, 2003. 11. Araldite Technical manual for “Adhesive AV 138M with Hardener HV 998”. 12. Pechiney Renalu Companny, Certification for Aluminium 2024-T3.

2T22. Sandwich structures

561

MODELING CORE FAILURE BY THE TSAI–WU CRITERION IN THE DESIGN OF FOAM-CORE SANDWICH BEAMS E. E. Gdoutos, V. D. Balopoulos, P. A. Kalaitzidis and M. Konsta Department of Civil Engineering, Democritus University of Thrace 12 Vassilissis Sofias St., Xanthi, 67100, Greece [email protected], [email protected], [email protected], [email protected] This work is part of an extensive program at the Laboratory of Applied Mechanics of D.U.Th. involving experimental and numerical research, to expand our knowledge of composite materials and propose enhanced techniques for rational design of sandwich beams and shells. In particular, it is a study of the importance of describing core failure in elastic sandwich beams by the Tsai–Wu criterion (not by simple shear), for a variety of support conditions and loading patterns. The Tsai–Wu criterion can account for combined normal and shear stresses in anisotropic materials. In describing sandwich core failure, it represents a conservative elaboration of its simple-shear counterpart and is used in combination with failure criteria for all other limit states. For the plane stress conditions of a beam section, the Tsai–Wu criterion takes the simple form:

Fc  Ft W2 V2 V 1  1  62 Fc Ft Fc Ft F6

1 (1)

where the second-order stress V 3 has been ignored and the material strength in compression (Fc), tension (Ft), and shear (F6) has been introduced. As a first approximation, we apply both criteria in the context of Bernoulli kinematics and engineering beam theory. We consider the foam core of a sandwich beam that satisfies common assumptions (almost constant shear stress, M ) without axial forces. The critical F c F t  1 , and fiber in any section is the most compressed one and its failure, according to the Tsai–Wu criterion (for length L, width b, core thickness h c , and face thickness h f ), is given by: (2) The parameters

and

(typical action over typical resistance),

P  [

and J  [

introduce scale is the load intensity, and

describe the dependence of section moment and shear on the non-dimensional

position along the beam (i.e., the influence of the support conditions and the loading pattern). For each given case of support and loading and each section location , equation (2) can be solved for , so as to obtain the position of the critical section and [ c r i t  L the critical load intensity

.

The process described above is implemented in MatLab and applied to a large number of cases (presented in the full paper). In this summary we include two indicative diagrams obtained for a sandwich beam with glass/epoxy faces and core made of PVC foam (Divinycell H100). In particular, Figure 1 presents the critical load ( ) as a function of beam length for a tip-

E. E. Gdoutos et al.

562

loaded cantilever, superimposing new results for core failure according to the Tsa–Wu criterion on earlier results (see [2]) for core failure in simple shear and face failure by wrinkling. Figure 2 presents the same information for a simply supported beam under parabolic loading.

FIGURE 1: Critical load vs length for tip-loaded cantilever sandwich beam

FIGURE 2: Critical load vs length for simply-supported sandwich beam under parabolic load

References 1.

Allen, H.G., Analysis and Design of Structural Sandwich Panels, Pergamon Press, London, UK, 1969.

2.

Gdoutos, E.E and Daniel, I.M., in Proceedings of the 17th National Conference of Italian Group of Fracture, edited by , Bologna, 2004, –.

3.

Daniel, I.M., Gdoutos, E.E., Wang, K. A. and Abot, J.L., International Journal of Damage Mechanics, vol. 11, 309–334, 2002.

2T22. Sandwich structures

563

NUMERICAL INVESTIGATION OF CRACK PROPAGATION IN SANDWICH STRUCTURES E. E. Theotokoglou Faculty of Applied Sciences, Dept. of Mechanics-Lab. of Strength Materials, The National Technical University of Athens, Zographou Campus, Theocaris Bld., GR-0157 73, Athens, Greece [email protected] Low-density foam core sandwich composite find an increasing use as structural materials. They are often used for high performance structural applications such as in the hull forms of racing yachts, patrol crafts, lifeboats and catamaran ferries. There is a growing emphasis on selecting different materials and their behavior under flexural loading. In addition, fracture mechanics analyses of low-density foam core have been performed by several authors [1-3] considering linear fracture mechanics on a macroscopic level. However only a limited amount of data are evaluated about the fatigue crack growth in the core of sandwich beams [3-5].

FIGURE 1. Crack propagation in the core of a sandwich beam. The purpose of the present work is to numerically investigate the fatigue crack propagation in the core of sandwich beams under flexural loading. At first a core-skin debond parallel to the beam axis is considered (Fig. 1), in accordance with experimental data [5]. When subjected to flexural loading, this debond will propagate slowly along the top interface and eventually kinked into the core as shear crack. Stress intensity factors are calculated using Finite Element Method, and assuming linear fracture mechanics and plane strain conditions. Results from the finite element analysis combined with the experimental data predict the crack growth behavior under flexural loading. The simplicity of the proposed procedure and the numerical model developed, make possible the prediction of the crack propagation for various types of sandwich beams under flexural loading.

References 1.

Gibson, LH. and Ashby, M.F., Cellular solid – structure and properties, 2nd ed. Cambridge University Press, 1997.

564

E. E. Theotokoglou

2.

Zenkert, D. and Backlund, J., Compos Sci Technol, vol. 34, 225-42, 1989.

3.

Harte, A.M., Fleck, N.A., Int. J. Fatigue, vol. 23, 499-507, 2001.

4.

Burman, M. and Zenkert, D., Fatigue crack initiation and propagation in sandwich structures, Doctoral thesis, Report 98-29, Department of Aeronautics, Royal Institute of Technology, Sweden, 1998.

5.

Kulkarni, N., Mahfuz, H., Jeelani, S. and Carlsson, L.A., Composite Structures, vol. 59, 499505, 2003.

2T22. Sandwich structures

565

LOCAL EFFECTS IN SANDWICH BEAMS: MODELLING AND EXPERIMENTAL INVESTIGATION M. Johannes, J. Jakobsen, V. Skvortsov1, E. Bozhevolnaya and O. T. Thomsen Institute of Mechanical Engineering, Aalborg University Pontoppidanstræde 101, 9220 Aalborg East, Denmark 1State Marine University of St. Petersburg, Russia [email protected] It is known that the joining of different cores in sandwich beams and panels leads to local effects at these core junctions. The local effects arise due to mismatch of the elastic properties of the adjoining core materials, and they manifest themselves by a rise of the in-plane stresses in the sandwich faces as well as of the shear and through-the-thickness stresses in the adjacent cores. These stress concentrations may cause local fracture of the weak core materials, but severe face damage is also a highly possible scenario. This may jeopardize the structural integrity of the sandwich element and cause its global failure. Skvortsov and Thomsen [1] were the first to shed light on the physics of the local effects at core junctions in sandwich beams subjected to transverse loading. Closed-form analytical estimates of the stress concentrations are given in this work, and the accuracy of these estimates was subsequently verified experimentally by Bozhevolnaya et al. [2]. These studies have demonstrated that the locally induced stresses are of considerable magnitude under transverse external loading. Thus the question arises what kind of local effects are induced in sandwich beams/panels subjected to axial in-plane loading, which also occurs commonly in practice. An analytical modelling of such a situation is performed on the basis of the exact 2-D theory of elasticity solution. This solution considers the mismatch of the global stress-strain state of the compliant and stiff cores far from the considered core junction. Here an axially applied force N will cause in-plane normal stresses in the face and cores, which can be approximated by

V f1(2) f

N , 2 h f (1  G 1( 2 ) )

V c1(2) f

N G 1( 2 ) h c (1  G 1( 2 ) )

,

G 1( 2 )

E 1( 2 ) h c 2E f h f

(1)

The locally induced stresses that arise at the junction area are described with the help of an extended Winkler foundation model, which couples the behaviour of the faces with the longitudinal in-plane stresses in the supporting core materials. The maximum local bending stress in the face and core shear stress are estimated to be

V

c

bend f

4

k fV

E c1 , E c2

f

6h f

f1

hc

O

W c1

c (1  c ) ,

4

6 E c1 h c E fhf

ª

V c1 f c « k 1 ¬

º 6Q c (1  Q c ) 1  k2O » O 1 Q c ¼

(2)

3

3

(3)

where kf, k1 and k2 are known coefficients close to unity, c quantifies the mismatch of the elastic core properties and describes the rate of decay of the local effects in the compliant core.

M. Johannes et al.

566

An example of a distribution of the face stresses of a sandwich beam subjected to uni-axial tension is shown in Fig. 1. It is seen that face stresses, which are shown along the outer face surface and the face-core interface, display drastic variations close to the junction (which is situated at x=100 mm).

FIGURE 1. Stress distribution in the face of a sandwich beam subjected to uni-axial tension An experimental investigation will be pursued for two different realistic combinations of joined core materials; one example corresponding to a junction between polymeric foam cores of different densities, and another example corresponding to the joining of a low density polymeric foam core and a stiff wooden reinforcing patch, as used for rigging purposes in shipbuilding. The nature of the local effects for the tensile in-plane loading condition will be studied by comparing experimentally determined strains of the sandwich beam faces with results from finite element modelling and estimations given by the analytical model. In addition to data acquired in the elastic regime of deformation, the sandwich beams will be loaded quasi-statically until the occurrence of fracture/failure, and the face strains, the overall deformation patterns, the loads where the on-set of fracture occurs as well as the modes/patterns of fracture will be monitored. The analytical and finite element model results will be compared with the experimental measurements, and various failure criteria will be evaluated in relation to their capacity to accurately predict failure of the core junction and thereby of the sandwich structures considered.

References 1.

Skvortsov, V. and Thomsen O.T., ‘Analytical Estimates for the Stresses in Face Sheets of Sandwich Panels at the Junctions between Different Core Materials’, In Proceedings of the 6th International Conference on Sandwich Structures (ICSS-6), Ft. Lauderdale, Florida, March 31-April 2, 2003, CRC Press, New York, 2003, 501-509.

2.

Bozhevolnaya, E., Thomsen, O.T., Kildegaard, A. and Skvortsov, V., Composites. Part B: Engineering, Vol. 34, pp 509-107, 2003.

2T22. Sandwich structures

567

TYPICAL IN-PLANE RESPONSE SURFACES FORPRISMATIC FOAM-CORE SANDWICH BEAMS V. D. Balopoulos, P. A. Kalaitzidis, D. A. Zacharopoulos and E. E. Gdoutos Department of Civil Engineering, Democritus University of Thrace 12 Vassilissis Sofias St., Xanthi, 67100, Greece [email protected], [email protected], [email protected], [email protected] This work employs the technique of response surfaces [1] to the 2-D statics of prismatic foam-core sandwich beams subject to typical support conditions and transverse loading. The goal is to obtain approximate functional forms for all responses that characterize the limit states of such beams (e.g., support reactions, extremes of deformation and stress) and, hence, influence their optimal design through the inequality constraints. This is part of a program of experimental and numerical research at the Laboratory of Applied Mechanics, to expand our knowledge of composite materials and propose enhanced techniques for rational design of sandwich structures. A response surface (or curve, or hyper-surface) is an interpolation of a quantity of interest (called the “response”) which is expensive to obtain either experimentally or numerically and depends on one or more a priori known parameters. First, the response is measured or computed at all points of a regular grid in the parameter space and, then, the resulting values are fitted with inexpensive functions. However, the ease of application of this technique and the information content of the results depend greatly on the choice of parameters and interpolating functions. An obvious requirement is to choose parameters that are mutually independent and have a clear physical meaning. An equally desirable, if less obvious, objective is that the dependence of the response on the parameters may be decoupled, at least approximately. To achieve these goals, one must have significant understanding of the response under study. The use of response surfaces is essential in the context of robust global optimization, for reasons of feasibility and efficiency explained at length in our separate work on the subject. Nevertheless, the results presented are useful in the design and analysis of prismatic beams in general, provided their shear flexibility is considerable and, hence, their response does not admit closed-form solutions. All investigations carried out in this work regard linear behavior, both geometrically (as ensured by the strict limits of serviceability) and materially. Furthermore, all orthotropic materials are considered aligned with the principal sectional axes, so that the state of pure bending is possible. Thus, the strain energy is proportional to the load amplitude, consists of distinct shear and bending contributions, and involves no cross-terms and no contribution from uniform stretch (geometric linearity). Sandwich beams with foam core are highly deformable in shear. Therefore, Bernoulli kinematics is inaccurate for describing their stress and strain fields and their sectional stiffness. Even Timoshenko kinematics may occasionally prove insufficient, especially in the recovery of intra-sectional fields from sectional strain measures and stress resultants. In such circumstances, the engineering split of 3-D behavior into 2-D (sectional) and 1-D (beam) behavior is salvaged by means of Variational Asymptotic Beam Sectional Analysis [2]. This method provides enhanced accuracy in the evaluation of sectional stiffness and in the recovery of sectional fields not only for prismatic rods but for pre-curved and pre-twisted ones as well. A piece of software, that relies on this method and goes by its initials (VABS), is available free for academic use from [3]. Due to the decoupling of the strain energy, the sectional stiffness is diagonal and beam behavior is governed by k ss (shear stiffness, units of force), k b b (bending stiffness, units of

V. D. Balopoulos et al.

568

moment u distance), and

(slenderness), where

is the approximate static depth

of the section. One may also scale the sectional strain measure and make of

to produce

commensurate with k s s . Both k s s and k b b are multiples

, with non-dimensional coefficients of proportionality that depend strongly on (geometry) and

(material), and only weakly on E c G c (i.e., on Q c ).

Finally, the intra-sectional stress field depends on the section characteristics, as quantified by Og , Om

, and Q c , and on the scaled measures of strain, İ , and stress,

.

The product of this work is three types of response surfaces, which interpolate: 1

the stiffness coefficients

and

those of “engineering” beam theory) as functions of 2

(produced by VABS and compared to

O g , O m , Q c ,

the support reactions, w m a x L , and ı , İ at the critical sections (obtained by solving separately for each combination of support and loading conditions and for “unit” amplitude, i.e., for total load equal to k ref ) as functions of k ref , and

3

the stresses at critical fibers of a section (produced by VABS and compared to those of “engineering” beam theory) as functions of  ı , İ , O g , O m , Q c .

The first type is simple and requires little work. The second type is easy, in principle, but tedious in practice, because of the numerous combinations that must be considered. Conversely, the third type is, in principle, the hardest to construct, because it depends on many parameters. However, only response surfaces for the corrections to the “engineering” stresses (that VABS introduces) are necessary and, since these corrections are small, rough fitting of the data is sufficient.

References 1.

Myers, H. M., Montgomery, C. D, Response Surface Methodology : Process and Product Optimization Using Designed Experiments, Wiley-Interscience, 2002

2.

Yu, W., Hodges, H. D., Volovoi, V., Cesnik, E.S. C., ‘On Timoshenko-like modeling of initially curved and twisted composite beams’, International Journal of Solids and Structures 39, 2002, 5101–5121

3.

Utah State University Department Mechanical and Aerospace Engineering, Dr Webin Yu Site http://www.mae.usu.edu/faculty/wenbin/

2T23. Novel testing and evaluation techniques

569

NON-DESTRUCTIVE EVALUATION OF YIELD STRENGTH USING A NOVEL MINIATURE DUMB-BELL SPECIMEN-AN EMPIRICAL APPROACH G. Partheepan, D. K. Sehgal1 and R. K. Pandey1 Research Scholar, 1Professor Department of Applied Mechanics, Indian Institute of Technology, Delhi, INDIA-110 016. [email protected], [email protected], [email protected] This paper describes a method used to extract yield strength of the material using a newly developed miniature specimen. An experimental setup is also developed to perform the miniature test. Miniature tests were conducted on the proposed dumb-bell specimen fabricated from different materials using the developed test setup. The miniature test output i.e. load-elongation diagrams are obtained for the materials chosen for the present study. Standard test methods for predicting mechanical properties require the removal of large volume of material samples from the in-service component, which is generally impractical where there is a restriction on the available specimen volume. The proposed specimen can be taken from in-service component without disturbing the integrity of the structure. A linear empirical equation is proposed for the determination of yield strength of the material. The yield strength of the material is obtained based on the miniature test result i.e. yield load (load at breakaway) and the miniature specimen geometrical parameter. The predicted yield strength value corroborates well with the experimental results. Researchers in the past used either thick specimen or thin specimen having number of machining operations. For the present study, a new dumb-bell shaped miniature specimen is designed as shown in Fig. 1. The procedure for making this specimen is easier as compared to the conventional sub size tension test specimens, which need a number of machining operations. More number of machining operations on the specimen may change the properties as well.

Figure 1. Design of miniature tensile specimen. The present work involves design of miniature specimen holder as the specimen used in the present case being miniature in nature could not be directly gripped in the testing machine, fixture for attaching the miniature specimen in the test machine along with the specimen holders. The present study is carried out in Zwick machine. The miniature tests were conducted on the specimens prepared from the materials selected for the present study. The tests are conducted at a speed of 0.05 mm/min and at room temperature. At least five specimens were tested from each material. Fig. 2 shows the miniature test load-elongation for the specimen from AR66 (Aluminum alloy) material.

G. Partheepan et al.

570

Figure 2. Miniature test load-elongation curve for AR66. The yield load (load at breakaway) is obtained from the miniature load-elongation curve for AR66 and also for other materials. Before testing the miniature specimens were measured for its geometrical parameters. Statistical analysis was performed on some input and output variables of the miniature test on different materials. It is to check the repeatability of test so that the test results can be used in predicting the material properties. It is observed that the statistical analysis results are very satisfactory and consent to use the test results in predicting the yield strength of the material. A new linear empirical relation for the prediction of yield strength based on yield load and geometry of the miniature specimen is developed as follows:

V

y

§ Py · 1 .7 6 3 9 ¨ ¸  6 5 .9 7 3 ©tw ¹

(1)

The results obtained from the empirical equation for different materials are in good agreement with the experimental results. Conclusions A new empirical correlation is proposed for the determination of yield strength of the unknown material using the miniature test results and its geometry. This miniature specimen can be prepared from material taken from any in-service components in a non-destructive manner. The result from the empirical correlation is found to be in good agreement with the experimental results.

2T23. Novel testing and evaluation techniques

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3D MEASUREMENT OF THE STRAIN FIELD SURROUNDING CRACK TIP Daniel Vavrik, Jan Bryscejn, Jan Jakubek1 and Jaroslav Valach Institute of Theoretical and Applied Mechanics of the Czech Academy of Sciences, Prosecka 76, Prague 9, Czech Republic 1Institute of Experimental and Applied Physics of the Czech Technical University in Prague, Horska 3a/22, 128 00, Prague 2, Czech Republic, E-mail: [email protected] [email protected] Finite elements method is widely used for numerical simulations of solid object behaviour in many applications questioning in some cases the necessity of physical experiments. Available databases of material behaviour are quite sufficient for simulations of linear systems. However for the simulations of nonlinear systems, it is still necessary to have experimental information’s. Unfortunately, the feedback based on strain measurement in several points only can lead to accurate but imaginary numerical solution. Full field strain measurement is routinely performed today. Let’s reduce the class of the analyzed object onto flat specimens only. Dependency on loading type and studied feature, either the in-plain or out-of plain experimental method is usually chosen. One of the highly non-linear problems is the failure of ductile specimen with stress concentrator especially when failure is accompanied by the developing of damage zone in the vicinity of the stress concentrator. Corresponding damage models have a number of parameters which is necessary to determine. The feedback based on in-plane strain measurement only can lead to a non-unique solution as well as without prior knowledge of material damage type. From this reason both in-plane and out-of plane displacement measurement is required. On the other hand monitoring the out-of plane displacement can detect the onset of intensive damage zone development [1]. It is possible to employ the combination of two different optical methods using only one camera to achieve 3D displacement/strain measurement. The proposed Coded Photometric Stereo method for the measurement of the out-of plane displacement and the optical grid method for the measurement of the in-plane strain field can be applied simultaneously. The Photometric stereo (PS) method allows topographic reconstruction of the object surface using its optical images [2]. PS utilizes the fact of close relation between the relative lightness of uniformly illuminated surface and the angle to the direction of light. It means that knowing the illumination geometry we can determine the slope (normal) of the surface at every point. Surface topography is obtained as an integration of this normal field. This fact can be used for the purpose of out-of plane measurements of loaded object deformations. Three images required by PS using three lights illuminating surface from different directions are sufficient for determination of both x and y slopes at any studied point of the surface regardless on its colour variations. Knowledge of both slopes is advantageous for the reconstruction integration especially in the case of locally irregular surfaces. For this reason three lights have been used in our experiment. Reconstructed topography is dimensionless, so dimension calibration must be done. It can be done by one point mechanical measurement of the elevation differences between two points of the studied surface or it is necessary to have some calibration object of known height/depth connected with the surface. Coded Photometric Stereo (CPS) is the enhanced PS method utilizing Red-Green-Blue (RGB) lights coding. Monochromatic RGB lights positioned around the observed area produce directional

D. Vavrik et al.

572

illumination. Three different scenes coded in one compose image can be separated using standard RGB colour channels of the digital camera we use. Out-of plane displacement is measured by CPS using these scenes. The compose image serves for the measurement of the in-plane displacement field by the grid method. The grid method analyzes the deformation of the surface measuring grid. The method of Interpolated Ellipses (MIE) has been selected for this purpose [3]. The MIE is a technique based on the optical monitoring of deformations during loading processes of hexagonal grids of dots deposited on the surface of the monitored specimen. Loading the specimen deforms a circle on the surface into an ellipse. Each ellipse is interpolated by six neighbouring dots of the hexagonal grid. Knowledge of the ellipse parameters directly yields the magnitude and the direction of principal strains on the specimen surface. Proposed combination of above described optical methods is suitable also for dynamical experiments as the 3D displacement/strain field can be determined from one image. Developing of the 3D displacement/strain field during loading of a flat high ductile specimen with crack will be presented. Calculated plastic strain intensity developing will be presented as well. Specimen will be loaded until failure will occur. Characteristic behaviour of the strain/ displacement fields regarding to damage zone evolution will be explored. As it is known from the experiments performed in the past [1,3] intensive damage zone developing is accompanied by the intensive developing of the plastic strain intensity [3] as well as by the characteristic delay in a contraction evolution [1].

References 1.

Vavrik, D.; Jakubek, J.; Pospisil, S.; Visschers, J.: In Proceedins of the 9th International Conference on the Mechanical Behaviour of Materials, Switzerland, Geneva, May 25-29, 2003

2.

Woodham, R. J.: Optical Engineering, 19, 139-144, (1980).

3.

Vavrik, D.; Zemankova, J.: Experimental Mechanics, Vol. 44, August 2004, pp. 327-335,

2T23. Novel testing and evaluation techniques

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RADIOGRAPHIC OBSERVATION OF DAMAGE ZONE EVOLUTION IN HIGH DUCTILE SPECIMEN D. Vavrik1, T. Holy, J. Jakubek, M. Jakubek and Z. Vykydal Institute of Experimental and Applied Physics of the Czech Technical University in Prague, Horska 3a/22, 128 00, Prague 2, Czech Republic, E-mail: [email protected] 1Institute of Theoretical and Applied Mechanics of the Czech Academy of Sciences, Prosecka 76, Prague 9, Czech Republic This work reports on new results of the experimental observation of material damage evolution in high ductile flat specimens manufactured from aluminium alloy. Failures in ductile materials precede intensive internal material damage evolution. Not only damage existence but also its quantification has to be determined for a numerical simulations purpose. An experimental method called “X-Ray Dynamic Defectoscopy (XRDD)” was developed from this reason [1]. The test sample is illuminated by X-rays during the loading process. Measured changes in transmission represent alterations of effective thickness of the specimen. The effective thickness changes are understood as weakening of the material due to damage volume fraction and transversal thickness reduction (contraction) resulting from loading stress. Alterations in the sample thickness due to void volume fraction are separated from the total thickness reduction using independent optical measurement of the out-of plane displacement field by the photometric stereo method. We observe time evolution of the damage zone shape and proportional volume fraction of voids (damage intensity) by XRDD. In-plane strain field and consequent plastic strain intensity at a surface is investigated by the optical Method of Interpolated Ellipses [2]. Failure of a high ductile specimen usually precedes a decrease of the loading force (material softening) under the condition of displacement control in the monotonic loading. This phenomenon is usually induced by a large plastic deformation and eventually by a related dynamic development of voids and micro-cracks inside the specimen (damage process). The experimental investigation of this highly interesting stage can be made accessible only under very well controlled loading. Unfortunately, the elastic energy stored in the loading equipment can result in sudden failure within very short time corresponding to the loading instability. We can follow this time interval with real fast readout system or, alternatively, we can prolong this time interval by reducing the elastic energy in the loading equipment. New designed loading frame fulfils the indicated requirements and enables extraordinary precise displacement loading control even beyond the maximal loading force. This transferable and highly stiff loading device is equipped by four stepper engines ensuring symmetrical loading of the specimen with stable position of the observed area in the X-ray beam. The loading force is recorded by a load cell and the prolongation of the specimen is measured by an extensometer. Loading force capacity of the device is 100 kN and weight only 25 kg, with dimensions 377x343x190 mm. These parameters allow to fix loading equipment onto PC controlled motorized stage during experiment; see Fig. 1 for whole experimental setup. It is possible to put loading frame together with the motorized stage into fully shielded box. Therefore X-ray radiographic transmission and tomographic observation is easy accessible.

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Fig. 1: Experimental setup. X-ray tube on the left, loading frame fixed on the loading stage in the middle, X-ray detector Medipix on the right. There are several principal requirements which are necessary to achieve the high resolution X-ray imaging: high quality of the X-ray beam, precision positioning of the observed object and high quality of the X-ray detector. As the X-ray sensor we are using the digital Medipix-2 [3]. The X-ray generator Hamamatsu has X-ray emission spot of the diameter 5 Pm and divergent cone beam. It allows magnification of factor 10 allowing resolution of the micrometer scale. Regarding the precision positioning of the observed object, stepper engines are employed in the motorized stage. This stage has two linear axes in a plane perpendicular to the beam direction and one rotation around vertical axis. Linear axes allow scanning objects bigger than X-ray detector area. Rotation allows computer tomography reconstruction. Each active part of the experimental setup is operated using universal serial bus USB. Fully operational and controllable are the motorized stage, the parameters and the exposition of the X-ray source, the acquisition of the X-ray images, optional acquisition of the optical images, the driving of the stepper motors of the loading frame, the data acquisition from the load cell and of the extensometers. It is possible to operate and control all these processes using one notebook thanks to this unification. In addition all these functions have automatically the same time base.

References 1.

Vavrik, D.; Jakubek, J.; Pospisil, S.; Visschers, J. (2005), Materials Science Forum, Vol. 480, pp. 231-236

2.

Vavrik, D.; Zemankova, J.: Experimental Mechanics, Vol. 44, August 2004, pp. 327-335

3.

Medipix collaboration: http://www.cern.ch/MEDIPIX/

2T23. Novel testing and evaluation techniques

575

CALIBRATION OF FRACTURE PARAMETERS BY INSTRUMENTED INDENTATION AND TEST SIMULATION Massimiliano Bocciarelli, Gabriella Bolzon and Giulio Maier Department of Structural Engineering, Politecnico di Milano piazza Leonardo da Vinci 32, 20133 Milano, Italy [email protected], [email protected], [email protected] Surface engineering is an emerging discipline in technologies leading to products such as electronic packages, magnetic recording media, optical devices and tribological protection of mechanical components. The fruitful use of thin coatings in these applications require an accurate characterisation of mechanical properties of these this layers after deposition, a process which can alter their characteristics with respect to the original bulk state. Elastic moduli, yield strength, fracture energy and interfacial adhesion play a crucial role on the correct functioning and longterm performance of coatings, avoiding cracking or delamination from the substrate. A spreading methodology for material characterisation is based on indentation tests. Fracture induced in brittle materials by indenters with sharp corners and delamination between film and substrate caused by indentation tests have been investigated by several researchers, e.g. Xiaodong et al. [Xiaodong, L., Dongfeng, D. and Bhushan, B., Acta Mater., vol. 45, 4453-4461, 1997.], Abdul-Baqi and Van der Giessen [Abdul-Baqi, A. and Van der Giessen, E., Int. J. Solids Struct., vol. 39, 1427-1442, 2002.], Li and Siegmund [Li, W. and Siegmund, T., Acta Mater., vol. 52, 2989-2999, 2004]. The model calibration technique proposed in Bolzon et al. [Bolzon, G., Maier, G., and Panico, M., Int. J. Solids Struct., vol. 41, 2957-2975, 2004.] and Bocciarelli et al. [Bocciarelli, M., Bolzon, G. and Maier, G., Mech. Mat., vol. 37, 855-868, 2005.] is based on indentation test, imprint mapping and inverse analysis. This method can be applied to the identification of fracture material parameters both for delamination in film-substrate systems and for the fracture characterisation of ceramic materials at the micro-scale. The novelty is represented by the mapping of the residual imprint (through atomic force microscope or laser profilometer, depending on the imprint size), and by the use of these deformation measures, besides the traditional indentation curves, for the parameter estimation through the minimisation of a function which represents the discrepancy between the experimental measurements and the same measurable quantities obtained by the numerical simulation of the experiment. Details can be found in Maier et al. [Maier, G., Bocciarelli, M., Bolzon, G. and Fedele, R., Int. J. Fracture, submitted, 2005.]. The test simulation has been performed by the finite element commercial code ABAQUS, using the large plastic strain capability provided therein Fracture and delamination processes have been simulated by means of interface elements, implemented in the code by the authors, endowed with the cohesive-crack model originally proposed by Rose et al. [Rose, J.H., Ferrante, J. and Smith, J.R., Physical Review, vol. 9, 675-678, 1981. ] and Xu and Needleman [Xu, X. P. and Needleman, A., J. Mech. Phys. Solids, vol. 42, 1397-1434, 1994.]. The purpose of this communication is to present some recent or current developments and the main results recently achieved by the authors in the growing area of fracture mechanics centred on the calibration of cohesive fracture models for quasi-brittle materials, by approaches which combine experimentation, experiment simulation and minimisation of the discrepancy between measured and computed quantities.

M. Bocciarelli et al.

576

References 1.

Xiaodong, L., Dongfeng, D. and Bhushan, B., Acta Mater., vol. 45, 4453-4461, 1997.

2.

Abdul-Baqi, A. and Van der Giessen, E., Int. J. Solids Struct., vol. 39, 1427-1442, 2002.

3.

Li, W. and Siegmund, T., Acta Mater., vol. 52, 2989-2999, 2004

4.

Bolzon, G., Maier, G., and Panico, M., Int. J. Solids Struct., vol. 41, 2957-2975, 2004.

5.

Bocciarelli, M., Bolzon, G. and Maier, G., Mech. Mat., vol. 37, 855-868, 2005.

6.

Maier, G., Bocciarelli, M., Bolzon, G. and Fedele, R., Int. J. Fracture, submitted, 2005.

7.

Rose, J.H., Ferrante, J. and Smith, J.R., Physical Review, vol. 9, 675-678, 1981.

8.

Xu, X. P. and Needleman, A., J. Mech. Phys. Solids, vol. 42, 1397-1434, 1994.

2T23. Novel testing and evaluation techniques

577

INTERNAL CRACK DETECTION AND ANALYSIS USING THERMOELASTIC STRESS ANALYSIS N. Sathon and J.M. Dulieu-Barton School of Engineering Sciences, University of Southampton Highfield, SO17 1JB, UK [email protected], [email protected] The detection of damage at early stage is of prime important to initiate timely and cost effective repair and maintenance. In a shell structures such as pipes or pressure vessels, cracks may initiate at the internal surface and propagate through the thickness. The cracks are usually semi-elliptical or semi-circular shape. These type of defects can be observed using traditional inspection techniques such as ultrasound. The aim of the current research is to devise an approach of using thermoelastic stress analysis (TSA) to detect, analyse and quantify the severity of these sub-surface cracks in terms of the stress field surrounding the crack. TSA is a non-contact technique concerned with the measurement of the surface temperature change of a solid elastic body under dynamic loading. The technique is based on the thermoelastic effect. The temperature change is measured using a highly sensitive infra-red detector. The relationship between the temperature change and the stress change under adiabatic condition can be expressed as [1]:

'T



DT Uc

3

¦ 'V

i

(1)

1 1

where T is the local temperature change, is the coefficient of thermal expansion, T is the surface temperature, is the density, c is the specific heat and delta sigma is the sum of the principal stress. Primarily TSA is a surface technique and has been used extensively to evaluate the SIFs from through cracks. In the late 1980s it was recognised that the technique can also be used to obtain sub-surface stresses provided that phase of temperature oscillation is available [2]. Some initial validations of this idea have been carried out experimental and by using numerical solutions [3]. The approach is based on the effect of heat conduction caused by the stress gradient and hence thermal gradient (see equation 1). At a typical loading frequency for TSA the assumption of an adiabatic state may not be valid around the region of damage such as a crack due to the very high stress gradient which results in an inconsistency of thermal amplitude and phase. This nonadiabatic behaviour is exploited in the present work to evaluate the severity of the sub-surface crack. This paper describes the behaviour of thermal response from the surface of solid body with embedded multiple sub-surface flaws at different severity in terms of thermal amplitude and phase. Finite Element modelling of the thermal conditions is carried out and the results from the numerical simulation are then compared with the TSA to confirm the feasibility of using the technique for internal crack severity evaluation.

N. Sathon and J.M. Dulieu-Barton

578

References 1.

Dulieu-Barton, J.M. and P. Stanley, Development and applications of thermoelastic stress analysis. Journal of strain analysis for engineering design, 1998. 33: p. 93--104.

2.

McKelvie, J. Consideration of the surface temperature response to cyclic thermoelastic heat generation. in Proc. 2nd Conf. on Stress Analysis by Thermoelastic Technique. 1987: SPIE.

3.

Lesniak, J.R. Internal Stress Measurement. in Proc. 6th Congress on Experimental Mechanics. 1988. Portland: SEM, BETHEL CT.

2T23. Novel testing and evaluation techniques

579

ULTRAHIGH-RESOLUTION TRANSVERSAL POLARIZATION-SENSITIVE OPTICAL COHERENCE TOMOGRAPHY: STRUCTURAL ANALYSIS AND STRAIN-MAPPING Karin Wiesauer, Michael Pircher1, Rainer Engelke2, Gisela Ahrens2, Gabi Grutzner2, Reinhold Oster3, Christoph K. Hitzenberger1 and David Stifter Upper Austrian Research GmbH, Hafenstr. 47 – 51, 4020 Linz, Austria [email protected] 1Centre of Biomedical Engineering and Physics, Medical University, Währingerstr.13, 1090 Wien, Austria 2micro resist technology GmbH, Koepenicker Str. 325, 12555 Berlin, Germany 3Eurocopter Deutschland GmbH, 81663 München, Germany Optical coherence tomography (OCT), originally developed and so far nearly exclusively used for biomedical applications (e.g., [1,2]), is a contact-free, non-destructive technique based on lowcoherence interferometry to image structures within translucent and turbid materials. Commonly, cross-sectional reflectivity images with a depth-resolution determined by the coherence length of the near-infrared light source are obtained. When OCT is performed in a polarization sensitive way (PS-OCT), additional information about birefringence within a material is obtained by mapping the retardation between ordinary and extraordinary rays [3]. Because birefringence is induced when strain occurs, PS-OCT provides depth resolved information about the internal stress within a sample. In this work, we apply PS-OCT for material analysis. The materials investigated, mainly plastics, polymers and compound materials, show feature sizes often in the range of only a few microns (e.g., diameter of glass-fibres, thickness of layers). The depth-resolution of 10 – 20µm, provided by superluminescence diodes commonly used as light sources, is too low for these applications. Using a femto-second (fs-)Ti:sapphire laser, we obtain ultra-high depth-resolution of around 2µm for typical plastic materials [4]. For the first time, ultra-high resolution imaging is combined with transversal en-face) scanning PS-OCT, where images at a defined depth parallel to the sample surface are obtained. With our setup, we are able to scan areas as large as 3x3mm2 within seconds, and we can switch immediately from transversal to cross-sectional scanning [4]. We demonstrate the advantages of transversal scanning for two different types of samples: a helicopter rotor blade showing cracks due to loading tests, and high-aspect ratio moulds in thick photoresist layers for micro electromechanical parts (MEMS) where the resist-wafer interface was investigated. Figure 1a) shows a cross-sectional reflectivity image of the rotor blade consisting of a glass-fibre – epoxy resin laminate. Beneath a fibre-free top layer, the first fibre bundles are observed a depth of around 700µm. However, the crack running perpendicularly to the scanning plane (arrow) is hardly visible. In contrast, the en-face reflectivity image (Fig. 1b)) taken at a depth as marked in a), clearly reveals the crack running horizontally across the crossing fibre bundles.

K. Wiesauer et al.

580

FIGURE 1. a) Cross-sectional and b) en-face reflectivity scans of a helicopter rotor blade with a crack, indicated by the arrows. Dotted lines: Positions of cross-sectional and en-face scans. In Fig. 2a), a cross-sectional reflectivity image of the photoresist mould on a gold coated wafer is displayed. Besides the resist layer thickness of 1.3mm, nearly no information about the structure itself is obtained. In contrast, the en-face reflectivity scan taken at the optical depth of the interface reveals the geometrical wheel structure (Fig. 2b)). In that case, a faulty wafer was investigated. The defect structures (ridges at the rear resist surface, indicated by the arrows) were detected contactless and non-destructively with the moulds still on the wafer. On the other hand, retardation images taken at the interface level of a faultless mould show the interfacial strain distribution (Fig. 2c)). The areas around the teeth of the wheels are clearly highly strained, and increased strain occurs in between adjacent wheels. Images like these add valuable information for the design and quality control of MEMS moulds, because areas with excessive stress where defects may occur are revealed.

FIGURE 2. Photoresist moulds on a gold coated wafer. a) Cross-sectional reflectivity scan with schematic drawing showing the different optical levels. b) En-face reflectivity scan at the interface of a faulty mould. The arrows indicate some of the defect structures. c) Interfacial en-face retardation scan of a good mould, showing the strain distribution (detail shown in the inset).

References 1.

Huang, D., Swanson E. A., Lin C. P., Schuhman J. S., Stinson W. G., Chang W., Hee M. R., Flotte T., Gregory K., Puliafito C. A. and Fujimoto, J. G., Science 254, 1178, 1991.

2.

Fercher, A. F., Hitzenberger C. K., Drexler W., Kamp G. and Sattmann, H., Am. J. Ophthalmol. 116, 113, 1993.

3.

Hitzenberger, C. K., Götzinger E., Sticker M., Pircher M. and Fercher, A. F., Opt. Express 9, 780, 2001.

4.

Wiesauer, K., Stifter D., Pircher M., Götzinger E., Hitzenberger C. K., Bauer S., Engelke R., Ahrens G. and Grützner, G., Opt. Express 13, 1015, 2005.

2T23. Novel testing and evaluation techniques

581

APPLICATION OF DIGITAL SHEAROGRAPHY IN DETERMINING OPENING MODE SIF IN EDGE CRACKS M. Ghassemieh, A. Ghazavizadeh1 and N. Soltani1 Civil Engineering Department 1Intelligence Based Experimental Mechanics, Mechanical Engineering Department The University of Tehran, Iran [email protected], [email protected], [email protected] In this paper the non-destructive technique of digital shearography is utilized in order to obtain stress intensity factor (opening mode) in edge cracks. Being a relatively new non-destructive evaluation technique, digital shearography was developed to eliminate some of the shortcomings of holography and has proven to be a powerful method to measure in-plane and out-of-plane strains. Digital shearography has several advantages over other optical methods such as simple setup, insensitivity to environmental stability, not requiring any special device for vibration isolation and yielding out-of-plane strain components directly. Its advantages have made it suitable for industrial environments and research centers (e.g. Steinchen et al. [1] and Hung [2]). In digital shearography, by digital subtraction of before and after loading speckle patterns recorded by a digital CCD-camera, shearograms are obtained which dark fringes represent contours of equal in-plane or out-of-plane deformation partial derivatives. Through combination of linear elastic fracture mechanics and optical (digital shearography) relations, first mode stress intensity factor of cracks and first partial derivatives of out-of-plane deformation are correlated. In order To minimize random experimental errors, information for several points are registered and least square method is used to obtain stress intensity factor. Fig.1 presents the proposed scheme of the test specimens. Cracks normal to the length are formed in the middle of the specimen length and placed at the edge. The geometric specifications of specimens are detailed in Table (1). Making

L W

4 creates a uniform tensile stress

FIGURE 1. Proposed scheme of the test specimens distribution in the specimen. The cracks were blunt, not sharp which may be a source of error in comparison with empirical values.

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582

Table 1.Geometric specifications of specimens

According to handbooks of crack stress analysis,(e.g. Tada [3]), the stress intensity factor in the opening mode for edge cracks is as follows K

I

Yı

ʌa

(1)

where 2

3

§ a · § a · § a · § a · Y 1.122  0.231¨ ¸  10.55 ¨ ¸  21.71 ¨ ¸  30.382 ¨ ¸ ©W¹ ©W¹ ©W¹ ©W¹

4

(2)

The above equations are used in order to compare and verify the results obtained from shearography tests. From Table (2) it can be concluded that the experimental results are in good agreement with empirical values, thus proving the potentials of this non-destructive technique in measurement applications as well as qualitative evaluations. Table 2. Empirical and experimental SIFs for different specimens and loadings

References: 1.

Steinchen, W., Yang, L.X., Kupfer, G., Mäckel, P., and Vössing, F., J. Aerospace Eng., vol. 212, 21-30, 1998.

2.

Hung, Y.Y., J. Nondestructive Testing, vol. 8, 55-67, 1992.

3.

Tada, H., Paris, P.C., and Irwin, G.R., The stress analysis of cracks handbook, 3rd edition, ASME Press, 2000.

2T23. Novel testing and evaluation techniques

583

FINITE ELEMENT MODELING OF PULSE TRANSIENT IR THERMOGRAPHY M. Krishnapillai, R. Jones, I. H. Marshall, M. Bannister1 and N. Rajic2 Mechanical Engineering, Monash University, Clayton, VIC, Australia 1Cooperative Research Centre – Advanced Composite Structures, 506 Lorimer Street, Fishermans Bend, VIC, Australia. 2DSTO-Platforms Sciences Laboratory, 506 Lorimer Street, Fishermans Bend, VIC, Australia [email protected] Given the life extension program being currently implemented in both the military and commercial aircraft regime the increased need to operate aircraft well beyond the original design life is becoming more prevalent with each life cycle that is passed. Nondestructive testing is critical for a safe aircraft life extension program. Infrared thermography is a non-contact, non-destructive examination technique that utilizes radiated electromagnetic energy to acquire subsurface defect information[1]. The material within which these defects exist, and upon which IRT can be applied, range from concrete to metals to the focal material of this research, carbon fibre reinforced plastics (CFRP). As a nondestructive evaluation technique thermography is gaining acceptance due primarily to the recent advancements in the quality of thermal data acquisition systems as well as the interest in broad area scanning procedures coupled with the potential for a truly non contact NDE system that can handle inspections of intricately complex structures, Maldague [1]. To date there has been considerable work done concerning the use of finite difference models, both 2D, Perez [2] and 3D, Plotnikov [3], to simulate the thermographic process. But the limits of these methods are such that to create a simulated structure, differential equations are required to be derived and manipulated to suit [2]. And in the case of a non-axisymmetric problem of complex geometry this method becomes unfeasibly unrealistic in shortening the time of analysis and inspection. The use then, of IRT as a nondestructive evaluation technique is becoming increasingly attractive in the detection of sub-surface defects in composite structures due primarily to its potential ability to predict subsurface information given a suitable calibration template. To date, extensive in-field damage data acquisition studies have been performed, the results of which provide extensive qualitative results. Yet given this establishment a restriction to damage prediction applies when considering a more complex geometry upon which experimental data has not been collected or in collection would lead prediction redundant. This study reports on the use of numerical FE models as a flexible tool to create and simulate the thermographic process. It looks at the response of an FE model to predict damage parameters with the intention of determining numerical relationships and modeling methods that may be used upon more complex non-axisymmetric geometry. As a result of this study a suitably calibrated finite element simulation technique has been generated and validated (an example of a typical FE model with thermal response can be seen in Fig. 1). This validation technique has also yielded its application towards modelling upon what can be considered the epitome of a complex component, the curved structure. What makes a part complex, in the thermal sense, is the presence of curved sections to which typical thermal mathematical relationships are extraordinarily difficult to apply. By establishing the relationships between thermal surface response, defect depth and location in a curved section we are able to demonstrate the fundamental advantages that pulse transient IR thermography offers.

M. Krishnapillai et al.

584

FIGURE 1. Flat Plate Numerical FE Model and Thermal Response

References 1.

Maldague XPV, Moore PO, editors. Infrared and thermal testing: Non-destructive Testing Handbook. Vol. 3, American Society for Nondestructive Testing, 2001.

2.

Perez I, Kulowitch P and Davis W. Modeling of pulsed thermography in anisotropic media. Naval Air Warfare Center Aircraft Division Technical Report NAWCADPAX--99-38-TR, 1999.

3.

Plotnikov YA. Modeling of the multi-parameter inverse task of transient thermography. 25th Annual Review of Progress in Quantitative Non-destructive Evaluation Conference, Snowbird, Utah. 1998.

2T23. Novel testing and evaluation techniques

585

A NEW TECHNIQUE FOR THE MACHINING OF NATURAL CRACKS N. P. Andrianopoulos and A. Pikrakis Department of Mechanics, Faculty of Applied Sciences, National Technical University of Athens, GR – 157 73, Hellas Tel.: +30 210 7721222 [email protected] Experimental Fracture Mechanics is based on the study of specimens containing “machinednatural” cracks, a term which is self-contradicting. In practice, an artificial (machined) notch of considerable thickness is opened in the specimen by using various techniques and, then, a “natural” crack extension of the notch is created through fatigue. This procedure is, in details, described by ASTM standards [1], where an artificial notch is considered as acceptable when, among other restrictions, it must have a radius of curvature of the tip equal to ~0.25X10-3m and the throughfatigue crack extension has a quiet uncontrolled length of (1-2)X10-3m. Geometrically, this “natural” crack satisfies two of the requirements of a slit to be a natural crack, i.e. no loss of mass and small (but not near- zero) tip-radius. In many cases, it is not straight or forms a small angle with the notch axis. In addition, this method cannot be applied in case of notches inclined to the loading axis and special loading apparatuses are required. To facilitate and improve ASTM standard many attempts have been presented (e.g. [2, 3]). However, an important side-effect of this method has not been discussed. It is that fatigue causes changes of unpredictable severity in the mechanical properties of the material, exactly in the tip area, where the final crack is expected to initiate. In this area material fails and around the tip of the “natural” crack plasticized zones and hardening processes are observed. Consequently, fracture criteria are based on a slippery ground. In the present work a new technique of crack machining is proposed in order to avoid some of these difficulties. For that, a steel mould is constructed (Fig.1). It consists of

Fig.1. A sketch of the mould. The fixing guide is not shown. four identical plane plates and a guide to keep them firmly in the proper position. Between the two plates of each face of the mould a thin sheet (thickness

Ro 2 A0  A1 a / t  A2 a / t Ri

@

(1)

The values of the plastic limit pressure obtained by this study are compared with the empirical solutions presented in Ref. [1] and with finite element based plastic limit pressure expression developed in Ref. [2]. The proposed analytical approximation of limit pressure provides very useful tools for assessing the integrity of pressurized tubes. The effects of crack depth and length on the failure pressure are evaluated for the considered tube geometry.

References 1.

Miller, A.G., Int J Pres Ves Pip, vol. 32, 191–327, 1988.

2.

Kim, YJ., Shim, DJ., Nikbin, K., Kim, YJ., Hwang, SS. and Kim, JS., Int. J. Pres. Ves. Pip., vol. 80, 527-540, 2003.

3.

Timofeev, B.T., Karzov, G.P., Blumin, A.A. and Anikovsky, V.V., Int. J. Pres. Ves. Pip., vol. 76, 393-400, 1999.

4.

ABAQUS User's guide and theoretical manual, Version 6.5, Hibbitt, Karlsson & Serensen, Inc., 2005.

2T28. Mesofracture mechanics

627

TENSILE SIMULATION OF POLYMERIC MATERIAL CONSIDERING THE MESO-SCALE STRUCTURE Akira Shinozaki, Kikuo Kishimoto and Inoue Hirotugu Department of Mechanical and Control Engineering, Tokyo Institute of Technology 2-12-1, O-okayama, Meguro-ku, Tokyo, 152-8552, Japan [email protected], [email protected], [email protected] Several studies related to meso-scale structure and mechanical properties have been made. De Gennes[1] discussed the motions for one chain performing wormlike displacements inside a strongly corss-linked polymer gel. Theodorou and Suter[2] suggested the method for the detailed atomistic modeling of well-relaxed amorphous glassy polymers. Using molecular dynamics simulations, Stevens[3] studied the effect of interfacial bond density and network size on interfacial fracture. Hiroo[4] studied the coarse-graining is applied to flexible polymer chains. Yashiro[5] discussed the mechanical properties from atomistic scale. Marc [6] studied the orientation and crystallization of polyethylene during uniaxial extension. These works have been clarified some aspects of mechanical properties. In fact, the mechanical properties of polymers are strongly influenced by meso-scale (10-9~103 m) structure, such as entanglement, molecular weight distribution, orientation, etc. It is important to understand the relationship between mechanical properties of macro-scale and meso-scale structure. But the study of relationship between mechanical properties and meso-scale structure is few. This study therefore aims to clear this relationship by the simulation considered the mesoscale structure by chain network model. Large strain deformation of this model is evolved via molecular dynamics analysis. Actually, molecular chains of Polymeric materials have many kinds of length, andentangled each other. The complex meso-scale structures are composed by molecular chain as described in Fig. 1. In this study, the structures are viewed molecular chain network model (Fig. 2). The molecular chain which is the most basically element of the network model, is represented by simple model such as the mass-spring model (Fig. 3). N successive atoms are combined into a single mass-spring segment.

FIGURE 1. Entangled Polymer chains.

FIGURE 2. Network model.

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FIGURE 3. Segment.

FIGURE 4. After concentrated model.

FIGURE 5. Deformation process of model A

FIGURE 6. Stress-Stretch ratio curve

In this work, two kinds of network model are generated. One is composed by linear chains (model A (Fig.2)) and another model has branches (model B). The network model is not equilibrium. Therefore the network model is concentrated (Fig.4). Then, the concentrated network model is simulated (Fig. 5). The simulation is assumed tensile test. Stress-Stretch ratio curve (Fig. 6) is obtained. From the simulation, it is clear that the branch strongly affects the young’s modulus and yield stress.

References 1.

P.G. de Gennes: J. Chem. Phys, Vol. 55, 572, 1971

2.

D.N. Theodorou, U.W,suter: Macromolecules, Vol. 18, P 1467, 1985

3.

M.J.Stevens: Macromolecules, Vol 34, P2710, 2001

4.

F.Hiroo, T. Jun-ichi, D. Masao: J. Chem. Phys, Vol. 116, P 8183, 2002

5.

Y.Kisaragi, I.Tomohiro, T. Yoshida: Internatinal Journal of Mechanical Sciences, Vol. 45, P 1863, 2003

6.

Marc S.Lavine, Numan Waheed, Gregory C. Rutledge: Polymer, Vol. 44, P1771, 2003

2T28. Mesofracture mechanics

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MICROFRACTURE AND STRAIN LOCALIZATION: A COMPUTATIONAL HOMOGENIZATION APPROACH C. Dascalu, G. Bilbie and R. Chambon Laboratoire Sols-Solides-Structures, CNRS – INPG – UJF BP 53, 38 041 Grenoble Cedex 9 [email protected], [email protected], [email protected] The aim of this work is to study the appearance instable behaviours (like strain localisation bands) in elastic solids, as a consequence of micro-fracture. A two-scale approach of computational homogenization (e.g. Kouznetsova et al. [2], Miehe [3]) is considered. The macroscopic behaviour is obtained by localization/homogenization exchanges with representative elementary volumes. Periodic boundary conditions are assumed for each elementary cell. In order to properly understand the relation between micro-fracture and strain localization, in this work we restrict our analysis to non-dissipative behaviours. On the level of the microstructure, we consider a large strain hyper-elastic material containing traction-free microcracks with unilateral contact. The appearance of instabilities is indicated by the loss of ellipticity of the equilibrium equations. To clearly identify the microcracks influence on the macroscopic stability, we assume stable microscopic constitutive laws. In this case, the macroscopic instabilities are completely due to the presence of the microcracks in the elementary cells.

FIGURE 1. Computational localization/homogenization scheme. A deformation gradient F is imposed on the boundary of a cell and the resulting mean Piola-Kirchhoff stress P is returned. The homogenization procedure is represented in Figure 1. If M ( X ) is the deformation map of an elementary volume, F  X its gradient and P  X the first Piola-Kirchhoff stress, the boundary conditions on the boundary are: M

where t



X  M  X

P ˜N

F ˜ X



 X  ; t ( X  )

 t(X  )

with N the external normal. We denote by F  X and

(1) P

 X the

corresponding mean values. This procedure provides an implicit (numerical) law P P  F . The computations are done with finite elements, for different hyperelastic laws. A finite-difference formula together with the obtained implicit law allow for the computation of the coarse-scale

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acoustic tensor Q (e.g. Rice [4]). The appearance of macroscopic instabilities is indicated by the loss of ellipticity : d e t Q

0

(2)

For a hyperelastic law of the type of that considered by Abeyaratne and Triantafyllidis [1], we represented in Fig. 2 the stability/instability regions in the plane elementary cell with two microcracks.

1  F1 1 ,1  F 2 2

for the

FIGURE 2. a) Stability/instability regions b) REV with two cracks We show that, even for a stable and non-dissipative microscopic behaviour, the presence of microcracks can give rise to an unstable macroscopic behaviour, typical for bands of localization of the deformation. We present macroscopic localization behaviours obtained with two-scale finite element computations.

References 1.

Abeyaratne, R., and Triantafyllidis, N., J. Appl. Mech., vol. 51, 481-486, 1984.

2.

Kouznetsova, V., Geers, M. G., and Brekelmans, W. A. M., Int. J. Numer. Meth. Engng., vol.54, 1235-1260, 2002

3.

Miehe, C., Comput. Methods Appl. Mech. Engrg., vol. 192, 559-591, 2003.

4.

Rice, J.R., Theoretical and Applied Mechanics, edited by W.T. Koiter, North-HollandPubl, Amsterdam, 1976, 207-220

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STRAIN AND FRACTURE AT MESOSCALE OF COATED MATERIALS S. Panin Institute of Strength Physics and Materials Science SB RAS 2/1 Academicheskii pr., 634021, Tomsk, Russia [email protected] Recently surface-strain mapping technique have found a wide application in experimental mechanics due to intensive development of image acquisition equipment (high–resolution TV- and photo–cameras) as well as possibility of fast and precise processing of experimental data with the use of personal computers. Most interesting and essential results on developing both experimental techniques and interpretation of results in terms of mechanics were achived in S.Corolina University in prof. M. Sutton’s group [1]. In so doing most attention was paid to fatigue fracture of heterogenious materils. Interesting results on mathematical processing of experimental data obtained by surface–strain mapping were gained in Great Britain in Prof. P.Whithers’ group [2]. In researches of Prof. V.Panin to carry out within the framework of physical mesomechanics, were shown that surface layers of a loaded solid are an individual structural level of strain origin and development. Prof. V.E. Panin [3,4] has shown that special state of surface layers causes fast shear stability loss under loading and gives rise to initial acts of plastic deformation there. In so doing the propagation of defect flows of a non-dislocation nature in surface layers plays the determining role. The development of the given processes is much pronounced in materials where dislocation plasticity is restrained by elements of internal structure. If surface layers are subjected to various treatment procedures or a protective (strengthening) coating is deposited onto material surface, the pattern of strain origin and development is substantially changed. The restriction of dislocation plasticity results in increase of local stress concentration level, while the character of strain development is governed by pattern of their occurrence and relaxation. The target of experimental study of coated materials being loaded under different schemes was associating shape and numerical parameters of loading diagram and characteristic patterns of strain development (localization). The estimation of strain localization can be obtained by calculating strain components (main plastic shear, strain rate intensity, shear and rotation component of distortion tensor) by numerical differentiation of data obtained by television–optical observation of surface of a loaded heterogeneous material. Another important reason for carrying out the investigations is optimizing modes for coating deposition as well as structural and geometrical factors. Frequently cracking of coatings occurs under loading which does not give rise to catastrophic failures of surface–hardened parts of machine. It is of importance to find out cracking pattern that diminishes the risk of strain localization while the estimation of the latter can be performed by processing optical images gained at the “coating–substrate” interface. It is shown that most optimal from the point of view of behaviour under mechanical loading is formation of coatings with nonflat “coating-substrate” interface and presence of a gradient transient layer. The latter hinders crack propagation into lower substrate layers and increasing composition strength by the additivity law. Experimental prove has given to the fact that fine cracking of the coating allow to avoid substantial strain localizations that can keep exploitation properties of surface–hardened parts of machine that does not completed with catastrophic consequences (fast failure).

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It is clearly demonstrtated that in materials with high-strength low-ductile coatings the interface is the site of fatigue crack origin. The decrease in distinction of elastic moduli of a coating and substrate results in nucleation of the crack on surface of the coating.

References 1.

Sutton, M.A., Helm, J.D., Boone, M.L., International journal of fracture, No. 109, 285, 2001.

2.

Clocksin, W.F., Chivers, K.F., Torr, P.H.S. et. al., In Proceedings International Conference on New Challenges in Mesomechanics, edited by Pyrz and Sih. Aalborg University Press, Vol. 2, 2002, pp. 467.

3.

Panin, V.E., Theor. and Appl. Frac. Mech., Vol. 37, 261, 2001.

4.

Panin, V., Physical Mesomechanics, Vol. 4, No. 3, pp. 5, 2001.

2T32. Micromechanisms in fracture and fatigue

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RELATING CLEAVAGE CRACK NUCLEATION TO CRACKED CARBIDES IN A533B STEEL A. Kumar and S. G. Roberts University of Oxford Department of Materials, Parks Road, Oxford OX1 3PH, U.K. [email protected], [email protected] At low temperatures, ferritic steels exhibit a change in fracture behaviour, from ductile fracture with high fracture energies accompanied by a high degree of plasticity, to brittle cleavage fracture whereby fracture occurs at transonic speeds at low fracture energies accompanied by very low degree of plasticity [1, 2]. This change from ductile to brittle cleavage fracture behaviour occurs over a range of temperatures, over which the behaviour is characterised by a competition of ductile microvoid coalescence and brittle cleavage fracture. The ductile to brittle transition temperature is dependant on strain rate, stress triaxiality due to notch acuity, microstructural and compositional factors [1, 2, 3]. The pervasiveness of ferritic steels in structural engineering and the nuclear power industry, means that a thorough understanding of the micromechanism of cleavage fracture is fundamental for the development of accurate models for predicting fracture stresses and lifetimes of components. The ductile to brittle transition behaviour of ferritic steels has been investigated by many researchers for over half a century. Stroh [2], Cottrell [3] and Lindley et al. [4] have developed theories describing the micromechanism of cleavage, in other words, the crack nucleation and propagation that precedes brittle cleavage fracture in these steels. Nowadays it is believed that cleavage in ferritic steels most probably starts in brittle second phase particles like carbides, fractured in the stress field of dislocations piled up at the particle ferrite interface. While there is some experimental evidence confirming fracture of grain boundary cementite during cleavage of ferritic steels, the evidence in the literature for fractured spheroidal brittle phase carbides dispersed throughout the ferrite matrix, is rather limited, ambiguous and sometimes contradictory [4, 5]. Moreover, studies on notched ferritic steel specimens by Stroh [2] and Zener [6] have shown that crack nucleation involving the attainment of a critical value of local plastic strain independent of the macroscopic applied tensile load, is the most difficult step in the cleavage fracture process. Yet studies by Hendrickson et al. [7] and Knott [8] have shown the influence of applied tensile stress in fracture, which suggests that cleavage fracture is propagation controlled whereby the catastrophic propagation of a microcrack is dependant on a normal applied tensile stress. Hence as Bošansky and Šmida [5] as well as Wang and Chen [9] point out that the origin of nuclei of cleavage cracks, the mechanism controlling cleavage fracture and the fracture criterion are still subjects of discussion. The purpose of this study was to investigate if, and under what loading conditions, spheroidal brittle carbides crack and act as the sites for cleavage crack nucleation. Also this study attempts to identify the controlling event during cleavage fracture and over the brittle to ductile transition temperatures. To investigate the role of spheroidal carbide particles in cleavage crack nucleation, uniaxial tensile tests have been carried out at temperatures from the “lower shelf” up to the transition to ductile behaviour on notched samples of spheroidised A533B steel, a commonly used reactor pressure vessel grade ferritic steel. Different spheroidisation heat treatments have been selected in order to obtain a microstructures with a variety of carbide particle distributions, ferritic grain sizes and Vickers hardness values. Fracture surfaces and cross-sections of completely fractured as well

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as part-fractured specimens have been examined by a Scanning Electron Microscope (SEM) and Energy Dispersive X-ray analysis (EDX) to identify cleavage nucleation sites and understand carbide fracture and its propagation into the ferrite. The results of the tests are reported and their implications for cleavage microcrack nucleation and controlling steps of cleavage fracture process in steels containing spheroidised brittle particles are discussed.

References 1.

Orowan, E., Rep. Prog. Phys., vol. 12, 185-232, 1948

2.

Stroh, A.N., Adv. Phys., vol. 6, 418-465, 1957

3.

Cottrell, A.H., Trans. Am. Inst. Min. Metall. Petrol. Engrs., vol. 212, 192-203, 1958

4.

Lindley, T.C., Oates, G. and Richards, C.E., Acta Metall., vol. 18, 1127-1136, 1970

5.

Bošanský, J. and Šmida, T., Mat. Sci. Eng., A vol. 323, 198-205, 2002

6.

Zener, C., The micromechanism of fracture, In Fracturing of Metals, American Society for Metals, Cleveland, Ohio, 1948

7.

Hendrickson, J.A., Wood, D.S. and Clarke, D.S., T. Am. Soc. Metal, vol. 50, 656-676, 1958

8.

Knott, J.F., J. Iron Steel Inst., vol. 204, 104-111, 1966

9.

Wang, G.Z. and Chen, J.H., Int. J. Fracture, vol. 89, 269-284, 1998

2T32. Micromechanisms in fracture and fatigue

635

MICRO-ENERGY RATES FOR DAMAGE TOLERANCE AND DURABILITY OF COMPOSITE STRUCTURES C. C. Chamis and L. Minnetyan NASA Glenn Research Center, Clarkson University Cleveland, OH 44135, Potsdam, NY 13699 [email protected], [email protected] For effective structural health monitoring for durability, it is important to quantify damage tolerance of a candidate structure. Since continuous fiber composites are able to arrest cracks and prevent self-similar crack propagation, composite structures have received a great deal of consideration for design with emphasis on damage tolerance. However, a number of design parameters such as fiber orientation patterns, choices of constituent material combinations, ply drops and hybridization, result in complex design options for composite structures. Thus, it is necessary to evaluate damage initiation in a composite structure and its fracture propagation characteristics for achieving a rational damage tolerant design. Compared with homogeneous materials, damage initiation and progression characteristics of fiber composites are much more complicated. Composite structures often contain some preexisting or induced flaws in matrix and fibers after fabrication of composites. At lower stresses, matrix is likely to be cracked because of flaw-induced stress concentrations and cause the matrix flaws to propagate across the composite. With the use of established material modeling and finite element modes, and considering the influence of local defects, through-the-thickness cracks and residual stresses, computational simulations have made it possible to evaluate the details of progressive damage and fracture in composite structures. In a computational simulation, damage evolution quantifier such as the damage volume, exhausted damage energy, and the Damage Energy Release rate (DERR) are used to quantify the structural damage tolerance at different stages of degradation. Low DERR levels usually indicate that degradation takes place with minor resistance by the structure. Structural resistance to damage propagation is often dependent on structural geometry and boundary conditions as well as the applied loading and the state of stress. In certain cases, such as the room temperature behavior of composites designed for high temperature applications, internal damage initiated as microcracks in the matrix become enlarged to be externally visible. Thus, matrix cracking and its effect on damage propagation/damage tolerance need be evaluated. Some simulations have been successful in predicting damage tolerance and failure load of composite structure by considering ply stresses and the corresponding stress limits for matrix crack growth. Damage initiation, growth, accumulation, and propagation to fracture are studied. Since the complete evaluation of ply and subply level damage/fracture processes is the fundamental premise of computational simulation, a microstress level damage index is added for the identification and tracking of subply level damage processes. Computed damage regions are similarly correlated with ultrasonically scanned damage regions. Simulation is validated by comparison with test data from Acoustic Ultrasonic (AU) testing. Results show that computational simulation can be used with suitable Non-Destructive Evaluation (NDE) methods for credible in-service monitoring of composites. A complete set of micromechanics equations used is published elsewhere for evaluating microstresses. Computational simulation is implemented via integrating three modules: (1) composite mechanics, (2) finite element analysis, and (3) damage progression tracking. The composite mechanics module is designed to analyze fiber composite structures with an updated composite mechanics theory. Its main function is to calculate ply and composite properties of laminates from

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the fiber and matrix constituent characteristics and the composite lay-up. Additionally, it determines the composite structural response and ply stresses from the FEM analysis results. In simulation, the composite mechanics module is called before and after each finite element analysis. The finite element analysis module is able to process linear and nonlinear static and dynamic analysis. Four-node anisotropic thick shell elements are usually used to model laminated composites. The finite element analysis module accepts laminate properties from the composite mechanics module and performs the structural analysis at each load increment. After structural analysis, the computed generalized node stress resultants and deformations are provided to the composite mechanics module. The composite mechanics module computes the developed ply stresses for each ply and checks for ply failure modes at each node. Failure criteria applied to detect ply failures are based on the maximum stress and modified distortion energy (MDE) criteria for combined stress effects. The overall evaluation of composite structural durability is carried out in the damage progression module that keeps track of composite degradation for the entire structure. The damage progression module relies on the composite mechanics module for composite micromechanics, macromechanics and laminate analysis, and calls the finite element analysis module for global structural analysis. If excessive damage is detected, the incremental loads are reduced and the analysis is restarted from the previous equilibrium stage. Otherwise, if the increment of loads is acceptable, another finite element analysis is performed but the constitutive properties and the finite element mesh are updated to account for the damage and deformations from the last simulation. Simulation is stopped when global structural fracture is predicted. If the ply is subject to combined stresses, its microstresses are obtained by simply superimposing results of all corresponding stress components. Ply transverse fractures usually begin in the matrix between fibers due to the elevated stress levels from stress concentration. Microstress level damage tracking is able to quantify the type of damage in the matrix by comparison of microstresses with constituent stress limits. A microstress damage index is defined as a binary number with 14 bits in the damage progression module. In this paper, the adhesive bond strength of lap-jointed graphite/aluminum composites is examined by computational simulation. Computed microstress level energy release rates are used to identify the damage mechanisms associated with the corresponding acoustic emission (AE) signals. Computed damage regions are similarly correlated with ultrasonically scanned damage regions. Results show that computational simulation can be used with suitable NDE methods for credible in-service monitoring of composites.

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MICROMECHANICAL OBSERVATION OF FRACTURE PROCESS IN MORTARS E. Schlangen and O. Copuroglu Delft University of Technology, CiTG, Microlab, P.O. Box 5048, 2600 GA Delft, The Netherlands [email protected] Cement-based materials like concrete and mortars are quasi-brittle materials. These materials show a softening behaviour when tested in uni-axial tension. An example of such a behaviour is shown in Fig. 1, which is a result obtained from a tensile test on mortar in the special micro-tensile testing machine explained in this paper. The shape of the curve and the area under the curve which is a measure for the fracture energy, is strongly related to the heterogeneity of the material, see for instance Schlangen and van Mier [1]. At the weak spots in the material (generally the interface at grain boundaries) first micro-cracks develop in the material when a load is applied. Subsequent loading will result in a localized crack that will propagate through the material. This mechanism is believed to take place in all cement based materials, but is hard to observe. Stable fracture in a tensile test can only be realised with a closed loop hydraulic testing machine. Observations of micro-cracking and localization of these cracks is a difficult task. However to be able to improve materials a complete understanding of the fracture process is necessary. Furthermore durability is a hot issue in cement based materials. Ingress of water and ions result in internal reactions of concrete and embedded steel reinforcement which can result in fast degradation of concrete structures [2]. Understanding the fracture process, the way micro-cracks and localized cracks propagate through the material, is thus important in order to control transport through the material and design the material in such a way that a long service life of structures is guaranteed.

FIGURE 1. Typical observed load-deformation curve of mortar. The present study deals with a new developed technique to be able to observe the fracture process (what happens at the crack tip) during a stable tensile test. A micro-tensile testing machine as shown in Fig. 2 is used to test various mortar materials. The mortars are chosen in such a way that components in the mortar have different local properties. This will then result in different fracture mechanisms and also a different load-deformations response. The tensile tests are performed on small specimens (15x15 mm cross section) with one notch. The crack mouth opening displacement measured on the specimen is used as feed back signal to control the test. The micro-tensile testing machine is constructed in such a way that it fits insight an ESEM. With the

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ESEM online images of the development of micro-cracks and propagation of the crack tip are obtained.

FIGURE 2. Micro tensile testing machine(left) and SEN-mortar specimen (right). The results of the various tests will be presented in the paper. A relation will be made between the local properties in the material and the fracture mechanism that takes place. The results of this investigation will provide very useful information to verify numerical models that simulate fracture processes on the micro-scale of cement-based materials, see for instance Schlangen and Copuroglu [3].

References 1.

Schlangen, E. and van Mier, J.G.M., Cem. Conc. Composites, 14: 105-118, 1992.

2.

Francois, R. and Arliguie, G., Magazine of Concrete Research, 51, 2, pp. 143-150, 1999.

3.

Schlangen, E. and Copuroglu, O., In Proceedings of the 5th International Conference on Computation of Shell and Spatial Structures, June 1-4, 2005, Salzburg, Austria

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639

MICRO-FRACTURE MAPS IN PROGRESSIVELY DRAWN PEARLITIC STEELS J. Toribio and F. J. Ayaso Department of Materials Engineering, University of Salamanca E.P.S., Campus Viriato, Avda. Requejo 33, 49022 Zamora, Spain Tel: (34-980) 54 50 00; Fax: (34-980) 54 50 02 [email protected] One of the major concerns in civil engineering construction and maintenance of prestressed concrete structures is the fracture performance of the high-strength prestressing steel wires which are the fundamental components in the afore-said composite material (prestressed concrete), since these wires suffer the highest levels of stress and may be damaged by the combined action of both mechanical and environmental agents. High-strength prestressing steels are manufactured from a previously hot rolled bar with pearlitic microstructure which is heavily cold drawn in several passes to obtain the commercial prestressing steel wire with increased yield strength obtained by a strain-hardening mechanism. Thus the final commercial product has undergone strong plastic deformations able to modify its microstructure. Thus, although cold drawing improves the (traditional) mechanical properties of the steel (i.e., those properties useful for regular service), the microstructural changes during manufacture [1-3] may affect the fracture performance of the material, specially in the presence of stress raisers like cracks or notches. In this paper the fracture performance of axisymmetric notched samples taken from prestressing steels with different levels of cold drawing is studied. To this end, a real manufacture chain was stopped in the course of the process, and samples of all intermediate stages were extracted. Thus the drawing intensity or straining level (represented by the yield strength) is treated as the fundamental variable to elucidate the consequences of the manufacturing route on the posterior fracture performance of the material. In addition, since samples with very different notch geometry are considered, the effect of stress triaxiality on fracture performance is also analysed. Fractographic analysis of the samples by means of scanning electron microscope (SEM) showed the microscopic topographies after failure and allowed the assembly of micro-fracture maps (MFM) covering the whole fracture surface and containing relevant information on the micromechanisms of fracture in the material, as shown in Fig. 1 for one of the notched geometries (that with the maximum stress triaxiality). In the matter of the influence of the stress triaxiality (constraint) on fracture processes in the vicinity of notches, the behaviour is more ductile in the case of blunt notches than in the case of sharp notches. With regard to the influence of the cold drawing degree, the fracture behaviour becomes more ductile as the strain hardening level of the steel increases, so that cleavage is predominant in the fracture area of slightly drawn steels, whereas the presence of micro-void coalescence (MVC) increases with the degree of cold drawing and becomes predominant in the case of the most heavily drawn steels in which cleavage can hardly be detected as an extended region.

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FIGURE 1. Micro-fracture maps (MFM) in notched specimens

References 1.

Dewey, M.A.P. and Briers, G.W., J. Iron and Steel Inst., vol. 2, 102-103, 1966.

2.

Embury, J.D. and Fisher, R.M., Acta Metall., vol. 14, 147-159, 1966.

3.

Langford, G., Metall. Trans., vol. 1, 465-477, 1970.

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A BRIEF HISTORY OF FRACTOGRAPHY S. P. Lynch and S. Moutsos Dept. of Materials Engineering, Monash University Clayton, Vic. 3168, Australia [email protected] Fracture surfaces have, no doubt, been studied throughout the history of mankind, probably starting with observations on stone-age tools. In the 16-18th centuries, the macroscopic appearance of fracture surfaces was used to assess the quality of metallic materials, with studies by Réaumur in 1722 [1] being the most notable (Fig. 1(a)). However, it was not until 1943 that fracture surfaces were first examined at high-magnifications (using optical microscopy up to 1,000x) (Fig. 1(b)) (Zapffe and Moore [2]), and that the first attempts were made to examine replicas of fracture surfaces using transmission-electron microscopy (TEM) (Barrett and Derge [2]). Early replicas had poor fidelity and resolution, and it was not until 1956 that Crussard et al. [3] pioneered high-resolution TEM fractography using shadowed, direct-carbon replicas (Fig. 2). This technique (and its subsequent variations) revolutionised fractography and led to a plethora of studies in the 1960’s and 70’s. It therefore seems appropriate to commemorate the 50th anniversary of high-resolution electron fractography with a review of how it, and subsequent scanning electron microscopy (SEM) and other techniques, have led to a better understanding of fracture processes. Such understanding has been invaluable in failure analysis and in developing improved materials. Milestone observations for a number of important modes of fracture in inert environments including cleavage, brittle intergranular fracture, dimpled overload fractures, and fatigue fractures, are described first, followed by examples of key observations for fractures produced in embrittling environments (Fig. 3). Fractographic features and aspects of fracture modes that are not well understood are also discussed.

FIGURE 1. (a) Sketches by Réaumur [1] showing a cleavage fracture, described as “little mirrors of irregular shape and arrangement” - one of seven classes of iron identified by him according to their fracture surface-appearance in 1722, and (b) Optical micrograph of cleavage fracture of iron showing river lines and twins (Zapffe and Moore, 1943 [2]).

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FIGURE 2. Two of the first high-resolution transmission electron micrographs of fracture surfaces of steels showing (a) fine river lines on a cleavage fracture, and (b) a dimpled overload fracture surface (Crussard et al., 1956 [3]). Such observations led to improved understanding of ductile and brittle behaviour, and clearly showed that dimples resulted from nucleation, growth, and coalescence of nano/micro-voids.

FIGURE 3. SEM of fracture surfaces produced by cracking of a high-strength martensitic steel in (a) liquid mercury, and (b) air, showing that crack growth can occur by a more localised microvoid-coalescence process in embrittling environments than in air. Such observations (in both hydrogen and liquid-metal environments) led to the development of localised-plasticity theories for environmentally assisted cracking (e.g. Beachem, 1972 [4], Lynch, 1988 [5]) involving, for example, adsorption-induced dislocation-emission (AIDE).

References 1.

de Réaumur, R. A. F., see Smith C.S., A History of Metallography, MIT Press, 1988.

2.

Zapffe, C. A. and Moore, G.A., Trans AIMME, vol. 154, 335-359, 1943, and discussion therein by C.S. Barrett and G. Derge, 353-355.

3.

Crussard, C., Borione R., Plateau J., Morillon Y. and Maratray F., J. Iron and Steel Inst., vol. 183, 146-177, 1956.

4.

Beachem, C. D., Metall. Trans., vol. 3, 437-451, 1972.

5.

Lynch, S.P., Acta Metall., Overview no. 74, vol. 36, 2639-2661, 1988.

C. SPECIAL SYMPOSIA/SESSIONS

C1. Nanomaterials and Nanostructures

1. Fracture and Fatigue at the Micro and Nano scales

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SIZE EFFECTS IN LEAD FREE SOLDER-JOINTS A. Betzwar-Kotas, G. Khatibi, A. Ziering, P. Zimprich, V. Groeger, B. Weiss and H. Ipser1 Institute of Materials Physics, University of Vienna Strudlhofgasse 4, A-1090 Vienna, Austria 1Institute of Inorganic Chemistry, University of Vienna Waehringerstrasse 42, A-1090 Vienna, Austria [email protected] Due to the environmental and health concerns the usage of lead based solders in electrical and electronic equipment is restricted. Recent regulations require the replacement of these solders by non toxic lead free solders, thus numerous scientific and technical investigations has been performed on the properties of the solder joints produced using these new materials [1]. Investigations on the effect of specimen size on properties of the bulk solders materials have shown that the bulk data can be used only if the solder joint size is larger than a representative volume [2]. Thus available bulk material data are not reliable if one considers the extremely small volumes ( 1 Pm (open marks). With the increase in Hp, the orientation change tends to increase regardless of the grain size. It is clear that T is larger in nanoscopic grains than in larger grains especially at higher Hp. The result of all the measured grains is shown in Fig. 5 for T between Hp = 0 and 16 % in relation to d. The orientation change is obviously larger for smaller grains. Below the range of d < 1 Pm, the orientation change tends to decrease linearly with d. Large T in small d region is considered to result either from the increase in misorientation within the grains, observed as plastic deformation by slip, or from grain rotation by grain boundary sliding without increase in the transgranular misorientation. Figure 6 shows the change of GOS between Hp = 0 and 16 % in relation with d for all the measured grains. 'GOS slightly increases with d, indicating that plastic deformation by slip is more likely to be introduced in coarser grains. Judging from the results in Fig. 5 and 6, it is concluded that grain rotation occurs among nanoscopic grains in ECAPprocessed Cu. The rotation angle of nanoscopic grains is measured to be about 4 degrees under Hp = 16 %. EBSD observation was found to be useful for the quantitative analysis of deformation mechanism in ECAP-processed materials with nanoscopic and submicron grains. By the combination of EBSD and atomic force microscopy, grain boundary sliding mechanism among nanoscopic grains will be clarified. The fatigue damage accumulation process and crack propagation behavior will also be precisely investigated taking into consideration the effect of microstructure such as crystallographic orientation, grain boundary and subsequent local strain distribution.

FIGURE 4. Orientation change T vs H. FIGURE 5. T vs d. FIGURE 6. 'GOS vs d.

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THE EFFECT OF EXTENSIONAL STRAINS ON MOLECULAR ORIENTATION, POLYMER FREE VOLUME DISTRIBUTION AND CRYSTALLIZATION Hai Dong1,2, Ruilan Guo1 and Karl I. Jacob1,3 1School of Polymer, Textile and Fiber Engineering 2 School of Material Science and Engineering 3G.W.W School of Mechanical Engineering Georgia Institute of Technology Atlanta, GA 30332-0295 [email protected], [email protected], [email protected] Mechanical properties and morphological attributes of polymeric fibers and films are highly depended on amount of draw induced in them [1]. Morphological characteristics, such as free volume distribution, crystallite size and orientation are nanoscale attributes that determine the mechanical and physical properties of the resulting polymeric material. In particular, stretching enhances the crystallization rate by orders of magnitude. Thus, understanding the changes in nanoscale morphological parameters when a polymer sample is subjected to axial extensional strains is of significant importance in predicting mechanical properties as well as to design polymeric materials for specific applications. Two nanoscale aspects will be explored: free volume evolution and nucleation and growth of crystallites. Free volume concept has long been used to understand mechanical and rheological properties as well as to explain and interpret many aspects related to polymers such as the glass transition, chain dynamics, physical aging and transport behavior [2-4]. The amount of free volume will affect many commercial polymer shaping operations, such as fiber spinning and injection molding [5]. Although the total free volume offers a quantitative basis for relating some properties of polymers [5,6], the distribution of free volume may also play a significant role in governing the underlying physics, such as in diffusion. Consequently, there have recently been some efforts in characterizing the free volume distribution by experimental techniques, utilizing, for example, positron annihilation lifetime (PAL) spectroscopy [7]. These experimental techniques are sometimes laborious and involve some ambiguities in interpreting the results quantitatively in terms of free volume distribution. In this work, the nature of free volume evolution and its distribution in a linear model polymer resembling polyethylene under extensional strain, using a combination of Molecular Dynamics (MD) and Voronoi tessellation has been investigated. It was observed that free volume is highly dependent on the probe size. When molecular orientation due to stretch increases, the total number of voids in the sample decreases along with the number average void size, while the number of larger unoccupied regions in the polymer increases which become more elongated due to stretch. The Voronoi tessellation shows that although the overall free volume is decreasing during stretching, the reduction is not evenly distributed within the region. Free volume associated with atoms located away from the ends of molecular chains is decreasing while the free volume associated with atoms located at the molecular ends increases with stretch. Results from this computational work are in good agreement with several experimental observations reported in the literature. Nucleation and crystal growth in polymers are significantly enhanced by extensional strains, resulting in better mechanical properties. Nucleation of a single molecular chain was compared with stress induced crystallization of polymer in the bulk, showing differing kinetics of nucleation and crystal growth as well as nanoscale structural differences in the resulting morphology. The

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evolution of crystallinity as well as the resulting crystalline orientation were quantified with MD simulations for various extensional strain levels. Thus, patterns of relationship between stain, molecular orientation, degree of crystallinity and amount of free volume were developed. Although MD simulations were carried out at very high strain rates, the results show good qualitative agreement with experimental results. Amount of free volume in polymers is very small, of the order of 1%, using the experimental probe size in PAL. During the nucleation and growth phase, crystalline regions are also very small. However, such nanoscale morphological structures have shown to have significant influence on the behavior of polymers. The effect of axial extensional strains on the evolution of these nanoscale structures and the mechanism for enhancement of polymer mechanical properties will be the focus of this talk.

References 1.

Dong, H., Jacob, K.I., Macromolecules, vol. 36, pp. 8881-8885, 2003.

2.

Wang, B., Wang Z. F., Zhang M., Liu W. H., Wang S. J., Macromolecules, vol. 35, 39933996, 2002.

3.

Haraya, K., Hwang S. T., J. Membr. Sci., vol. 71, 13-27, 1992.

4.

Kobayashi, Y., Haraya, K., Hattori, S., Sasuga, T., Polymer, vol. 35, 925-928, 1994.

5.

Engelsing, K., Mennig, G., Mechanics of Time-Dependent Materials, vol. 5, 27, 2001.

6.

Doolittle, A. K., J. Appl. Phys., vol. 22, 1471, 1951.

7.

Doolittle, A. K., The Technology of Solvent and Plasticizers, Wiley, New York, 1954.

8.

Kobayashi Y., Zheng W., Mwyer E. F., McGervey J. D., Jamieson A. M., Simha R. Macromolecules, vol. 22, 2302-2306, 1989.

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MICROROTATION-AUGMENTED ENERGY-MINIMIZATION FOR 3D NANOCRYSTALLINE CU STRUCTURES M. A. Tschopp and D. L. McDowell School of Materials Science and Engineering Georgia Institute of Technology Atlanta, GA 30332-0245 [email protected] Molecular dynamics simulations are frequently used to study deformation mechanisms at the nanoscale. However, the lattice orientations of grains in the starting nanocrystalline (nc) configurations are typically based on either random orientations (Van Swygenhoven and Derlet [1]; Schiøtz et al. [2]) or orientations specifically chosen to be high angle grain boundaries (Yamakov et al. [3]), which may not be either global or local minimum energy configurations. Our hypothesis is that global or local minimum energy configurations are more representative of actual nc grain structures. Consequently, the objective of this research is to use atomistic simulations to study the grain boundary character and deformation response for more energetically realistic initial configurations in 3D nc-Cu with an algorithm that augments traditional methods for forming polycrystals during the energy minimization process with microrotational perturbances of the lattices. In our simulations, we examine the effect of lattice microrotations on the generation of 3D Voronoi-constructed nc grain and grain boundary structures with an embedded-atom method potential for Cu (Mishin et al. [4]). The microrotation algorithm couples a modified Monte Carlo method with molecular statics to show that an initial grain structure with high angle grain boundaries will evolve towards a lower energy grain structure via the introduction of small rotations of grains prior to energy minimization for each Monte Carlo step. In this way, symmetric and asymmetric coincident site lattice (CSL) boundaries naturally become more prominent within the nc sample due to their lower energy; this is particularly relevant to nc grain ensembles where the surface energy is dominant. Fig. 1 shows a schematic of the microrotation algorithm used to generate the starting nc grain structure for deformation simulations. In this schematic, the initial configuration is generated with random grain lattice orientations. The microrotation algorithm randomly selects a grain and rotates the lattice orientation to create a trial configuration. Through an iterative process, the minimum energy grain boundary structure for this rotation is found using a nonlinear conjugate gradient energy minimization algorithm. Last, an energy criteria decides whether to accept or reject the trial microrotation based on a comparison of the potential energy of the trial configuration to that of the previous configuration. This procedure repeats until the configuration converges to either a global or local energy minimum. The simulation results compare an initial configuration generated using random grain lattice orientations with a configuration that was evolved using the microrotation algorithm to show how the microrotation algorithm affects two specific parts: (i) the nanocrystal grain boundary character statistics and (ii) the inelastic deformation response of Cu. The first part examines the effect of the microrotation algorithm on CSL grain boundary statistics in nc grain structures and compares the CSL statistics computed with the microrotation algorithm to experimentally determined CSL grain boundary statistics. The second part compares the effect of the microrotation algorithm on the atomistic deformation characteristics of nc grain structures; we incorporate different mean grain sizes to compare the effect of the microrotation algorithm in

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nanoscale regimes dominated by either: (i) grain boundary-mediated deformation processes or (ii) dislocation nucleation and emission processes.

FIGURE 1. Flow chart for the microrotation algorithm. The significance of these results is that generating and deforming a more energetically realistic nc configuration provides a more accurate understanding of grain boundary character and deformation mechanisms with decrease of grain size into the nc regime. In addition, the microrotation algorithm addresses CSL content in nc materials for atomistics in a more realistic fashion.

References 1.

Van Swygenhoven, H., Derlet, P.M. and Hasnaoui, A., Physical Review B, vol. 66, 024101-14, 2001.

2.

Schiøtz, J., Vegge, F., Di Tolla, F.D., Jacobsen, K.W., Physical Review B, vol. 60, 1197111983, 1999.

3.

Yamakov, V., Wolf, D., Phillpot, S.R. and Gleiter, H., Acta Materialia, vol. 49, 2713-2722, 2001.

4.

Mishin, Y., Mehl, M.J., Papaconstantopoulos, D.A., Voter, A.F. and Kress, J.D., Physical Review B, vol. 63, 224106-1-16, 2001.

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MECHANICS AND ELECTROMECHANICS OF SINGLE CRYSTALLINE PIEZOELECTRIC NANOWIRES Min-Feng Yu, Zhaoyu Wang, Jie Hu and Abhijit Suryavanshi Department of Mechanical and Industrial Engineering, University of Illinois at UrbanaChampaign, Urbana, IL 61801, USA. [email protected] Significant interest exists for the scientific study and the commercial application of piezoelectric materials with nanoscale dimensional properties [1-4]. With the recent advance in the synthesis of piezoelectric nanomaterials of high crystalline quality and low dimensionality [5-6], it is now possible to study the size and dimensionality effect in mechanics and electromechanics related to piezoelectricity. We report here such a study with single crystalline barium titanate (BaTiO3) nanowires. Specifically, the mechanical property and the piezoelectric behaviour of individual BaTiO3 nanowires having diameters down to several tens nanometer are studied with piezoresponse force microscopy (PFM) and with tensile electromechanical testing method. The BaTiO3 nanowires utilized in the study are synthesized through a solid state reaction route at high temperature in sodium chloride medium [5]. Fig.1 shows the representative electron microscopy images of the nanowires. The excellent size uniformity and high crystallinity are shown. Additionally, in situ TEM Energy Dispersive X-ray spectroscopy has confirmed that that the nanowire is composed of Ba, Ti and O with Ba/Ti ratio close to 1.

FIGURE 1. (a) Scanning electron microscopy image of an individual BaTiO3 nanowire; (b) Transmission electron microscopy image of a nanowire showing the clearly resolved perfect lattice structure in nanowire; (c) Diffraction image taken from an individual nanowire showing its high crystallinity. In order to reveal the nanoscale piezoelectric behavior in nanowire, PFM, which is a technique developed based on atomic force microscopy (AFM), is used. In PFM, a small ac testing signal is applied across the sample with a conductive AFM tip. Due to the converse piezoelectric effect, the applied electrical field induces a vertical or shear local displacement of the sample, which induces a vertical or torsional deflection of the AFM probe cantilever. The induced displacement (down to as small as 0.1 pm) can be measured with an ultrahigh sensitivity lock-in amplifier. PFM thus allows the detection of magnitude and phase of the piezoelectric response, which then allows the determination of the piezoelectric constants, as well as the local polarization state and domain structure in the sample. Figure 2 shows the measured piezoresponse results from an individual

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BaTiO3 nanowire having a diameter of 95nm. The measured d11 and d15 piezoelectric responses indicate that the BaTiO3 nanowire is primarily polarized along the length direction. (We define the direction perpendicular to the length direction as direction 1 and the length direction as direction 3 following the traditional nomenclature.) The d15 response is close to 60 times high as the d11 response, indicating the strong shear response behaviour of the nanowire, a property similarly existed in bulk BaTiO3 crystal [7]. Additional PFM studies, such as domain switching dynamic study, hysteresis loop study and PFM imaging, have confirmed that BaTiO3 nanowire is polarized along the length direction and has minimal polarization at zero bias along the direction perpendicular to the length direction. For the quantitative study of the mechanical and piezoelectric properties of BaTiO3 nanowire, a uniaxial tensile electromechanical testing flexure stage is developed. Integrated with the stage include a miniaturized capacitive displacement sensor and a MEMS based force sensor, which provides the sub-nanometer displacement resolution and nano-Newton force resolution required for the electromechanical characterization of BaTiO3 nanowire. The description of this measurement tool and the result obtained from the tensile testing will be further detailed in the talk.

FIGURE2. The acquired d11 (a) and d15 (b) piezoelectric response curve.

References 1.

Naumov, I. I., Bellaiche L. and Fu, H., Nature, 432, 737, 2004

2.

Dawber, M., Jung D. J., and Scott, J. F., Appl. Phys. Lett. 82, 436, 2003.

3.

Ghosez P.and Rabe K. M., Appl. Phys. Lett. 76, 2767, 2000.

4.

Alexe M., Harnagea C., Hasse D., and Gösele U., Appl. Phys. Lett. 79, 242, 2001.

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Urban, J. J., Yun W. S., Gu Q., and Park, H. J. Am. Chem. Soc. 124, 1186 (2002).

6.

Mao, Y., Banerjee S., and Wong S. S., J. Am. Chem. Soc. 125, 15718, 2003.

7.

Jaffe B., Piezoelectric Ceramics, Academic Press, London, 1971.

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MULTISCALE SIMULATION FOR HIGH SPPED PROPAGATION OF DISORDERED REGIONS W. Yang, X. Li and Z. Guo Department of Engineering Mechanics, Tsinghua University Beijing, 100084, China [email protected] We propose a new multi-scale simulation scheme which seamlessly combines the conventional molecular dynamics (MD) with the continuum mechanics formulated under the material point method (MPM). In MPM, modified interpolation shape functions are adopted to reduce artificial forces on the background hierarchical grids. The method is applicable to several kinds of potentials including the Lennard-Jones, EAM and a bonding-angle related potential for silicon. Examples of high energy Cu-Cu and Si-Si cluster impact are presented. The kinetic energy of the cluster is the critical process parameters. The evolution of displaced atoms is found to depend on the underlying lattice structures. For the case of Cu-Cu cluster impacts, stacking faults play an important role. The displaced atoms, visualized in the method of “local crystalline order”, propagate in an anisotropic manner. This implies the anisotropy in energy transformation process through impacts with multi interactions among cluster and surface atoms. With the help of the present multi-scale scheme, the computation capacity implemented in a personal computer could reach a system composed of 900 millions atoms. The case of Si-Si cluster impacts is also examined where the damage spreads in a more isotropic manner. For the case of cluster impact on a beam with pre-existing cracks, the high energy impact may seal the crack with amorphous matters and induces an efflux of atoms ahead of the crack mouth, as shown in Figure 1.

FIGURE1. Local crystalline orders at 2.5ps (left), 5.0ps (center) and 7.5ps (right) after impact A multiple time step algorithm, called reversible reference system propagator algorithm, is introduced for the long time molecular dynamics simulation. In contrast to the conventional algorithms, the multiple time method has better convergence, stability and efficiency. The method is validated by simulating free relaxation and the hypervelocity impact of nano-clusters. The time efficiency of the multiple time step method enables us to investigate the long time interaction between lattice dislocations and low-angle grain boundaries. By use of the MTS method, we examine the convergence and stability of rRESPA method, and show its performance in some different systems. The MTS method obviously has better convergence and stability than the

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conventional algorithms. Moreover, this method updates the slow degrees of freedom less frequently than the fast ones, and thus speed up the simulation. By simulating the interaction between lattice dislocations and GBs, one observes not only the complete interaction process of dislocations and GBs, but also phenomena such as dislocations transmission through the GB, dislocations absorption into the GB, and dislocations coalescence into a micro-crack. These phenomena will provide help in the study of the interaction of dislocations and GBs. The multiple time step method is also used to investigate the generation of dislocation loops from a Frank-Read source. Setting in a background of a bicrystal lattice, the formed dislocation loops may pile-up at the grain boundary and then reinitiate at the neighbouring grain. Various kinds of partial dislocations and branched stacking faults may also manifest, such as shown in Figure 2, giving a rich variety for the propagation of disordered regions.

FIGURE 2. Snapshot of interaction between lattice dislocation and GB (14.5 ps)

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SURFACE-STRESS-DRIVEN PSEUDOELASTICITY AND SHAPE MEMORY EFFECT AT THE NANOSCALE W. Liang and M. Zhou Woodruff School of Mechanical Engineering Georgia Institute of Technology, Atlanta, GA 30332 [email protected] The pseudoelastic deformation of some shape memory alloys (SMAs) such as Au-Cd, Au-Cu-Zn, Cu-Zn-Al, and Cu-Al-Ni proceeds through the reversible movement of twin boundaries (Ren and Otsuka [1]). The behavior of these materials is commonly referred to as rubber-like due to its resemblance to the behavior of soft and pseudoelastic rubber (Otsuka and Wayman [2]). A similar behavior and a shape memory effect (SME) are discovered in single-crystalline Cu nanowires with lateral dimensions between 1.76 and 3.39 nm through molecular dynamics simulations. This behavior at the nanoscale is due to reversible crystallographic lattice reorientations through the movement of twin boundaries within the FCC crystalline structure (Fig. 2), allowing Cu nanowires to exhibit recoverable strains of up to more than 50% which are well beyond the recoverable strains of 5-8% of most SMAs. The reorientation is driven by high internal stresses resulting from the surface stress and high surface-to-volume ratios of the nanowires. This phenomenon only occurs in nanowires within the size range of 1.76-3.39 nm and is not observed in bulk Cu. Furthermore, it is temperature-dependent and hence gives rise to an SME. Specifically, the critical temperature for spontaneous reorientation upon unloading increases from 100 to 900 K as the wire size increases from 1.76 to 3.39 nm, making it possible to design nanoscale components of varying sizes for operation over a wide range of temperature. Such an objective is more difficult to achieve with conventional bulk SMAs since their transition temperatures (martensite start and finish temperatures, austenite start and finish temperatures) only vary with material structures and composition, not size. Moreover, the nanowires have very short response times which are on the order of nanoseconds due to their extremely small dimensions compared with bulk SMAs. These unique properties can lead to important applications at the nanoscale, including sensors, transducers, and actuators in nano-electromechanical systems (NEMS).

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FIGURE 1. Reversible lattice reorientations upon loading and unloading in single-crystalline Cu nanowires; (a) original -axis/{111}-surface wire with rhombic cross-sections, = 70.5° and = 109.5°, (b) stretched -axis/{001}-surface wire with square cross-sections, (c) (110) atomic plane containing the > @ wires axis and the long diagonal ([001]) of the rhombic crosssection in the original wire, (d) the same (110) atomic plane after lattice reorientation, containing the new wire axis ([001]) and a diagonal ( [110] ) of the new square cross-section. Atomistic simulations have also yielded the same rubber-like behavior and SME in Au nanowires with similar levels of recoverable strains and different critical temperatures and critical sizes. Since other FCC metallic (e.g., Pt and Ag) nanowires have similar structures and properties as those of Cu and Au nanowires (Rodrigues and Ugarte [3]), it is tempting to speculate that a similar behavior may also be found in them, with comparable levels of recoverable strains as those for Cu and Au wires. Of course, their critical temperatures and critical sizes would depend on their surface stress levels and the differences between their {001} and {111} surface energies. If such an effect is proven true, these materials could provide a whole class of nano building-blocks with unique rubber-like behaviors and SMEs operative over a wide range of temperatures and sizes.

References 1.

Ren, X. and K. Otsuka, Nature, vol. 389, 579-582, 1997.

2.

Otsuka, K. and Wayman, C.M., Shape Memory Materials, Cambridge University Press, New York, 1998.

3.

Rodrigues, V. and Ugarte, D., In Simulation and Modeling of Mechanical Deformation of Nanowire in Nanowire Materials, edited by Z.L. Wang, Kluwer Academic/Plenum Publishers, New York, 2003, 177-209.

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THERMOMECHANICAL BEHAVIOR OF ZINC OXIDE NANOBELTS A. Kulkarni and M. Zhou G. W. Woodruff School of Mechanical Engineering Georgia Institute of Technology 801 Ferst Drive, Atlanta, GA 30332-0405, U.S.A. [email protected] Belt-like ZnO nanostructures with rectangular cross-sections have recently been synthesized through vapor deposition (Pan et al.) [1]. These nanobelts can serve as building blocks for functional nano-systems. The integration of these nanostructures in systems requires understanding of their inherent properties, functionalities and behavior. An atomistic framework is developed to evaluate the thermomechanical behavior of these nanobelts. Molecular dynamics simulations are performed to characterize the response to uniaxial tensile loading. The ultimate tensile strength, strain at failure and Young’s modulus are obtained as functions of temperature, size and growth orientation. The results are compared with the behavior of bulk ZnO.

FIGURE 1. (a) unit cell of ZnO, (b) orientations of nanobelts, and (c) loading scheme The nanobelts in three growth directions are generated by assembling the unit wurtzite cell along the [0001] , [0110], and [2110] crystalline axes, see Fig. 1(a)-(b). The interactions between the atoms are described by a Buckingham type potential which accounts for both electrostatic and short range pair-wise effects. Following the geometric construction, dynamic relaxation is carried out to yield free-standing nanobelts at 300 K. Two distinct configurations are observed. When the lateral dimensions are above 10 Å, nanobelts with rectangular cross sections are observed. Below this critical size, tubular structures involving two concentric shells similar to double-walled carbon nanotubes are observed in the [0001] and [0110] orientations. The tubular structures have low energy [0001] lateral surfaces, indicating a transformation driven by surface energy minimization. Approximation to quasi-static tensile loading is achieved through the specification of boundary velocities at the ends of the nanobelt during loading steps and subsequent relaxation at fixed lengths during equilibrating steps (Fig.1 (c)). Deformations of belts with [2110] and [0110] orientations exhibit three stages, including initial elastic stretching, wurtzite-ZnO to graphitic-ZnO

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structural transformation, and cleavage fracture. On the other hand, [0001] belts do not undergo any structural transformation and fail through cleavage along [0001] planes. Calculations show that the ultimate tensile strength (UTS) and Young’s modulus of the belts are size-dependent and are higher than the corresponding bulk ZnO values. Specifically, as the lateral dimensions decrease from 30 to 10 Å, significant increases between 38-76% and 31-53% are observed for the UTS and Young’s modulus, respectively, as shown in Table 1. This effect is due to the size-dependent compressive stress induced by tensile surface stress in the nanobelts (Diao et al.) [2]. TABLE 1. Young’s modulus and UTS as functions of nanobelt lateral dimensions (T = 300 K)

[0110] and [2110] nanobelts with multi-walled tubular structures have higher values of elastic moduli (~430 GPa) and UTS (~36 GPa) compared to their wurtzite counterpart, echoing a similar trend in multi-walled carbon nanotubes. The influence of temperature on properties is also determined. Between 100 to 1000 K (note that Tm =2250 K ), approximately 18%, 9% and 51% decreases in the Young’s modulus are observed for the [0001] , [0110], and [2110] orientations. This observation is consistent with what is reported for bulk ZnO (Gadzhiev) [3].

References 1.

Pan, Z.W., Z.R. Dai, and Z.L. Wang, Science, vol 291(9), 1947-1949, 2001.

2.

Diao, J., K. Gall, and M.L. Dunn, Nano Letters, vol 4(10), 1863-1867, 2004

3.

Gadzhiev, G.G., High Temperature, vol 41(6), 778-782, 2003.

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NATURAL MODES OF C60 CAGE VIA CARBON-CARBON BONDING ELEMENT Pan Zeng, Xue-Gui Yang and Jing Du Department of Mechanical Engineering, Tsinghua University Beijing 100084, PR China [email protected] Science and technology related to C60 cage have attracted the attention and research interest of thousands of scientists and engineers over the past decade (Kroto et al. [1]). This attraction stems from C60’s beautiful symmetry, dazzling chemical and physical properties, and potential applications in nanotechnology (Zhang et al. [2]). The simulations are widely used to study or predict the vibrational behaviours of C60 cage (Wu et al. [3], Jiang et al. [4]). The available approaches can be mainly catalogued into the group theory model and the ab inito calculation (Adams et al. [5], Koruga et al. [6]). However, there has not yet been a more completed investigation for vibration of C60 cage in Raman domain from both the computational model and the experiments. So a direct computational model of covalent atom structure is our objective. To this end, a new bond-based direct computational approach is developed to investigate the mechanical behaviours of C60 cage. This approach works through element technology and molecular mechanics (Chang et al. [3]), called Carbon-Carbon Bonding Element (CCBE), which is defined on a bond with two atoms (Fig.1). There are 6 DOFs defined to describe the force-energy relationship of co-valent bond via molecular mechanics. Further the cluster model with a bondbased hexagon ring structure is built (Fig.2). Three important characteristics of covalent atom structure, i.e., length, angle, energy, are totally considered in computational model. The force constants can be identified by Raman spectra of C60 cage. The CCBE has some important characteristics, for example, it is a discrete model, and the constants of element matrix can be directly related to the force constants of co-valent bond. As for the scale of computation, the CCBE also has an obvious dominance. For a system with N atoms the DOFs will be 3N, and the equation to be solved will be linear when only considering a small deformation near original equilibrium position.

FIGURE 1. Representation of CCBE

FIGURE 2. The cluster model with CCBE

A C60 cage has a novel structure with 60 carbon atoms. Its 174 DOFs should be corresponding to total 174 natural modes. But only about 20 orders of modes can be directly detected by means of Raman spectrum. The modelling technology of Carbon-Carbon Bonding Element is used to analyze the total natural modes of C60 cage. So all information of natural modes of C60 cage has been presented and investigated (Fig.3 and 4). The comparison with experiment of Raman spectrum (Koruga et al. [6]) shows that the modelling method based on Carbon-Carbon Bonding

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Element is convenient and efficient in predicting the vibration behaviour of C60 cage (Table 1). This study represents an effort to develop a precise numerical method for applications in nanostructure modelling.

FIGURE 3. Ag(1) natural mode of C60

FIGURE 4. Hg(1) natural mode of C60

TABLE 1. The natural frequencies of C60 molecule in the Raman domain

References 1.

Kroto, H. W., Heath, J. R., et al., Nature, vol.318, 162, 1985

2.

Zhang, Q. L., O’Brien, S. C., et al., Chem. Phy. Letters, vol.90, 525, 1986

3.

Wu, Z C, Jelski, D A, and George, T. F., Chem. Phy. Letters, vol.137, 291-294, 1987

4.

Jiang, Q., Xia, H., Zhang, Z and Tian, D., Chem. Phy. Letters, vol.192, 93-96, 1992

5.

Adams, G. B., Page, J. B., et al., Physical Review B, vol.44, 4052, 1991

6.

Koruga, D., Hameroff, S., et al., Fullerene C60, Amsterdam: North-Holland, 1993

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FRACTURE OF NANOCRYSTALLINE ALUMINUM C. San Marchi, S. L. Robinson, N. Y. C. Yang and E. J. Lavernia1 Sandia National Laboratories, 1University of California, Davis 7011 East Ave., MS-9402, Livermore CA 94551 [email protected] Bulk nanocrystalline (NC) alloys are an exciting new class of materials that have only recently established their potential for real-world applications. The tensile yield strength of nanocrystalline 5083 aluminum produced by consolidation of cyromilled powders is about twice that of conventional 5083 as shown in Fig. 1. The material is extruded which accounts for the anisotropy in tensile properties and has a grain size on the order of 50 nm. The elongation to failure is lower than for conventional coarse-grained 5083, however not much different from similar high strength alloys such as 5082-H19: 370 MPa yield strength, 4% elongation [1]. In addition, these materials are thermally stable; heating tensile bars to 500C for 2 hours results in only modest loss in room temperature strength.

FIGURE 1. Tensile stress-strain curves of nanocrystalline 5083 aluminum. The fracture surfaces reveal that deformation is primarily ductile and that second phases (oxides, silicides and intermetallics) contribute to damage. These second phases are also highly refined due to the cyromilling process and are typically submicron in size. In addition, these second phase particles are believed to provide the excellent thermal stability observed for these nanocrystalline alloys produced by crymomilling. Fracture toughness tests in 3-point bending are underway and preliminary fracture toughness values are in the range of 15 to 20 MPa m1/2 for nanocrystalline 5083.

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FIGURE 2. Fracture surface of nanocrystalline 5083 tested in tension, longitudinal orientation.

References 1.

Hatch, J.E., Aluminum: Properties and Physical Metallurgy, American Society for Metals, Metals Park OH, 1984.

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WEAR AND FATIGUE IN SILICON STRUCTURAL FILMS FOR MEMS APPLICATIONS Daan Hein Alsem, Robert Timmerman1, Eric A. Stach2, Christopher L. Muhlstein3, Michael T. Dugger4 and Robert O. Ritchie5 Department of Materials Science and Engineering, University of California at Berkeley Materials Sciences Division, Lawrence Berkeley National Laboratory One Cyclotron Road MS 72/150, Berkeley, CA 94720 [email protected] 1Department of Applied Physics, University of Groningen Nijenborgh 4, 9747 AG Groningen, The Netherlands [email protected] 2School of Materials Engineering, Purdue University 501 Northwestern Avenue, West Lafayette, IN 47907 [email protected] 3Department of Materials Science and Engineering, Pennsylvania State University 202B Steidle Building University Park, PA 16802 [email protected] 4Materials and Process Sciences Center, Sandia National Laboratory PO Box 5800, Albuquerque, NM 87185-0889 [email protected] 5Department of Materials Science and Engineering, University of California at Berkeley Materials Sciences Division, Lawrence Berkeley National Laboratory One Cyclotron Road MS 62/203, Berkeley, CA 94720 [email protected] Recent advances in the application of micromachined structures have increased the demand for more reliable structures. Stiction, fatigue and microwear [1] are large issues in the reliability of microelectromechanical systems (MEMS), especially now that designs become more demanding. Silicon is an excellent construction material at the micro-scale, because of highly developed processing methods directly related to semiconductor electronics processing and its high strength. However, it is an inherently brittle material and reliability is the limiting factor as far as commercial and defence applications are concerned. Since the surface to volume ratio of these structures is very large, surface forces become dominant and classical models for failure modes cannot always be applied. Whereas bulk silicon is not susceptible to fatigue, micron scale silicon is. This poses considerable limitations to MEMS design and reliability. Muhlstein et al. [2] have posed a “reaction-layer” fatigue mechanism where a stress induced thickened oxide layer accommodating moisture assisted cracking is thought to cause fatigue in silicon at the microscale. Even though more experimental confirmations for this mechanism has been found [3], the question of why the oxide layer thickens under influence of high local cyclical stresses is still uncertain, and an alternative fatigue mechanism has been suggested by Kahn et al. [4]. This presentation will present a new series of data on fatigue resonator devices, as used in [2] and [3], fabricated at the Sandia SUMMITTM polysilicon process. These devices differ from the previously used devices in that their post-release silicon oxide layers are much thinner (~2 nm vs.

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~30 nm in previous studies). These results will provide additional insight into the mechanism causing fatigue of micro-scale polysilicon. Additionally, detailed wear debris investigation have been conducted on side-wall friction devices run in ambient air, also fabricated in the Sandia SUMMITTM polysilicon process. Electron microscopy techniques were used to image and analysis wear debris in these silicon MEMS. This study showed that the debris particle size is ~50-100 nm and the debris forms agglomerates a large as ~500 nm. Comparing abrasive wear tracks, wear debris, grain size and surface roughness, it follows that after an initial adhesive wear mechanism, where ~50-100 nm particles are removed from the surface by fracture through the grains (size ~400 nm) an abrasive wear mechanism regime occurs and creates wear plough tracks with the width similar to the size of the debris particle agglomerates. Surface roughness can aid in adhesion processes, but since it is considerably smaller (~10 nm) than the wear particles and wear tracks, surface asperity fracture does not appear to contribute to the wear debris in later stages of wear. It is interesting that the debris particles are indeed amorphous and have a high oxygen content, but do not completely consist of SiO2. This fact in combination with the post-release oxide layers in these films being only ~2 nm, tells us that debris particles are formed by silicon from the film that amorphizes and subsequently partly oxidizes [5]. Some numerical support for the suggested mechanisms, as well as additional experimental evidence on sub-surface cracking of the silicon during wear will be presented in order to provide insight into the potential role of delamination as a micro-scale wear mechanism.

References 1.

A. D. Romig Jr. , M. T. Dugger, P. J. McWhorter, Acta. Mater., vol 51, 5837, 2003

2.

C. L. Muhlstein, E. A. Stach, and R. O. Ritchie, Acta. Mater., vol 50, 3579, 2002

3.

D.H. Alsem, E. A. Stach, C. L. Muhlstein and R. O. Ritchie, Appl. Phys. Lett., vol 86, 41914 - 1-3, 2005

4.

H. Kahn, R. Ballerini, J. J. Bellante, and A. H. Heuer, Science, vol 298, 1215, 2002

5.

D.H.Alsem, E.A. Stach, M.T. Dugger, M. Enachescu, R.O. Ritchie, Journal of Thin Solid Films, submitted, 2005.

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INDENTATION INDUCED THROUGH THICKNESS FILM FRACTURE ON ENGINEERING ALLOYS D. F. Bahr, K. R. Morasch and A. Alamr Mechanical and Materials Engineering, Washington State University PO Box 642920, Pullman WA 99164-2920 USA [email protected] In thin film systems, failure often occurs via fracture mechanisms, with either through thickness cracking or interfacial delamination leading to failure of the device or layer. In spite of this common failure mechanism, many of the testing methods for analyzing fracture in thin film systems are focused on the applied problems of thin film adhesion measurements. While this is an important goal in many industries, particularly in the microelectronics community, for engineering applications there many situations where film fracture thorugh the thickness of the film, and not film adhesion, is the controlling factor in the life of a component. Measuring the stress at which fracture occurs in these thin film systems requires testing methods amicable to both the small scale of the films as well as the complex relationship between the mechanical properties of the film and the substrate. One method for testing thin film fracture is indentation driving fracture. A number of tests, particularly those of Chechenin et. al. [1] and Weppleman and Swain [2] have shown it is possible to produce indentation induced cracks in thin hard films on ductile substrates. Other studies have extended these tests to a broad range of systems; Pang and Bahr studied TiO2 on Ti [3], RodriguezMarek et. al. tested passive films on stainless steels [4], and Morasch and Bahr [5] and Bahr and co-workers [6] examined Al2O3 on Al. The current paper will focus on more recent examinations of engineering alloys, particularly stainless steel and anodized aluminum. These films generate clear indentation induced fracture, as shown in Fig. 1 for a conical indentation using a 1 m radius of curvature tip to indent a 200 nm thick anodized aluminum film on samples of 1100 series aluminum. This fracture pattern clearly occurs outside the contact radius, a, in this case the effective radius of fracture, c, is approximately 2.3 times the contact radius.

FIGURE 1. Indentation Induced Film Fracture in Anodized Aluminum The load depth curves for these indentations can be analyzed in terms of energy, rather than stress intensities, as has been done in previous work [3-6]. The load depth curve for an aluminium substrate, an anodized film which exhibits a small radial crack in the contact region, and a large

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circumerential crack. Using this energy analysis and the measured elastic properties of the porous anodic film, the toughness of anodized aluminium oxide is 0.3 J/m2. This paper will present an energy based analysis of the aluminium system as well as similar studies of a stainless steel. The stainless steel system was tested during electrochemical film growth, and shows clear examples of the effects of both alloy and surrounding environment on the strength of passive films. Both in situ and ex situ testing was carried out to examine the effects of environment on the testing procedures. Increasing the salt concentration in the electrolyte from 0.01M NaCl to 0.1M NaCl and changing the substrate on which the film was grown from 904L to 304 stainless steels reduced the applied tensile stress needed to fracture the film formed at a metastable pitting potential from 1.74GPa to 1.63GPa and from 1.76GPa to 1.63GPa, respectively. The measured strength of films measured in ambient conditions after removal from the electrolyte was greater than when the films were measured in situ. However, the trends in film strength as a function of environment varied by are the same between in situ and ex situ testing, suggesting the two tests are both feasible methods of analyzing environment effects of film strength.

References 1.

Chechenin, N.G., Bottiger, J., Krog, J.P. Thin Solid Films vol. 261, 228-235, 1995

2.

Wepplemann, E., Swain, M.V., Thin Solid Films vol. 286, 111-121, 1996

3.

Pang, M., Bahr, D.F. J. Mater. Res., vol. 16, pp. 2634-2643, 2001

4.

Rodriguez-Marek, D., Pang, M., Bahr, D.F., Metall. Mater. Trans, A. vol. 34A, 1291-1296, 2003

5.

Morasch, K.R. and Bahr, D.F., J. Mater. Res., vol. 20, 1490-1497, 2006

6.

Bahr, D.F., Woodcock, C.L., Pang, M., Weaver, K.D., Moody, N.R., Inter. J. Frac. vol. 119/ 120, 339-349, 2003

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SURFACE NANOSTRUCTURED ALUMINUM BY SEVERE PLASTICS DEFORMATION E. I. Meletis, K. Y. Wang1 and J. C. Jiang2 Materials Science and Engineering The University of Texas at Arlington, Arlington, Texas 76019 USA 1Center for Advanced Microstructures and Devices 2Mechanical Engineering Department Louisiana State University, Baton Rouge, Louisiana 70803 USA [email protected] Severe plastic deformation (SPD) has been known to be an effective method for producing nanostructured materials [1]. Examples of SPD methods are mechanical alloying and mechanical attrition to prepare nanostructured powders. The same concept can be used to develop a nanocrystalline surface region in bulk materials thus enhancing surface sensitive properties [2]. Recently, we used ultrasonic shot peening (USSP) to surface harden commercially pure aluminum (Al 1100). In this process, steel balls placed in the vial, vibrate at high frequency and impact the surface inducing plastic deformation at high strain rate. The repeated multidirectional impacts onto the material surface result in severe plastic deformation in the near surface layer leading to nanocrystallization. Microhardness measurements as a function of depth revealed a twofold increase in surface hardness followed by a hardness gradient consistent with a gradient in grain size. The hardness profile was stabilized after 1 hr of processing time.

FIGURE 1. Variation of hardness as a function of depth and USSP processing time at cryogenic temperature.

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FIGURE 2. Variation of friction with sliding distance and processing time. The final hardness (or grain size) reflects the equilibrium between deformation hardening and recovery from heating generated during processing. Due to low melting point of Al, recovery is expected to have a significant effect on the minimum grain size attainable by this process impeding further hardening. In the present study, an attempt was made to suppress the recovery process by conducting USSP experiments at cryogenic temperatures. The objective was to manipulate the kinetics and achieve a smaller grain size and thus higher hardness. Fig. 1 presents the microhardness depth profile as a function of processing time at cryogenic temperature. The microhardness achieved was 1.0 GPa that is about 25% higher than that obtained with USSP conducted at room temperature (or 2.5 times higher than that of unprocessed 1100 Al). Similarly, the microhardness shows a sharp initial increase and reaches a plateau after about 1 hr of processing. Based on a Hall-Petch relationship, such hardness is expected to correspond to a grain size of about 25 nm [3]. In our previous room temperature USSP experiments, the grain size at the surface was found to be around 100 nm. The tribological response, Fig. 2, shows that a processing time of more than 30 min results in a rather stable initial friction. Also, a significant reduction in the coefficient of friction for a sliding distance of about 600 m is observed. Thus, processing at lower temperatures offers the opportunity to achieve smaller grain sizes and significant enhancement in mechanical properties.

References 1.

Koch, C.C., Nanostruct. Mater., vol. 2, 109-129, 1993.

2.

Gleiter, H., Prog. Mater. Sci., vol. 33, 223-315, 1988.

3.

Zhou, F., Lee, J., Dallek, S. And Lavernia, E.J., J. Mater. Res., vol.16, 3451-3458, 2001.

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CONTRIBUTION OF LOCALIZED DEFORMATION TO IGSCC AND IASCC IN AUSTENITIC STAINLESS STEELS Gary S. Was, Zhijie Jiao and Jeremy T. Busby University of Michigan 2355 Bonisteel Blvd., Ann Arbor, MI 48109 USA University of Michigan 2355 Bonisteel Blvd., Ann Arbor, MI 48109 USA P.O. Box 2008, Oak Ridge National Laboratory Oak Ridge, TN 37831 [email protected], [email protected], [email protected] It is known that the irradiation-induced microstructrual and microchemical changes in austenitic alloys may affect the irradiation-assisted stress corrosion (IASCC) susceptibility. However, a recent study [1] shows that IASCC susceptibility is more likely to be linked to the mechanical properties such as yield stress and hardness that arise from the microstructrual change. A higher yield stress generally corresponds to a lower level of uniform elongation but a higher degree of localized deformation. Localized deformation, induced by low stacking fault energy (SFE) and/or irradiation damage, may play a key role in IGSCC and IASCC susceptibility of austenitic stainless steels and nickel-base alloys. Proton irradiation and constant extension rate tensile testing (CERT) were used to examine the potential impact of SFE and irradiation on deformation mode and IASCC. Three model alloys (E : UHP-304, H : 304+Si and L : 304+Cr+Ni) having a spread in SFE were selected for this study. Two batches of samples were irradiated with 3.2 MeV protons at 360°C to 1.0 and 5.5 dpa respectively, and then incrementally strained in 288°C Ar atmosphere to 3%, 7% and 12%. After each strain level, the degree of strain localization, as determined by channel height, width and spacing were quantified using SEM and AFM on replicas of the surfaces of the deformed samples. Results were compared to those from SCC tests in simulated LWR environments to determine if localized deformation is a controlling factor in IASCC. At 3% strain, irradiation dose has a significant positive effect on channel height. The higher the dose, the larger is the average channel height, Fig. 1. However, as the strain increases, the significance of this effect decreases. At 7% strain, the average channel height for alloy E at 1.0 dpa is nearly equal to that at 5.5 dpa. The average channel height follows the order, alloy H > alloy E > alloy L, at 3% strain for both doses. Alloy L has the lowest height of the three alloys for all conditions. The average channel width does not change much regardless of strain and dose. As expected, the spacing between channels decreases with increasing strain levels. At low dose, the average channel strain increases with increasing strain for all three alloys, Fig. 2. However, channel strain for alloys H and E saturates at 7% strain. Alloy L has the lowest average channel strain of all three strain levels. Alloy H has the highest average channel strain at low strain (3%). The magnitude of average channel strain follows the order of alloy H > alloy E > alloy L. The order is inverse of that for the magnitude of stacking fault energy. The alloy with lowest SFE has the highest average channel strain. At high dose, average channel strain for alloys H and E is saturated even at 3% strain. Alloy L is still the lowest of all three alloys.

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FIGURE 1. Average channel height in alloys E, H and L at doses of 1.0 and 5.5 dpa

FIGURE 2. Average channel strain in alloys E, H and L at doses of 1.0 and 5.5 dpa

At low dose, the degree of strain localization in channels increases with increasing strain level and it saturates at higher strain level. At high dose, strain localization is saturated at low strain level (3%) for alloys H and E. At low strain levels ( alloy E > alloy L, which is the inverse order of the stacking fault energy. Alloy L has the smallest degree of strain localization at all strain levels and both doses. The alloy with the highest SFE has the least degree of deformation. Alloy H with the lowest SFE is most susceptible to IASCC, and alloy E has a moderate IASCC susceptibility. Alloy L with the highest SFE is resistant to cracking. The degree of localized deformation at the point of crack initiation is most likely to be the controlling factor for IASCC susceptibility.

References 1.

K. Fukuya, M. Nakano, K. Fujii, T. Torimaru and Yuji Kitsunai, Journal of NUCLEAR SCIENCE and TECHNOLOGY, Vol. 41, No. 12, p. 1218-1227Jones, G. A., Applied Fracture Mechanics, Soringer, Berlin, Germany, 1978.

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A STUDY OF CRACK-DISLOCATIONS INTERACTION WITH 3D DISCRETE DISLOCATION DYNAMICS I. N. Mastorakos and H. M. Zbib School of Mechanical and Material Engineering Washington State University Pullman, WA 99163 [email protected], [email protected] Although in recent years there has been an attempt to model crack – dislocation interactions [1, 2], the work has been limited to two dimensions and for certain special cases. In this work we address the problem within a three-dimensional discrete dislocation dynamics frame-work coupled with a dislocation density model for cracks. Representing 2D cracks by dislocation density distributions is a well-known and widely applied technique in planar cracks. Dislocation density represents the slope of the crack opening displacement at a given position on the crack. Thus, the stress field due to the relative displacement of an infinitesimal segment of the crack surfaces can be used as Green's function which can be integrated over the crack surface to represent the stress field due to the crack at any given point in the medium surrounding the crack. Furthermore, with the application of the superposition principle, the stress-free crack surface condition can be satisfied. This technique can be extended to 3D cracks, where, instead of straight dislocations, infinitesimal dislocation loops are considered (for a review of this technique see [3, 4]). In this case, the crack plane is considered as a distribution of infinitesimal dislocation loops with Burgers vector b ( b , b , b ) . To describe the displacement field produced by such a dislocation loop of area dS, a Cartesian coordinate x

system Oxyz is defined so that the dislocation loop lies in the plane z

y

z

z c (Fig. 1).

The problem that has to be solved is a planar crack of penny or elliptical shape, which is embedded in an infinite body and is subjected to an arbitrary loading. Because of the nature of the loading, the crack will experience both opening and shearing mode displacements. A continuous distribution of infinitesimal dislocation loops, each of area dS and Burgers vector b ( b , b , b ) is applied to the crack faces to model the three relative displacements of them. The tractions on the crack plane induced by the distribution are: x

y

z

V 3i ( x )

³K

ij

( x , x c) b j ( x c) d S

S

(1)

where i 13 , j is the number of loops, and Kij ( x, xc) is a known function. The boundary condition to be satisfied is that the crack faces are stress – free, which leads to the following integral equation:

³K S

ij

( x , x c ) b j ( x c ) dS

 t i0 ( x ) (2)

In order to solve the above equation, we have to deal with the third degree singularity that appears in the kernel Kij ( x, xc) . This type of singularity is universal, meaning that in all problems

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involving crack representation by dislocations the singularity remains the same regardless of the geometry concerned. Having solved the integral equation, the interaction of different shape cracks with different dislocation types (edge, screw and mixed) and various loading types (fatigue, creep, creep-fatigue, etc.) can be examined with the use of Discrete Dislocation Dynamics [5]. Figure 2 shows the stress distribution around a crack as a result of interaction with a nearby dislocation.

References 1.

Van der Giessen, E, Deshpande, V.S., Cleveringa, H.H.M. and Needleman, A., J. Mech. Phys. Solids, vol. 49, 2133-2153, 2001.

2.

Deshpande, V.S., Needleman, A. and Van der Giessen, E., Acta Mater, vol. 51, 1-15, 2003.

3.

Hills, D.A., Kelly, P.A., Dai, D.N. and Korsunsky, A.M., Solution of Crack Problems, Kluwer Academic Publ., Dordrecht, 1996.

4.

Weertman, J., Dislocation Fracture Mechanics, World Scientific, Singapore, 1996.

5.

Zbib, H.M. and Diaz de la Rubia, T., Int. J. Plasticity, vol. 18, 1133-1163, 2002.

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NUMERICAL SIMULATIONS AND MEASUREMENTS OF CRACKS PARALLEL AND NEAR INTERFACES IN GRADED STRUCTURES Ivar Reimanis, Keith Rozenburg, John Berger, Matthew Tilbrook1 and Mark Hoffmann1 Metallurgical and Materials Enginering and Engineering Division Colorado School of Mines Golden, CO 80401, USA 1School of Materials Science and Engineering, University of New South Wales, Sydney 2052, New South Wales, Australia [email protected] The driving force and mode mixity for cracks near interfaces was examined via experimental measurements of the crack tip displacement field with moire interferometry, verified using boundary element modeling, and further explored with finite element modeling. The stress intensity factor was obtained by a collocation method in which the Westergaard crack tip expansions are used for displacements [1]. The method of fundamental solutions was employed so that displacements across the material interface could be used [2]. Boundary element simulations provide verification of the method and allow a comparison with experiment. Systematic finite element simulations enable a study of how residual stresses may affect crack trajectories and driving forces. Cracks near interfaces experience a stress field that is highly sensitive to the crack location. The present work examines the major factors that influence crack growth when a crack is parallel and very near an interface in a bimaterial configuration, such as that shown in Fig. 1. The elastic mismatch, plastic mismatch and the residual stress gradient typically present in such structures influence the crack driving force and trajectory. These are studied here with a combination of experimental and numerical methods. Conventional methods for applying moire interferometry to analyze cracks near interfaces are limited because the displacement field on both sides of the interface cannot be utilized. For example, in the Cu-W composites specimens examined here, the fracture process zone is on the order of 100 Pm, and so for cracks within that distance from the interface ( e.g., t < 100 Pm in Fig. 1), the size of the displacement field necessary to extract the stress intensity factor through the Westergaard expansions extends into the material across the interface. Expansions from the method of fundamental solutions [2] are used to incorporate displacements from material across the interface, and these expansions are coupled to those from the Westergaard expansions by imposing continuity conditions across the interface. The process is verified with synthetic data generated from a simple boundary element model. It is then applied to a test specimen (Fig. 1) comprising a Cu-W bimaterial composite. Finite elements results on the same geometry are then used to show that residual stresses play a large role in determining the crack driving force and trajectory, but that this effect is mitigated by the presence of plasticity.

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FIGURE 1. Four point bend specimen used in fracture experiments and numerical simulations.

References 1.

Sanford, R. J. ., Mechanics Research Communications, 6, 289-294, 1979

2.

Fairweather, G, and Karageorghis, A. Advances in Computational Mathematics, 9, 69-95, 1998.

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DEFORMATION AND FAILURE PROCESSES OPERATING IN ULTRA-FINE GRAIN METALS K. Hattar, I. M. Robertson, J. Han1, T. Saif1, S. J. Hearne2 and D. Follstaedt2 Dept. of Materials Science and Engineering, University of Illinois, Urbana IL 61801. 1Dept of Mechanical and Industrial Engineering, University of Illinois, Urbana IL 61801. 2Sandia National Laboratory, PO Box 5800Albuquerque, New Mexico, NM 87185 [email protected], [email protected], [email protected], [email protected], [email protected], [email protected] Nanograined metallic materials typically have higher yield and tensile strength, lower stiffness and better resistance to environmental degradation and wear than their large-grained analogs. We currently lack an understanding of how the fundamental deformation processes change as a function of grain size and therefore we interpret the macroscopic response by scaling-down the processes that operate in large-grained systems. The disparity between model predictions and experiment suggest we have yet to include the necessary physical processes. Molecular dynamics computer simulations of deformation and failure processes in nanograined materials have been used extensively to determine the deformation processes. It has been suggested that for high stacking-fault energy materials such as Al, the deformation mode changes from perfect to partial dislocation processes at a grain size of about 18 nm and to grain boundary mediated processes at smaller grain sizes. A similar transition occurs in low stacking-fault energy materials except no perfect dislocations are involved in the deformation mechanism. These results have been summarized in the form of a deformation map[1]. Farkas et al.[2], using MD simulations, have shown that both intergranular and transgranular fracture can occur and that the fracture process is accompanied by dislocations and grain boundary mechanisms. Intergranular fracture occurs through the linkage of nanocracks that form at triple junctions. They also show that grain boundaries perpendicular to the crack propagation direction can arrest the crack. These deformation and failure processes remain to be validated experimentally. Using an in-situ TEM straining device[3], fabricated from silicon using microlithographic techniques, it is possible to observe the deformation processes and simultaneously measure the load and displacement for free-standing thin metallic films with a columnar grain structure. The deformation and failure processes for Al and Au films of different thicknesses have been investigated[4] and the results from these studies are the subject of this presentation. For 125 nm thick Al films the average grain size was 130 nm but grains as small as 35 nm and as large as 420 nm were also present. During tensile testing, no general plasticity was observed in the gauge section and the fracture mode was intergranular with no accompanying dislocation activity. Sharp cracks advanced rapidly through regions containing small grains but they were arrested when a properly oriented large grain was encountered. The crack blunted by extending along the boundary of the arresting grain. During this blunting process dislocation emission and deformation twinning occurred in vicinal grains. Figure 2a shows a dislocation structure existing in only a few grains along the fracture surface. Emission of perfect and partial dislocations occurred from regions of the grain boundary and not from the crack tip. Voids or microcracks nucleated and grew on grain boundaries ahead of the arrested crack, and crack advance occurred through linkage of the microcracks with the primary crack. It was found that the progress of the arrested crack could be halted in favor of nucleating and propagating a new crack. For thicker Al films, dislocation activity occurred in the gauge section prior to the initiation of the failure crack. The failure mode was again intergranular. It was accompanied by dislocation

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activity that extended several grains into the gauge section, see Figure 2b. In contrast to the thinner Al film in which the failure crack was perpendicular to the tensile axis, the failure crack in the thicker film was at 45º. The thick Al film showed similar behavior to a 200 nm thick Au film. The possible reasons for the difference in behavior (length scale effect, grain boundary distribution and type, grain boundary and film chemistry, etc) will be discussed in this presentation.

FIGURE 2. Dislocation structure along fracture surface of a) 125 nm and b) 500 nm thick Al film deformed in tension at room temperature.

References 1.

Yamakov V., Wolf D., Phillpot S.R., Mukherjee A.K., and Gleiter H., Nature Mater. vol. 3, 43 (2004).

2.

Farkas D., Van Swygenhoven H., and Derlet P.M., Phys. Rev. B vol. 66, 060101 (2002).

3.

Haque M.A. and Saif M.T.A., Sensors and Actuators, A vol. 97-98, 239 (2002).

4.

Hattar K., Han J., Saif M.T.A., and Robertson I.M., J. Mater. Res. vol. in press (2005).

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SIMULATION OF CROSS-SECTIONAL NANOINDENTATION IN INTERCONNECT STRUCTURES WITH COHESIVE ELEMENTS D. Gonzalez, J. Molina, I. Ocana, M. R. Elizalde, J. M. Sanchez. J. M. Martinez-Esnaola, J. Gil-Sevillano, G. Xu1, D. Pantuso1, T. Scherban2, B. Sun1, B. Miner1, J. He1 and J. Maiz1 CEIT and TECNUN (Universidad de Navarra), P. Manuel Lardizabal 15, 20018 San Sebastián, Spain 1Intel Corporation, Hillsboro 97124 (OR), USA [email protected] The thermo-mechanical robustness of interconnect structures is a key reliability concern for integrated circuits. The miniaturization process and the package/silicon interaction result in an increase of the thermal stresses whilst new low-k materials with degraded mechanical properties are used, increasing the likelihood of adhesion failure in the interconnect structures. In this context, the cross-sectional nanoindentation technique (CSN and MCSN) [1-5] has been recently developed by the authors as a technique to characterize the interfacial adhesion of real interconnect structures. A Berkovich indenter is used to initiate fracture in the silicon substrate near the interconnect structure. As a result, the cracks propagate through this structure, preferentially along the weakest interfaces. An example is shown in Fig. 1, illustrating the outcome of the experiment for two identical interconnect structures, where the material at the interface indicated by the arrows was varied. The cracks generated in the corners of the indents propagate through the interconnect structure and are finally arrested by the ductile copper capping. The amount of delamination of the interface of interest could be directly used as a qualitative quick monitor of good/bad adhesion in this case.

FIGURE 1. Examples of the MCSN technique applied to different structures: (a) good adhesion and (b) bad adhesion of the interface indicated by the arrows. In this work, these experiments have been modeled using the commercial finite element program ABAQUS. The final goal is to obtain a numerical tool capable of predicting crack propagation and crack path in real complex interconnect structures. This paper shows the calibration of the model by comparison of the simulations with the experimental results obtained on test samples. In order to incorporate the fracture behaviour of the various materials and interfaces present in the structure into the numerical analysis, user-defined elements have been created based on the cohesive zone theory, which specifies the traction-separation law at the crack front. The cohesive law has been directly derived from a potential function. Based on this theory, a non-standard finite

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element (referred here as “cohesive element”) has been implemented as a user defined subroutine in the general purpose finite element program ABAQUS. The CSN experiments give insight into the preferred crack paths, as shown in Fig. 1. The experiments are also used to calibrate the model as follows. Various possible crack paths are introduced in the model through cohesive elements characterised by their fracture energy and strength. As a function of these fracture properties, different crack paths are predicted in the numerical simulations. By comparison of the numerical predictions of applied load and crack path with the experimental results, the unknown cohesive fracture properties of the relevant interfaces can be extracted. Fig. 2 shows the numerical simulation of a particular MCSN experiment. The model is able to predict crack path and sudden changes in direction (kinking) depending on the combination of mechanical and fracture properties of the materials and interfaces, as observed in the experiments.

FIGURE 2. FEM modelling result of a particular MCSN experiment.

References 1.

Sánchez, J.M., El-Mansy, S., Sun, B., Scherban, T., Fang, N., Pantuso, D., Ford, W., Elizalde, M.R., Martínez Esnaola, J.M., Martín Meizoso, A., Gil Sevillano, J., Fuentes, M., Maiz, J., Acta Materialia, vol. 47, 4405-4413, 1999

2.

Elizalde, M.R., Sánchez, J.M., Martínez-Esnaola, J.M., Pantuso, D., Scherban, T., Sun, B., Xu, G., Acta Materialia, vol. 51, 4295-4305, 2003

3.

Scherban, T., Pantuso, D., Sun, B., El-Mansy, S., Xu, G., Elizalde, M.R., Sánchez, J.M., Martínez-Esnaola, J.M., International Journal of Fracture, vol. 119/120, 421-429, 2003

4.

Molina, J., Ocaña, I., González, D., Elizalde, M.R., Sánchez, J.M., Martínez-Esnaola, J.M., Gil Sevillano, J., Scherban, T., Pantuso, D., Sun, B., Xu, G., Miner, B., He, J., Maiz, J. In Proceedings of the 11th International Conference on Fracture, Topic 14: Electronic Materials, Paper 4002, 2005

5.

Ocaña, I., Molina, J., González, D., Elizalde, M.R., Sánchez, J.M., Martínez-Esnaola, J.M., Gil Sevillano, J., Scherban, T., Pantuso, D., Sun, B., Xu, G., Miner, B., He, J., Maiz, J., In Mater. Res. Soc. Symp. Proc., Vol. 863 © 2005 Materials Research Society, B1.2.1-B1.2.6, 2005

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FRACTURE BETWEEN TWO SELF-ASSEMBLED MONOLAYERS K. M. Liechti and D. Xu University of Texas, Aerospace Engineering and Engineering Mechanics 210 E. 24th Street, WRW 110C 1 University Station, C0600 Austin, TX 78712-0235 [email protected] The objective of this work was to determine the interfacial toughness of .two silicon surfaces that were each coated with self assembled monolayers (SAMs) and pressed together. The SAMs were mixtures of two species. Each SAM made the same covalent bond with the Si, but differed in the terminal group at the other end on the molecule. One of the SAMs had a very active end group whereas the other did not. As a result, the degree of adhesion between the surfaces was controlled by the areal density of the active end group. Previous studies [1-4] of fracture control using SAMs used specimens in which the SAMs were deposited on a suitable substrate and interacted at the other end with an epoxy. Thus the current study removes the epoxy with a view towards simplifying interactions. Zhuk et al. [1] used methyl (CH3) and carboxy (COOH) terminal groups on 15-carbon alkanethiols to control adhesion between gold and epoxy. The thermodynamic work of adhesion of epoxy on the coated surface was linearly proportional to the COOH/CH3 fraction in solution up to about 80%, and was constant thereafter. A series of superlayer fracture experiments revealed that the interfacial fracture toughness increased strongly with the thermodynamic work of adhesion. The rate of toughening increased with the work of adhesion, suggesting that more and more plastic dissipation was excited in the epoxy layer. Kent et al. [2] and Reedy et al. [3] used mixed monolayers of dodecyltrichlorosilane (DTS) and bromo-undecyltrichlorosilane (BrUTS) to control adhesion between aluminum and epoxy. Both make strong covalent bonds with the aluminum. The methyl terminal group on the DTS again makes weak, non-polar interactions with the epoxy. The authors indicate that the BrUTS forms an alkyl ammonium bromide compound with the amine crosslinker that was used to cure the EPON 828 epoxy. As a result, an ionic bond was achieved with the epoxy through R-NH2+Br-R’ bonds. Between 10 and 20% bromine termination, there was a strong increase in the tensile and shear strengths of the aluminum/epoxy interface as determined by cruciform and napkin ring shear experiments. Asymmetric double cantilever experiments were used to determine the toughness of the interface, which increased linearly with the bromine fraction. The linear relationship was ascribed to the linear increase in the thermodynamic work of adhesion with bromine fraction [2]. In contrast to the gold/epoxy experiments, any plastic dissipation effects were apparently the same for all bromine fractions, even though the toughness of the aluminum/BrUTS/DTS/epoxy was much higher than that of the gold/COOH/CH3/epoxy interface in moist environments. The fracture mode-mix in the asymmetric double cantilever beam experiments was -8° at a reference length of 10 Pm, whereas it was about 50° in the superlayer experiments. In working with the same mixture of SAMs and an epoxy, Mello and Liechti [4] found that increasing the bromine content altered the fracture mechanism and increased the interfacial toughness of a sapphire/epoxy interface. The tractionseparation law for the sapphire epoxy interface became dependent on mode-mix with the addition of a SAM to the sapphire surface. This was in contrast to the uncoated sapphire specimens whose traction-separation law was independent of mode-mix, had a 50% higher maximum traction and a ten-fold lower critical separation. It seemed that the bromine interaction with the epoxy was high enough to pull epoxy chains from the epoxy matrix.

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In the current study, laminated beam specimens were fabricated by functionalizing Si(111) surfaces of small Si beams with mixture self-assembled amine and carboxylic acid monolayers of low defect density. Each areal density of hydrogen bonds distinguished a separate monolayer adhesive. The beams were prepared and then pressed together in a controlled environment The laminated beams were then placed in the miniaturized loading device and loaded in displacement control while the reactive loads were measured. Crack opening displacements were be measured by crack opening interferometry [5] using an infrared microscope. As currently configured, the interferometer measures crack opening displacements (COD) to with a resolution of 30nm, 300nm from the crack front. The fracture surfaces were probed via XPS, ISS and AFM. The spectroscopic data was compared with that generated following formation of the monolayer adhesives and used to determine the locus of failure or the weak link in the various monolayer adhesives that are considered. AFM was used to determine fracture surface topography. At the time of abstract submission, preliminary and encouraging results have been obtained. These are expected to mature by the time the conference proceeding paper is due.

References 1.

Zhuk, A. V., Evans, A. G., Hutchinson, J. W. and Whitesides, G. M., J. Mater. Res., 13, 35553564, 1998.

2.

Kent, M. S., Yim, H., Sorenson, J., Matheson, A., Reedy, E. D. and Majumdar, B., Proceedings of the 23rd Annual Adhesion Society Meeting, 323-325, 2003.

3.

Reedy, E.D., Kent, M.S. and Moody, N. R. Proceedings of the 23rd Annual Adhesion Society Meeting, 502-504, 2003.

4.

Mello, A. W. and Liechti, K. M. J. Appl. Mech., to appear 2005.

5.

Liechti, K. M. Chapter 4 in Experimental Techniques in Fracture, (ed. J. S. Epstein), VCH Publishers, New York, 1993.

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NANOTUBE NANOACTUATOR Min-Feng Yu, Jie Hu, Zhaoyu Wang and Abhijit Suryavanshi Department of Mechanical and Industrial Engineering, University of Illinois at UrbanaChampaign, Urbana, IL 61801, USA. [email protected] Having provided the foundation for sensing and actuation applications, piezoelectricity has been intriguing subjects for many studies. The application of piezoelectric materials for high-resolution actuation and positioning in scanning probe microscopy has enabled the manipulation and characterization of matters at nano- and atomic scale. Its application in high-resolution sensing has allowed unprecedented ease in control and measurement of force and displacement. However, as an indispensable part for any technology development, the study of nanoscale sensor and actuator that make use of piezoelectricity and that take advantage of the significant progress in the development of nanomaterials is still lacking. The inherent unique properties of nanomaterials possess potentially better engineering figure of merits for developing new materials and creating new devices with better performance [1]. Here, we report the study of piezoelectricity in BN nanotube, which reveals that BN nanotube is piezoelectric. The study corroborates directly with a recent theoretical study by Mele and Král predicting the existence of piezoelectricity in BN nanotube [2]. BN nanotube, structurally similar to carbon nanotube, was made through high temperature chemical vapor deposition growth [3]. Its mechanical rigidity was found to be comparable to carbon nanotube (Young’s modulus around 1 TPa), and its lattice structure was found to be mostly zigzag. The diameter of the BN nanotubes was between 30 and 150 nm, and its length up to tens micrometers. Most of the synthesized BN nanotubes were found to be high quality, as shown in Fig. 1. We prepare a BN nanotube sample for atomic force microscopy (AFM) study by depositing the nanotubes on an Au coated conductive substrate.

FIGURE 1. Transmission electron microscopy images showing (a) the multi-walled structure and (b) the highly graphitized lattice structure of an BN nanotube. Piezoresponse force microscope (PFM), one of the new techniques developed from AFM, was applied to study the local piezoelectric response in BN nanotube based on the converse piezoelectric effect. For the measurement, an ac testing signal is applied between a conductive AFM probe (which is in contact with the top surface of an individual BN nanotube) and the conductive substrate (which is in contact with the back surface of the BN nanotube). The induced structural deformation is then directly measured from the deflection of the AFM cantilever with the aid of high sensitivity electronics. Shown in Fig. 2 is the measured piezoelectric response from a selected spot on a BN nanotube. A linear response of the piezoresponse amplitude on the applied

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ac amplitude is clearly seen. This response corresponds to a piezoelectric coefficient of 0.09 pm/V for this BN nanotube. The piezoelectric response is also found to increase with the increased DC bias additionally applied on the BN nanotube, as shown in Fig. 3. The piezoelectric coefficient increases from 1.4 pm/V at DC bias of 2 V, to 1.9 pm/V at 5 V and to 3.4 pm/V at 10 V. Such dependence is indicative of the improved polarization alignment in BN nanotube according to the traditional point of view on piezoelectricity. However, for BN nanotube, to understand the exact origin of the polarization and the observed piezoresponse behavior calls for further investigation.

FIGURE 2. (a) An AFM image showing a 63 nm diameter BN nanotube on an Au coated substrate, (b) the measured local piezoelectric response from the BN nanotube.

FIGURE 3. The dependence of the piezoelectric response on the applied DC bias. In this talk, our extensive study on the piezoelectric behavior of BN nanotubes will be further detailed, which includes the study of the piezoresponse phase change behavior related to the polarization state, the converse piezoresponse behavior under mechanical load and the direct piezoelectric effect of individual BN nanotubes.

References 1.

R. H. Baughman, et al., Science, 284, 1340 (1999).

2.

E. J. Mele and P. Kral, Phys. Rev. Lett. 88, 056803 (2002)

3.

C. C. Tang, Y. Bando, and T. Sato, Chem. Phys. Lett. 362, 185 (2002).

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NANOCRACK DETECTION IN VIBRATING NANOWIRES R. Ruoff, L. Calabri, N. Pugno, X. Chen, W. Ding and K. Kohlhaas Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA Department of Structural Engineering and Geotechnics, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Italy Department of Mechanics and Industrial Technology, Universita degli Studi di Firenze, Via di Santa Marta 3, 50139 Firenze, Italy [email protected], [email protected], [email protected] Crystalline boron (B) nanowires (NWs) have been synthesized by the CVD method with preformed metal catalyst particles. We have experimentally investigated their dynamical resonance (i) and mechanical strength (ii). Both the two independent methods suggest the possible presence of nanocracks in the tested B NWs. Nanocrack detection can in principle be achieved by analytical calculations quantifying crack position and depth. (i) The nanodynamical experimental apparatus is summarized in Fig. 1, [1]. The mechanical resonances of cantilevered B NWs were excited and the resonance peak frequencies measured, Fig. 2. Shifts in the natural frequencies were observed, suggesting the possibility of the presence of nanocracks; other possible shift causes, such as intrinsic NW curvature, non-ideal clamps, presence of spurious masses, large displacements, etc., are also discussed. Assuming the existence of a nanocrack, analytical calculations were performed to quantify its depth and position based on the measured frequency shifts. (ii) A newly developed and rapid electron beam induced deposition method was used to clamp the B NWs and test them in tension inside an SEM with a home-built nanomanipulator [2]. Highresolution SEM images were acquired at each loading step, and two independent methods of analysis of each image were used to obtain the corresponding tensile load. The B NW geometries were measured by TEM after the tests. The stress vs strain, Young’s modulus, and tensile strength of the B NWs were obtained through data analysis. The strength measurements strongly suggest the presence of nanocracks in the B NWs. Assuming the existence of a nanocrack, placed at the fracture section, its depth is quantified by applying Quantized Fracture Mechanics [3] starting from the measured fracture strengths. The possibility of detecting nanocracks through mechanical resonance of nanostructures is thus exemplified. The challenge on the experimental side in the future will be ensuring that other contributors to shifts in mechanical resonance, are not present or have a strong enough different functional dependence, that the nanocrack contribution can be “uncovered” if present. We gratefully acknowledge the grant support from the NSF (#020079; #030450); ONR #N000140210870 (support for W. Ding), and NASA BIMat URETI # NCC-1-02037 (support for X. Chen).

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FIGURE 1. Experimental apparatus for driving mechanical resonance of NWs.

FIGURE 2. Mechanical resonance of a curved BNW naturally held at an AFM cantilever tip without any deliberate fabrication of a clamp.

References 1.

Chen, X., Zhang, S., Wagner, G., Ding, W., Ruoff, R.S, Journal of Applied Physics, vol. 95(9), pp. 4823-4828, 2003.

2.

Yu, M.F., Lourie, O., Dyer, M.J., Moloni, K., Kelly, T.F., Ruoff, R.S., Science, vol. 287, 637640, 2000.

3.

Pugno, N.M., Ruoff, R.S., Philosophical Magazine, vol. 84/27, 2829-2845, 2004.

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FRACTURE OF ATOMIC LAYER DEPOSITED NANOLAMINATE FILMS N. R. Moody, J. M. Jungk1, T. M. Mayer1, R. A. Wind2, S. M. George2 and W. W. Gerberich3 Sandia National Laboratories, Livermore, CA 94550 USA 1Sandia National Laboratories, Albuquerque, NM 87158 USA 2University of Minnesota, Minneapolis, MN 55455 USA 3University of Colorado at Boulder, Boulder, CO 80309 USA [email protected] Strength, friction, and wear are dominant factors in the performance and reliability of materials and devices fabricated using microsystem technologies. While adequate for some applications, asfabricated strength and wear properties are insufficient for use of these devices in many dynamic applications. Applying films is one method to enhance device performance and reliability. Atomic Layer Deposition (ALD) is ideally suited for this application as it creates conformal and potentially stress free films. [1] Of particular interest are ALD tungsten and alumina films where bulk crystalline counterparts exhibit high hardness and good frictional resistance. However, recent studies on single layer ALD tungsten films show they exhibit a pronounced susceptibility to channel cracking and delamination while single layer ALD alumina films exhibit significantly lower hardness than desired. [2,3] We therefore began a study of atomic layer deposited nanolaminate-based composites using alternating layers of nanocrystalline tungsten and amorphous aluminum oxide nanolaminates to determine if properties could be tailored to meet microdevice needs. [4] The films were deposited in four, eight, and sixteen bi-layer systems to form 100 nm thick films on silicon substrates. In all samples, the alumina layer thickness was held constant at 4 nm and the metal layer was adjusted to fill the remaining volume. (Table 1) Nanoscratch techniques were then employed to evaluate the resistance to fracture of each film system at loads characteristic of microsystem operation. These tests using a 50 nm radius Berkovich diamond tip revealed a strong reverse length-scale effect where an increasing number of bilayers led to a decrease in fracture resistance. (Figure 1) Unlike the results from single ALD tungsten films where scratch tests initiated extensive channel cracking and film debonding, there was no widespread delamination in the nanolaminate films. A micromechanical method, based on the crack lengths induced by the nanoscratch tests and applied loads, was employed to provide a first order estimate of fracture toughness for the nanolaminate films. [5] The stress intensity solution for a mode I crack under these conditions is given by, K Ic

2 pb

b

1/ 2 a

Sa

sin

1 b

a

(1)

where p is the pressure opening the crack, b is the radius of the indenter in the groove, and a is the half-crack length. Using this relationship, the fracture toughness for each nanolaminate film was determined from the scratch track widths, crack lengths, and nanoscratch test loads. The values are given in Table 1. These results show that a maximum in the fracture resistance exists between the single layer blanket film of ALD tungsten and scale of bilayer nanolaminate structure of ALD tungsten and ALD alumina thereby providing a means to tailor wear resistant film performance. This work was supported by Sandia National Laboratories, a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company for the United States Department of Energy's

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National Nuclear Security Administration under contract DE-AC04-94AL85000. WWG also thanks NSF for its support.

FIGURE 1. Scratch fractures in single layer and bi-layer nanolaminate films. [2,4]

Table 1. Single layer and bi-layer film properties Film SL W 4 BL 8 BL 16 BL

Alumina Thick- Tungsten Thickness Volume Fraction ness (nm) (nm) Tungsten 200 100 4 21.1 84.1 4 8.4 67.7 4 2.1 34.4

Fracture Toughness MPa-m1/2 0.33 0.46 0.35 0.30

References 1.

Mayer, T.M., Elam, J.W., George, S.M., Kotula, P.G. Goeke, R.S., Applied Physics Letters 82, pp. 2883-2885 (2003).

2.

Moody, N. R., Jungk, J. M., Mayer, T. M., Wind, R. A., George, S. M., Gerberich, W. W., Proceedings ICF11, to be published.

3.

N. R. Moody, Sandia National Laboratories, Livermore, CA, unpublished research.

4.

Jungk, J. M., Moody, N. R., Mayer, T. M., Wind, R. A., George, S. M., Gerberich, W. W., Proceedings ICF11, to be published.

5.

Hoehn,J. W., Venktaraman, S. K., Huang, H., Gerberich, W. W., Mater. Sci. Engng, A192/ 193, pp. 301-308 (1995).

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INFLUENCE OF MICROSTRUCTURE, STRENGTH AND ADHESION ON AU ELECTRODEPOSITS Nancy Yang, J. Kelly, T. Headley and C. San Marchi Sandia National Laboratories [email protected] Electrodeposition is extremely effective for applying uniform thin metal coatings on a complex microdevices, which otherwise are inaccessible by other coating techniques. We are actively developing electrical contact coatings for Ni-based microsystem using the LIGA* microfabrication process 1-2, Fig. 1. The requirements for the coating are high strength, wear resistance and good adhesion to the Ni substrate. The candidate coating that meets these criteria is electrodeposited Au coating (referred to here as Hard Au), plated from a commercial sulfite electrolyte with organic additive (Technigold 25E). In this study, we focus on the metallurgical factors that determine the strength of the Au coating material and influence adhesion of the Au coating to the Ni microsystem substrate. Experimental results show that this Hard Au derives it high strength from nano-sized features of its microstructure (Fig. 2). The hardness of the Hard Au is about 2 GPa, which is about 4 times harder than coatings plated without the organic hardening additive from gold sulfite electrolytes (Fig.3). Hardness and fracture resistance of the coatings are highly dependent on the combination of the size of the microstructure and the stress in the coating. The nanocrystallite size (determined from XRD peak broadening) is 50 nm. In addition, the microstructure exhibits small spherical pores 10nm in diameter (Fig. 3) in the bulk and clusters of these pores along the Au-Ni interface. These nanopores are characteristics of the Hard Au coatings, presumably related to the hydrogen generation and entrainment during electroplating. The resultant microstructure of the Hard Au coating is dictated by the concentration of the organic hardening additive in the electrolyte and can be controlled to some extent by varying the concentration. Hard Au coatings produced from electrolyte with the highest concentration of hardening additive feature a significantly more complicated nanocrystalline microstructure, with more twinning and more porosity, in addition to higher hardness. As a result these coatings have more residual stress and are more susceptible to delamination from the substrate. In this presentation, we will discuss correlation between microstructure and plating variables. The effect of microstructure on coating strength and adhesion to the Ni-substrate will also be discussed.

FIGURE 1. Contact spring made by LIGA* microfabrication process

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FIGURE 2. Typical microstructure of Hard Au

FIGURE 3. Hardness as a function of hardening additive in Hard Au electrodeposits.

References 1.

J. J. Kelly, N. Yang, T. Headley and J. Hachman, J. electrochemical Society, 150 (6) C445C450, 2003.

2.

C. San Marchi, N. R. Moody, M. J. Cordill, G. Lucadamo, J. J. Kelly, T. Headley, N. Yang: "Structure-property relationships of Au films electrodeposited on Ni", Materials Research Society Symposium Proceedings; 2004; v.821, p.5-10.

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FRACTURE OF SUBMICRON THIN METAL FILMS DURING CYCLIC LOADING S. Eve, D. Wang, C. Volkert, N. Huber and O. Kraft Institut für Materialforschung II, Forschungszentrum Karlsruhe and Institut fur Zuverlässigkeit von Bauteilen und Systemen Universitat Karlsruhe (TH) Forschungszentrum Karlsruhe, Postfach 3640, 76021 Karlsruhe, Germany [email protected] One current trend in microelectronics and MEMS is to develop micro devices based on plastic substrates. This allows for new applications, for instance, by integrating such flexible devices into the personal environment like textiles. Furthermore, the use of polymers offers a high potential for cost effective production for mass products. Depending on the application, devices on plastic substrates are fabricated by forming the polymer, and depositing and patterning one or several thin films onto the substrate. One reliability issue in such devices is the stretchability of the thin films during mechanical and/or thermal loading conditions. Under monotonic loading, however, it has been shown that cracking of metal films on compliant substrates only occurs, when large strains (>10%) are reached. In contrast, cyclic mechanical or thermal loading conditions with typical strain ranges between 0.1% and 1% lead to damage formation such as cracking, surface roughening and delamination [1,2]. For instance, a micro-spectrometer with a 400 nm thick gold film on 1.28 mm thick PMMA substrate shows after 5 thermal cycles between -40 to +55°C severe damage. The thin metal film and the substrate have very different thermal expansion coefficients. When applying a temperature change, this results in high residual stresses and in cyclic deformation leading to cracking, roughening, and also delamination of the film, as observed by scanning electron microscopy, limiting the device lifetime. The stability of the couple metal-film/polymer-substrate during thermal cycling and a good comprehension of the relevant damage mechanisms are essential for the prediction and improvement of the reliability of such systems. This includes an acceleration of the fatigue testing, since standard thermal cycling tests often used for reliability assessments are restricted to a small number of cycles and may take several days. Therefore, we employ mechanical methods to characterize the fatigue behavior of thin metal films on an elastic substrate. These methods include uniaxial tensile loading of metal films on polyimide substrates as described in [2]. Beside that, we have developed a fatigue experiment, which allows for testing in an equi-biaxial loading condition. This is to simulate the strain state that occurs during a thermal cycle in a given temperature range. It is based on the ring-on-ring test; the specimen is supported by a ring and a concentric ring of smaller diameter loads the opposite face. It produces a biaxial tensile strain and stress state inside the smaller ring. For the film on substrate specimen, support and loading rings are applied on both sides of the specimen in order to allow the mechanical simulation of thermal fatigue test with alternating tensile and compressive strain in the film. This new experimental method has been used to characterize the fatigue behaviour of films for different material combinations; i.e. aluminum and gold as the film materials sputtered onto PolyMethylMethAcrylate (PMMA) and PolyCarbonate (PC) for the substrate. In both type of tests, uni-axial as well as equi-biaxial loading of the film/substrate composites, the substrate material is expected to deform elastically while the film may undergo plastic deformation in both tension and compression. Owing to this sample structure, the film stress cannot be determined from the externally applied load. However, the stress-strain behavior of the

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films has been analyzed for several samples using in-situ X-ray diffraction during uni-axial straining of the samples. The development of the fatigue damage has been studied during interrupted tests, the samples were investigated using various techniques, including optical microscopy, scanning, and transmission electron microscopy (SEM, TEM) as well as focused ion beam microscopy (FIB). Quite recently, a study on the effect of length scale (both film thickness and grain size) on fatigue-induced damage morphology in Cu films revealed that the dimensions of the fatigue extrusions decreased with decreasing film thickness from 3.0 µm to 200 nm and that the characteristic dislocation structures, such as those found in bulk fatigued metals, were only found in the largest grains of the 3.0 µm thick film [3,4,5]. In contrast, only individual dislocations were observed in films thinner than 1 µm. For a deeper understanding of these mechanisms, a more detailed investigation of the influence of film thickness in the regime of 50 to 500 nm on the fatigue mechanisms is currently being performed.

References 1.

Kraft, O., Schwaiger, R., and Wellner, P., Material Science. Engineering A, vol. 319-321, 919, 2001

2.

Mönig, R., Keller, R.R., and Volkert, C.A., Review of Scientific Instruments, vol. 75, 49975004, 2004

3.

Schwaiger, R., Dehm, G., and Kraft, O., Philosophical Magazine A, vol. 83, 693, 2003

4.

Zhang, G.P., Schwaiger, R., Volkert, C.A., and Kraft, O., Philosophical Magazine Letters, vol. 83, 477, 2003

5.

Zhang, G.P., Schwaiger, R., Volkert, C.A., Arzt, E., and Kraft, O., Journal of Materials Research, vol. 20, 201-207, 2005

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MICROMECHANICS OF DAMAGE EVOLUTION IN SOLID PROPELLANTS N. Aravas1, F. Xu and P. Sofronis University of Illinois at Urbana-Champaign, Department of Mechanical and Industrial Engineering 158 Mechanical Engineering Building 1206 West Green Steet Urbana, IL 61801 1Department of Mechanical and Industrial Engineering University of Thessaly, Volos, Greece. [email protected] Solid propellants are composite materials with complex microstructure. In a generic form, the material consists of polymeric binder, ceramic oxidizer, and fuel particles (e.g. aluminum). Damage induced by severe stress and extreme temperatures is manifested in particle cracking, decohesion along particle/polymer interfaces, void opening or even polymer crazing at low temperatures and inert propellants. In this work, the effect of damage due to void formation on the material macroscopic response is investigated from a solid mechanics perspective. First, issues related with the constitutive behavior of the individual phases in the absence of damage are reviewed. Next, with the use of rigorous composite homogenization theory, a macroscopic constitutive law is proposed that accounts for continuous void nucleation and growth upon straining. Numerical calculations for the uniaxial tension test capture most of the experimentally observed features, namely an initial elastic regime, a viscoplastic regime in which void formation competes with hardening in the matrix, a softening regime, and a macroscopic volume expansion which continuously increases with straining.

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DEFORMATION AND FAILURE MECHANISMS IN METALLIC NANOLAYERED COMPOSITES R. G. Hoagland, J. P. Hirth, and A. Misra Los Alamos National Laboratory, Los Alamos, NM 87545 [email protected] Layered composites composed of two or more dissimilar metals can be easily created with precisely controlled layer thickness (to within one atomic layer) by various vapor deposition techniques. For equithickness composites with layer thicknesses greater than 100 nm, typically, flow strengths display a Hall-Petch type dependence on layer thickness, i.e., VY = kh-1/2 + V0, where h is the layer thickness, k the Hall-Petch constant and V0, a background strength or friction stress. For composites with thinner layers this relation is no longer obeyed, but instead the strength becomes less dependent on h and reaches a maximum at an h of about 1 – 5 nm, as shown in Figure 1, Misra, et al [1]. Although, at maximum, the strength is lower than predicted by Hall-Petch, these materials are still very strong, with flow strengths exceeding 1 GPa and, in some cases, approaching the theoretical shear strengths of the constituents. Even at these high strength levels the materials are deformable, plastically. Cu/Nb, for example is easily rolled to large reduction in thickness except as noted below, Misra [2].

Figure 1. Flow strength, represented here in terms of hardness, of several multilayered composites increases as the layer thickness decreases. In this graph, the abscissa is h-1/2 and so in the linear portions on the left side of the graph, the data obey a Hall-Petch relation. Peak strength occurs in the range of 1 - 5 nm. We discuss the origins of the strengthening mechanisms in these materials. Important differences exist in the types of operative strengthening mechanisms between systems where the two components have the same crystal structure and are epitaxially related and systems where the components have different crystal structures. In the former case, lattice mismatch, that creates large coherency stresses with alternating signs from one layer to the next, is primarily responsible for strength, Hoagland et al [3]. This observation suggests a simple description of maximum strength in terms of lattice mismatch. Other factors include modulus mismatch and a form of work hardening caused by accumulation of residual dislocations at interfaces due to repeated penetration of the interfaces by the passage of slip from one material into another, Henager et al [4].

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In the latter case where the component materials have different crystal structure, the interfaces, if weak in shear, attract glide dislocations. Once in the interface, these glide dislocations become trapped because of dislocation reactions or core spreading. These effects reduce the stresses near the dislocation core making it less able to nucleate, by whatever means, a glide dislocation in the neighboring crystal. This reduces the ease of transport of slip across the boundary thereby making the interface an effective obstacle to slip. We show evidence, derived from atomistic modeling, of dislocation – interface interactions, Hoagland et al [4]. We discuss an elasticity model that enables prediction of the magnitudes of the interactions. This model shows that some types of dislocations interact much more strongly with shearable interfaces than others. The model also suggests that, as the layer thickness is reduced, a greater fraction of existing glide dislocations will become trapped in interfaces leading to dislocation starvation. This is consistent with observations of greatly reduced ductility during rolling of Cu/Nb composite films with layer thicknesses of less than 4 nm. Acknowledgements: The authors are pleased to acknowledge the support of this work by the U. S. Dept. of Energy, Office of Basic Energy Sciences.

References 1.

Misra, A, Hirth, JP, and Kung, H, Phil. Mag. A, vol. 82, 2935, 2002.

2.

Misra, A. Zhang, X., Hammon, D., and Hoagland, R. G. , Acta Mat., vol. 53, 221, 2005.

3.

Hoagland, R. G. Mitchell, T. E., Hirth, J. P., and Kung, H., Phil. Mag., vol. 82, 643, 2002.

4.

Henager, C. H., Kurtz, R. J., and Hoagland, R. G., Phil. Mag., vol. 84, 2277, 2004.

5.

Hoagland, R. G., Kurtz, R. J., and Henager, C. H., Scripta Mat., vol. 50, 775, 2004.

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DISLOCATION SOURCE SENSITIVITY OF PLASTICITY AND FRACTURE IN TUNGSTEN J. E. Talia and R. Gibala Department of Mechanical Engineering Wichita State University Wichita, Kansas USA [email protected] Department of Materials Science and Engineering University of Michigan Ann Arbor, Michigan USA [email protected] We have examined the effect of dislocation sources introduced on the surface of single-crystal and polycrystalline tungsten on the plastic flow and fracture behavior at temperature in the range 77 K to 590 K. The experiments utilize the phenomenon of surface film softening observed in many body-centered cubic metals, such as observed by Sethi and Gibala [1-3]. In investigations like these, it is observed that application of surface films of approximately 50-200 nm in thickness to bcc metal substrates can decrease the yield and flow stress, increase the ductility, and correspondingly reduce the large temperature dependence of the yield and flow stress at homologous temperatures T below approximately 0.15Tm, where Tm is the absolute melting temperature. The large temperature dependence of the yield and flow stress at T/Tm < 0.15 is associated with the high Peierls-Nabarro stress of screw dislocations in the bcc structure. By contrast, edge dislocations in bcc metals have high mobility at low temperatures. Mechanistically, it has been shown that for the coated materials under applied stress, large densities of mobile edge dislocations can be generated in the substrate metal at the film-substrate interface. These edge dislocations can move into the substrate and effect plasticity at the reduced flow stresses observed. In this investigation, additional use is made of surface modification (roughening) of the substrate surface to afford control over the density of potential dislocation sources at the film-substrate interface in coated materials. The results are described below. The experiments have been done on high purity (> 99.999%) single crystals with an approximate [213] tensile axis orientation that were grown by triple-pass electron-beam zone melting of undoped polycrystalline tungsten in a vacuum of less than 5 x 10-5 Pa. These materials were machined into tensile specimens of 3.2 mm in diameter and 25 mm in length, with a gage diameter of 1.5 mm and gage length of 12.5 mm. The final specimens were electropolished and then outgassed at temperatures in the range 1300 K to 1500 K at pressures below 10-6 Pa. Experiments on polycrystalline materials were performed mainly on the as-received, warmworked tungsten of about 99.95% purity. The material had an elongated grain structure along the tensile axis, with grains about 1-5 microns wide and about 10-50 microns long and an approximate [110] crystallographic texture. For ease in reproducing deposition conditions from experiment to experiment, the surface films chosen for these experiments were tungsten oxide films deposited anodically at room temperature. Most of the results presented are for an 80 nm film deposited at 15 volts. Surface dislocation sources on the substrate surfaces were introduced by two different methods: manual surface abrasion with metallographic papers of different grit sizes in the range 220-600 or, with better control, chemical etch pitting of the surface by metallographic techniques, as used historically to disclose dislocations that emerge on specimen surfaces. The abraded or etchpitted surfaces were then oxide coated, as described above. Most mechanical testing was done in

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tension at a shear strain rate of 3 x 10-4/s, and various types of experiments were conducted over the temperature range from 77 K to 590 K. The experimental results fall into four broad categories. (1) Surface roughening by etch pitting or surface abrading of the two tungsten materials reduced the plasticity and promoted a more brittle fracture relative to corresponding baseline materials. These processes introduced surface flaws of larger size than existed on the reference surfaces. (2) Deposition of surface oxide films on the unetched or unabraded materials resulted in enhanced plasticity and reduced yield and flow stresses relative to baseline properties. Thus, a somewhat conventional version of surface film softening was observed in these experiments [1-3]. (3) When etch pitting or surface abrasion of the substrates was combined with subsequent oxide coating of the roughened surface, greatly enhanced plasticity over that given in (2) was observed. (4) To a first order, the extent of softening in surface-roughened and oxide-coated material, whether measured by enhanced plasticity, reduced flow stress, or extent of brittle fracture, correlated with the degree of surface roughening. In effect, the presence of the coating converted roughening acting as flaws in (1) into potential dislocation sources. Quantitative correlations in addition to the full complement of results are given in the paper. In summary, we have demonstrated that introduction of dislocation sources by etch pitting or abrasion of the surface of tungsten in single-crystal and polycrystalline forms can promote enhanced plasticity of the subsequently oxidized material. The experiments provide fundamental data of the type needed for more complete constitutive analysis of dislocation dynamics and its interaction with fracture processes. As the relative dimensions of the substrate decrease toward nanometer length scales, the effects we see at millimeter dimensions should become more and more significant.

References 1.

Sethi, V.K. and Gibala, R., Acta Metall., vol. 25, 321-332, 1977.

2.

Sethi, V.K. and Gibala, R., Phil. Mag., vol. 37, 419-429, 1978.

3.

Sethi, V.K. and Gibala, R., in Surface Effects in Crystal Plasticity, edited by R. and J. Fourie, Noordhoff, Leyden, The Netherlands, 1977, 599-610.

Latanision

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DELAMINATION OF THIN METAL FILMS ON POLYMERS A. Pundt, E. Nikitin, and R. Kirchheim Universität Göttingen Institut für Materialphysik, Tammannstr. 1, 37077 Göttingen, Germany [email protected] Hydrogen absorption in niobium films on polycarbonate (PC) gives rise to large compressive in plane stresses which finally lead to a delamination of the metal from the substrate. Delamination occurs via straight and wrinkled buckles and can be observed with an optical microscope (cf. Fig. 1). By doping the Nb-film electrochemically with hydrogen the increasing stresses are measured by determining the curvature of the PC-substrate. For a 200 nm thick Nb-film the corresponding compressive stress is shown in Fig. 2 as a function of hydrogen concentration. The initial linear increase of the stress is in accordance with the known volume expansion caused by H-atoms in Nb. Deviations from the linear response start at the same time when buckles are formed.

FIGURE 1. Buckles formed in a 100 nm thick niobium film sputter deposited on a polycarbonate substrate of 1 mm thickness. The Nb-film was doped electrochemically with hydrogen which initiated compressive stresses in the adhering Nb-layer leading to partial delamination as buckles. With increasing hydrogen content the network of buckles is changing. The corresponding critical stress for buckling is measured for 50, 100 and 200 nm thick Nbfilms which were covered on both sides with a 10 nm thick Palladium film. It was shown by Pundt et al. [1] that the critical stresses for buckling are much larger than the ones needed to exceed Euler’s instability criterion. They are required to overcome the adhesion between Pd and PC. From a simple energy balance between the adhesion energy and the released elastic energy the following equation can be derived: V cr

r V in 

2JE D (1  Q 2 )

(1)

where Vcr is the critical stress for buckle formation, Vin is the initial stress in the Nb-film (where the positive sign is referring to tensile stress), D is the film thickness, J is the adhesion energy between film and substrate and E and Q are Young’s modulus and Poisson’s ratio of the metal film. In accordance with Eq. 1 measured critical stresses are plotted in Fig. 3 versus the inverse square root of film thickness. The slope of the corresponding straight line yields a value of about 1 J/m2 for the adhesion energy and the intercept gives an initial compressive stress of about 600

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MPa. The precision of the evaluated adhesion energy can be improved by measuring initial stresses and/or the shape of the buckles. The concept of producing compressive stresses in a film on a substrate by dissolution of atoms or molecules in the film and measuring critical stresses for buckling is applicable to other systems besides Nb on PC. For instance dry and hard lacquer films on metals buckle when they are exposed to a vapour of Dichlormethan. In addition, a thin metal film can be placed between the hydrogen dissolving metal, i.e. Niobium and the polymer. Then the adhesion between the thin film and the polymer has to be used in Eq. 1.

FIGURE 2. Compressive stress within the 200 nm thick Nb-film as a function of hydrogen concentration. Buckeling of the film is observed at the same time when the measured stress (open circles) deviates from the linear relationship The critical stress for buckling is defined as the stress, where these deviation reach 10%.

FIGURE 3. Critical stresses for buckling obtained from stress measurements as presented in Fig. 2 and plotted versus inverse square root of film thickness D cf. Eq. 1).

References 1.

Pundt, A. Nikitin, E. Pekarski. P. and Kirchheim, R., Acta mater. 52, 1579-1587, 2004

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FRACTURE MECHANICS OF ONE-DIMENSIONAL NANOSTRUCTURES Weiqiang Ding, Lorenzo Calabria, Kevin M. Kohlhaas, Xinqi Chen and Rodney S. Ruoff Department of Mechanical Engineering, Northwestern University 2145 Sheridan Road, Evanston, IL 60208-3111 [email protected] aDipartimento di meccanica e tecnologie industriali, Universita di Frienze Via di Santa Marta, 50139, Florence, Italy One-dimensional (1D) nanostructures such as nanotubes and nanowires have attracted considerable attention in recent years due to their promise of applications in sensing and materials reinforcement. Over the past decade various 1D nanostructures has been synthesized. To develop applications with these nanostructures, it is important to first understand their fundamental properties. Our work focused on characterizing the mechanical properties of these novel 1D nanostructures. One of the methods we employed to characterize 1D nanostructures is tensile testing, which is a commonly used testing method to characterize the tensile properties of materials. During quasistatic tensile loading, a piece of material is loaded in tension until it fractures. The specimen elongation and applied load is typically recorded during the loading process. The tensile strength, Young's modulus and other tensile properties such as fracture strength and ultimate strain of the material are then determined from the stress-strain relationship. Conventional tensile test machines are not suitable for nanostructure characterization. Here we studied the tensile properties of 1D nanostructures with our home-built nanomanipulator [1] inside a scanning electron microscope. The two types of nanostructures we investigated are crystalline boron nanowires and multiwall carbon nnaotubes (MWCNTs). The crystalline boron nanowires have been synthesized with the chemical vapor deposition method. [2] Their average diameter was ~ 60 nm and they are tens of microns in length (Figure 1a). Arc-grown MWCNTs were purchased from Materials and Electrochemical Research Corp. They are 6 – 20 nm in outer diameter and 1 – 5 um in length (Figure 1b).[3]

FIGURE 1. SEM images of (a) crystalline boron nanowires and (b) multiwall carbon nanotubes. Nanoscale tensile tests on these nanostructures were performed with the nanomanipulator inside a LEO 1525 field emission gun SEM. AFM cantilevers were used as the manipulation tool and force sensing element. Individual nanostructures were picked up from the source and clamped between two opposing AFM cantilever tips (Figure 2a) with the electron beam induced deposition method.[4] Tensile load was then applied to each nanostructure tested through nanomanipulation. With the increase of the tensile load the nanostructure eventually fractured.

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A MWCNT consists of many concentric cylindrical shells, and the interaction between the individual shells is the relatively weak van der Waals force. When a MWCNT is tensile loaded, the outer layer is primarily loaded and consequently fractured with inner layers being pulled out from the outer shell fragment (Figure 2b), in a ”sword-in-sheath” manner.[5]

FIGURE 2. SEM images of (a) a boron nanowire being clamped between two AFM cantilever tips under a tensile load; (b) sword-in-sheath fracture of a multiwall carbon nanotube. A series of SEM images were taken during the tensile loading process. From image analysis the cantilever deflection and nanostructure elongation were obtained. The diameter of the boron nanowires were measured inside SEM. The diameter of MWCNTs were measured with highresolution TEM. The tensile stress and tensile strain of the nanostructure at each loading step were obtained from data analysis, and a stress-strain diagram were plotted. From the stress-strain relationship the tensile properties of the MWCNTs and boron nanowires were evaluated.

Acknowledgements This work was funded by NSF EEC-0210120, and in part by ONR #N000140210870 (partial support, W. Ding) and by the NASA BIMat URETI # NCC-1-02037 (support for X. Chen). The SEM and TEM work was performed in the EPIC facility of NUANCE Center at Northwestern University. We appreciate receiving the boron nanowires from C. Otten (Buhro group, Washington University-St. Louis.)

References 1.

Yu, M.F., Dyer, M.J., Skidmore, G.D., Rohrs, H.W., Lu, X.K., Ausman, K.D., Von Ehr, J.R., and Ruoff, R.S., Three-dimensional manipulation of carbon nanotubes under a scanning electron microscope. Nanotechnology, 1999. 10(3): 244-252.

2.

Otten, C.J., Lourie, O.R., Yu, M.F., Cowley, J.M., Dyer, M.J., Ruoff, R.S., and Buhro, W.E., Crystalline boron nanowires. Journal of the American Chemical Society, 2002. 124(17): 4564-4565.

3.

http://www.mercorp.com/mercorp/nano.pdf.

4.

Ding, W., Dikin, D.A., Chen, X., Wang, X., Li, X., Piner, R., Ruoff, R.S., and Zussman, E., Mechanics of hydrogenated amorphous carbon deposits from electron beam induced deposition of a paraffin precursor. Journal of Applied Physics, 2005. 98: 014905.

5.

Yu, M.F., Lourie, O., Dyer, M.J., Moloni, K., Kelly, T.F., and Ruoff, R.S., Strength and breaking mechanism of multiwalled carbon nanotubes under tensile load. Science, 2000. 287(5453): 637-640.

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EFFECTS OF STRUCTURE AND BONDING AT SURFACES AND INTERFACES ON FRACTURE S. P. Lynch, S. Moutsos, B. Gable, S. Knight, D. P. Edwards and B. C. Muddle Monash University Clayton, Vic. 3168 Australia, DSTO, P.O. Box 4331 Melbourne 3001 [email protected] It is well known that segregation of impurity elements at grain boundaries can facilitate intergranular fracture. However, it is not so widely recognised that segregation of major alloying elements in some materials, e.g. lithium and magnesium in aluminium alloys, may also be embrittling. Moreover, it appears that certain structural arrangements may be required in addition to segregation, and that ‘two-dimensional’ grain-boundary phase transitions are probably responsible for ductile-to-brittle fracture transitions with decreasing temperature (e.g. Hart [1], Lynch et al.[2]). For a given testing temperature, ductile-to-brittle fracture transitions may also occur with increasing ageing time due to increasing levels of segregation. Intergranular chemistry and structure can influence fracture resistance via effects on decohesion or dislocation emission from crack tips or via effects on slip transmission across boundaries, but the relative importance of these effects is not well established. Evidence for the above hypotheses are reviewed, with a focus on recent work on a variety of Al-Li alloys in different ageing conditions, and with grain sizes ranging from several hundred nanometers to several hundred micrometers. High-resolution TEM and SEM fractography, thinfoil TEM, atom-probe microscopy, and other techniques have been used. It is concluded that particular grain-boundary structures and chemistries facilitate decohesion and dislocationemission from crack tips, and thereby promote low-energy intergranular fracture by a very localised microvoid-coalescence process in some systems (Fig. 1). Ultra-fine grained alloys exhibited similar behaviour to large grained alloys (Fig. 2). Structure and bonding at crack tips could also be affected by adsorption of atoms from the external environment (in addition to the intrinsic grain-boundary structure), with potential effects on cohesion and dislocation emission. Exactly how structure and bonding at crack tips are affected by adsorption is not known, but the dramatic phenomenon of adsorption-induced liquid-metal embrittlement (e.g. Lynch [3]) demonstrates that significant effects must occur. Surface relaxations and reconstructions are known to occur at planar surfaces, are known to be influenced by adsorption, and can extend for several atomic distances beneath surfaces (e.g. [Van Hove [4], Woodruff [5]). There may well be greater effects at stressed (non-atomically sharp) crack tips with high-index, stepped surfaces, and at crack-tip/grain-boundary intersections, than at low-index, unstressed surfaces. Thus, effects on dislocation emission (involving the creation of a surface step and a dislocation core by shearing of atoms within a few atomic distances of crack tips) should be expected. Fractographic evidence that adsorption-induced surface-lattice perturbations can facilitate dislocation emission and decohesion from crack tips are outlined. Finally, the implications of these results for fracture of nanocrystalline materials are considered.

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FIGURE 1. (a) SEM, and (b) TEM of replica of low-energy intergranular fracture of a very underaged 8090 Al-Li-Cu-Mg alloy tested at -196ºC. Lithium segregation at grain boundaries is probably responsible for ‘brittle’ fracture. Note that the TEM of the replica (shadowed at a low angle ~10º) reveals what appears to be very shallow dimples not resolved by SEM (with a fieldemission gun, low kV, and small working distance).

FIGURE 2 (a) TEM of thin-foil, and (b) SEM of low-energy intergranular fracture produced at -196ºC, of a fine-grained mechanically alloyed 905-XL Al-Li-Mg-C-O alloy.

References 1.

Hart, E. W., Scripta Metall., vol. 2, 179 - 182, 1968.

2.

Lynch S.P., Muddle B.C., and Pasang, T., Philos. Mag. A, vol. 82, 3361-3373, 2002.

3.

Lynch, S.P., Acta Metall., Overview No. 74, vol. 36, 2639-2661, 1988.

4.

Van Hove, M.A., In Materials Science and Technology: A Comprehensive Treatment, edited by R. W. Cahn et al., vol. 1, 485-453, 1991.

5.

Woodruff, D. P. (Ed.), The Chemical Physics of Solid Surfaces, vol. 10, Elsevier, 2002.

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APPLICATION OF THE NEW STATIC PHOTOELASTIC EXPERIMENTAL HYBRID METHOD WITH NEW NUMERICAL METHOD TO THE PLANE FRACTURE MECHANICS Jai-Sug Hawong1 , Jeong-Hwan Nam2, O-Sung Kwon3 and Konstantin Tche3 1School of Mechanical Engr, Yeungnam Univ. Gyung San City, Gyung-Buk, Korea, 712-749 2Visiting Researcher, School of Mechanical Engr, Yeungnam Univ., Korea, 712-749 3Graduate Student, School of Mechanical Engr, Yeungnam Univ.,Korea, 712-749 [email protected] Dynamic photoelastic experimental method [1,2] and photoelastic experimental analysis for othotropic material [3,4] have been widely studied [1,2] since 1950. Photoelastic experimental method has been widely applied to the static and dynamic fracture mechaics [5,6] since 1970. During this time, R.J. Sanford [7] suggested the non-linear least square method using NewtonRaphson numerical method with Gaussian elimination method. We have used this method and this conception for determination of stress intencity factor using photoelastic experimental method [8]. The non-linear least square method have been applied to the photoelastic experimental hybrid method which can be used to obtain the static and dynamic stress intensity factor and stress concentration factor [9,10,11]. The Newton-Raphson numerical method with Gaussian elimination method have been used in the non-lineal least square method for the photoelastic experimental method. In this research, the photoelastic experimental hybrid method with Newtion-Raphson numerical method is called old technique. However, old technique is often diverged and unstable in high stress distribution as vicinity of crack tip. Therefore, the main aim of this research is to develop the photoelastic experimental hybrid method with Hook-Jeeves’ numerical method(is called new technique in this research) which is more precise and stabler than old technique and is diverged any case. The detail aims of this research are as follows. 1

To develop the new photoelastic experimental hybrid method with Hook-Jeeves’ numerical method and to certify the validity of the new technique.

2

To certify the validity of application of the new technique to high stress distribution such as plane fracture problem.

3

To certify the validity of the application of Hook-Jeeves’ numerical method to the static photoelastic experimental method.

In this research, the new static photoelastic experimental hybrid method with Hook-Jeeves numerical method has been developed: This method is more precise and stable than the photoelastic experimental hybrid method with Newton-Rapson numerical method with Gaussian elimination method. Using the new static photoelastic experimental hybrid method with HookJeeves numerical method, we can separate stress components from isochromatics only, stress intensity factors can be determined and plane fracture mechanics can be analyzed. The new statics photoelastic experimental hybrid method with Hook-Jeeves should be used in the full field experiment than the photoelastic experimental hybrid method with Newton-Rapson with Gaussian elimination method

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References 1.

D. Post, Photoelastic Stress Analysis for an Edge Crack in a Tensile Field, Experimental Stress Analysis, pp. 99~116, 1953.

2.

Irwin, G.R., Proc. SESA, pp. 93~96, 1958.

3.

M. Ramulu, Dynamic Crack Curving and Branching, Dissertation, University of Washington, 1982.

4.

J.S. Hawong, A.S. Kobayashi, M.S. Dadkhah, B. S.-J. Kang, and M. Ramulu, Experimental Mechanics, pp. 146~153, 1985.

5.

D.G. Smith and C.W. Smith, Engr. Fract. Mech, Vol. 4, pp. 357~366, 1972

6.

Tada, H., Experimental Mechanics, Vol. 1, pp. 390~396, 1974.

7.

Robert J. Sanford, Engr. Fracture Mech. pp. 621~633, 1979.

8.

Jai Sug Hawong, Dong Chul Shin, Hyo Jae Lee, Experimental Mechanics, Vol. 16 no. 2, pp. 165~174, 2002.

9.

J.S. Hawong, C.H. Lin, S.T. Lin, J. Rhee and R.E. Rowlands, Journal Stresses in Orthotropic Composite Material, Vol. 29, No. 18, pp. 8~13, 1991.

10.

Dong-Chul Shin, Jai-Sug Hawong and O-sung Kwon, Transactions of KSME(A). Vol. 25, No. 3, pp.434~442, 2001.

11.

Jai-Sug Hawong, Dong-Chul Shin and Un-cheol Back, Engineering Fracture Mechanics, Vol. 71, pp. 233~243, 2004.

29. Reliability and Failure Analysis of Electronics and Mechanical Systems

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RISK ANALYSIS OF BURIED PIPELINE USING PROBABILISTIC METHOD Ouk Sub Lee1, Dong Hyeok Kim2 and No Hoon Myoung3 School of Mechanical Engineering, InHa University #253, Yonghyun-Dong, Nam-Ku, Incheon, 402-751, Korea [email protected] Department of Mechanical Engineering, InHa University #253, Yonghyun-Dong, Nam-Ku, Incheon, 402-751, Korea [email protected] Department of Mechanical Engineering, InHa University #253, Yonghyun-Dong, Nam-Ku, Incheon, 402-751, Korea [email protected] Natural gas is currently one of the most widely used sources of energy and its use is increasing. The buried pipelines transporting gas and fluid are mostly installed underground and near the highly populated zones and have various types of defects such as corrosion and environmentassist-cracking. The prediction of the remaining strength of pressurized pipelines containing corrosion defects has been frequently carried out using deterministic methods. These methods use the nominal values for both load and the resistance parameters. However, it is well known that the load and resistance parameters have uncertainties resulted from the measurement of the dimensions of defects, the manufacture of the pipe, the operating conditions of pipelines, and etc. The major factors for the failure of pipelines transporting the high-pressure gas are known to be mechanical damage and corrosion. The corrosion is a process through which metal is degraded by the interaction with its environment. Several models are used to predict wall loss due to corrosion. The technique to predict pipeline failure due to corrosion damage is necessary to determine the corrosion tolerance when we design and want to keep the pipelines in reliable state, Lee and Kim [1], Caleyo et al. [2]. For the case that the internal pressure is acting at the corroded pipeline, the failure pressure model is used to assess for remaining strength of pipeline. The failure pressure model that is most commonly used is ANSI/ASME B31G model. The failure pressure equation of ANSI/ASME B31G model for the pipeline corrosion is classified by the corrosion shape of parabola and rectangular. And the MB31G model is used for the purpose of reducing the conservatism and assumption of ANSI/ASME B31G model [2]. In this paper, using this two of failure pressure models and three of wall loss model which is corrosion model, the effects of varying boundary conditions on the failure probability of buried pipeline are investigated and the results from FORM (first order reliability method) and SORM (second order reliability method) are compared and systematically studied for the buried pipelines with corrosion defects. And the FORM and SORM are used in order to estimate the failure probability of the buried pipelines with corrosion defects. When the FORM and SORM are used to estimate the failure probability, it is assumed that every variable is normal distribution and the probability distribution is determined by its mean and standard deviation. The failure probability is calculated using the FORM and SORM that is one of the methods utilizing reliability index. The FORM and SORM are denoted from the fact that it is based on a first-order Taylor series approximation and second order Taylor series approximation of the LSF, respectively, which is defined as below, Halder and Mahadevan [3], Melchers [4].

Z

RL

(1)

O. S. Lee et al.

714

where R is the resistance normal variable, and L is the load normal variable. Assuming that R and L are statistically independent normally distributed random variables, the variable Z is also normally distributed. The reliability index for the non-linear model is estimated by the process shown in Fig. 1. So we can calculate the failure probability using the reliability index, and the reliability of buried pipelines with corrosion defects can be estimated using the failure probability.

FIGURE 1. Process to determine of the reliability index.

References 1.

Lee, O. S. and Kim, D. H., Key Engineering Materials, Vol. 270~270, 1688~1693, 2004.

2.

Caleyo, F., Gonzalez, J. L. and Hallen, J. M., Int. J. of Pressure Vessels and piping, Vol. 79, 7786, 2002.

3.

Halder, A. and Mahadevan, S., Probability, Reliability and Statistical Method in Engineering Design, John Wiley & Sons, 2000.

4.

Melchers, R. E., Structural Reliability Analysis and Prediction, John Wiley & Sons, 1987.

29. Reliability and Failure Analysis of Electronics and Mechanical Systems

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RELIABILITY ESTIMATION OF SOLDER JOINT BY ACCELERATED LIFE TESTS Ouk Sub Lee1, No Hoon Myoung2 and Dong Hyeok Kim2 School of Mechanical Engineering, InHa University #253, Yonghyun-Dong, Nam-Ku, Incheon, 402-751, Korea [email protected] Department of Mechanical Engineering, InHa University #253, Yonghyun-Dong, Nam-Ku, Incheon, 402-751, Korea [email protected] Department of Mechanical Engineering, InHa University #253, Yonghyun-Dong, Nam-Ku, Incheon, 402-751, Korea [email protected] The thermal stresses induced by difference in Coefficient of Thermal Expansion between FR-4 board and 63Sn-37Pb solder joint directly affect the reliability of 63Sn-37Pb solder joint. This research, thus, focuses to investigate the crack initiation and propagation behaviour around solder joint by imposing a designed Accelerated Life Tests Procedure on solder joint by using a newly manufactured Thermal Impact Experimental Apparatus. The fracture mechanism of the solder joint was found to be highly influenced by thermal stresses. Fig. 1 illustrates a solder joint assembly deformed under thermal cycling. Arrows in Fig. 1 show thermal stresses induced around a solder joint under thermal cycling. And solder joint is deformed by thermal stresses.. ' L is the deformation of solder joint by thermal stresses.

Figure. 1 An illustration of thermo-mechanical deformation in solder joints under thermal cycling.( h = height of solder joint, L is distance from neutral point to solder joint In this paper, the reliability of solder joint was evaluated by using the modified Coffin-Manson law and a failure probability model in terms of thermal frequency and temperature. The total number of cycles to failure, N f , is assumed as being dependent on the plastic strain amplitude, ' H p , the fatigue ductility coefficient,

H cf , and fatigue ductility exponent, c . The

relationship among these variables in the Coffin-Manson law is described as Eq(1).

'H p 2

H cf ( 2 N f ) c

(1)

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The First Order Reliability Method(FORM) is denoted from the fact that it is based on a firstorder Taylor series approximation of the limit state function(LSF) which is defined as below.

Z

(2)

RL

where R is the resistance normal variable, and L is the load normal variable. Assuming that R and L are statistically independent normally distributed random variables, the variable Z is also normally distributed. The event of failure occurs when R  L , that is Z  0 . The probability of failure(PF) is given as below.

(3) where

P Z and V Z are the mean and standard deviation of variable Z , respectively, new

variable U is U

( Z  P Z ) / V Z , and ) is the cumulative distribution function for a

standard normal variable and

E is the safety index or reliability index.

The detail properties of silicon chip, PCB(FR4) and solder joint are shown in Table 2. TABLE 1. Material properties of flip chip package.

References 1.

Rao, R.T., Fundamentals of Microsystems Packaging, McGrawHill, New York, USA, 2001.

2.

Achintya, H., Sankaran, M., Probability, Reliability and Statistical Method in Engineering Design, John Wiley & Sons, New York, USA, 2000.

3.

Deborah, D.L.C., Materials for electronic packaging, Butterworth-Heinemann, Boston, USA, 1995.

4.

Michael, P., Handbook of electronic package design, Dekker, New York, USA, 1991.

29. Reliability and Failure Analysis of Electronics and Mechanical Systems

717

ANALYSIS OF ENGINEERING PLASTIC BEHAVIORS IN THERMAL STRESS CONDITION Seon Il Ham, Dong Jun Choi and Sang Duck Park Samsung Electronics Co., Ltd Customer Satisfaction Management Center 416 Maetan 3-Dong Paldal-Gu Suwon-Si Gyonggi-Do 442-742 KOREA Phone: 82-31-200-1064 FAX: 82-31-200-2165, [email protected] Recently, various plastics are used for improvement of reliability and thermal stability of electronic goods. But, it is difficult to choose suitable balance of grade resin to each other product property. Selection of high efficiency resin is becoming inescapable circumstance according to the development of product quality. Using an inexpensive and reasonable resin, that sustains a uniform performance of product quality. It makes a robust product and increases a company's competitive power. Hereupon, I introduce example that use ESPI methods of thermal deformation analysis of product using in our company product. I try to refer to a structural weak point detection of thermal condition of electronic goods instead of mechanical and chemical measurement of specimen type. Keywords: ESPI(Electronic speckle pattern interferometry), NDT (Non contact destructive testing)

Fig. 1 Tandem Laser Scanning Unit LD (Laser Diode) Base Specimen 1

Fig. 2 Tandem Laser Scanning Unit LD Base Specimen 2 Fig. 1 and Fig. 2 are test sample of colour laser printer unit. It makes engineering plastics material NORYL. Top and bottom base units compare deformation before thermal stress and after thermal stress conditions. LSU main frame and LD base unit are thermal deformation each behaviours. It makes Optical Path Difference of laser printing unit. In this experiment, we make adjust material property and bead structure of thermal stress condition.

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718

References 1.

Jones. R., and Wykes. C., Holographic and speckle interferometry, Univ. Press, Cambridge, 1989

2.

Vest CM. Holographic interferometry. New York: Wiley, 1979

29. Reliability and Failure Analysis of Electronics and Mechanical Systems

719

A MECHANISTIC MODEL FOR THE THERMAL FATIGUE BEHAVIOR OF THE LEAD-FREE SOLDER JOINTS Ilho Kim, Tae-Sang Park and Soon-Bok Lee Department of Mechanical Engineering KAIST (Korea Advanced Institute of Science and Technology) 373-1, Guseong-dong, Yuseong-gu, Daejeon, 305-701, Korea(ROK) [email protected] There have been many publications on solder joint life prediction models in the last few years. Many researchers have carried out mechanical fatigue and creep tests on bulk specimens in order to develop a more accurate life prediction model. Some others measured the deformation of the specimen and made the relationship between the deformation and the fatigue life. Other researchers have carried out thermal cycling tests and made life prediction model using the FEA results. The mechanical tests with bulk specimen show different trends of material property with that of solder ball joints. Because the representative volume affects material properties as an experimental results as shown by Bonda and Noyan [1]. If we test the solder ball joints mechanically, temperature condition of the specimen is isothermal. But actually solder joints are subjected to the cyclic temperature condition with the thermal gradients. Thermal cycling tests well describe the real operating condition. However it is very difficult to measure the stress and strain of the solder joints. Generally, the stress and strain of the solder joints was predicted using the finite element method. In this paper, we propose a new mechanistic life-prediction model that can compensate the weaknesses in the mechanical fatigue test and the thermal cycling test. The mechanical tests were performed with a micro-tension tester which has very high sensitivity. Fig. 1 shows the micro-tension tester. Fig. 2 shows the specimen which consists of 9 solder balls (diameter: 760), upper PCB and lower PCB. The isothermal fatigue test was performed under various temperature and loading conditions and the creep test was also performed.

Figure 1. Schematic diagram and a photograph of the micro-tension tester

Figure 2. Test specimen

Figure 3. A schematic diagram of pseudo power cycling tester

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Figure 4. Temperature profile of pseudo power cycling tests Thermal cycling tests were performed with pseudo-power cycling test method, which applied heats to the specimen by conducting as shown in Fig. 3. It has merits of both chamber cycling method and the power cycling method. The pseudo-power cycling method can apply various temperature ranges easily, and the temperature condition is more realistic. The temperature profile described in this study is shown in Fig. 4. [3] A new mechanistic life prediction model for the thermal fatigue was developed and its validity has been approved using the finite element method and the experimental results.

References 1.

Bonda, N.R., Noyan, I.C., IEEE transactions on components, packaging, and manufacturing technology, vol 19, no 2, 208-212, 1996

2.

Park, Tae-Sang, A study on mechanical fatigue behaviours of ball grid array solder joints for electronic packaging, Doctoral Thesis, KAIST, DME985155, 2004

3.

Kim, Ilho, A study on thermal fatigue behaviour of BGA package, Master’s Thesis, KAIST, MME20023132, 2003

29. Reliability and Failure Analysis of Electronics and Mechanical Systems

721

MECHANICAL BEHAVIOR OF METALLIC THIN FILM ON POLYIMIDE SUBSTRATE Dong-Cheon Baek, Sung-Yeol Kim and Soon-Bok Lee Department of Mechanical Engineering KAIST (Korea Advanced Institute of Science and Technology) 373-1, Guseong-dong, Yuseong-gu, Daejeon, 305-701, Korea(ROK) [email protected] Stress state of metallic thin film on polyimide substrate under tensile loading was analyzed using analytic solution and finite elements methods. To obtain the material properties of the film, tensile test of copper film on Kapton substrate was performed as an illustrating example of metallic thin film on polyimide substrate and the measurement technique of the mechanical behaviour of metallic submicron film was verified. In addition, in situ tensile atomic force microscopy (AFM) observations of the crack evolution are studied and successive damaging phenomena are described and finally analyzed with the help of finite element calculations.

FIGURE 1. Tensile test apparatus Thin films are used in many technical applications, such as semiconductor devices, microelectro-mechanical systems, hard or decorative coatings. The mechanical behavior of very thin layers is difficult to study and sometimes strongly influenced by the substrate properties, as in nanoindentation measurements reported by Bhattacharya and Nix [1]. While the stress state is very complicated in nanoindentation, mechanical properties of thin film can be obtained directly from uni-axial tensile testing. However, tensile testing of free standing film has many technical difficulties, such as fabrication procedures depending on film materials and handling problem. An alternative for tensile testing of thin films is to deform films still attached to their substrates proposed by O. Kraft et al. [2]. The strain applied to both the film and substrate is the same, and the measured force is the sum of the forces on both layers:

FT

F f  Fs

(1)

where FT , F f and Fs are, respectively, total measured force of specimen, force on film and force on substrate. The force on substrate can be obtained within the elastic range of substrate. To

D.-C. Baek et al.

722

minimize the contribution of the substrate to load, thin substrates of low elastic modulus with large elastic range need to be used. This technique has the advantage of studying the thin film under the real conditions of technical application and handling of specimens. In the present paper, stress state of metallic thin film on polyimide substrate under tensile loading was analyzed using analytic solution and finite elements methods considering warpage in transverse section of loading due to the mismatch strain induced by different Poisson’s ratio. To show the feasibility of this method, copper film on Kapton substrate was performed as shown in Figs 1-2. Strain was measured directly on surface of specimen using dual microscope which is optical pattern-matching apparatus made by Park et al. [3].

FIGURE 2. Stress-strain curve of Cu film In addition, in situ tensile atomic force microscopy (AFM) observations of the crack evolution are studied when an external tensile load is applied step-by-step to the specimen using small tensile test device. The successive damaging phenomena are described and finally analyzed with the help of finite element calculations.

References 1.

Bhattacharya, A.K., Nix, W.D., International Journal of Solids and Structures, vol. 24, 12871298, 1988

2.

Kraft, O., Schwaiger, R., Wellner, P., Materials Science & Engineering. Properties, Microstructure and Processing. A, Structural Materials, vol. 319, 919-923, 2001

3.

Park, T.S., Baek, D.C., Lee, S.B., Sensors and Actuators. A Physical, vol. 115, 15-22, 2004

31. Multiscaling in Molecular and Continuum Mechanics - Scaling in Time and Size from Macro to Nano

723

MACRO-, MESO- AND MICRO-DAMAGE MODEL BASED ON SINGULARITY REPRESENTATION FOR ANTI-PLANE DEFORMATION G. C. Sih and X. S. Tang School of Mechanical Engineering, East China University of Science and Technology, Shanghai 200237, China Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015, USA School of Bridge and Structure Engineering, Changsha University of Science and Technology, Changsha, Hunan 410076, China [email protected] Recent development of sub-micron devices in microelectronics and cell structure evolution in microbiology has indicated the need to understand how defects or imperfections initiate or migrate at the microscopic and atomic scale, where the chemical compositions are very unstable. Slight changes can built up and lead to significant alterations of the macroscopic behavior. Such effects have not received sufficient attention in the past at such lower scale. They are potential sources that can effect the initial stresses and strains at the microscopic and atomic scale, the magnitude of which depend on the evolution of the system. These initial disturbances will interact with energy transmitted through the system by external means. Macroscopically speaking, a system may be regarded to be in equilibrium but this does not necessarily apply to the lower scales. Hence, modeling of the macro/meso/micro behavior of physical systems requires the capability to cover scale range several orders of magnitude in lineal dimension. In contrast to the current trend of using molecular dynamics for treating multiscale physical systems where massive calculations are performed that involves millions and more atoms for simulation, this work focuses attention near the singular tip of a defect or imperfection at the nanoscale. Such an approach is justified from the findings of painstaking electron microscopy works that have traced the crack-tip signatures to the nano-scale [1]. Instead of crunching out numbers of unmanageable proportions, it suffices to model the dominant defect tip region. The same idea that has been applied so successfully to the tip of a macro-crack in fracture mechanics although the problem of multiscaling is considerably more challenging where effects at the micro-scale or smaller must be related to those at the macro-scale by the use of a meso-scale zone because the gap between macro- and micro-scale can be too coarse. Demonstrated in this work is the development of a macro/meso/micro model that covers the lineal scale of 10-11 to 100 by application of the volume energy density function. Boundary constraints and defect geometries are shown to play a role at the smaller scale in the same way as those at the macroscopic scale. Since the objective here is to illustrate the concept of the singularity representation approach, anti-plane deformation is assumed. The corresponding case of in-plane deformation [2,3] follows the same line of thought but more complicated. Since scale divisions are chosen arbitrarily, discontinuities between any two scale ranges cannot be avoided in general in view of the multiple choice of geometric and loading parameters that cannot be possibly be anticipated in advance. Moreover, in order to justify the use of equilibrium mechanics theories, the scale ranges have to be kept sufficiently small. The connection between scales becomes a major issue in this approach. Scale invariant criteria based on force or energy must then be used. This is reminiscent of the early works [4] dealing with size effects. What the model does is to simulate the non-equilibrium process by a series of equilibrium states connecting two scale ranges at one time. In this way, macroscopic behavior can be connected to imperfections at the dislocation level [5].

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The connection necessitates the knowledge of how the homogeneity of a system changes as the scale is switched. The explicit determination of this cross scale change in homogeneity is made possible because of the simplicity of the anti-plane deformation model.

References. 1.

Private communication with M. S. Bruemmer from Pacific Northwest National Laboratory, Richland, WA, USA, February 23, 2005.

2.

G. C. Sih and X. S. Tang, Simultaneity of multiscaling for macro-meso-micro damage model represented by strong singularities, J. of Theoretical and Applied Fracture Mechanics, 42(3) (2004) 199-225.

3.

G. C. Sih and X. S. Tang, Scaling of volume energy density function reflecting damage by singularities at macro-, meso- and micro-scopic level, J. of Theoretical and Applied Fracture Mechanics, 43(2) (2005) 1-21.

4.

G.C. Sih, Implication of scaling hierarchy associated with nonequilibrium:field and particulate. Prospects of me-somechanics in the 21st century, G.C. Sih and V.E. Panin, eds. Special issue of J. of Theoretical and Applied Fracture Mechanics, 37, (2002) 335-369.

5.

G. C. Sih and X. S. Tang, Screw dislocations generated from crack tip of self-consistent and self-equilibrated systems of residual stresses: atomic, meso and micro, J. of Theoretical and Applied Fracture Mechanics, 43(3) (2005) (in press).

31. Multiscaling in Molecular and Continuum Mechanics - Scaling in Time and Size from Macro to Nano

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MULTISCALING EFFECTS IN TRIP STEELS G. N. Haidemenopoulos and N. Aravas Department of Mechanical & Industrial Engineering University of Thessaly, Volos, Greece [email protected] Low-alloy TRIP steels are a relatively new class of steels with excellent combinations of strength and formability, making them particularly suitable for sheet forming applications in the automotive industry. The steels possess a multiphase microstructure containing ferrite, bainite and retained austenite. During cold forming operations, such as stretch forming, the retained austenite transforms to martensite under the action of the applied stresses and strains. This deformationinduced martensitic transformation of the retained austenite is responsible for the transformationinduced plasticity (TRIP) effects found in these materials. These effects include significant improvements in ductility and formability. TRIP steels offer a unique example for the study of multiscale effects in materials in the sense that experimental observations and models, derived at different scale levels, can be combined for the understanding and the design of these materials. At the microstructural level, TRIP effects depend on the volume fraction and the distribution of phases and more specifically the volume fraction and stability of retained austenite. Themodynamic stability and strain-induced transformation of the austenitic dispersion are in turn influenced by microstructural parameters, such as size and composition, and by macroscopic parameters, such as stress state triaxiality. Computational thermodynamics and kinetics methods are applied, at the microstucture scale, for the modeling of austenite stability [1]. Carbon stabilization is taken into account during the austenite to bainite transformation, and austenite stability is calculated as a function of annealing time. Typical results are shown in Fig.1 where the calculated retained austenite volume fraction is plotted vs annealing time and the results are compared with experimental measurements of retained austenite with a saturation magnetization method. The results aid the design of heat treatments for the processing of TRIP steels.

FIGURE 1 Retained austenite as a function of annealing time Multiphase TRIP steels are essentially composite materials with evolving volume fractions of the individual phases. The effective properties and overall behavior of TRIP steels are determined by using homogenization techniques for non-linear composites. A methodology for the numerical integration of the resulting elastoplastic constitutive equations in the context of the finite element

G. N. Haidemenopoulos and N. Aravas

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method is developed and the constitutive model is implemented in a general-purpose finite element program. The model is calibrated by using experimental data of uniaxial tension tests in TRIP steels[2]. The problem of necking of a bar in uniaxial tension is studied in detail. The constitutive model is used also for the calculation of ``forming limit diagrams" for sheets made of TRIP steels; it is found that the TRIP phenomenon increases the strain at which local necking results from a gradual localization of the strains at an initial thickness imperfection in the sheet.

FIGURE 2. Forming limit curves for two different values of initial thickness inhomogeneities.The solid lines correspond to the TRIP steel, whereas the dashed lines are for a non-transforming steel. The dark triangles are experimental data. Typical results of the calculations are shown in Fig.2 for a transforming (TRIP) and a nontransforming steel for two different values of initial thickness imperfection. Included in Fig.2 are experimental data from formability measurements. Work is underway to further refine the model in order to describe more accurately the forming limits of the material.

References 1.

A.I. Katsamas, G.N. Haidemenopoulos and N. Aravas, Steel Research Int., vol.75, No.11 ,737-743, 2004.

2.

I. Papatriantafillou, N. Aravas and G.N. Haidemenopoulos, Steel Research Int., vol.75, No.11,730-736, 2004.

31. Multiscaling in Molecular and Continuum Mechanics - Scaling in Time and Size from Macro to Nano

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A HYPER-SURFACE FOR THE COMBINED RATE AND SIZE EFFECTS ON THE MATERIAL PROPERTIES Zhen Chen1, Luming Shen1, Yong Gan1 and H. Eliot Fang2 1Department of Civil and Environmental Engineering University of Missouri-Columbia, Columbia, MO 65211-2200, USA 2Computational Materials & Molecular Sciences Department Sandia National Laboratories, Albuquerque, New Mexico 87185-1411, USA [email protected] The recent interests in developing multiscale model-based simulation procedures have brought about the challenging tasks of bridging different spatial and temporal scales within a unified framework. However, the research focus has been on the scale effect in the spatial domain with the loading rate being assumed to be quasi-static. Although material properties are rate-dependent in nature, little has been done in understanding combined loading rate and specimen size effects on the material properties at different scales. In addition, the length and time scales that can be probed by the molecular level simulations are still fairly limited due to the limitation of computational capability. Based on the experimental and computational capabilities available, therefore, an attempt is made here to formulate a hyper-surface in both spatial and temporal domains to predict combined size and rate effects on the mechanical properties of materials. As shown in an asymptotic scaling analysis without considering the rate effect [1], the relationship between the nominal strength V N and different sizes D of geometrically similar structures exhibits a two-sided asymptotic support in the log D  log V

space. Hence, a

N

simple set of equations could be chosen to represent the size effect on the quasi-static strength V 0 in the spatial domain, as follows:

(1) where Du is the specimen size at which the ultimate strength V u is reached, and Dm the minimum macro-scale size beyond which the strength V m becomes size-independent. As can be seen from Eq. (1), the slope of the size-dependent portion with D u  D  D m is given by d log V 0 d log D



S 2

log log

u  log V m cos D m  log D u

V

· ¸¸ ¹

§ S log D  log D u ¨¨ © 2 log D m  log D u

(2)

which can be normalized to be d log V 0 log V u  log V m / d log D log D m  log D u



S 2

§ S log D  log D u cos ¨¨ © 2 log D m  log D u

· ¸¸ ¹

(3)

As can be found from Eq. (3), the normalized slope could be fully determined with the smallsize asymptotic limit and large-size asymptotic limit, and is in the range between 

S and zero. 2

Z. Chen et al.

728

Although the question on a reasonable small-size asymptotic limit remains open [1], the proposed formulation might provide a simple means to characterize the size-dependence of certain materials under quasi-static loading conditions. To describe the dependence of the material strength on the strain rate H , Cowper and Symonds’s model is adopted as follows:

§ H p V H 1  ¨¨ Vo © H r

· ¸¸ ¹

1/ q

(4)

in which H p denotes the plastic strain rate, V 0 is the quasi-static strength, and Hr and q are two model parameters that can be determined with two experimental data points of V H . The size effect on the model parameters were not considered in the original model. As compared with the plastic strain, the elastic strain can be neglected so that H p = H could be assumed. As can be found from the open literature, however, there exists a critical strain rate for single-crystal metals, below which the material strength becomes rate-independent. The critical strain rate is increased with the decrease of the specimen size. In other words, the model parameters Hr and q in Eq. (4) could be assumed to be size-dependent if this model is used to predict the rate-dependent strength with the strain rate above the critical strain rate. Thus, a three-dimensional hyper-surface with respect to both spatial and temporal domains could be formulated to describe combined size and rate effects on the material strength, as below. Based on Eq. (4), the hyper-surface is assumed to have a two-sided asymptotic support in the

log

V Vo H space. The small-size asymptotic limit and large-size asymptotic limit are  log Vo H r

represented by Hrs , V os , q s and parameters

Hr

Hrl , V ol , ql , respectively. The size dependence of model

and q can therefore be described as follows:

log H r  log H rl log H rs  log H rl

q  ql q s  ql

§ S log D  log D rs 1  sin ¨¨ © 2 log D rl  log D rs

§ S log D  log D rs 1  sin ¨¨ © 2 log D rl  log D rs

· ¸¸ ¹ (5.1)

· ¸¸ ¹ (5.2)

for D rs  D  D rl with Drs and Drl being the specimen sizes at the small-size asymptotic limit and large-size asymptotic limit, respectively. It follows from Eqs. (4) and (5) that the threedimensional hyper-surface takes the form of log V H , D

log V

o

D  log

º ª § 1 log H  log H r D ·¸¸ » «1  10 * * ¨¨ © q D ¹¼ ¬

(6)

in the log H  log D  log V space. To demonstrate the features of the proposed hypersurface, the mechanical properties of both tungsten and diamond specimens of various sizes under various loading rates are investigated.

Reference 1.

Bazant, Z.P. Scaling of Dislocation-Based Stain-Gradient Plasticity. J. Mech. Phys. Solids. 50:435-448, 2002.

34. Cracks in Micro- and Nanoelectronics

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A NEW METHOD FOR LOCAL STRAIN FIELD ANALYSIS NEAR CRACKS IN MICRO- AND NANOTECHNOLOGY APPLICATIONS B. Michel, D. Vogel1, N. Sabate2 and D. Lieske3 1Fraunhofer Institute for Reliability and Microintegration IZM Berlin 2University of Barcelona 3Infineon Technologies AG Dresden Gustav-Meyer-Allee 25, D-13355 Berlin, Germany [email protected], www.bernd-michel.com The paper presents a new reliability approach based on local stress and deformation analysis by means of digital image correlation methods. The so-called nanoDAC- (deformation analysis by correlation technique) method is applied in connection with creep and fatigue crack evaluation concepts. This will lead to improved lifetime estimations of microsolder joints in electronic packaging and in MEMS and NEMS interconnection technologies as well. Various kinds of flip chip, CSP and other packaging concepts for sensors, chips and MEMS will be discussed based on the nanoDAC analyses of critical interconnection regions. Special attention will be given to interface cracking taking also into account humidity and vibration effects of the components.

Stress and Strain Measurements in Very Small Regions A new approach to the local measurement of residual stresses in micro- and nanostructures is described in the presentation. The presented technique takes advantage of the combined millingmaging features of a focused ion beam (FIB) equipment to scale down the well-known classical hole drilling method. This method consists of drilling a small hole into a solid containing inherent residual stresses and measuring the displacements/strains caused by the local stress release, that takes place around this hole. In the presented case, the displacements caused by the milling are determined by applying digital image correlation techniques (DIC) to high resolution micrographs taken before and after the milling process. The residual stress value is then obtained by comparing the measured displacements with the analytical solution of the ideal displacement fields. The feasibility of this approach and some generalization has been demonstrated on a micromachined silicon nitride membrane showing that this method has very high potential for practical applications in the field of MEMS, silicon chip interconnection technologies and related topics. The authors call this new method FIBDAC. It received the 2005 Fraunhofer award for science and technology. Besides the FIBDAC method the authors also present another example using the DIC approach. It deals with fracture toughness evaluation by means of so-called nanoDAC technique, i.e. nanodeformation analysis around tiny cracks using atomic force microscopy. NanoDAC is a special microDAC variant of digital image correlation approach where local deformation fields at the crack tip before and after loading steps are compared applying digital image correlation methods providing these images by means of AFM, AFAM or other SPM techniques. The methods enable to derive local stress intensity factors and more general fracture quantities as well for micro- and nanostructures (e.g. MEMS, NEMS etc.).

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730

References 1.

Vogel, D., Sabaté, N., Wunderle, B., Keller, J., Michel, B., Reichl, H., Nanoreliability for Mechanically Loaded Devices, Int. Congress of Nanotechnology 2005 (ICN 2005), San Francisco, USA, 1-4 Nov. 2005.

2.

Michel, B., Keller, J, NanoDAC – a New Technique for Micro- and Nanomechanical Reliability Analysis of Lead-free Solder Interconnects, Int. Conf. on Lead-Free Soldering, Toronto, Canada, 24-26 May 2005.

3.

Michel, B., Testing at Micro and Nanoscale, EuroSIME, European Conf. on Thermal, Mechanical and Multiphysics Simulation and Experiments in Microelectronics, Berlin, 18-20 April 2005.

4.

Auersperg, J., Vogel, D., Michel, B., Crack and delamination risk evaluation of thin silicon based microelectronic devices, 11th Int. Conf. on Fracture (ICF 11) Torino, 20-25 March 2005.

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EXPERIMENTAL INVESTIGATIONS FOR FRACTURE ANALYSIS OF SOLDER JOINTS IN MICROELECTRONIC AND MEMS APPLICATIONS H. Walter1,4, C. Bombach2, R. Dudek, W. Faust3 and B. Michel4 1AMIC GmbH Berlin, Germany, Volmerstraße 9B, D-12489 Berlin 2Nanotest und Design GmbH Berlin, Germany 3 Fraunhofer IZM Chemnitz, Germany 4 Fraunhofer IZM Berlin, Gustav-Meyer-Allee 12, D-13355 Berlin, Germany [email protected] In Microelectronic and MEMS (Micro-Electro-Mechanical Systems) applications the volume of solder joints decreases rapidly due to higher packaging density. In recent years, many solder alloys have been developed and used. Many of lead-free-solders show a complex material behaviour due to different mechanical and thermal properties throughout the sandwich which can influence the mechanical and thermal reliability as well as the life time. For this reason, ensuring the solder joint reliability is one of the most critical design aspects of electronic assemblies. To predict the failure of solder joints with the help of the FE-Simulations tools, the description of solder behaviour is needed. The mechanical behaviour of solder is non-linear and temperature dependent. Solder alloy in consideration are above 0.5 of their melting point at – 40°C, so creep processes are expected [1,2]. The failure behaviour of solder is a complex sequence and depends on microstructures, like grain coarsening, micro-voiding, recrystallization, micro-cracking and macro-cracking on alloying content, soldering temperature profile and dissolution of metallizations. Changes of the microstructure can significantly effect the mechanical properties of the solders. Inhomogeneity of solders, espacially of Sn-based lead free solders, can cause local fatigue driven multiple cracking (3,4). Furthermore, plate-like intermetallic compounds (IMC) may cause crack initiation and brittle fracture at interface to metallization, especially if the joint thickness becomes comperable to the IMC-thickness respectively (Figure 1).

The failure criterion used for recording lifetime might vary based on either electrical failure or mechanical cracks. For the analysis the temperature and stress dependent inelastic behaviour (Creep and stress relaxation) no standard testing methods could be used for these applications. combination of numerical testing methods and experimental are necessary. A comprehensive mechanical characterization of solder alloy properties for tensile, shear, creep and fatigue

H. Walter et al.

732

properties were investigated. Thereby, this paper presents experimental test methods and results by means of modified grooved lap specimens [5]. The analysis of shear stress and strain in solder joints is of interest for development of analytical models that describe the shear deformations of solder joints due to global thermal expansion mismatch between components and PCB. It could be seen, that a couple of Sn-based lead free solder shows both primary and secondary creep behaviour under cycling loading conditions. Primary creep and plastic strain may not be negligible in applications with high temperature ramp rate or under thermal cycling conditions with short dwell time. For the description of the low cycle fatigue behaviour of solder alloys different failure hypotheses are necessary. In addition to the defect free analysis concepts, a defect tolerant analysis concept can be used. The last concepts based on fracture and damage mechanics hypotheses. Fracture mechanics approaches using a critical crack tip parameters (J-Integral) with the assumes that fatigue is limited to propagation of micro cracks [6]. Continuum damage approaches using a viscoplastic constitutive framework with damage evolution capabilities. The application of fracture mechanical concept enables an accurate interpretation of result of the FE-analysis to estimate the reliability and lifetime duration.

References 1.

Dudek,R.,Walter,H.,Döring,R.,Michel,B. : The World of Electronic Packaging and System Integration, edited by Michel,B., Aschenbrenner,R., IZM special edition, Berlin 2005, 56 -65

2.

Schubert,A.,Dudek,R.,Auerswald,E.,Gollhardt,A.,Michel,B.,Reichl,H.: Micromaterials and Nanomaterials, Issue 03/2004, 30 – 41

3.

Wiese,S. : The World of Electronic Packaging and System Integration, edited by Michel,B., Aschenbrenner,R., IZM special edition, Berlin 2005, 497-593

4.

Schubert,A.,Dudek,R.,Auerswald,E.,Gollhardt,A.,Michel,B.,Reichl,H.: Proceedings of 53rd Electronic Components Technology Conference , 2003, 603-610

5.

Deplanque,S.,Nüchter,W.,Spraul,M.,Wunderle,B.,Dudek,R.,Michel,B., In Proceedings of EuroSIME 2005, Berlin

6.

Ghavifekr.H.B.,Michel .B., Sensors and Actuators, A 99, 2002, 183-187

34. Cracks in Micro- and Nanoelectronics

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SIMULATION OF INTERFACE CRACKS IN MICROELECTRONIC PACKAGING J. Auersperg1,2, B. Seiler3, E. Cadalen4, R. Dudek3 and B. Michel2 1AMIC Angewandte Micromesstechnik GmbH, Volmerstraße 9B, D-12489 Berlin, Germany 2Fraunhofer Institute for Reliability and Microintegration Berlin (IZM), Dept. Mechanical Reliability and Micro Materials, Gustav-Meyer-Allee 25, D-13355 Berlin, Germany 3CWM Chemnitzer Werkstoffmechanik GmbH, Otto-Schmerbach-Str. 19, D-09117 Chemnitz, Germany 3THALES Microelectronics S.A., Z.I. de bellevue 35221 Chateaubourg, France [email protected] Increasing use under harsh environmental conditions - extreme temperatures, in particular often lead to fatigue and failure of advanced electronic packages and related systems. As a result, its thermo-mechanical reliability becomes more and more one of the most important preconditions for adopting it in industrial applications. Residual stresses from several steps of the manufacturing process, thermal and static and dynamic mechanical loading conditions along with the fact that microelectronic packages are basically compounds of materials with quite different Young's modules and thermal expansion coefficients contribute to interface delamination, chip cracking and fatigue of interconnects. Consequently, numerical investigations by means of nonlinear parameterized FEA, fracture mechanics concepts are frequently used for design optimizations using sensitivity analyses [1]. So, numerical design studies help to optimize designs of electronics applications at the earlier phase of the product development processes. Unfortunately, this methodology typically accounts for classical stress/strain evaluation or life time estimations of solder interconnects using modified Coffin-Manson approaches. Delamination or bulk fracture mechanisms usually remain unconsidered. This contribution intends to figure out and discuss ways of using fracture mechanics numerical approaches in connection with parameterized FEA attached to response surface method (RSM)based DOE-methodology. For improving such methods, the evaluation of mixed mode interface delamination phenomena of several polymeric substrate/underfiller-, substrate/encapsulant- and ceramics/encapsulant-specimens under bending have been combined with experimental deformation measurements. The simulation models were prepared to introduce residual stresses, satisfy the boundary/ loading conditions of the experiments, simulate the measured crack tip location vs. loading time history and determine interface fracture parameters.

J. Auersperg et al.

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FIGURE 1. Image analysis with uniDAC, sample molding compound on ceramics Measured force vs. deflection curves, deformation fields as results of optical inspection and deformation analysis as well as determined crack tip vs. deflection curves using the gray scale correlation technique as shown in Fig 1 represent the input for the delamination modelling by means of nonlinear FEM. The interface delamination investigations outlined here base on fracture mechanics approaches for bimaterial crack problems. They take into account the special mixed mode situations in case of interface fracture as discussed by Sun and Qian [1]. Because of the goals of these investigations, the energy release rate G (ERR), the interface stress intensity factors K (SIF) and their phase angle O 1 ,

O2,

lim ro0

2 Sr /

§ r · ¨ ¸ © lk ¹

 iH D

­ V 12 ½ ° ° /  1 ® V 22 ¾ °V ° ¯ 32 ¿

O3@

where r is the distance from a crack tip, and lk is an arbitrary characteristic length.

(1) (2) denotes

the diagonal matrix. O1, O2, and O3 are eigenvectors of the interface. These stress intensity factors of an interface between dissimilar anisotropic materials are very useful to evaluate the strength of jointed interfaces. We proposed a new numerical method based on the energy method to calculate the stress intensity factors of an interface crack between dissimilar anisotropic materials [3]. In this paper, we extended the previous method for three-dimensional problems. This numerical method is usually used with the finite element method. In three-dimensional problems, the cost of preparing huge input data is troublesome for actual users, especially in industries. In the presented method, the stress intensity factors are automatically calculated using the contour integral method and the moving least square method. Users of this method need to prepare a small amount of data for the SIF calculation.

J-integral of an interface crack in three-dimensional structure is calculated by following equation.

(3)

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756

FIGURE 1. Contour integral of a three-dimensional crack. where W is the density of strain energy, Ti is traction, ui is displacement, * is the contour of integral and A is the area inside the contour as shown in Fig. 1. To reduce the cost of data preparation, each term of this equation is automatically calculated from the nodal displacements along a crack front using the moving least square method. The J-integral must be separated into each mode of stress intensity factors. Because the stress intensity factors of an interface crack between dissimilar anisotropic materials are not independent. Each mode of stress intensity factors depends on others. We utilized the superposition method for the separation. In this technique, asymptotic solutions shown as Eq. (1) for three sets of stress intensity factors are superposed on the target problem which should be solved. If we superposed three independent asymptotic solutions on the target problem, three modes of stress intensity factors will be obtained. We applied this technique to some typical three-dimensional problems of interface cracks between anisotropic materials. Obtained stress intensity factors did not depend on the path of contour integral except too close path around a crack tip. This method can calculate the stress intensity factors of an interface crack between dissimilar materials in a 3D jointed structure accurately. This method needs only nodal displacements along a crack front obtained by a commercial FEM code and small amount of data those indicate the shape of a crack and the locations of contours of J-integral.

References 1.

Hwu. C, Explicit Solutions for Collinear Interface Crack Problems, International Journal of Solids and Structures, 30, 1993, 301-312.

2.

Stroh, A. N., 1962, Steady State Problems in Anisotropic Elasticity, Journal of Mathematical Physics, 41, 77-103.

3.

Toru Ikeda, Koh Yamanaga, Masaki Nagai and Noriyuki Miyazaki, Stress Intensity Factors Analysis of an Interface Crack between Anisotropic Dissimilar Materials under Thermal Stress, Proceedings of European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2004), Jyväskylä Finland, 2004, CD-ROM.

43. Interfacial Fracture in Composites and Electronic Packaging Materials

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MOLECULAR DYNAMICS OF INTERFACIAL FRACTURE T. E. Tay, V. B. C. Tan and M. Deng Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117576 [email protected] There is growing realization that many fracture phenomena straddle various length scales. This is particularly so in interfacial fracture between dissimilar materials and in composites, where conventional continuum mechanics approaches do not explicitly model the interfacial failure mechanisms at the molecular level. Consequently, several issues such as the effects of local mode mixity on fracture toughness have not been satisfactorily resolved. With recent advances in molecular dynamics (MD) and multi-scale modelling techniques, the chasm between molecular or nano-scale characteristics and macro-scale properties relevant to fracture is beginning to be narrowed, and may eventually be bridged. This presentation begins with a brief review of MD and multi-scale simulation and their relevance to interfacial fracture and damage in fiber-reinforced composite materials. Much of the MD literature in fracture concerns metallic systems, with few publications in MD of polymeric systems [1-2]. There are also very limited experimental investigations of crack initiation in polymeric interfacial systems at the molecular level [3]. Although many challenges remain, some pertinent parameters such as strength of adhesion may be related to the molecular and chemical interactions. We present recent results of a classical atomistic MD simulation of a diffused polymer interface (Fig. 1) [1], and a coarse-grain MD simulation of a highly cross-linked epoxysilane system (Fig. 2). For the latter case, ab initio MD is used to develop the intermolecular force fields, which are in turn employed in the coarse-grain (CG) bead-spring models. The CG technique enables modeling of highly cross-linked polymer systems and permits bond scission, a prelude to the nucleation of micro-voids and cracks.

FIGURE 1. A polycarbonate-silane (PC-AMPTES) interface atomistic MD model.

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FIGURE 2. Failure at an epoxy-silane-glass interface in a coarse-grain MD model.

Reference 1.

Deng M., Tan V.B.C. and Tay T.E., Polymer, vol. 45 (18), 6399-6407, 2004.

2.

Stevens, M.J., Macromolecules, vol. 34, 1411-1415, 2001.

3.

Kent, M.S., Reedy, E.D., Yim, H., Matheson, A., Sorenson, J., Hall, J., Schubert, K., Tallant, D., Garcia, M., Ohlhausen, T. and Assink, R., J. Maters. Res., vol. 19 (6), 1682-1695, 2004.

C. SPECIAL SYMPOSIA/SESSIONS

C2. Engineering Materials and Structures

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NUCLEATION, GROWTH AND INSTABILITY OF THE CAVITATION IN RUBBER E. Bayraktar1,2, K. Bessri1 and C. Bathias1 1ITMA/CNAM- Arts et Métiers, School of Mechanical Engineering, Paris, France 2Supmeca/LISMMA-Paris, School of Mechanical and Manufacturing Engineering, France [email protected], [email protected], [email protected] Elastomeric Matrix Composites (EMCs) subjected to static and fluctuating loads basically fail due to the nucleation and growth of defects. In fact, higher hydrostatic pressure influences mechanical behaviour of EMCs. In other words, the change in behaviour of EMCs due to the nucleation of cavitations under the hydrostatic pressure is evaluated for understanding of the mechanics underlying the damage mechanism. Two types of specimens are used in this study; Natural rubber, NR vulcanised and reinforced by carbon black and Synthetic rubber (styrene-butadiene-rubber, SBR). It is generally accepted that under static loading conditions, elastomeric Matrix Composites (rubbers) are considered as isotropic hyperelastic incompressible materials. Because a rubber material element cannot be extended to infinite stretch ratio, a damage mechanism at large strain is considered. Cavitation in rubber particles plays an important role in the toughening mechanism of rubber-modified plastics [1-7]. Indeed, cavitation in elastomers is thought to be initiated from flaws, which grow primarily due to a hydrostatic tensile stress, and ahead of the crack there will be not only a high stress perpendicular to the plane of the crack but also significant stress components in the other direction. [1-3, 5, 7]. The most popular idea about the cavitation phenomenon says that the cavitation is related to the existence of the gas bubbles trapped in the material during the production stage and the growing of the cavities would then be the result of the growing the gas bubble. Instable failure mechanism at the end of the cavitation is not well known too. Here, an experimental study was carried out on the cavitation phenomenon of the pancake shaped specimens from NR and SBR (smooth and notch). Initiation and propagation stages of cavity and also the instability conditions of the cavities have been determined by simple static tensile testing. In order to complete the exploration of the cavitation in NR and SBR, we have conducted a comparative study on the effect of the hydrostatic pressure and the effect of the stress triaxiality at the tip of the notch. So, tensile tests conducted on the smooth and notched specimens, of whom the depths varied from 2 to 8 mm, showed that a very strong hydrostatic pressure at the centre of the specimen governs the damage. However, the effect of the stress triaxiality increases at the tip of the notch. So, a real competition between the hydrostatic pressure and the stress triaxiality should be attended just from the beginning of the deformation, which characterises the damage mechanism of the NR and SBR. In-situ observations of uniaxial tensile testing are also presented by using Xrays computed tomography, CT, (medical scanner) and compared with those of the scanning electron microscopy (SEM).

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References 1.

Rivlin R. S. and Thomas A. G., Journal of polymer science, 10, Vol. 291-318, 1953.

2.

Chang W. J. and Pan J., J. of Mater. Science, Vol. 36, 1901-1909, 2001.

3.

Lake G. J., Thomas A. G. and Lawrence C. C., Polymer, Vol. 33, (19), 4069-4074, 1992.

4.

Bayraktar E., Antolovich S. and C. Bathias, In Proceedings of ICFC3 on the 3rd International Conference on Fatigue of composites, 13-15 September 2004, Kyoto -Japan

5.

Gdoutos E. E., Schubel P. M. and Daniel I. M., Strain, Vol. 40, 119-125, 2004.

6.

Jancar J., Dianselmo A. and Dibenedetto A. T., Polymer, Vol. 34, (8), 1684-1694, 1993.

7.

Bayraktar E., Montembault F. and Bathias C., Journal of Materials Science and Technology, Vol. 20 (1), 27-31, 2004.

4. Fracture and Fatigue of Elastomers

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ENGINEERING FRACTURE MECHANICS FOR CRACK TOUGHNESS CHARACTERISATION OF ELASTOMERS Katrin Reincke1, Wolfgang Grellmann1 and Gert Heinrich2 1Institute of Materials Science, Martin-Luther University Halle-Wittenberg,D-06099 Halle/Saale, Germany2 Leibniz Institute of Polymer Research, Hohe Straße 6 D-01069 Dresden, Germany [email protected] Elastomer materials are used in a wide application range and subjected to different loading from which material failure can result. Because this failure is caused by initiation and propagation of cracks, application of fracture mechanics methods for material assessment is obvious and the assessment of materials fracture properties have fundamental importance. Many papers in the literature deal with fracture mechanical investigations of elastomers under cyclic loading. However, fracture mechanical experiments under quasi-static and especially impact-like loading have been described to a lesser extent. This paper shows performance, analysis and results of different methods of technical fracture mechanics and their possibilities for the assessment of crack resistance behaviour of elastomeric materials. Experimental methods that are described in detail are the instrumented notched tensile impact test (NTI) and a quasi-static fracture mechanics test. By using these two tests, it is possible to get information on the materials resistance against unstable and stable crack initiation and propagation, respectively. The instrumented NTI test (see Fig. 1) can be favourably performed with thin and/or flexible specimens. Due to recording of the load–extension (F–l) diagram, a fracture mechanical analysis is possible for these materials/specimens. This means, one can determine toughness parameters Jd describing the resistance against unstable crack propagation under impact-like loading conditions (pendulum hammer speed up to 3.7 m/s) also for elastomers.

FIGURE 1. Experimental configuration of the instrumented notched tensile impact test (a) and a schematic representation of a load–extension diagram of a razorblade-notched elastomeric specimen An example of application of instrumented NTI tests is shown in Fig. 2. Two elastomeric materials were exposed different times to lye at a temperature of 95 °C. In Fig. 2 a, one can see Jd as a function of exposure time; Fig. 2 b shows the dependence of the conventional tear resistance W on the exposure time. It can be seen that the resistance against initiation and propagation of an unstable crack decreases with increasing exposure time; a similar result was found for W. However, while for Jd no significant differences between the two elastomers were found, this means, both materials have the same crack resistance behaviour, for the value W, elastomer 2 shows higher tear resistance. In contrast to Jd, in the industrial praxis W is used for a description of

764

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the resistance of elastomeric materials against tearing of an existing crack. In this case, if one uses only W, an overestimation of the crack resistance behaviour of elastomer 2 is done.

FIGURE 2.Crack toughness related to unstable crack propagation Jd (a) and tear resistance W (b) as function of exposure time for two different elastomers Furthermore, a quasi-static fracture mechanics test will be described in the paper. This test is a single-specimen test, where the deformation and fracture process is recorded with a video camera. Aim of the experiment is to record crack resistance curves for a quantitative characterisation of the stable crack initiation and propagation behaviour. Examples of such crack resistance curves are shown in Fig. 3 for NR vulcanizates with different amounts of an organically modified nanodispersed layered silicate (OMLS). Increasing the amount of layered silicate leads to a change in crack propagation behaviour. At low filler contents, the nature of crack propagation can be described with stick-slip behavior, while at higher amounts a steady tearing occurs. This means, the strain crystallization of the rubber matrix is disturbed.

FIGURE 3. Crack resistance curves of NR compounds filled with different contents of an organically modified layered silicate

4. Fracture and Fatigue of Elastomers

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MULTIAXIAL FATIGUE CRACK INITIATION ON FILLED RUBBERS : STATISTICAL ASPECTS L. Laiarinandrasana, A. Bennani and R. Piques Centre des Matériaux – Ecole Nationale Supérieure des Mines de Paris- UMR CNRS 7633 BP87 – F 91003 Evry Cedex - FRANCE [email protected] Nowadays, white reinforcement fillers such as precipitated silica particles are more and more used in many industrial products. In particular, they are reported to increase tear resistance and to reduce internal heating. In this work, two precipitated silica reinforcements, which essentially differ in their specific surface area, are considered. They have been incorporated into a natural rubber matrix. Two reinforced rubber materials have thus been elaborated. Experiments on both filled rubber materials consist of cyclic tension/compression and torsion tests, carried out on dog-bone shaped specimens. All tests have been pursued until crack initiation defined as a visible millimetric crack on the outer surface of the specimens. Microscopic examinations are utilised in order to find out the location of the crack and to depict the microcrack growth mechanisms. It seems that, first, void nucleation occurs at the interface between coarse inclusions and the rubber matrix; then, the crack propagates up to 1mm in size through the "composite" filled rubber materials. The mechanical behaviour of both materials has been modelled by means of finite element (FE) analyses. This allows assessment of the local stress state inside the specimen. Then, with the help of local parameters computed by FE analysis, the fatigue lifetime is characterised. In particular, it has been reported [1] that the fatigue lifetime plots of both compounds seemed to merge into a unique curve, which will be considered as the deterministic one. The statistical aspects are carried out by determining the mean amount of particles per unit volume, D by using a quantitative mapping technique. Thus, 1/D corresponds to the mean volume Vu containing one inclusion. By considering that the probability to find no inclusion within a volume V reads:

P

§ V · exp ¨¨  © Vu ¹

(1)

it comes out that the volume VX that has the probability X to contain one particle is :

VX

V u ln(1  X )

(2)

where ln stands for naeperian logarithm. Then, void nucleation occurs when the largest principal stress in the vicinity of a coarse particle is greater than a critical value Vc. Let VV be the volume of material in the investigated geometry where the stress is greater than Vc. The aforementioned statistical approach can be applied by setting: VX = VV. It allows to plot fatigue curves (Vmax versus number of cycles to crack initiation) with various amounts of risks of crack initiation: e.g. 10%, 50% and 90%. Experimental scatter will be compared with 10% and 90% risks fatigue curves bounds. The statistical treatment of the fatigue database has been implemented as a post-processor into a FE code. The extension of this

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probabilistic approach to fatigue lifetime plots accounting for the mean/minimum stress effects is also investigated.

Reference 1.

Laiarinandrasana, L., Bennani, A., Cantournet, S. and Bomal, Y., to appear In Proceedings of the Fourth European Conference on Constitutive Modelling of Rubber, Stockhölm 27-29 June 2005

4. Fracture and Fatigue of Elastomers

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FRACTURE CRITERIA OF RUBBER-LIKE MATERIALS UNDER PLANE STRESS LOADINGS A. Hamdi1*, M. Nait-Abdelaziz1, N. Ait Hocine2 and P. Heuillet3 1LML, UMR CNRS 8107, Polytech’Lille, Villeneuve d’Ascq, France 2Laboratory of Rheology, Brest, France 3LRCCP, 94400 Vitry Sur Seine, France *adel.hamdi@polytech’lille.fr The use of rubber like materials is now very widespread in industry. Thus, establishing a failure criterion which allows to predict the ultimate properties of the rubbery parts in structures, is of a great interest to make easier the dimensioning of such components. Our general purpose in this work is to build such a criterion. The first part of this paper deals with some fracture elongations criteria reported in the literature. Indeed, since the first work of T.L. Smith [1] on the ultimate properties of rubbers, several authors [2-5] have proposed some fracture criteria based upon strains, stresses or energy. These are examined using experimental data determined from simple and biaxial tension tests on unfilled and carbon black filled elastomers. Four materials have been tested under quasi-static and monotonic loadings, at room temperature and under strain rate of 0.015 s-1. By examining the obtained results, the limits of these criteria which have been initially established to fit unfilled elastomers ultimate properties are highlighted. So, in the second part, an original failure criterion based on an equivalent elongation concept is introduced. This equivalent elongation IJseems to be linearly dependent on a given biaxiality ratio

ln( O2 b ) . Thus, from such an evolution, analytical expressions of the principal elongations at ln( O1b ) break can be written as function of the biaxiality ratio n and IJ evolution parameters. A quite good agreement is highlighted when comparing the failure experimental data with the analytical expressions. n

FIGURE 1. Evolution of the normalized equivalent elongation as function of the biaxiality factor n

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References 1.

Smith T.L., “Dependence of the Ultimate Properties of a GR-S Rubber on Strain Rate and Temperature”, Journal of polymer science, vol. XXXII, 99-113, 1958.

2.

Smith T.L., Rinde J.A., “Ultimate Tensile Properties of Elastomers. V. Rupture in Constrained Biaxial Tensions”, Journal of polymer science, part. A2, vol.7, 675-685, 1969.

3.

Dickie R.A., Smith T.L., “Ultimate Tensile Properties of Elastomers. VI. Strength and Extensibility of a Styrene-Butadiene Rubber Vulcanizate in Equal Biaxial Tension”, Journal of polymer science, part. A2, vol. 7, 687-707, 1969.

4.

Kawabata S., “Fracture and Mechanical Behavior of Rubber-like Polymers Under Finite Deformation in Biaxial Stress Field”, Journal Macromol. Sci. -Phys., B8 (3-4), 605-630, 1973.

5.

Nevière R., Pfiffer A., Stankiewicz F., “A strain based design criterion for solid propellant rocket motors” Congress OTAN : Symposium on Combat Survivability of Air, Sea and Land Vehicules, Aalborg, Danmark, 23-26 September 2002.

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PREDICTION OF RUBBER FATIGUE LIFE UNDER MULTIAXIAL LOADING A. Zine1, N. Benseddiq1, M. Nait-Abdelaziz1 and N. Ait Hocine2 1Lille University of science and technology, France; 2University of Brest, France [email protected] The process of fatigue failure of rubbers is generally described by two phases : crack initiation and crack propagation. This study concerns the crack initiation in such materials submitted to a cyclical loading. Concerning this aspect, either criteria based upon maximum stretch or strain energy density have been developed in the literature [1, 2, 3]. More recently, a parameter predicting the onset of primary crack and its probable orientation has been introduced by Mars [4, 5]. This criterion is based on the so-called “cracking strain energy density (CSED)” Wc and postulate that crack initition will occur in the plane in which the value of Wc is a maximum. The cracking strain energy density parameter represents only the portion of strain energy density available to initiate a crack in a given plane. It is defined incrementally as the dot product of traction vector

&

& with

V

the strain increment vector dH on this material plane (figure 1):

dW c

&

&

V .d H

& & ( r T .V ).( d H.r )

(1)

The CSED parameter can be written, assuming finite strains, as: &

dW

c

&

U R T C S dE R & & Uo RTC R

&

&

U R T (2E  I) S dE R & & Uo R T (2E  I) R

& U / U o is the ratio of the deformed mass density to the undeformed mass density, R

(2) is the unit

vector in the undeformed configuration, defining material plane of interest, S is the 2nd PiolaKirchhoff stress tensor, E is the Green-Lagrange strain tensor and C is the Green deformation tensor.

Figure 1 : Wc/W as function of the plane orientation and of the maximum stretch ratio In this work, assuming finite strains, this parameter has been analytically determined in the cases of simple tension, biaxial tension and simple shear loading. These expressions have been derived by assuming a neo-hookean strain energy density function W. As shown in fig. 1, for the

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particular case of biaxial tension, the results obtained from such relationships denotes the capability of this criterion to predict the orientation plane in which the primary crack would be expected to occur in a material. The criterion has been then implemented in a finite elements code and results obtained for classical strain states have been compared to analytical results. As shown in figure 2, a good agreement has been highlighted. The results have also shown that the ratio Wc/W is not dependent on the analytical form of the strain energy density function. Fatigue experiments have also been achieved on 2 kinds of rubbers on PS and uniaxial tension specimen. The results show that the cracking strain energy density is good predictor of rubber fatigue life.

Figure2: evolution of the CSED as function of the stretch ratio O1

References 1.

Cadwell, S.M., Merrill, R.A., Sloman, C.M., Yost, F.L. (1940), Dynamic fatigue life of rubber, Industrial and Engineering Chemistry, Analytical Edition; 12, pp.19-23.

2.

Beatty, J.R. (1964) Fatigue of rubber, Rubber Chemistry and Technology; 37, pp.1341-1364.

3.

Roberts, B.J, Benzies, J.B. (1977), The relationship between uniaxial and equibiaxial fatigue in gum and carbon black filled vulcanizates In Proceedings of Rubbercon ’77, vol. 2.1.. pp. 2.1-2.13.

4.

Mars, W. V.( 2002). Cracking Energy Density as a predictor of fatigue life under multiaxial conditions, Rubber Chemistry and Technology, 75, pp. 1-18.

5.

Mars, W. V., A. Fatemi, A. (2001) Criteria for Fatigue Crack Nucleation in Rubber Under Multiaxial Loading. Constitutive Models for Rubber II, D. Besdo, R. Schuster, J. Ihlemann (eds.), Swets and Zeitlinger, Netherlands, pp. 213-222.

4. Fracture and Fatigue of Elastomers

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MODELING OF BIAXIAL FATIGUE OF NATURAL RUBBER Shanyan Dong1, Claude Bathias2, Karine Le Gorjo3, F. Hourlier4 and J. F. Vitorri5 1 ITMA, Ph.D. Student, Conservatoire National des Arts et Métiers, 2 rue Conté, 75003, Paris, France. Tel: 00 33 1 40 27 26 58. [email protected]. 2 ITMA, Professor and director of ITMA. Conservatoire National des Arts et Métiers, 2 rue Conté, 75003, Paris, France. Tel: 00 33 1 40 27 23 22. [email protected]. 3 Project manager. HUTCHINSON S.A. – Centre de Recherche, rue Gustave Nourry, BP 31, 45120, Châlette-sur-Loing, France. 4 PAULSTRA 26, bld de Péringondas, F-28207, Châteaudun Cedex, France. 5 Technocentre RENAULT, 1 rue du Golf, Guyancourt Cedex 78 288, France. Numerous rubber components experience multiaxial cyclic stresses in service. From a practical point of view, there is a great need for predicting the effects of complex loading histories on the fatigue life of rubber parts. This paper studies the modeling of fatigue natural rubber under biaxial loading by using a specimen called pancake, in which both uniaxial and multiaxial loading can be introduced. The specimen is shown in Fig. 1 left. The filled nature rubber is fixed between two steel plates to form a shape of pancake. A tomography method is used to examine the fatigue damage inside the specimen, which is helpful to have a good understanding of the fatigue damage initiation and propagation during the fatigue test. The medical tomographic scanner system of our laboratory is shown in Fig.1 right. The work of this paper include the following aspects: stressstrain response analysis, stress-strain behavior with load cycles, the fatigue life and the observation of failure plane associated with the nucleation of fatigue cracks, and their subsequent growth, the exploration of the fatigue damage initiation and propagation inside the specimen by tomography method and the observation of the crack surface by Scanning Electron Microscope.

FIGURE 1. Pancake specimen and tomography scanner system. First, a FEA simulation is carried out to study the stress-strain response of the specimen under multiaxial loading. A plane strain condition prevails in the pancake specimen. The biaxial effect on the stress-strain response is discussed. A comparison between the FEA results and experimental results is made and a satisfied agreement is obtained. On the pancake specimen, fatigue tests are conducted over a wide range of load histories, including pure tension, pure torsion, proportional and non-proportional combined tension-torsion

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loading. A set of video cameras are set up around the specimen to monitor the nucleation of fatigue cracks and their subsequent growth. Then the effect of the biaxility on fatigue failure plane and crack growth rate are analyzed. The ability of existing multiaxial equivalences criteria (maximum principal strain, strain energy density, octahedral shear strain) to predict fatigue behavior is explored. In order to study the fatigue damage inside the specimen in specific stage of fatigue process, first, we accomplish certain fatigue test without stop to know the whole fatigue process. Then we repeat the same condition on another specimen. After some specific cycles of test according to the fatigue stage which we are interested, we take off the specimen from the fatigue test machine, and then we scan the specimen in the tomographic scanner system to examine the damage inside at this cycle. After the scanning, we continue the fatigue test until next number of cycle which we want, and repeat the scanning. We repeat this operation several times until the specimen is cracked. Thus we can get a history of the fatigue damage inside in different stage of fatigue process. From the damage histories, we can find that the damage first inside the specimen near the center. With the propagation of the first damage, other damages appear. Two or more damage nearby can coalesce to form a bigger damage. There is often a major damage which propagates faster than the others. The major damage may dominate the fatigue process. The crack surface is observed using Scanning Electron Microscope. Then the mechanism of the crack propagation under biaxial loading is discussed.

4. Fracture and Fatigue of Elastomers

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MODELING OF CRACK PROPAGATION IN ELASTOMERIC MATERIALS USING CONFIGURATIONAL FORCES T. Horst and G. Heinrich Leibniz Institute of Polymer Research Dresden Hohe Straße 6, D-01069 Dresden, Germany [email protected] Service life prediction of elastomeric materials is clearly of high practical and scientific interest and has attracted the attention of chemists, engineers and physicist. The failure of components is often associated with the initiation and extension of cracks. Hence, the fracture mechanics approach is very fruitful in understanding such destructive processes. Fracture toughness of elastomeric materials is much higher than surface energy due to the existence of dissipative processes with and without time scale in the bulk. Tailoring the materials by blending the elastomers and adding fillers can influence this value significantly. These noncatastrophic dissipative processes were induced mostly near the crack tip as a result of polymerpolymer, polymer-filler and filler-filler interactions due to blend morphology and filler structure preventing the breakage of polymer chains and thus the extension of the crack, see Hamed [1]. Characterizing fracture of elastomeric materials tearing energy was introduced as the amount of energy G required to advance a fracture plane by one unit area. Separating the dissipated energy Ediss outside of the process zone by thermodynamical consideration of fracture, see Maugin and Trimarco [2], the total dissipation, that is the total bulk energy lost ) per unit time, can be written as

)

G ˜ v  E diss

(1)

provided that the local dissipative behaviour is described by means of internal variables of state where G is the configurational force of non-Newtonian nature acting as a driving force on the crack tip as generalization of the J-integral, and v is the crack tip velocity. Following the argumentation of irreversible thermodynamics, see e.g. Maugin [3], an equation describing crack propagation can be derived from a crack dissipation potential Dcrack via

v

w D crack (G ) wG

(2)

The observed S-shape curve in the plot G vs. v, see Fig. 1, derived from a nonconvex crack dissipation potential is capable of explaining steady as well as stick-slip tearing where the crack advances in a continuous and discontinuous manner respectively, see Maugis [4]. This general point of view can be modified for the application to elastomeric materials by accounting for temperature and inertia effects, emphasized by Persson et al. [5] resulting in a scenario similar to the ductile-brittle transition.

T. Horst and G. Heinrich

774

FIGURE 1. Qualitative relation between the configurational force and the crack tip velocity Based on these considerations we emphasize the influence of viscoelastic properties on the crack propagation taking into account structural aspects of elastomeric materials. The application of these concepts in Finite Element Analysis leads to further understanding of the peculiarities observed in fracture.

References 1.

Hamed, G.R., Rubber Chem. Technol., vol. 67, no. 3, 529-536, 1994

2.

Maugin, G.A. and Trimarco, C., In Configurational Mechanics of Materials, edited by Kienzler, R. and Maugin, G.A., Springer, Wien, 2001

3.

Maugin, G.A., The Thermodynamics of Nonlinear Irreversible Behaviors, World Scientific, Singapore, 1999

4.

Maugis, D., J. Mater. Sci., vol. 20, 3041-3073, 1985

5.

Persson, B.N.J., Albohr, O., Heinrich, G. and Ueba, H., J. Phys.: Condens. Matter, in press

4. Fracture and Fatigue of Elastomers

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DETERMINATION OF INTER-FIBRE-FAILURE IN COMPLEX, REINFORCED COMPOSITES V. Trappe and H. Ivers Federal Institute of Materials Research and Testing (BAM) Unter den Eichen 87, 12205 Berlin, Germany [email protected] Fibre Reinforced Plastics (FRP) produced as complex textile composites are increasingly employed for weight and cost reasons in transportation systems (aircraft, railway, automotive). With the rapid development of modern manufacturing methods, there is a need for new measuring methods and realistic theoretical approaches for design and calculation purposes. Advanced FRP structures have to endure high mechanical and environmental loading. Therefore the durability and reliability depends much more on the micro mechanical properties as on the global strength. For example pure intralaminar micro cracking – without any delaminations of layers and fibre fracture leads to a distinct strength reduction of carbon fibre reinforced plastics (CFRP). Micro cracking is non-detectable for conventional X-ray-radiography and ultra sonic measurements [1]. State of the art: layer-wise strength analysis Determination of the inter fibre fracture of a single layer is typically employed to estimate the layer-wise strength of a complex laminate. Thereby, the influence of the neighbouring layers is ignored. This often leads to large deviations between theory and reality (s. Fig. 1). Additionally, the problem occurs that for many semi-finished materials with complex textile reinforcement, i.e. fabrics, nettings or knitting fabrics, no single layer strength can be stated. Thus, the indication of material parameters (inter-fibre-break-strength), essential for the construction, is not possible and an understanding of the failure processes in complex layer composites impractical.

Non destructive evaluation, X-ray refraction and effects X-ray refraction topography [2] is caused by the effect of refraction at the interface of materials of different refractive indices as well known from visible light passing glass lenses. In the experimental set-up a collimated X-ray beam passes the sample. At a fixed angle the refracted signal is measured and additionally a signal proportional to the absorption. A characteristic refraction value C is determined, which is proportional to the surface per unit volume. The intensity of the refracted beam will increase if the difference of the refractive index rises at the observed interfaces. Hence the intensity will be higher for materials with debonded fibres or pores

V. Trappe and H. Ivers

776

than without (s. Fig. 2). By calibration the real as well as the relative inner surfaces are measured. The relative increase 'C is sufficient in most cases and used in further investigations. Scanning the whole area of the sample gives a topographic map of inner surfaces (s. Fig. 2).

Solution A new method for a quantitative determination of transverse and shear strength in a complex laminate solves the denoted problems by “online-refraction”. Therefore a combination of mechanical loading and non destructive-testing with the X-ray refraction technique results in fundamentally new understanding of the micro-mechanical properties of FRP. The objective is to understand the nonlinear mechanical failure behaviour of this material class by measuring the physical properties employed in computational models for failure predictions. The experimental data show, how the nonlinear and linear mechanical characteristics of GFRP laminates with +/-45 and/or 0 /90 woven fabrics of linen style correlate with the increase of the "online" refraction (increase of micro crack density 'C). The layer-wise strength analysis reflects neither quantitatively nor qualitatively these failure processes.

References 1.

TRAPPE, V., HARBICH, K.-W., ERNST, H.: „Damage State of CFRP characterized nondestructively by X-Ray-Refraction-Topography and Ultrasound“; 48th International SAMPE Symposium, Long Beach, USA 2003, Proceedings Vol. 48-1 S. 1228-1239

2.

HENTSCHEL, M.P., HARBICH, K.-W., LANGE, A.: „Non-destructive evaluation of single fibre debonding in composites by X-ray refraction“, NDT&E International, Vol. 27, 5 (1994) p. 275

4. Fracture and Fatigue of Elastomers

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THE TEST FREQUENCY DEPENDENCE OF THE FATIGUE BEHAVIOR OF ELASTOMERS Z. Major1, Ch. Feichter2, R. Steinberger2 and R. W. Lang1,2 1Institute of Materials Science and Testing of Plastics, University of Leoben 2Polymer Competence Center Leoben GmbH Leoben, Austria [email protected] In engineering applications elastomers are frequently exposed to complex combinations of mechanical loads (monotonic, static, intermittent and cyclic loads). A better understanding of the material resistance against crack initiation and propagation becomes of increasing practical importance. Real elastomer parts and components are loaded over a very wide range of loading frequency (1 to 105 Hz) [1]. It is also a well known phenomenon that viscoelastic materials may reveal a hysteretic type heating during cyclic loading [2]. Furthermore, this temperature increase is influenced by various factors, i.e., loading frequency, amplitude, the viscoelastic loss and the heat capacity and conductivity of the elastomer type [3 and 4]. Hence, the main objectives of this paper are: (1) to develop and implement adequate test methods and data reduction schemes to determine the test frequency dependence of the crack initiation and growth resistance of elastomers under cyclic (fatigue) loading conditions and (2) to investigate the effect of hysteretic heating in elastomers. The tests were performed on several elastomer types typically used in engineering applications. The fatigue tests were run on a high rate servohydraulic test system (MTS 831.59 Polymer Test System). A pure shear specimen configuration with a faint waist in the mid-section was used in this study. The test frequency was varied between 0.2 and 50 Hz keeping all other test conditions constant.

FIGURE 1. Frequency dependence of the hysteretic heating during cyclic loading. The specimen temperature and the spatial and temporal temperature distribution was measured during the cyclic loading using a full-field thermal analysis system (Altair, Cedip, F). Based on these results, to simplify the experimental set-up single non-contact temperature sensors were applied to the near crack tip region (near field) and in the specimen ligament (far field) for recording the temperature. A significant test frequency dependence of both the crack growth behavior and the hysteretic heating was observed. Moreover, the temperature increase and the crack growth was found to

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strongly depend on the elastomer type. To gain more insight into the dependence of the heating effect on the viscoelastic parameters, the hysteretic stress-strain curves were also recorded and analyzed. In addition, dynamic characterization tests were also performed to determine the amplitude and temperature dependence of the loss modulus values for various elastomer types.

FIGURE 2. Frequency dependence of the tearing energy, T, at crack propagation rate, da/dN, of 10-4 mm/cycles.

References 1.

Heinrich, G., et al., 2005, Crack Propagation in Rubber-like Materials, ICF 11, Torino

2.

Strobl, G, 1997, Physics of Polymers, Springer, Berlin.

3.

Mars, W.V., Fatemi, A. and Cooper, W. V., 2004, Rubber Chemistry and Technology, Vol. 77, 392-408.

4.

Kerchman, V and Shaw, Ch., 2003, Rubber Chemistry and Technology, Vol. 76, 386-405.

5. Integrity of Dynamical Systems

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Invited Contribution

NONLINEAR MODEL FOR REINFORCED CONCRETE FRAMES LOADED BY SEISMIC FORCES D. Kovacevic Civil Engineering Department, Faculty of Technical Sciences University of Novi Sad, Serbia & Montenegro [email protected] This paper is a review of one possibility for numerical modeling of in-plane reinforced concrete frames loaded by seismic actions. Objective of this research is the formulation of one enough sophisticated and, for engineering practice, reasonably convenient numerical model. Particularly, the main goal is to adopt the "optimal" model - compromise between complexity and quality of approximation. Physical discretization and mathematical approximation is based on finite element method (FEM) concept. Finite element (FE) stiffness and geometric matrix are defined by LaGrange updated formulation. Mass matrix is adopted as a lumped mass matrix neglecting the rotational inertia. Damping matrix is assumed as a proportional to initial stiffness matrix of FE system. Beam FE cross-section is divided in certain number of finite thickness concrete and steel layers, which behavior under the cyclic loading is modeled by corresponding uniaxial constitutive rules, Fig. 1.

FIGURE 1. Reinforced concrete cross-section approximated by finite layers and uniaxial constitutive rule for concrete The uniform cracks distribution, i.e. "smeared cracks approach" is accepted in zones where concrete tension strength is reached. Steel-concrete bond relation is modeled indirectly - by socalled "tension stiffening effect". Linear strain distribution is adopted along the height of the cross-section, because of negligible shear influence in the total deformation field for the typical beam. In this way, the well-known "shear locking" effect (overestimated the participation of shear deformation in the total deformation energy) is avoid. In contrast to shear in strict sense, axial and shear stresses interaction influence, as a cause of inclined cracks appearance must be included in model. The proposal for inclusion the frame joint deterioration, as well as, interaction of shear and flexural forces (inclined cracks effects), in this model, is given additionally. Straight, plane, two-joint beam FE approximates a RC element (beam, column). Two displacements and one rotation per joint are the degrees of freedom (DOF). Third degree

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L'Hermite polynomials and a linear functions are adopted as the interpolation functions for transversal and longitudinal displacements field. For numerical integration of dynamic equilibrium, the Newmark integration procedure (with 5ms increment) is applied as well as a modified Newton-Raphson iterative procedure for balancing the residual loads. As an illustration of previous propositions, presented are the results of the four numerical tests - one linear and three nonlinear analysis of one simple reinforced concrete frame loaded by three seismic actions: San Fernando, Parkfield and Imperial Valley earthquakes. Attained results indicate that proposed numerical concept is one "good compromise" solution. Compromise is made between the accuracy, as an essential parameter, and, on the other hand, simplicity, as everyday design practice task. The objective of presented research was to find the middle way in nonlinear analysis of mentioned structures. Opposite to standard beam FE models [1], that include only the concrete and reinforcement behavior modeling, suggested beam FE model considers frame joint deterioration as well as interaction of shear and flexural forces too, Kovaevi [2]. Final verification and implementation of this modeling concept proves in parametric test analysis i.e. in comparison with the experimental data and results obtained by application of some complex model. It is direction of future research on this modeling concept.

References 1.

Behavior and Analysis of Reinforced Concrete Structures under Alternate Actions Inducing Inelastic Response, Vol. 1: General Models, CEB Bulletin d'information No 210, Lausanne, 1991.

2.

Kovaevi, D., In Numerical Modeling of Reinforced Concrete Frames Loaded by Seismic Actions, Ph.D. Thesis, Civil Engineering Faculty, University of Belgrade, 2001.

5. Integrity of Dynamical Systems

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Invited Lecture

MONITORING THE DURABILITY PERFORMANCES OF CONCRETE AND MASONRY STRUCTURES BY ACOUSTIC EMISSION TECHNIQUE A. Carpinteri and G. Lacidogna Department of Structural Engineering and Geotechnics Politecnico di Torino Corso Duca degli Abruzzi 24, 10129 Torino, Italy [email protected] [email protected] The contribution of non-destructive and instrumental investigation methods is currently exploited to measure and check the evolution of some negative structural phenomena, such as damage and cracking, and to predict their subsequent developments. The choice of the technique for controlling and monitoring reinforced concrete and masonry structures is strictly correlated to the kind of the structure to be analysed and on the data to be extracted, Carpinteri and Bocca [1]. Among these methods, the non-destructive methodology based on Acoustic Emission (AE) proves to be very effective, Carpinteri et al. [2]. This technique makes it possible to estimate the amount of energy released during the fracture process and to obtain information on the durability performances of the monitored structures, Carpinteri and Lacidogna [3,4]. The AE monitoring equipment adopted by the authors consists of PZT transducers fitted with a preamplifier and calibrated on inclusive frequencies of between 100 and 400kHz. The transducers are connected to switchboards equipped with an amplifier and a pass-band filter, one threshold level measuring system, a recorder and an oscillation counter. The threshold level of the signal recorded by the system, fixed at 100PV, is amplified to up to 100mV. The amplification gain, determined as the ratio between the voltage at output Eu and that at input Ei according to the formula dB = 20 log10 Eu/Ei, turns out to be 60 dB. This signal amplification value is the one commonly adopted in the assessment of AE events in concrete. Oscillation counting capacity is assigned a limit of 255 every 120 seconds of signal recording. In this manner, a single event is the result of 2 recorded minutes [4]. From the literature (Ohtsu [5], Shah and Zongjin [6]) we find that the amplitude of the direct non-amplified signal is of the order of 100PV, neglecting the attenuation phenomena due to the distance of signal generation; hence, it can be assumed that the measurement system has the ability to detect the most significant AE events of material cracking. By means of this system, the intensity of a single event is by definition proportional to the number of counts N recorded in the time interval (Event Counting). Clearly, this hypothesis is fully justified only in the case of slow crack growth, Holroyd [7]. With this system, in addition, a localization procedure based on time delays measured by few (e.g., 2-6) spatially distributed AE sensors is applicable to localize the main sources of the damage process. By means of the AE technique, an extensive experimental analysis on masonry and reinforced concrete structures under service loads has been carried out [2,3]. In some cases the main cracks sources are localized in the volume or on the surface of the structure. For surface sources, direct observations confirm the validity of the localization procedure. Strictly connected to the energy detected by AE is that dissipated by the monitored structure. The energy dissipated during crack formation in structures made of quasi-brittle materials plays a fundamental role in the behaviour of a structure throughout its life. Strong size effects are clearly

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observed on energy density dissipated during fragmentation. Recently, a multiscale energy dissipation process has been shown to take place in fragmentation, from a theoretical and fractal viewpoint, Carpinteri et al. [8]. Based on Griffith’s assumption, of local energy dissipation being proportional to the newly created crack surface area, the fractal theory shows that the energy will be globally dissipated in a fractal domain comprised between an Euclidean surface and volume. According to the fractal concepts, an ad hoc theory is herein employed to detect and monitor concrete and masonry structures performances by means of the AE technique. The fractal theory takes into account the multiscale character of energy dissipation and its strong size effects. This makes it possible to introduce a useful energetic damage parameter for structural assessment based on a correlation between AE activity in a structure and the corresponding activity recorded on a small specimen obtained from the structure and tested to failure [2]. Moreover, by applying Fractal and AE criteria, the safety of structures undergoing damage and degradation processes can be efficiently evaluated.

References 1.

Carpinteri, A., Bocca, P., Damage and Diagnosis of Materials and Structures, Pitagora Ed., Bologna, Italy, 1991.

2.

Carpinteri, A., Lacidogna, G. and Pugno, N., In Proceedings of 5th International Conference on Fracture Mechanics of Concrete and Concrete Structures (FraMCos-5), edited by V. C. Li, C. K. Y. Leung, K. J. Willam, S. L. Billington, 2004, 31-40.

3.

Carpinteri, A., Lacidogna, G., Journal Facta Universitatis, Series: Mechanics, Automatic Control and Robotics, vol. 19, 755- 764, 2003.

4.

Carpinteri, A., Lacidogna, G., System for the assessment of safety conditions in reinforced concrete and masonry structures, Italian Patent N. To 2002 A000924, deposited on 23 October 2002.

5.

Ohtsu, M., Magazine of Concrete Research, vol. 48, 321-330, 1996.

6.

Shah, P., Zongjin, L., ACI Materials Journal, vol. 91, 372-381, 1994.

7.

Holroyd, T., The Acoustic Emission & Ultrasonic Monitoring Handbook, Coxmoor Publishing Company’s, Oxford, 2000.

8.

Carpinteri A, Lacidogna G, Pugno N., International Journal of Fracture, vol. 129, 131-139, 2004.

5. Integrity of Dynamical Systems

783

Invited Lecture

BIFURCATION CONTROL OF PARAMETRIC RESONANCE IN AXIALLY EXCITED CANTILEVER BEAM H. Yabuno and M. Hasegawa Graduate School of Systems and Information Engineering University of Tsukuba Ten-no dai, Tsukuba 305-8573 JAPAN [email protected] Bifurcation control of parametric resonance in an axially excited cantilever beam is theoretically and experimentally investigated. In the cases when the excitation frequency is in the neighborhood of twice the natural frequencies, the parametric resonance is produced through the trans-critical bifurcation and the cantilever overcomes also saddle-node bifurcation at the finite amplitude which is a discontinuous bifurcation [1] [2]. In state of the passage through resonance, jumping phenomena occurs due to the discontinuity of the bifurcation. Our control objectives is to avoid the occurance of the jaump phenomena in the state of the passage throught resonance. We have proposed a bifurcaion control method for parametric resonance in a single degree of freedom system. In this research, the method is expanded to the paremetric resonance produced in the acontinuous system, i.e., cantilever beam. Then, a control method for the avoidance of the paremetric resonance is proposed. Also, the validity of the mehod is experimentally confirmed. First, we derive the equation of motion of the cantilever beam by taking into account the effect of the curvature nonlinearrity [3]. The governing equation is theoretically analyzed by using the method of multiple scales [4]. The obtined averaged equation is autonomus for which the bifurcaion analyisis is easily performed. The above mentioned discontinuous bifurcations (saddlenode bifurcation and subcritical pitchfork bifurcation) are investigated with respect to the excitation frequency and their bifurcation points are detected.

FIGURE 1 Analytical model Next, we consider a control method for the avoidance by using a piezo actuator. We derive the equation of motion under the effect of the bending moment by the actuator. It is assumed that the bending moment is proportional to the input voltage. The averaged equation under the control input is derived again by the method of multiple scales. We set the control input to be proportional to the velocity of the beam and the cubic nonlinear term with respect to deflection. The design of the feedback gains are designed based on the averaging equation. Furthermore, we use an experimental set-up as in Fig. 2. We confirm the validity of the theoretically proposed control system. The displacement of the beam at a point is measured. By

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this data is feedback to actuate the piezo actuator. Under the control, we observe the passage through resonance, and compare with the case of no control. As a result, it is confirmed that the proposed control method is valuable for the avoidance of the jumping phenomena in the case of passage through resonance.

FIGURE 2 Experimental setup

References 1.

Yabuno, H., Nonlinear Dynamics, Vol. 12, 263-274,1997.

2.

Yabuno, H., Murakami, T., Kawazoe, J., and Aoshima, N., ASME J. Vibration Acoustics, Vol 126, 149-162, 2004.

3.

Anderson, T. J., Nayfeh, A. H., and Balachandran, B., ASME J. Vibration Acoustics, Vol 118, 21-27, 1996.

4.

Nayfeh, A. H. and Mook, D. T. , Nonlinear Oscillations Wiley New York 1979.

5. Integrity of Dynamical Systems

785

Invited Lecture

ADAPTIVE PROPERTIES OF DYNAMIC OBJECTS I. I. Blekhman and L. A. Vaisberg “Mekhanobr–tekhnika” Corp., Institute for Problems in Mechanical Engineering of RAS Bolshoy pr. V.O., 61, St. Petersburg, 199178 Russia [email protected] By adaptability we understand an ability of objects to retain their individuality and main functional properties, accommodating to the change in outer conditions. Then in case of technical objects we mean that their main qualitative and quantitative parameters of functioning remain within the limits, acceptable for the consumers. In most cases adaptability contains such fundamental notions as stability and steadiness. Speaking roughly, we will say that the stationary condition (particularly, the equilibrium position) or motion is stable if in time it does not change much under the action of certain excitations. We will say that the stationary states or regimes of motion of an object are steady if certain (significant for all practical purposes) parameters of those states or motions remain within a certain domain A when the parameters of the system and the parameters of outer excitation remain within a certain domain B. The notion of adaptability differs essentially from that of self-organization by which is usually meant the emergence of new properties in a system, the latter becoming the integration of separate objects interacting with each other. Self-organization does not mean that the object is intended to fulfill a certain practical aim. Though, there are cases when the adaptability of the system is provided by its ability to be self-organized. Self-synchronization of dynamic objects (briefly discussed in the report) is a bright example of it. It should be noted that for some strange reason the phenomenon of self-organization eludes the attention of the adherents of synergetics, while this phenomenon is one of the expressive examples of self-organization. The more complicated and highly organized the object, the more adaptive, as a rule, it is. The adaptability of living organisms is well known. It can be explained by a natural selection: only those organisms which were able to adapt to the changes in the outer conditions have survived in the process of evolution. It is surprising, however, that some technical systems also possess a certain adaptability. This presentation is devoted to the description of some examples of the adaptability of mechanical objects that the authors came across in their scientific and engineering practice. Perhaps specialists in other branches can give other, no less dramatic examples. We consider here the following examples of adaptation in technical systems: 1

Self-synchronization of dynamic objects, in particular, vibro-exciters, i.e. unbalanced rotors, actuated by the asynchronous engines. This phenomenon consists in the fact that two or more objects, generating oscillation or rotation with different frequencies, when united into a single system, generate oscillations with equal or multiple frequencies.

2

Adaptive properties of the devices with self-synchronized vibro-exciters – an auto-balance beam - and vibrational machines. In the former devices the inertial elements of a beam automatically compensate the changing unbalance of the rotor, while in the latter the

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rotors of the exciters automatically record the changing position of the center of gravity of the solid body they are installed on. 3

A pendulum with a vibrating axis of suspension (the Stephenson-Kapitsa pendulum) is automatically located in the direction of the most intensive oscillations of the axis of suspension.

4

The particle which is being deformed in the field of a standing wave tends to approach either the nodes or the loops of the wave, depending on its elastic and inertial properties, and also on the oscillation frequency.

5

The profiles of a working chamber of crushers are worn out in the process of work in such a way that the wasted energy, the rate of wear and the strain of the critical parts are minimized. It is remarkable that after a certain period of work, the so called working period, the profiles acquire a configuration, obtained as optimal, as a result of a rather intricate theoretical investigation.

6

A chain of generators of a certain type with a sequentially reduced oscillation frequency possesses the following adaptive property. If the links between first generator, which possesses the highest frequency of the generated oscillations and the next one, function adequately, then the first generator will dampen the vibrations of the other generators. In case the first generator stops working or its link with the next generator is broken, the latter “wakes up” and dampens by its oscillations all the other generators, located further and so on. This effect underlies the adaptation properties of the system of exciting the rhythm of heart contractions. It should be noted that the adaptation properties of some machines are not accidental, but are the result of the purposeful work of investigators, designers and inventors, though based only on intuition. In fact, any well designed machine possesses, in one way or another, adaptive properties.

It is natural that the adaptability of a technical device can be provided by the use of the means of control and of mechatronics. These approaches, very expensive as a rule, can be characterized as a struggle against nature, while in this presentation we consider it to be the use of its gifts. One of the effective means of providing the adaptive properties of the machines is the transfer from the cinematic bonds in their mechanism to the dynamic ones, i.e. to the enrichment of the additional degrees of freedom. There are two glowing examples of it. In the closing part of the presentation some general principles are considered which underlie the effects of adaptation in the mechanical systems. In particular, there are suppositions that in a number of cases adaptability is a consequence of the extreme properties of the appropriate processes. Along with that the authors realize that these interpretations just give the answers to the question “how” but not to the questions “why”, which is characteristic of modern physics. The brilliant Euler and his contemporaries, as well as many outstanding scientists nowadays believe that the presence of the extreme principle is the design of the Creator. The researchers who are of materialistic views argue that these principles are the produce of the human brains, because practically all the physical regularities can (if one tries) be interpreted mathematically, as a realization of certain extreme statements. The authors of this presentation would rather share the first point of view.

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Invited Contribution

INFLUENCE OF ADDENDUM MODIFICATION COEFFICIENT ON THE GEAR'S LOAD CAPACITY I. Atanasovska and V. Nikoli-Stanojevi Faculty of anagement in Industry, JNA 63, 37000 Krusevac, Serbia, Faculty of Mechanical Engng, Univ. of Kragujevac, Sestre Janji 6, 34000 Kragujevac, Serbia [email protected] There are many factors that influence at the mechanical behavior of gears. The gear’s mechanical phenomenons are greatly conditioned by teeth’s profile. One of the values that is most important and influential is the addendum modification coefficient value (x1, x2). This paper gives the description of the procedure developed for researching the influence of addendum modification coefficient value on the load capacity of cylindrical involute gears with straight teeth. The numerical method – Finite Element Method (FEM) – is used for the determination of stress state for meshed teeth’s flanks and roots. The model of meshed gears’ teeth contact in FEM is made to enable the simultaneously monitoring teeth’s flanks stress state and teeth’s roots stress state. It’s important to notice that the accuracy of FEM calculations is greatly conditioned by accuracy of model’s geometry and also by the choice of the boundary conditions that simulate the real working conditions in the best way. According to this, the FEM models each consist of three gear’s teeth are developed and described in this paper. The special program for tooth’s profile drawing is developed and built in present FEM software. This program makes possible the developing of the FEM models with ideal gears’ geometry both for period with two tooth pairs in contact as well as for single tooth pair meshing period. During the developing of the FEM model for meshed gear pair the special attention is paid to the simulation of contact conditions on meshed teeth’s flanks. The “point-to-surface” contact finite elements are chosen for tooth contact simulation. Very high level of coincidence between the behavior of contact zone obtained by the developed FEM procedure and the behavior of contact zone at real gear pairs. The particular characteristics of the “point-to-surface” contact finite elements are used during the FEM calculations. During the developing of gears’ meshing simulation this paper pays special attention to the developing of the procedure for load distribution calculation and for obtaining its influence on the load capacity of meshed gear pair. This is in accordance with the fact that the teeth stiffness is the most influential value for load distribution among simultaneously meshing tooth pairs. Also, this is in accordance with the fact that the load distribution is the most influential mechanical phenomenon for the deformation and stress state of gear pairs as well as for theirs load capacity. The stiffness of tooth pair directly depend on the values of the loads trensferred by the tooth pairs that is simultaneously in contact. As a consequence, for period with two tooth pairs in contact the developed procedure used iterations for obtaining the values of stiffness and load for each tooth pair in contact. The FEM models made for a single real gear pair are used for analysis and verification of developed procedure. Obtained results are compared with corresponds many different aspects. The very high coincidence is obtained. In order to compare the stress states of meshed teeth's flanks and roots during the meshing period for gear pairs with different values of addendum modification coefficients the comparative diagrams are made and shown in this paper. All values useful for the researching of mechanical phenomenons at gear pairs (tooth stiffness c', tooth deformation u', load distribution q, teeth’s

788

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flanks stress state VH, teeth’s roots stress state VF1, VF2) are monitored through the comparative diagrams. Many conclusions about the influence of addendum modification coefficient at tooth defformation and gear load capacity are obtained from that diagrams. These diagrams are used for making the special procedure and diagram sets which enable one to make the right choice for the values of the addendum modification coefficients for a particular gear pair in accordance with the general goal – increasing the gear's load capacity. The exponential functions which describe how the maximum teeth’s flanks stress values and the maximum teeth’s root stress values depend on the values of addendum modification coefficients for a particular gear pair are defined using numerical methods. Many conclusions about the influence of addendum modification coefficient at tooth defformation and gear load capacity are obtained from that diagrams. These diagrams are used for making the special procedure and diagram sets which enable one to make the right choice for the values of the addendum modification coefficients for a particular gear pair in accordance with the general goal – increasing the gear's load capacity. The exponential functions which describe how the maximum teeth’s flanks stress values and the maximum teeth’s root stress values depend on the values of addendum modification coefficients for a particular gear pair are defined using numerical methods. The developed procedure for choosing the optimal values of addendum modification coefficients described in this paper gives possibility for easy recognizing the influence of these values on the all gear’s mechanical phenomenons. It is so especially for the influence of described values on the load distribution which is extremely important factor for gear’s load resistance, as well as for reducing vibrations, shocks and noise during the gear pair working

5. Integrity of Dynamical Systems

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Invited Contribution

MICROMECHANICAL MODELLING OF FRACTURE-INDUCED ANISOTROPY AND DAMAGE IN ORTHOTROPIC MATERIALS Vincent Monchiet, Ion-Cosmin Gruescu, Djimedo Kondo and Oana Cazacu1 Laboratoire de Mecanique de Lille, UMR CNRS 8107, Universite Lille 1, France [email protected], [email protected], [email protected] 1GERC, University of Florida, Shalimar, USA [email protected] Matrix cracking is commonly recognised as one of the main inelastic deformation mechanisms of Brittle Matrix Composites. The modelling of such phenomenon still presents some difficulties which are mainly related to the description of the interaction between the initial anisotropy and the cracks-induced anisotropy. The present study concerns a new micro-macro approach of the non linear behavior and damage propagation in this class of materials. First, we present an analytical method for the determination of Eshelby tensor S (or equivalently the Hill tensor P) associated to an arbitrarily oriented crack embedded in an orthotropic elastic medium (see the representative elementary volume on Figure 1). The crack is modeled as an infinite elliptic cylinder along a symmetry axis of the solid matrix, and with a low aspect ratio. The new analytical results provided by the present study show the strong interaction between the primary anisotropy and the crack-induced anisotropy. Several validations of the new results are presented through their agreement with some existing results in literature for particular configurations of the cracks system. The incorporation of these analytical results in a Mori-Tanaka homogenization scheme allows to determine the macroscopic elastic properties of the orthotropic matrix containing a general distribution of cracks. A last part of the study is devoted to a modelling of the damage process in initially orthotropic materials. For this purpose, we propose a physically-motivated damage criterion based on an energy release concept and accounting for the interaction between the primary anisotropy and the induced damage. Identification of the model requires 5 parameters with clear physical meaning. For illustration purpose, these parameters are calibrated on experimental data provided by Gasser et al. on a Ceramics Matrix Composites (See Figure 2). The predictive capabilities of the anisotropic damage model and comparisons for off-axes loading experimental data on the same material provide a large validation of the proposed approach. Evolution of the overall stiffness tensor components will be also presented at the conference.

FIGURE 1 : Representative Elementary Volume : anisotropic solid matrix weakened by cracks

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FIGURE 2 : Tensile loading and calibration curve on uniaxial axis loading ( M

0q) )

FIGURE 3 : Model predictions and validation on off- axis loading test ( M 20q) ) and M 45q) )

Reference 1.

Gasser, A. "Sur la modélisation du comportement mécanique des composites céramiquecéramique à temperature ambiante", Ph.D. Thesis, ENS Cachan, 1994. In French

5. Integrity of Dynamical Systems

791

Invited Lecture

VIBRATION CONTROL DEVICES AND THEIR APPLICATION K. Nagaya Department of Mechanical Engineering, Gunma University Kiryu, Gunma 376-8515, JAPAN [email protected] The vibration control is of importance for preventing fractures of machines and structures. Recently various control methods have been developed. However, vibration control devices have not been discussed thoroughly. The present report introduces various vibration control devices developed in our laboratory[1]-[13]. 1

Vibration isolation systems using electromagnetic actuator

It is difficult, in general, to suppress the transmissibility from the base to the vibrating body to be less than one by using usual vibration control methods such as PID, optimal regulator, etc. In order to isolate the base vibration, we presented a permanent-electromaget actuator [1],[2] and the method of control, in which vibration disturbances are cancelled directly, and velocity feedback is performed to suppress resonance peaks. When the actuator and control method are used, the vibration disturbance is perfectly isolated, and the transmissibility becomes almost zero. 2

Vibration suppression for structures using magnetic dampers

A vibration absorber is available to control vibrations in wide frequency range. In order to suppress vibrations we present a magnetic damper. The sound noise due to plate vibrations is suppressed, and when an appropriate arrangement is made for the absorber, high frequency vibrations can also be suppressed [3]. In order to suppress vibrations of large flexible structures such as aircraft wings, a dam per will be applicable. Since eigenfrequencies of an aircraft wing are small, it requires the following for the damper(1)The damping force has to be large for low frequency because the vibration frequency of the wing is small, (2)it works for small displacement, (3) its size has to be small which can be stacked in the wing, and (4) passive damper is desirable because the maintenance has to be free in the damper. This article presents a new type linear damper, which satisfies the conditions as just mentioned. The damper consists of a number of thin plates with slits. MR fluid is filled in the damper, so that magnetic fields freeze MR fluid. The resisting torque is generated when the plates slides due to the shear of slits of the plates. The damper works against the bending moment of the wing. Theoretical and experimental results are obtained[5]. 3

Tunable absorber for suppressing vibrations

Since, vibration amplitude for machines and structures is zero at anti-resonance frequency. In order to create the anti-resonance, we provided a tunable absorber. Auto tuning control method is developed[4]. The absorber is utilized to a milling machine. 4

Silencer consisting two-stage Helmholtz resonator

A Helmholtz resonator has advantages over other noise control methods, in that it does not require energy to function and it can be applied to high-frequency noise. In this article, a noise reduction method based on Helmholtz resonator is discussed in reference to application to a blower. However, as the frequency of noise generated by a blower, although high, varies over time, the Helmholtz resonator is ineffectual if applied directly. In order to reduce varying highfrequency noise, a new type of silencer, comprised of a two-stage rotary auto-tuning resonator, is

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proposed[8]. A fast Fourier transform (FFT) analysis of noise obtained by a noise meter is used for control. 5

Counteracting moment devices for controlling vibrations of buildings

The present article provides a method of vibration control for a beam carrying a mass at its tip subjected to earthquakes. A vibration isolation mechanism consisting of a gear train for the beam is presented[6]. Theoretical analysis for the beam is developed, and to validate the method and the analysis, experimental tests are carried out for a model of the present mechanism. The device is also applied to multi-level buildings[7]. It is clarified that the vibration displacements and the moments in the beam are suppressed significantly. 6

High-TC superconducting levitation systems and its vibration control

The modeling and analysis of a high TC suoerconducting levitation system are discussed[9][11]. First, the analytical expressions for obtaining the non-linear levitation force given by the present author are clarified; and then a vibration control method is presented. In which feedback currents involving frequency weights are used. Optimal coefficients of the transfer function of the controller are obtained by minimizing the cost function. Hence, the spillover instability due to the non-linear vibrations will be reduced. Numerical calculations have been carried out for some typical problems. To validate the present method, experimental tests have been carried out. The superconducting levitation system is also applied to pulse motors[12]-[13]. The levitation system is somewhat new, because in our system, the superconductor supports at its one end, and the permanent magnet supports the other end of the rotor shaft. This means that, the system requires only one superconductor, and stable levitation is possible without levitation control. The vibration control method is also presented. To validate the system, experimental tests have been carried out.

References 1.

K.Nagaya and H.Kanai, Journal of Sound and Vibration, 180-4 (1995), pp.645-655.

2.

K.Nagaya and M.Ishikawa, IEEE Trans. on Magnetics, 31-1(1995), pp.885-896.

3.

K.Nagaya and L.LI, J. Acoust. So. America, 104-3((1998), pp.1466-1473.

4.

K.Nagaya A.Kurusu, S.Ikai and Y.Shitani, Journal of Sound and Vibration 228-4 (1999), pp.773-792.

5.

T. Pranoto, K.Nagaya and A.Hosoda, Journal of Sound and Vibration, 276 (2004), pp.919932.

6.

K.Nagaya and T.Fukushima, Intelligent beam transforming earthquake force into vibration control force and its optimal design”, Journal of Sound and Vibration, 218-3(1998), pp.445461.

7.

K.Nagaya, T.Fukushima and Y.Kosugi, J. Acoust.Soc.America, 105-5(1999), pp.2695-2703.

8.

K.Nagaya, Y.Hano and A.Suda, J. Acoust. Soc. America, 110-1(2001), pp.289-295.

9.

K.Nagaya, IEEE Trans. on Magnetics, 32-2(1996), pp.445-451.

10. K.Nagaya and S. Shuto, IEEE Trans. on Magnetics, 32-3(1996), pp.1888-1996. 11. K.Nagaya, M.Tsukagoshi and Y.Kosugi, J.Sound Vib., 208-2(1997), pp.299-311. 12. K.Nagaya, Y.Kosugi, T.Suzuki and I.Murakami, IEEE Trans. on Appl. Superconductivity, 94(1999), pp.4688-4694. 13. K.Nagaya, T.Suzuki, N.Takahashi, and H.Kobayashi, IEEE Trans Appl. Superconductivity, 11-4 (2001), pp.4109-4115.

5. Integrity of Dynamical Systems

793

Invited Lecture

MEASUREMENTS OF DYNAMICAL SYSTEM INTEGRITY AND FRACTURE MECHANICS K. S. Hedrih Faculty of Mechanical Engineering University of Nis, Institute of Mathematics SANU Belgarede Yu-18000 Niš, ul. Vojvode Tankosia 2/22, Serbia and Montenegro [email protected], [email protected] I. What is the Dynamical System ? Problems in dynamics have been fascinating physical scientists (and mankind in general) for thousands years. Modern dynamical system theory has relatively short history. It began with Poincaré (1880, 1890, 1899), who revolutionized the study of nonlinear differential equations by introducing the qualitative techniques of geometry and topology rather than strict analytic methods to discus the global properties of solutions of these systems. Robert Devaney in his book [1] wrote: “The simple examples of dynamical systems show how dynamical systems occur in the “real world” and how some very simple phenomena from nature yield rather complicated dynamical systems”. The answer is quite simple: take a scientific calculator and input any number whatsoever. Than, start striking one of the function keys over and over again. This iterative procedure is an example of a discrete dynamical system: x 0 , f x 0 , f  f x 0 , f  f  f x 0 ,......, f  f .... f  f x 0 . The basic goal of the theory of Dynamical Systems is to understand the eventual or asymptotic behavior of an iterative process. If the process is a discrete process such as iteration of a function, then the theory hopes to understand the eventual behavior of the points x , f x , f 2 x , f 3 x ,..., f k x ,..., f n x . Functions which determine dynamical systems are also called mappings, or maps, for short. Mathematical phenomenology and analogy [2] is very useful in the investigation of kinetic properties and processes in the dynamical systems with disparate nature. A very important notation in the study of dynamical systems is the behavior or persistence of the system under small changes or perturbations. This is the concept of structural stability. The notion of structural stability is extremely important for practical application. II. Characterization of a dynamical system: Material model with material structures (construction with structural elements); Mathematical description of material structure dynamics (geometry and material of construction, constitutive stress-strain relation depending of material properties [3], time rate changes in the system structures, material coefficients, coefficients of inertia tensor, coefficients of stiffness……and other material properties; coupled tensor fields properties of material…); Stress and strain states of dynamical system structure on the boundary surfaces (defined by boundary conditions for free and for loaded system, external surface contour excitations, contour displacements); Stress and strain states [4] of dynamical system structure at initial time moment or with all history before initial moment on the observation in all material structures and on the boundary surfaces (by initial condition satisfying the boundary conditions for free and for loaded system); States of dynamical processes in dynamical system; State of stress and strain in the material, and also state of displacements of structure points and also states of other coupled fields depending on the type of material structure. III. Types of dynamical system integrity [5,6] Ideal integrity of dynamical system is when properties of the material structure system and its own kinetic parameters do not change under external excitations; Partial integrity of dynamical system is when properties of the material structure system or its own kinetic parameters do not change under external excitations. Modified integrity of dynamical system is when properties of the material structure system or its own kinetic parameters change under external excitations in the proposed intervals.

K. S. Hedrih

794

Rheonomic integrity of dynamical system is when properties of the material structure system and its own kinetic parameters are functions of time and do not change under the external excitations. Integrity of subprocesses in dynamical systems (In the linear oscillatory system own modes are mutual independent processes and single frequency processes with one own frequency each). Integrity of the real structure material in dynamical system (Measurements of integrity of the real structure material are defined by development of material sciences and the fracture mechanics theory [7] and [8]. Papers written by the British scientist A. A. Griffith (1920, 1924) are of permanent importance for the early formative period of fracture mechanics. He was the first to consider the energy balance approach to the crack problem, the important aspects of which have been reviewed by Panasyuk (1993) [9]. IV. Chaotic Clock Models: A paradigm for vibrations and noise in machines and integrity of machines. For examining natural clocks [10] of reductors (power transmission), as well as sources of nonlinear vibrations and noise in its dynamics, it is necessary to investigate properties of nonlinear dynamics, and phase portraits, as well as structures of homoclinic orbits, layering and sensitivity of this layering of homoclinic orbits and bifurcation of homoclinic points. The natural clocks of nonlinear dynamics of coupled rotors are studied, as well as integrity of machines with respect to the fatigue of the material structure of power transitions [11]. Key words: Homoclinic orbits and points, separatrice layering, trigger, coupled singularities, bifurcation, vector method, mass moment vectors, phase plane and portrait, couple triggers, the form of number eight or it multiplicand, Chaotic Clock Models, integrity, machines. V. Single and multifrequency vibration regimes in the sandwich system with discontinuity. By using two examples of free and forced vibrations of the elastically connected multi body systems and corresponding system with a discontinuity in an elastic connection, we show some basic properties and measurements of the integrity of basic dynamical system. The integrity of dynamical subprocesses in the behavior of the whole system and its subsystems or in component processes and as response of the whole system to corresponding system with discontinuity have been studied by using methods of Bernoulli’s particular integral and Lagrange’s method of constants variation. It is shown that one- and two frequency subprocess regimes change into multi-frequency regimes induced by discontinuity in the system, which represents the loss of integrity of the system structure and marks the appearance of the loss of integrity of basic subprocesses [6]. The presence of multifrequency regimes in one of the modes of vibrations is an indicator of discontinuity in dynamical system and of loss of previous integrity. VI. Concluding remarks. For the measures of dynamical system integrity it is possible to take one of the sets of kinetic parameters, the changes of which in the critical values range are sources of bifurcation processes or of the appearance of nonprogrammed processes in dynamical system with possible appearance of structure discontinuity. Acknowledgment Parts of this research were supported by the Ministry of Sciences, Technologies and Development of Republic Serbia trough Mathematical Institute SANU Belgrade Grants No. 1616 Real Problems on Mechanics and Faculty of Mechanical Engineering University of Niš Grant No. 1828 Dynamics and Control of Active Structures.

References 1. 2. 3.

4. 5. 6. 7. 8. 9. 10.

11.

Devaney R., (1989), An Introduction to Chaotic Dynamical Systems, Addison-Wesley Publishing Company, Inc. p. 336. Petrovi Mihailo, Fenomenološko preslikavanje, Srpska kraljevska akademija, Štamparija Planeta, Beograd, 1933. Goroško O.A. and Hedrih (Stevanovi), K., Analitika dinamika (mehanika) diskretnih naslednih sistema, (Analytical Dynamics (Mechanics) of Discrete Hereditary Systems), University of Niš, 2001, Monograph, p. 426. (in Serbian). Raškovi, D., (1985), Teorija elastinosti (Theory of Elasticity), Nauna knjiga, 1985, 414. Rega G. and. Lenci S., (2004), Identifying, Evaluating, and Controlling Dynamical Integrity Measures in Nonlinear Mechanical Oscillators, Booklet of Abstracts, WCNA Orlando 2004, pp.13-14. Hedrih (Stevanovi), K., Integrity of dynamical systems, Booklet of Abstracts, WCNA Orlando 2004, pp. 25-32. Gdoutos E. E., Fracture Mechanics, An Introduction, Kluwer Academic Publishers, Dordrecht, 1993. Hedrih (Stevanovi) K., Jovanovi D. B., (2003), Mehanika loma i ošteenja (Damage and fracture mechanics) – matematika teorija – renik pojmova i prilozi, Mašinski fakultet u Nišu, str. 208. Ukrainian Siciety on Fracture Mechanics 1992-2002, Spolom, Lviv 2002, p. 273. Moon F,C.: Chaotic Clock Models: A Paradigm for Noise in Machines, Booklet of Abstaracts, IUTAM Symposium on Chaotic Dynamics and Control of Systems and Processes in Mechanics, Università di Roma “La Sapienza”, Roma, Italy, 2003, pp. 41-44. Hedrih (Stevanovi) K., (2004), Homoclinic orbits layering in the coupled rotor nonlinear dynamics and chaotic clock models: A paradigm for vibrations and noise in machines, Proceedings ICTAM04 Abstracts Book and CDROM Proceedings, pp. 320, SM17S-10624.

5. Integrity of Dynamical Systems

795

Invited Contribution

MODELING OF THE SURFACE CRACKS AND FATIGUE LIFE ESTIMATION Katarina Maksimovic, Stevan Maksimovic and Vera Nikolic-Stanojevic1 VTI- Aeronautical Institute, Katanieva 15, 11000 Belgrade, Serbia, 1Faculty of Mechanical Engng, Univ. of Kragujevac, Sestre Janji 6, 34000 Kragujevac, Serbia. [email protected] Part-through cracks such as corner or surface cracks are one of the most common cracks in structural components. The paper focuses to develop analytic expresses for the stress intensity factor (SIF) for the surface crack in 3-D solid type structural components and crack growth. For this purpose three-dimensional finite-element analyses were used to develop an analytic equation for the stress-intensity factors. Traditionally, damages in structural components are assumed to have an elliptic shape that are loaded with cyclic loads and load spectra. Semi-elliptic surface cracks frequently initiate and grow in the vicinity of high stresses, stress concentrations, thermal stresses and other non-linear stress fields. Accurate stress intensity factors for such cracks are necessary for reliable prediction of fatigue crack growth rates or fracture. The slice synthesis approach used herein to computation of surface flaw stress intensities. To validate the analytic derived tress intensity facors for semi-elliptic surface cracks, finite element method is used. Threedimensional finite elements were used to model a plate containing a semi-elliptic surface crack. The propagation of semi-elliptical surface initiated fatigue cracks has been considered. Analytic model for the stress intensity factors, derived in this work, are used for crack growth analyses and fatigue life predictions. Fatigue life under a load spectrum was predicted using these analytic stress intensity factors.. The finite element analyses were made using MSC/NASTRAN, with 20-noded isoparametric three-dimensional solid elements. In order to model the square root singularity at the crack tip, three-dimensional prism elements with four mid-side nodes at the quarter points (a degenerate cube with one face collapsed) were used and the separate crack tip nodal points were constrained to have the same displacements [1]. The quarter-point displacement FEM was employed in present work to evaluate stress intensity factors along semi-elliptic crack front. This method uses the out-of -plane displacement value at the quarter-point behind the crack tip. With the square-root singularity simulated this method has been verified to be of good accuracy for calculating of the stress intensity factors of a variety of practical cracked geometries [2]. In order to readily use these results in crack growth prediction computer routines, equations relating stress intensity to crack shape, and depth to plate thicknes ratio, have been empirically established based on the slice synthesis model 3

KA

V

Sa

3

¦¦ A

ij

i 0 j 0

3

KB

V

Sa

3

¦¦ B i 0 j 0

ij

§c· ¨ ¸ ©a¹

§c· ¨ ¸ ©a¹

i

i

2

2

§a· ¨ ¸ ©t ¹

§a· ¨ ¸ © t ¹

i

(1) i

where: KA is the stress intensity at depth; KB is the stress intensity at surface, s -applied stress,

(2) a-

crack depth, c - half surface length, t -plate thicknes; Aij and Bij are the coefficients (represent the displacements over the ntire crack face, the continuity expression is evaluated at 13 points). Figure 1 shows typical finite element model of structural component under tensile loading. To

K. Maksimovic et al.

796

check he validity of the above method for SIF evaluation by the semi-analytic the slice synthesis approach, comparison between the calculated SIF results of surface cracks in plate and the solution obtained by finite elements is shown in figure 2. For this purpose plate with semi-elliptic surface crack under tension stress s=83.3 [N/mm2] is analyzed. Geometry properties of this plate are: w=60 mm, t=10 mm, c=10 mm, a=10 mm.

FIGURE 1. Finite element mesh of semi-elliptic crack

FIGURE 2. Comparisons between analytic and FE results for SIF calculations Good agreement between analytic determined SIF with finite elements is evident. These analytic determined SIF can be reliable used in fatigue life estimation of surface cracked structures.

References 1.

K. Maksimovic, V. Nikolic-Stanojevic and S. Maksimovic, Efficient Computation Method in Fatigue Life Estimation of Damaged Structural Components, FACTA UNIVERSITATIS, Vol. 4, No. 16, 2004.

2.

R. S. Barsoum, Triangular quarter-point elements as elastic and perfectly-plastic crack tip elements, Int. J. Numer. Meth. Engng., 11, pp. 85-98, (1977).

5. Integrity of Dynamical Systems

797

Invited Contribution

STRUCTURAL DAMAGE DETECTION VIA THE SUBSPACE IDENTIFICATION METHOD Marina Trajkovic1,2, Dragoslav Sumarac3 and Marina Mijalkovic2 of Mechanics, Ruhr-University Bochum, D-44780 Bochum, Germany 2Department of Civil Engineering and Architecture, Aleksandra Medvedeva 14, 18 000 Nis, Serbia and Montenegro 3Department of Civil Engineering, Bulevar Kralja Aleksandra 73, 11 000 Belgrade, Serbia and Montenegro [email protected], [email protected], [email protected] 1Institute

Based on theoretical preposition from reference Xiao et al. [1], concerning The subspace identification method as one of the possible variants of inverse dynamic analyses, behaviour of real structural systems with real load and really noise contaminated input/output data were investigated in this work. The change of dynamic parameters (stiffness, damping), as a consequence of structural history (erosion, friction, fatigue, internal damages and cracks), has an impact on decrease of reliability and serviceability of a structure or, drastically, causes its collapse. Having in mind that structural damage is small or inside the system, hence the detection cannot be done visually, the authors propose one useful and non-destructive dynamic parameters evaluation tool - vibration monitoring of the structure. The report of the original investigation conducted on real models with real impulse load in laboratory is also given, Fig. 1. The hypothesis that the damage occurrence or the decrease of integrity of structural system leads to the change of the dynamic characteristics of the structure is tested during the investigation.

The authors propose the Scilab, a free MatLab clone, as a powerful tool for numerical computations and data analysis. A special software for experiment monitoring and for determination of relevant mechanical characteristics as well as location of possible damage of construction has been developed (for complete code see Trajkovic [2]). The results of the experimental part of the work, Fig. 2., were used as the entrance data for the software both in the case of complete set of data (number of sensors which measure acceleration of the structure as a response of the load is equal to the number of degrees of freedom) and in the case of incomplete

M. Trajkovic et al.

798

data (for the systems with a large number of degrees of freedom) where the missing values are calculated through the iteration algorithm.

With the progression in programming languages and software packages, computer-aided engineering methodology has significantly improved the practice of structural engineering. Hence, the experimental results as well as the values obtained using numerical methods have been compared with the results of structural analysis and simulation of the same model performed with the finite-element software package ANSYS. Considering that within the mentioned subspace identification method there still are some unsolved issues and that it is a topical research issue in the world, the authors emphasise the observed problems, and offer some ideas for potential overcoming of the method inadequacies.

References 1.

Xiao, H., Bruhns, O.T., Waller, H., Meyers, A., Journal of Sound and Vibration 264/4, 601623., 2001.

2.

Trajkovic, M., Investigation on dynamic properties of linear systems, Edition Academia, Andrejevic Endowment, Beograd, Serbia and Montenegro, 2004.

3.

Trajkovic, M., Monitoring dynamic properties of linear systems, Master thesis, Ruhr University Bochum, Germany, 2002.

5. Integrity of Dynamical Systems

799

Invited Lecture

CLOCK MECHANISM AS BASE OF ARTILLERY SAFETY AND ARMING DEVICES M. Ugrcic Military Technical Institute, Ratka Resanovica 1, 11132 Belgrade, Serbia & Montenegro [email protected], [email protected] The coupled cogged pear consisted of the pallet and escape wheel is the most important part of the clock mechanism (Fig. 1) that is the base of the function of all types of the mechanical watches. In this case, the elastic force of compressed spring or gravitation’s force of bonded weights support a driving (propulsion) and regular function of the clock mechanism. Besides the mentioned, the clock mechanism has been used largely to design the safety and arming devices for all modern types of fuzes for artillery projectiles because of the precision, physical stability, and primordially its-self reliability. In this case, the axial forces of inertia or centrifugal forces of bonded mobile masses drive the mechanism. The safety and arming device (S&A device), as a subsystem for safety and arming is a special part of artillery fuze consisted of the mechanism that takes broken mechanically the explosive train in the fuze and absolutely makes it safe and secure during the storage, transportation, and handling as well as in the beginning phase of projectile launching. The mechanism makes possibility to reinstate the initial explosive train (arming) only then the projectile crosses to muzzle safety distance (assigned to minimum 400 of calibers, i.e. projectile diameters).

FIGURE 1. 3-D view and components of the train of coupled gears in the clock mechanism The determination of optimum design parameters of this very responsible and relatively complex mechanism is not possible without an appropriate calculating method. The mathematical modeling of the safety and arming device is based on main dynamics equations of motion for the rigid material system and equations of the impact mechanics. Just a procedure is a rather complicated and long, that was reason to show in the paper, as well as to explain, only the final equations for motion of the mechanism elements. The mathematical model of the compound movement of mechanism carried out for each phase of three main motions: coupled motion, free motion, and impact. On the basis of derived mathematical model of S&A device motion, the program code OAMFOR for resolving of differential equations of the clock mechanism motion and numerical

M. Ugrcic

800

simulation of its function is developed. The program makes possibilities to optimize mechanism and perform arming zone as well. Some calculation results with variation of the significant parameters of the clock mechanism are shown (Fig. 2). Finally, the S&A device have been tested experimentally by firing from real artillery systems 76 and 105 mm of calibers. Some of the experimental results are shown and compared with results of numerical simulation. Both functions of S&A device safety and arming where successfully approved.

FIGURE 2. Safety zone s depending on design parameters b and Ȝ of real clock mechanism (numerical simulation)

References 1.

Lowen, G.G., Tepper, F.R., Dynamics of the Pin Pallet Escapement, Tech. Report, ARRADCOM, Dover, 1982.

2.

Lowen, G.G., Tepper, F.R., Computer Simulation of Artillery S&A Mechanism (Involute Gear Train and Straight-side Verge Runaway Escapement), Tech. report, ARRADCOM, Dover, 1982.

5. Integrity of Dynamical Systems

801

Invited Contribution

TWISTING DEFORMATION EVOLUTION OF DRILLING ROPES N. P. Puchko Kiev State Shevchenko University Ap.18, 16, St.Garmatna, Kiev, 03067, Ukraine [email protected] The drilling ropes are used for lifting or lowering of measurement instruments into boreholes. The spatial orientation of instrument container affects the measurement accuracy of layer occurrence depth and analysis of the layer properties. In this paper an evolution of twisting deformation of the drilling rope in processes of lifting, lowering and stopping in the borehole is studied. The specific character of rope deformation is conditioned by its rheological properties and ability to come untwisted under a longitudinal loading. The longitudinal - twisting deformations of ropes are described by equations

U

w 2U wt

U r2

EF

2

w 2T w t2

w 2U wx

kEF

 nEF

2

w 2U w x2

w 2T wx

2

f

 EF



³ GJ

P RT

³

 GJ P  k 2 EF

f

2

ww xT  kEF ³ R

U

2

(t  W )

f

f



§ w 2U w 2T ·¸ k Ru (t  W )¨ dW  f ( x , t ) , 2 ¨ wx w x 2 ¸¹ © f

(t  W )  k 2 EFRU (t  W )

f

w 2U w x2



2

ww xT d W  m( x, t ) , 2

(1)

where U ( x, t ) and T ( x, t ) are the longitudinal and twisting displacements of the rope cross sections, EF and GJp – instantaneous longitudinal and twisting rope rigidities, Ru (t  W ) and RT (t  W ) are the relaxation kernels of the longitudinal and twisting deformations, is a linear mass, k is an untwisting coefficient.

Owing to the significant viscosity of liquid solution in the borehole the longitudinal and twisting vibrations of the rope with load are quickly faded. The rope untwisting (or twisting) is conditioned by the action of the force of weight, the distributing force of external viscous friction which is depended upon the velocity of rope lifting or lowering. It is described by the equation § 2 ¨w T GJ p ¨  ¨ w x2 ©

t

³

f

RT ( t  W )

· wT ¸ dW ¸  E  k U ( g  a ( v )) wt wx ¸ ¹ w 2T

2

where is a coefficient of external viscous friction,

E

wT wt

0

(2)

– a moment of a force of external viscous

friction U a(v) , – the longitudinal distributing force of external viscous friction. The boundary conditions for the function T ( x, t ) under lowering have the next outlook:

N. P. Puchko

802

§ wT wT · ¸  km0 ( g  a (v ) under x l (3) T l (t ), t ) T 0 ( x) under x=l , ¨¨ E  GJ p 0 wt wx¸ ¹

©

Under lifting t

T l (t ), t )

§ wT ·

³ ¨¨© w x ¸¸¹ 0

˜ l(t ) dt x l

, § wT wT · ¨¨ E 0 ¸  GJ p w w x ¸¹ t ©

km0 ( g  a (v))

under

x

l0

(4)

where m0 – a mass of instrument container. The solution of equation (2) is presented in the form

T ( x, t ) T0 (l )  ( x  l ) ) (t )

(5)

It is found by the direct methods like Galerkin’s method and has a view § ¨

t

· ¸

T l0 , t T 0 (l ) exp ¨  O (l ) dt ¸  ¨ ©

³

¸ ¹

0

§ § t ·· kg § U ( l0  l ) · ¨ ¨ ¸¸ ¨ m0  ¸ ¨ 1  exp ¨  O (l ) d t ¸ ¸ GJ p © 2 ¹¨ ¨ ¸¸ © 0 ¹¹ ©

³

(6)

where l(t) and l0 are Lagrange’s coordinates of the upper and lower points of the drilling rope, §

O (l ) GJ p l(t ) ¨ E 0  ©

l0  l · ¸ 3 ¹

.

At first glance it would seem that the observed in practice regularities of untwisting-twisting of the drilling rope with instrument container during the processes of lifting, lowering and stopping in the borehole are the paradoxical ones. But the obtained solution (6) explains these peculiarities. Under a first lowering and stopping a transition process determined by the initial untwisting of rope occurs. Under next liftings, lowerings and stoppings the process of untwisting-twisting has become periodic. In the case of the ideal elastic rope a curve described the twisting displacement evolution of the measurement instruments container was obtained by the calculation. The relaxation of strain, a magnitude of lifting or lowering velocities and duration of stopping distinctly affects the magnitudes of untwisting-twisting. However in the case of sufficient duration of these stages the rope behaviour approximates to the calculated data.

5. Integrity of Dynamical Systems

803

Invited Lecture

HEREDITARY STRAIN THEORY OF SYNTETIC AND STEEL ROPES O. O. Goroshko Kiev State Shevchenko University Ap.32, 22, av.Lesnoj, Kiev, Ukraine, 02166 [email protected] The steel and syntetic ropes are widely used as the elements of transport, sea, drilling and other structures. Millions tones of hightquality steels and organic materials are used for the production of power ropes every year. The distinguishing properties of the ropes are: 1)untwisting, when the ropes are under tension; 2) hereditary (rheological) character of deformation which is due to contact interaction of wires and the changes of the lay angles. A model of natural twisting rod is selected as a model, which describes the rope deformation. Then longitudinal and twisting deformations U ( x, t ) and 4( x, t ) are coupled by the relationship u ( x , t )  k 4 ( x, t )

U ( x, t )

(1)

where u(x,t) – elastic rope lengthening. The untwisting rope moment of rope longitudinal tension is defined by the dependence  k P ( x, t )

M ( x, t )

(2)

where P(x,t) is the acting force. The coefficient k in formulas (1) and (2) has a dimension of length and defines the connection between the lengthening and twisting. At the same time k is an arm of an twisting moment. The relationship between a force, a moment and deformations in the rope cross sections is defined by the equation in the relaxation form t § · w u ( x,W ) ¸ ¨ wu EF ¨ d W ¸,  Ru (t  W ) wx ¨wx ¸ f © ¹ t § · w T ( x,W ) ¸ ¨ wT M ( x, t ) GJ p ¨ d W ¸.  RT (t  W ) wx ¨ wx ¸ f © ¹

³

P ( x, t )

³

(3)

According to d’Alambert principle and the relationships (3) the dynamical equations of longitudinal and twisting deformations have an outlook

U

w 2M wt

U r2

EF

2

w 2T wt

2

w 2U wx

GJ

p

2

 kEF

 k 2 EF

w 2T wx

2

t

 EF

2

ww xT

2

 kEF

§ w 2U w 2T · Ru (t  W )¨ 2  k 2 ¸ dW  f ( x, t ) ¨ wx w x ¸¹ © f

³

w 2U wx

2

t

 kEF

³R

f

u (t

W )

w 2U w x2

dW 

O. O. Goroshko

804

t



§

³ ¨¨© GJ

p RT

( t  W )  k 2 EFR u (t  W )

f

w 2T ·¸ dW  m ( x, t ) w x 2 ¸¹

(4)

Here Ru (t  W ) and RT (t  W ) are the relaxation kernels of the longitudinal efforts and twisting moments, which are defined experimentally, EF and GJp – instantaneous longitudinal and twisting rope rigidities, f ( x, t ) and m( x, t ) are the distributing force and moment. In a general case the problem of nonlinear dependence of the kernals Ru (t  W ) and RT (t  W ) upon the longitudinal rope strains is discussed. It was established that the time of rope relaxation may vary by an order depending upon the longitudinal strains and it may decrease upon increasing strain. The kernals of relaxation of standard hereditary bodies are used for the description of the relaxation of longitudinal strain and twisting moments under fixed average value of strain. The dependency of the rhelogical properties of syntetic ropes upon a humidity is discussed. The experimental data for the definition of the rheological parameters of the dry and humid syntetic ropes applied in the trawl technique are given. The dynamic deformation of the ropes under a variation of their length with regard to nonholonomic conditions at the point x rope running on a cylinder is investigated. The nonholonomic conditions take the form: t

U (l (t ), t )

³ 0

t

T (l (t ), t )

³ 0

w U (l , t )  l (t ) dt wx w T (l , t )  l (t ) dt wx

l (t ) of

,

(5)

These conditions determine a carrying mechanism of the rope deformation through the boudary point of rope running on or running out a cylinder. A nature of elastic crawling over a rope under its passage through a pulley is explained. The strain relaxation in a rope reeling part at lifting and its manifestation in the processes of the dynamical deformation at the next rope lomering is taken into account. The critical velocities of the load lifting by rheological ropes under excess of which the dynamical process has become nonsteady are defined. Under these velocities the amplitudes of vibrations of dynamical efforts increase. The conditions under which the rheological dynamical equations (4) can be put into the canonical form were established. There were determined the velocities of propagation of two groupes of longitudinal-twisting waves in the rheological rope. The applied problems of static and dynamical ropes deformation are solved. There were considered the questions of fatigue destruction of ropes and ways of the fatigue strenght estimation of ropes.

5. Integrity of Dynamical Systems

805

Invited Lecture

BRITTLE AND DUCTILE FAILURE IN THERMOVISCOPLASTIC SOLIDS UNDER DYNAMIC LOADING R. C. Batra and B. M. Love Department of Engineering Science and Mechanics, M/C 0219 Virginia Polytechnic Institute and State University Blacksburg, VA 24061, USA Tel. 540-231-6051; [email protected] Plane strain transient finite thermomechanical deformations of heat-conducting particulate composites comprised of circular tungsten particulates in nickel-iron matrix are analyzed using the finite element method to delineate the initiation and propagation of brittle/ductile failures by the nodal release technique. Each constituent and composites are modeled as strain-hardening, strainrate-hardening and thermally-softening microporous materials. Values of material parameters of composites are derived by analyzing deformations of a representative volume element whose minimum dimensions are determined through numerical experiments. These values are found to be independent of sizes and random distributions of particulates, and are close to those obtained from either the rule of mixtures or micromechanics models. Brittle and ductile failures of composites are first studied by homogenizing their material properties; subsequently their ductile failure is analyzed by considering the microstructure. It is found that the continuously varying volume fraction of tungsten particulates strongly influences when and where adiabatic shear bands (ASB) initiate and their paths. Furthermore, an ASB initiates sooner in the composite than in either one of its constituents. We have studied the initiation and propagation of a brittle crack in a precracked plate deformed in plane strain tension, and a ductile crack in an infinitely long thin plate with a rather strong defect at its center and deformed in shear. The crack may propagate from the tungsten-rich region to nickel-iron-rich region or vice-a-versa. It is found that at the nominal strain-rate of 2000/s the brittle crack speed approaches Rayleigh’s wave speed in the tungsten-plate, the nickel-iron-plate shatters after a small extension of the crack, and the composite plate does not shatter; the minimum nominal strain-rate for the nickel-iron-plate to shatter is 1130/s. The ductile crack speed from tungsten-rich to tungsten-poor regions is nearly one-tenth of that in the two homogeneous plates. The maximum speed of a ductile crack in tungsten and nickel-iron is found to be about 1.5 km/s. We have also performed mesoscale analysis of ductile failure in tungsten heavy alloys comprised of tungsten particulates immersed in nickel-iron matrix. Plane strain tension/ compression, plane strain simple shear and axisymmetric deformations have been analyzed. It is found that the mesoscale analysis predicts the initiation of an ASB much sooner than that predicted by the analysis of the equivalent homogenized body. Furthermore, the ASB initiation criterion for a particulate composite is quite different from that for a homogenized body. Even though the ASB initiation criterion for a monolithic material has been satisfied at numerous points, a coherent shear band develops much later. The location and orientation of the ASB can be determined by analyzing results of the complete simulation rather than when the analysis is in progress. For the multiscale analysis we first analyze transient coupled thermo-mechanical deformations of a homogenized body with values of thermophysical material parameters equivalent to those of the particulate composite. Time histories of deformation variables on the bounding surfaces of the centrally located 1 mm x 1 mm subregion of the 5 mm x 5 mm region are recorded. These are then

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used to study plane strain coupled thermomechanical deformations of the 0.5 mm x 0.5 mm subregion of the 1 mm x 1mm region with the remaining part comprised of the equivalent homogeneous material of the 5 mm x 5 mm body. It is found that the multiscale analysis of the problem gives an ASB initiation time of ~ 22 µs as compared to ~ 58 µs in the equivalent homogenized body and ~ 50 µs in the macroanalysis of deformations of the 0.5 mm x 0.5 mm region containing randomly distributed 50% volume fraction of 50 µm diameter tungsten particulates.

References: 1.

R. C. Batra and B. M. Love, Adiabatic Shear Bands in Functionally Graded Materials, J. Thermal Stresses, Vol. 27, 1101-1123, 2004.

2.

R. C. Batra and B. M. Love, Crack Propagation due to Brittle and Ductile Failures in Microporous Thermoelastoviscoplastic Functionally Graded Materials, Engineering Fracture Mechanics (in press).

5. Integrity of Dynamical Systems

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Invited Contribution

SOME ASPECTS OF DYNAMIC INTERFACIAL CRACK GROWTH R. R. Nikolic and J. M. Veljkovic Faculty of Mechanical Engineering, Sestre Janjic 6, 34000 Kragujevac DP ZASTAVA MASINE, Trg Topolivca 4, 34000 Kragujevac Serbia and Montenegro [email protected], [email protected] The scientific describing of the crack initiation and crack growth mechanics on bimaterial interfaces is of vital importance for understanding the failure processes in materials like composites and ceramics. An important failure mechanism in fiber or whisker reinforced ceramic composites is the debonding between the matrix and the reinforcing phases. This process of debonding can take place either quasi-statically or dynamically, depending on the loads nature that the composite structure is subjected to. If the interface is weakened by existence of flaws, they can serve as initiators of a crack, which, under adequate circumstances, can propagate in an unstable manner. Such situations lead to necessity of analyzing the dynamic interfacial crack growth. To formulate the mechanism of initiation and dynamic crack growth in bimaterial systems, it is necessary to know the whole 3D structure of the field around the tip of the moving interfacial crack. In this paper is presented the asymptotic analysis of the strain field around the tip of a crack that propagates along an interface. The asymptotic methodology is applied in order to reduce the problem to solving the Riemann-Hilbert problem. By that the displacements potentials are obtained that are used for explicit determination of the stress field in the vicinity of the tip of the nonuniformly propagating crack. The fields at the crack tip are determined for velocities within interval zero and less than two transversal wave velocities. The obtained analytical results were compared to experimental results of dynamic growth in different bimaterial systems, obtained by the optical method Coherent Gradient Sensor (CGS) and by high-speed photography. This comparison serves for demonstrating the necessity of using the complete expression in the analysis of the optical data and in exact prediction of the dynamic fracture behavior. The stress and displacement components, for each material, are expressed in terms of displacement potentials. By applying the asymptotic methodology the equations of motion are reduced to a system of coupled partial differential equations in terms of displacement potentials. The term coupled equations is used in the sense that the higher order solution will depend on the lower order solutions. Combination of the homogeneous and particular solution satisfies the boundary conditions on the crack faces and along the interface. By applying the boundary conditions on the interfacial crack faces and the bonding conditions along the interface the problem of nonuniform crack growth is reduced to solution of the RiemannHilbert problem. As a solution of this problem the displacement potentials are obtained. Those equations are then used to present the stress distribution as a function of the angle at the crack tip. These stress distributions as a function of angle for different velocities at the crack tip on the interface were not met in the literature, yet. These diagrams are shown here for the first time. From them (Fig.1a) one can notice the stress Vrr jump across the interface under the pure Mode I conditions. In pure Mode II conditions this jump does not exist. The same result is obtained for the case of the stationary crack. The maximum of stress VTT, in conditions of pure Mode I is moved towards the material 1 with the velocity increase, what corresponds to conditions of the mixed mode for the stationary crack.

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By solving the Riemann-Hilbert equation and Stieltjes transforms the asymptotic elastodynamic field is obtained. The most important characteristics of this field is that in appearance of two terms in these equations that are completely different from terms found in solution for the crack which propagates nonuniformly in the homogeneous medium. The first term is completely related to the interfacial nature of the crack growth, since it depends on the oscillatory index H. The second term depends on the complex dynamic stress intensity factor that is characteristic for interfacial crack, and on the crack tip velocity and its time derivative. In this paper is given the new approach to asymptotic analysis of the strain field around the interfacial crack tip. The programming routine Mathematica was applied and the solutions are compared to those obtained by Yang et al. [1] and Liu, Lambros and Rosakis [2]. Based on obtained results and that comparison we concluded that the complete expression from [2] has to be applied for the analysis of the dynamic interfacial crack growth. This also proves superiority of the analytical results obtained by Mathematica routine relative to numerical results obtained from references.

FIGURE 1. a) Angular stress distribution for bimaterial combination PMMA/steel for Mode I conditions. b) Asymptotic analysis results, for the crack velocity v=720 m/s; c) Intereferogram obtained for impact load, obtained by the CGS method. Bimaterial combination Homalite-100/Al Red lines are contours of the asymptotic analysis results

References: 1.

Yang, W., Suo Z. and Shih C. F., Proc. R. Soc. Lond. A 433, pp. 679-697, 1991.

2.

Liu C., Lambros J. and Rosakis A. J., J. Mech. Phys. Solids Vol. 41. pp. 1887-1954, 1992.

5. Integrity of Dynamical Systems

809

Invited Contribution

ON STABILITY PROBLEMS OF PERIODIC IMPACT MOTIONS S. Mitic Faculty of Occupational Safety University of Nis Yu-18000-Nis, Zetska 4/9, Serbia and Montenegro, Yugoslavia fax: +381 18 49 962 [email protected], [email protected] Behavior of mechanical systems exhibiting impacts is of great relevance in many practical engineering problems. Mechanical systems with impact interactions have wide applications in engineering as the most intensive source of mechanical influence on materials, structures and processes. Periodic oscillations with impacts take place very often in machine dynamics, structure machine, vibration engineering, vibration ecology problems as well as in ambient buildings and city structures etc. Oscillatory systems exhibiting impacts are of great relevance in many practical engineering problems. Stability problems of one group of periodic impact motions can be solved in the analytical form. “Accurate” method of “adjustment” by Kobrinski [1] was first developed and later different models of impacts introduced by Babicki [2], Masri and Caughay [3] and other were developed. If dynamic model of vibro-impact system is described with differential equations whose solutions can be found, the coordinative increments of positions and speeds can be expressed with help of small increments of integration constants and phases. After determining small increments of coordinative positions and speeds for the two following intervals, there should be used adjustment conditions, i.e. limit conditions and periodical conditions expressed in shape of small increments of coordinative positions and speeds as well as time, in the moment of impact which appears between that two following intervals. Then the recurrence links are obtained between small increments of arbitrary constants for two following intervals in shape of linear systems of homogeneous equations, of final differences in relation to small increments. The question of periodic vibro-impact process stability is solved considering recurrent relations, which link small disturbances of integration constants. These constants can be expressed in the shape of the product:

GC ji h j E i , where h j does not depend on i interval, and E is a constant number. So the question of stability is reduced to the problem of determining E . System of linear equations with small disturbances, has obtained, is homogeneous and has nontrivial solution if determinant of system is equal zero. The roots of characteristic determinant characterize stability of examined vibro-impact regime. For vibro-impact system with n / 2 degrees of freedom, characteristic determinant has n roots. If root modules of characteristic equations are less then one, then for the great number of impacts the movement is stable. The case when module of at least one root of characteristic equation is equal to one or it is higher and then bifurcation appears. On the basis of this method, the analytical procedure for determining stability of the periodic motion pendulum with rigid barriers, which limit the amplitude variation from its central position, was treated. It is considered in both the normal (downward) position and in the upright (inverted) position. The overall dynamics of the harmonically excited pendulum include impacts with the rigid arresters. This method is used for determining the characteristic equation for assessing stability of vibroimpact pendulum system’s periodic motion. Also, this method is used for determining the characteristic equation for assessing stability of the vibro-impact system’s periodic motion that consists of mass, spring, damper and a rigid arrester set at a particular distance from the mass’s

S. Mitic

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equilibrium position. The mass, acted upon by one or two asynchronous excitation forces, thus inducing the mass’s oscillatory motion interrupted by impacts upon the rigid arrester. New direction in developing theory about vibro-impact systems appears with development of bifurcation and chaos theory, which is enabled with improving computer technique and with using numerical and experimental methods (Moon and Rand [4], Shaw and Holmes [5], Peterka and Kotera [6], etc.). After 80‘s, a great number of authors are occupied with different models of vibroimpact systems where basic oscillatory system is described with linear differential equations, but complexity of problem as nonlinear exists because of the influence of impacts which provoke free oscillations of system additionally in relation to forced oscillations. In later years, it can be noticed from accessible literature that Peterka and Kotera gave significant contribution in their works, and they are giving generalized solutions about transitions between different types of impact motion and ways of how motion of system develops from periodic to chaotic. It is characteristic of vibro-impact systems that at simple deterministic system with periodic initiative, reactions are various, from possibilities of periodic to chaotic motion. In the case of vibro-impact system, Peterka [7], after analytical procedure on the basis of adjustment” method (small disturbances of amplitude and phase), with use of numerical procedure, were determined limits of stability with determining number E . The transition between periodic and chaotic impact motion on the limit of saddle-node bifurcation is very sensitive to system parameter change, which come from the character of saddlenode instability. Laws of transition from periodic to chaotic impact motion are explained with help of their areas of existence and stability, bifurcation characteristics and phase trajectories, of symmetrical and asymmetrical periodic process, and phase trajectories for vibro-impact system where oscillator is described with Duffing’s differential equation with one periodic initiative force, where the initiative of scratching impacts can be seen. In relation to stereotype oscillatory theory by which reaction is periodical if initiative is periodic, in theory of vibro-impact systems that becomes unbearable, reaction can be of chaotic character, because of bifurcation occurrence, and because of unpredictable additional impacts which reduce kinetic energy and amplitudes of motion system. Although the system is returning to the condition before bifurcation, initiative force is providing energy, amplitudes are growing and additional impacts are arising again with possible effect of chaotic motion. Keywords: stability, vibro-impact system, periodic motion, chaotic motion, bifurcation, phase trajectories.

References 1.

Kobrinskii, A.E., Kobrinskii A. A., Vibroudarni sistemi, Moskva, Nauka, 1973.

2.

Babicki.I. , Teorija vibroudarnih sistema, Moskva, 1978.

3.

Masri S.F., Caughay T. K.,O. S. of the I.D., Trans. of ASME, september, 586-592,1966.

4.

Rand, R.H. and Moon, F.C., B. C.. Int. J. Non Linear Mechanics, Vol.25, No.4: 417-432,1992

5.

Shaw S.W., Holms P.J., A P. F.I. O. , Journal of Applied Mechanics, Vol. 50/849-657,1983.

6.

Peterka. F. and Kotera, T., R.of E., Acta Technica CSAV. No.1 : 92-117, 1982.

7.

Peterka, F., D. of M.S., EUROMECH-2nd ENOC. Prague 1996

5. Integrity of Dynamical Systems

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Opening Invited Lecture

DYNAMICAL INTEGRITY OF NONLINEAR MECHANICAL OSCILLATORS S. Lenci and G. Rega Dip. Architettura, Costruzioni e Strutture, Università Politecnica delle Marche, via Brecce Bianche, 60131, Ancona, Italy Dip. Ingegneria Strutturale e Geotecnica Università di Roma “La Sapienza” via A. Gramsci 53, 00197, Roma, Italy [email protected], [email protected] This work overviews and continues recent investigations of the authors [1, 2] on the dynamical integrity of nonlinear mechanical systems and other oscillators. In fact, it has been realized that attractors must be paralleled by uncorrupted basins for safe practical applications [2, 3]. Eroded basins constitute a critical state for the structure corresponding to its impending failure, which can be instantaneous in the presence of perturbations or uncertainties. On the other hand, using the structure only when erosion is prevented may be too much conservative, because it can actually survive safely well above the relevant threshold if the erosion is not sharp. These considerations triggered detailed investigations of the safe basin erosion, which is basically constituted by four steps [2]. 1

Choice of the right definitions of “safe basin” and integrity measure. They may vary, e.g., (i) if one is interested in transient or steady dynamics, and (ii) if fractality of the basin can be accepted or must be disregarded, and have to be chosen according to the specific problem. Also the availability of fast algorithms for computing the integrity measure plays a role, because all of the following steps are very time consuming.

2

Investigation of the basins evolution. This item can be done only by extensive and systematic numerical simulations. However, key information, either exact or approximate, have to be obtained by studying the global bifurcations responsible for the main metamorphoses of basin boundaries, which sometimes enlighten on and explain in detail the hidden complex dynamical mechanisms.

3

Construction of the erosion profile for a varying system parameter, e.g., the excitation amplitude. This step is crucial because it permits to estimate how the dynamical integrity depends on the considered parameter. Moreover, it is very important in practical applications because it possibly allows for optimal choices of the parameter, if the erosion profile has maxima, or suggests to stay far apart from dangerous sharp falls of the profile. Indeed, it has been noted [2] that the erosion profiles are usually sharp in the neighborhood of resonance frequencies, whereas they are dull elsewhere.

4

Study of the collapse of the safe basin. In fact, the erosion ends with the onset of out-ofwell phenomena, namely, with the occurrence of scattered attractors, for multi-well hardening oscillators, or escape (which can have different physical meaning, e.g., overturning for rigid blocks, capsizing for ships, collapse to the substrate for electrodynamically actuated microbeams, etc.), for softening oscillators. According to the various cases, the structure itself may collapse or survive (in a desirable or unwanted way) after this event.

The second point that will be addressed is how it is possibly to maintain the dynamical integrity under severe conditions, or, equivalently, how it is possible to reduce or shift the safe basin erosion. In this respect, a technique previously developed by the authors [1] for controlling

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nonlinear dynamics and chaos will be applied. The method consists in optimally eliminating appropriate homo/heteroclinic bifurcations by varying the shape of the excitation, and it is based on the observation that the erosion phenomenon is usually triggered by the global bifurcation of a given (usually hilltop) saddle, although it can also involve other topological events [2, 3]. The elimination, or shift in parameter space, of this bifurcation – which is the key point of the method – is thus expected to have positive effects in terms of dynamical integrity of the system. Several uncontrolled and controlled erosion profiles of various mechanical oscillators will be built, investigated in detail and compared with each other to the aim of verifying the performances of control. Indeed, control method and dynamical integrity are intimately connected. In fact, the control permits to shift erosion, i.e., to maintain integrity. On the other hand, the ability of control in shifting the erosion profile is an important tool to check its practical effectiveness. Apart from overall developments, in this paper previous works are extended in at least two specific directions. First, further mechanical systems are considered and compared with each other, possibly in different dynamical regimes. This permits to enlighten on various aspects which were not adequately studied. Second, special attention is devoted to a new class of solutions, namely the rotating solutions of the mathematical pendulum, which are different from fixed points and oscillating solutions (of various mechanical systems) considered in previous works, and are likely related to different topological phenomena. Moreover, they are important in nowadays practical applications. Another novelty of this class of solutions is that they are born by a saddle-node bifurcation at a certain level of excitation amplitude. This is quite different from the solutions studied in previous works, which have no triggering bifurcation and exist also in the unforced case. In terms of erosion profiles this is expected to entail strong differences. In fact, while in the latter case the integrity measure is a decreasing function of the excitation amplitude and provides the well known “Dovercliff” erosion profile [3], in the former case the profile initially increases due to the onset of solution basin up to reaching one or more local maxima, then it is eroded by the incursion of unsafe fractal tongues from outside and eventually collapses. This question, which has also some effects in terms of normalization of the erosion profiles needed to compare different systems, will be discussed in detail.

References 1.

Lenci, S. and Rega, G., A unified control framework of the nonregular dynamics of mechanical oscillators,” J. Sound Vibr., vol. 278, 1051-1080, 2004.

2.

Rega, G. and Lenci, S., Identifying, Evaluating, and Controlling Dynamical Integrity Measures in Nonlinear Mechanical Oscillators, in press, Nonlinear Analysis, T.M.&A, 2005.

3.

Thompson, J.M.T., Chaotic Behavior Triggering the Escape from a Potential Well, Proc. Royal Soc. London A, vol. 421, 195-225, 1989.

8. Modelling of Material Property Data and Fracture Mechanisms

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FATIGUE CRACK INITIATION AND PROPAGATION AT HIGH TEMPERATURE IN A SOFTENING MARTENSITIC STEEL B. Fournier1,2, M. Sauzay1, M. Mottot1, V. Rabeau1, A. Bougault1 and A. Pineau2 1CEA, DEN-DMN-SRMA, Batiment 455, 91191 Gif-sur-Yvette cedex, France. 2ENSMP, Centre des Matériaux P.-M. Fourt, UMR CNRS 7633, BP 87, 91003 Evry, France. [email protected] Martensitic steels of the 9Cr1Mo family have been selected for advanced power generation systems, in particular because of their high thermal conductivity and low thermal expansion coefficient [1]. Typical in-service conditions with repeated start- and stop-operations lead to loadings of creep-fatigue type at high temperature (between 673 and 873 K) , with very long hold times (typically one month). Submitted to cyclic loading these martensitic steels are known to soften both under pure fatigue and under creep-fatigue loading [2,3]. Pure fatigue and creepfatigue mechanical tests were performed for different cyclic and creep applied strains. Fig. 1 shows that the number of cycles to failure decreases with increasing applied creep strain but the time to failure strongly increases. The interaction between fatigue and creep damage is illustrated by the map drawn in Fig. 2. SEM and optical observations of both the body and the fracture surfaces and of longitudinal sections were performed. In pure fatigue, the usual striations are observed but the observation of the tortuous propagation paths of secondary cracks (Fig. 3) reveals the strong influence of environment and recalls the paths usually observed under fatigue-corrosion interactions. In creepfatigue tests both transgranular and intergranular propagation are observed on the same sample. The environment is found to have a strong influence on the crack propagation. The more damaging effect of hold times in compression is attributed to the environment effect [4], the mean stress effect and a higher crack nucleation rate. The number of secondary cracks is the smallest for pure fatigue tests, and is higher for compression than for tension hold times. Short secondary cracks are found to be completely filled with oxide, whereas for long secondary cracks the amount of oxide depends on the nature of the hold period. In addition, the growth of the oxide layer is found to be strongly different depending on the type of loading. WDS measurements reveal that both inner and outer oxidation take place and differences in the oxide layer compositions are observed. An attempt is made to use the results of these mechanical tests and metallurgical observations to model the creep-fatigue-oxidation interactions in this steel.

FIGURE 1. Evolution of a) the number of cycles to failure and b) the time to failure for increasing creep strain in creep-fatigue tests with 'Ht=0.7% at 823K.

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FIGURE 2. Interaction between fatigue and creep damage.

FIGURE 3. Observation of secondary cracks in longitudinal sections for a) a pure fatigue test at 823K and b) a creep fatigue test at 823K.

FIGURE 4. Observation of secondary cracks on the specimen surface, with the oxide layer etched away, in a creep-fatigue test at 823K with a) compression hold time and b) tension hold time.

References 1.

Swindeman, R.W. et al., Pressure Vessels and Piping, 507-512, 2004.

2.

Kim, S., Weertmann, J.R., Metall. Trans. A19, 999-1007, 1988.

3.

Lukas, P., Kunz, L., Sklenicka, V., Mat. Sci. Eng. A129, 249-255, 1990.

4.

Hecht, R.L., Weertman, J.R.. Metall. Trans. A24, 327-333, 1993.

8. Modelling of Material Property Data and Fracture Mechanisms

815

TRANSFERABILITY OF CLEAVAGE FRACTURE PARAMETERS BETWEEN NOTCHED AND CRACKED GEOMETRIES C. Bouchet1, B. Tanguy1, J. Besson1, A. Pineau1 and S. Bugat2 1Ecole des Mines de Paris, Centre des Materiaux, Evry Cedex, France 2EDF Les Renardieres, Ecuelles, Moret-sur-Loing, France [email protected] In the recent past, the local approach to fracture has shown its capacity to be a predictive tool in many complex cases of structural integrity assessment [1]. Brittle fracture of steels is one of the fields where local approach has brought a lot of understanding (e.g. effect of prestraining, effect of dynamic loading [2]). In the nuclear industry, local approach to fracture is often used as a complementary tool to the code (e.g. ASME) in order to reduce the empirical margins and to contribute to a better understanding of the physical mechanisms which can lead to fracture. Most of the successful models devoted to the description of cleavage fracture are based on the weakest link assumption. One of the pioneering models devoted to low temperature cleavage fracture, the Beremin model [3], has linked the fracture probability with the defects population through the Weibull stress concept. Besides its physical bases, the success of this model relies on the small number of parameters that has to be calibrated. In the original study, notched tensile specimens with different radii were used to calibrate the parameters over a given range of temperatures, the model was then applied successfully to predict lower shelf fracture toughness values of an A508 cl.3 steel. However the capacity of the model to predict cleavage fracture toughness values with the same set of parameters when temperature increases, i.e. on the lower part of the transition region, has been questioned in the litterature[4]. One underlying problem is that for the same temperature, extensive plasticity may develop in notched tensile specimens whereas it remains confined in deep-cracked geometries because of constraint conditions. On the other side, the use of different temperatures for parameters calibration and toughness predictions raises concerns about the temperature effect on the parameters, which were assumed to be temperature independent in the original model. In order to investigate the transferability of cleavage fracture parameters in the lower part of the transition region, a large experimental program was carried out on an A508 cl.3 pressure vessel steel. The scope of this study is firstly to give some insights on the evolution of cleavage fracture mechanisms with increasing temperature for notched tensile and deep-cracked geometries. Secondly, based on a large number of specimens to deal with statistical aspects, several strategies have been carried out to calibrate the cleavage fracture parameters using the Beremin model. Experimental investigations include a large set of quasi-static mechanical tests : notched tensile (NT) specimens with 3 different radii tested at five temperatures (-150°C, -130°C, -100°C, -70°C,-40°C) covering pure cleavage fracture up to full ductile behavior, deep-cracked CT specimens with 2 different thicknesses (12.5 and 25 mm) tested over a large temperature range, with elastoplastic fracture toughness values ranging from 45 up to 600 MPa.m1/2 . Range of macroscopic failure strains for notched tensile specimens are given in Tab. 1. Besides mechanical tests, a fractographic investigation was done for each tested specimen using scanning electron microscopy. Both the nature of the site at the origin of the cleavage initation and its position on the fracture surface was studied. Evolution of the nature of the cleavage triggering sites with temperature is given for the different geometries. It is shown that for a given temperature and for a fracture mode which remains macroscopically brittle, manganese sulfide inclusions play an

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increasing role in the notched tensile geometries whereas such inclusions were not found in deepcracked geometry. TABLE 1. Macroscopic failure strain range for the tensile notched specimens (*:fully ductile)

Based on Axisymetric and 3D F.E. simulations, the local parameters (principal maximum stress, plastic strain and triaxiality ratio) were calculated at the site of cleavage initiation for all the tests performed. Several strategies were then carried out to determine the Beremin model parameters. In a first step, the parameters were determined at a fixed temperature and using the different notched tensile geometries (with the 3 different radii). In a second step, the results obtained in the whole range of temperatures for one given geometry were used. Finally, the whole set of experimental data was used. The values of the different sets of parameters are then discussed. Capacity of the model to predict the fracture toughness data is then discussed based on the observed fracture micromechanisms.

References 1.

Burstow, M.C., Beardsmore, D.W., Howard, I.C., Lidbury, D.P.G., Int. J. Pressure Vessels and Piping, Vol. 80, 775-785, 2003.

2.

Minami, F., Kazushige, A., J. of Pressure Vessel Tech., Vol. 123, 362-372, 2001.

3.

Beremin, F.M., A., Met. Trans., Vol. 14A, 2277-2287, 1983

4.

Wiesner, C.S., Goldthorpe M.R., Journal de Physique IV, Vol. 6, C6-295—C6-304, 1996

8. Modelling of Material Property Data and Fracture Mechanisms

817

RELATION BETWEEN CRACK VELOCITY AND CRACK ARREST M. Hajjaj1,2, C. Berdin1, P. Bompard1 and S. Bugat2 1Laboratoire de Mecanique des Sols, Structures et Materiaux, Grande Voie des Vignes, 92295 Châtenay-Malabry, France 2Electricite de France, R&D Division, Département MMC, Les Renardieres, 77818 Moret-surLoing cedex, France [email protected], [email protected], [email protected], [email protected] Initiation fracture toughness is a material parameter well established to predict crack initiation. An improved fracture design for security component could be obtained in predicting crack arrest. Arrest fracture toughness can be used for that purpose. However, this parameter although studied for a long time [1] is still questionable, even though a standard test procedure was developed in [2]. The influence of dynamic effects on crack arrest are often invoked and the assessment of arrest toughness under static analysis could lead to a dependence with specimen geometry [ 2]. The purpose of this paper was to determine the mechanical state ahead of a crack tip during crack propagation at high velocity and arrest under quasi-static loading, in order to later study a local fracture criterion. Crack arrest experiments were performed using a notched disk taken from a A533 Cl.B type steel, submitted to a thermal shock. This test was initially developed at Ecole des Mines de Paris [3]. The specimen consists in a ring with a radial fatigue pre-crack issued from on its outer surface (Fig. 1). It is first cooled at -196°C and its inner surface is then warmed up at about 600°C in 10s using an electromagnetic inductor. After brittle crack initiation, crack propagates towards areas of increasing toughness due to temperature rise. Crack arrest occurs after a few centimetres of high speed propagation. Temperature field is measured by thermocouples introduced inside the specimen. Crack velocity, which is about 600m.s-1,is measured by crack gages. A deceleration during the last few millimetres of propagation was noted. Detailed experimental results are reported elsewhere [Hajjaj 4]. Finite element modeling was used in order to obtain mechanical states at initiation, during the propagation and at arrest of the crack. The element size at crack tip was down to 50 Pm. Temperature loading was prescribed according to the experimental measurements. Temperature dependence of the elastic-plastic behaviour of the material was accounting for. Strain rate dependence was modelled through a Cowper-Symonds law. The release node technique was used to represent the crack propagation. Different assumptions were made about the crack velocity: an imposed constant crack velocity during crack propagation up to crack arrest, or crack deceleration prescribed as measured in experiments. Considering high crack velocity, dynamic computations were performed.

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FIGURE 1. Precracked ring specimen : a crack length, W, width of the ring (left); Stress intensity factor assessment during crack propagation (right). Stress and displacement analyses at the crack tip showed that elastic singularity is dominant as expected in viscous material [Kalthoff 1990 5]. The results are represented in terms of stress intensity factor (Fig. 1). Crack velocity history has a major influence on the mechanical state ahead of the crack tip: the stress intensity factor, i.e. the opening stress ahead the crack tip, highly increases and then decreases since the crack decelerates. Post-arrest analyses showed that it oscillates at the frequency of the first opening mode of the cracked specimen. In the case of the constant crack velocity, this vibration mode occurs only after crack arrest, whereas, in the case of the crack deceleration, it takes place during the last millimetres of propagation at low velocity. Different computations showed that this is not explained by different times to arrest. Comparison between stress intensity factors at arrest crack (the last points of the two curves in Fig. 1) indicates that there can be a large uncertainty of the mechanical state at arrest assessment, due to crack speed assumption. It seems therefore essential to account for the actual crack velocity in order to predict crack arrest, either in generation or propagation modelling.

References 1.

Bluhm, J.I., In Fracture V, edited by H. Liebowitz, Academic Press, New York, 1969, 2-60.

2.

Kalthoff , J.F., In Crack Dynamics in metallic materials, edited by J.R. Klepaczko, SpringerVerlag, New York, 1990, 69-254.

3.

Bouyne, E., Joly, P., Houssin, B., Wiesner, C.S., Pineau, A, Fat. Fract. Eng. Mat., vol. 24, 105-116, 2001.

4.

Hajjaj, M., Bugat, S., Berdin, C., Bompard, P., in Proceedings of ASME Pressure Vessels and Piping Conference, 2004.

5.

Freund, L.B., Dynamic fracture mechanics, Cambridge university Press, 1990.

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MECHANISMS OF DAMAGE AND FRACTURE IN TRIP ASSISTED MULTIPHASE STEELS G. Lacroix, Q. Furnemont, P.J. Jacques and T. Pardoen Departement des Sciences des Materiaux et des Procedes, Universite catholique de Louvain, IMAP, Place Sainte Barbe 2, B-1348, Louvain-la-Neuve, Belgium [email protected], [email protected], [email protected] A wide range of applications, especially in the automotive industry, require both large ductility and high strength, two properties that are unfortunately antagonist. TRIP-assisted multiphase steels, i.e. steels consisting of an intercritical ferrite matrix with retained austenite, bainite and martensite dispersed phases [1] provide extremely good combination of these two properties. In TRIP steels, the mechanical contribution adds to the chemical free enthalpy as a driving force for martensitic transformation of the metastable austenite. This transformation acts like an additional workhardening source that allows to increase both ductility and tensile strength [2]. The martensite transformation of metastable austenite has been reported to have either a beneficial or a detrimental effect on fracture toughness [3,4], depending probably on the complex relationship between austenite stability, austenite volume fraction and martensite brittleness. In this work, three different steel compositions have been studied in order to vary the initial austenite content and two heat treatments have been defined in order to vary the austenite stability. Fracture test were carried out on precracked Double Edge Notched Tension (DENT) specimens in order to characterize the damage mechanisms and the toughness of these steels. At a microscopic scale, the size of the transformed zone at the crack tip was measured by Orientation Imaging Microscopy (OIM). The damage sites and crack path have been characterized in the near crack tip region by SEM. The macroscopic toughness was measured by loading several DENT specimens to reach different amount of crack advance. The Crack Tip Opening Displacement (c) and the J integral at cracking initiation were determined. These two parameters quantify the cracking initiation toughness. Some DENT specimens with different ligament lengths were also loaded up to fracture. These tests allowed to estimate the essential work of fracture (we) which is a more physical parameter for quantifying the resistance to crack propagation in thin plate than the tearing resistance extracted from a JR curve. From the combination of the microscopic and macroscopic results, the damage mechanisms and the initiation fracture process were determined precisely (see Fig. 1): the transformation of all the austenite in martensite takes place very early in the fracture process zone during the crack opening process[5], then damage develops by decohesion between the ferrite and the martensite [5], followed by the coalescence along the interface between the ferrite and the second phase.

FIGURE 1. Damage mechanisms and fracture process (F=ferrite, B=bainite, A=austenite and M= martensite lathes).

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Figure 2 compares the we values and the Jc values. Whereas Jc seems to be strongly linked to the austenite content, we presents another behavior that can be explained by the different austenite stability. The necking and the damage contribution have been partitioned for the J integral and we [6]. Both quantities contain a contribution cracking from necking and from material separation. The separation of these two contributions has allowed to understand the variations shown on Fig. 2 as well as the difference between we and Jc.

FIGURE 2: Macroscopic toughness values (We and J) as a function of the austenite content.

References 1.

Jacques, P.J., Cornet, X. , Harlet, Ph., Ladrière, J. and Delannay, F., Metall. Trans. A, 1998, 29A, 2382.

2.

Jacques, P. J., Furnémont, Q., Mertens, A. and Delannay, F., Philosophical Magazine A, vol. 81 (7), 1789-1812, 2001.

3.

Chen, J.H., Kikuta, Y., Araki, T., Yoneda, M. and Matsuda, Y., Acta Metall., 1984, 32, 1779.

4.

Antolovich, S.D. and Singh, B., Metall. Trans., 2, 1971, 2135-2141.

5.

Jacques, P. J., Furnémont, Q., Pardoen, T. and Delannay, F., Acta Materialia, vol. 49, 139152, 2001.

6.

Pardoen, T., Hachez, F., Marchioni, B., Blyth, P.H. and Atkins, A.G., J. Mech Phys solids, 52, 423-452, 2004.

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THE ROLE OF SUB-BOUNDARIES IN THE BRITTLE FRACTURE OF POLYCRYSTALLINE MATERIALS Gareth Hughes1, Peter Flewitt1, Fabio Sorbello1, Gillian Smith2 and Alan Crocker2 1Interface Analysis Centre, University of Bristol, Bristol, BS28BS, UK 2Department of Physics, University of Surrey, Guildford, GU27XH, UK [email protected] , [email protected] Grain boundaries are resistant to the propagation of cleavage cracks in polycrystalline materials. Indeed, the importance of grain boundary orientation on the propagation of cracks, and in particular brittle cracks has been recognised by various workers [1,2]. In a polycrystalline material, the effective cleavage planes and therefore cracks in adjacent grains do not meet each other in a line in the common boundary, except in special circumstances. Therefore if the polycrystal is to separate into two parts some additional failure at the grain boundary must occur; this can take the form of multiple cleavage, brittle intergranular failure or ductile fracture [3]. However, in different metals and alloys, a range of other boundaries and interfaces are encountered, which can modify the propagation of brittle cracks, and in particular cleavage. Examples are twins observed in bcc and hcp metals, martensite and bainite in ferritic steels and more generally, interphase boundaries. Although the importance of these boundaries on the initiation and propagation of cracks has been recognised for many years, there has been little attempt to address the interactions involved. Various techniques are available to examine the detail of these local crack boundary interactions ranging from simple optical microscopy to high resolution scanning electron microscopy and in some cases, scanning probe techniques. More recently, Hughes et al. [4] have demonstrated that focussed ion beam (FIB) techniques, which combine high resolution imaging and milling, can be used to study the interaction between cleavage and grain boundaries in hcp materials. In this paper, we consider the influence of twin boundaries in bcc and hcp metals and alloys. The experimental results are then compared with the predictions obtained from microscale geometrical models, as described by Crocker et al. [3]. Several materials have been investigated to consider different twin sub-boundaries. These include a bcc nominal iron-3%-silicon steel, hcp zinc and Zircaloy. Each material has been heat treated to optimise the grain size and the brittle fracture mode so that the role of the twin boundaries on crack propagation can be investigated over a range of temperatures. The main instrument for investigation of the fracture surfaces has been the FEI Strata FIB201 focussed ion beam system, capable of producing high resolution images with microstructural information from both surface and sub-surface regions. Specimens of both hcp zinc and the bcc Fe-3%Si transformer steel were fractured at low temperature, spanning the lower shelf end of the brittle to ductile transition curve. The experimental observations for hcp zinc have shown that cleavage cracks can propagate either across twins or along twin boundaries. Hence the computer models to describe fracture in hcp zinc have been revised to incorporate both of these interactions between {10-12} twins and either basal (0001) or prismatic {10-10} cracks. Initially, the models have one twin per grain, which, when combined with either basal or prismatic cleavage contributions, predicts that a small amount of grain boundary accommodation is required. This prediction is consistent with the lack of observed grain boundary failure at low temperatures, where twinning is observed. Further investigations into the effect of twins and sub-boundary failure will be discussed through the examination of the brittle fracture of commercial Zircaloy alloy.

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Again, for the lower temperature fractures of bcc Fe-3%Si steel, {112} twins in the material are visible, emergent on {001} cleavage facets, where there is limited cracking along the twin interface. This is also accompanied by a localised form of accommodation, which has little effect on overall propagation of the cleavage crack. Again the computer models have been revised to accommodate the role of {112} twins. The implication of these results from experiments conducted over a range of temperatures spanning the brittle to ductile transition for both hcp and bcc materials will be discussed, with respect to the fracture mechanisms. The links between the geometric modelling and experimental work will be examined, with a view to explaining how the models have been developed, and comparisons between modelling predictions and experimental findings will be discussed. Finally, progress on experimental work and related modelling on the influence of bainitic substructure, developed in the prior austenite grains of an A508 steel, on the propagation of cracks will be discussed.

Acknowledgements The project from which this work is taken involves collaborations with Professors JF Knott (University Birmingham, UK) and V Randle (University of Wales-Swansea, UK) and is supported by the EPSRC. Professor Flewitt would like to thank BNFL British Nuclear Group, for allocating him time to work at the University of Bristol.

References 1.

Crocker, A.G., Smith G.E., Flewitt P.E.J. and Moskovic R., Materials Science Forum, 294296, 674, 1999

2.

Argon A.S. and Qiao Y., Philos. Mag. A, 82A, 3333-3347, 2002

3.

Crocker A.G., Flewitt P.E.J.and Smith G.E., Int. Mat. Rev. 50, 99, 2005

4.

Hughes G.M., Smith G.E., Crocker A.G. and Flewitt P.E.J., Mats. Sci. and Tech., to be published, 2005

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THREE-DIMENSIONAL MODELLING OF FRACTURE IN POLYCRYSTALS Gillian Smith1, Alan Crocker1, Gareth Hughes2 and Peter Flewitt2 1Department of Physics, University of Surrey, Guildford, Surrey GU2 7XH, UK 2Interface Analysis Centre, University of Bristol, Bristol BS2 8BS, UK [email protected], [email protected] A great deal of research has been carried out on modelling the fracture of polycrystalline materials. However, this has been largely restricted to 2-D models and special cases of 3-D models, e.g. Smith et al. [1], Crocker et al. [2]. Using 2-D models, brittle cleavage cracks in adjacent grains meet at a point in their common grain boundary. A crack can therefore propagate from grain to grain without the necessity of any grain boundary failure. In real materials this is not the case. Cleavage cracks in adjacent grains do not in general meet in a line in their common grain boundary so that some grain boundary failure or an equivalent accommodation mechanism, such as multiple cleavage or ductile tearing, must occur. For this and many other reasons it is important to develop satisfactory 3-D models, Smith et al. [3]. The simplest that have been used are in the form of a body-centred cubic array of identical, regular tetrakaidecahedra (14-hedra). These have suggested that of the order of 30% of brittle fracture is in the form of accommodation grain-boundary failure. This does not include complete grain boundaries that fail because of some inherent weakness. The figure of 30% is much greater than most reported experimental values and therefore there is a need for more realistic 3-D models. One approach has been to construct prismatic grains on a random array of 2-D polygonal cells. This is a good approximation of the structure of columnar grains in weld metal and again suggests that in brittle fracture about 30% of accommodating grain boundary failure is needed.[1] However, as the prisms are effectively of infinite height, this figure gradually increases as fracture propagates. A general 3-D model has therefore been developed. This has the form of a cube within which randomly positioned grain nuclei are generated. Grains grow radially from these nuclei until they meet their neighbours and thus generate randomly-shaped grains with flat polygonal faces. Information about these grains and their connectivity is held in the computer using parent-child links, relating grains to faces (F), edges (E) and vertices (V). This paper will describe applications of an example of this model with 45 grain nuclei. Only 5 of these grains are completely enclosed within the model, which at first was surprising but in fact is to be expected. The remaining 40 grains meet the surface and of these 29 have one or more faces in common with the interior grains. Striking features of the grains are the occurrence of many relatively small faces, several elongated faces, and vertex angles very different from the ideal equilibrium angle of 109.5o. The interior grains have 13 to 15 faces, 33 to 39 edges and 22 to 26 vertices, the averages being 14.2, 36.6 and 24.4, satisfying Euler's formula, V – E + F = 2. These values are close to those for the regular 14-hedron: F = 14, E = 36, V = 24. The average number of edges per face is 5.03 for the model compared with 5.14 for the 14-hedron. To fracture the model a stress axis is defined and each grain is allocated a crystallographic orientation and therefore cleavage planes appropriate to the material being investigated. Relative energies are then assigned for the available fracture mechanisms depending on the temperature. A crack is nucleated in the most favourably oriented grain and it is assumed that the projection of the fracture front on the plane perpendicular to the stress axis increases radially with time. When this crack reaches a grain boundary the weakest path is chosen for propagation. As fracture progresses

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the amounts of transgranular and intergranular brittle and ductile fracture and their associated energies are recorded. When applied to a model representing ferritic steels three orthogonal {001} cleavage planes are used. The amount of grain boundary failure around the grain in which the initial cleavage crack nucleates is then about 15% but as fracture propagates this soon rises to 27%, similar to the 30% found in earlier models. In this case it is assumed that multiple cleavage and ductile failure do not occur. The model is also being used to investigate the fracture of polycrystalline zinc. It was anticipated that this would be a relatively simple exercise as it was expected that cleavage only occurred on the basal (0001) plane. However experimental work on zinc has demonstrated that cleavage also occurs on prismatic planes and along twin boundaries so that the situation is complex, Hughes et al. [4]. Currently the surface grains in the above model are being studied and a crack nucleated in one of the interior grains is being allowed to propagate to the surface of the model. Cracks are also being nucleated at the surface of the model rather than in the interior. Different weighting factors are being examined for cleavage, grain boundary and ductile failure and distributions of fracture energies are being introduced. The alternative accommodation mechanisms of multiple or stepped cleavage and ductile failure are also being considered. Grain substructures, such as twin boundaries and bainitic boundaries, are being introduced following experiments that demonstrate the importance of these features. It is also proposed to use larger models with more complete interior grains. Selected results from this work will be reported and compared with the associated experimental research.

Acknowledgements The project upon which this paper is based, which involves collaboration with Professor John Knott at the University of Birmingham and Professor Valerie Randle at the University of Wales at Swansea, is supported by EPSRC. Professor Flewitt would like to thank BNFL British Nuclear Group for allocating him time to work at Bristol University.

References 1.

Smith, G. E., Crocker, A. G., Moskovic, R. and Flewitt, Philos. Mag. A, vol. 82, 3443-53, 2002.

2.

Crocker, A. G., Flewitt, P.E.J. and Smith G. E., Int. Mater. Rev., vol. 50(2), 99-124, 2005.

3.

Smith, G., Crocker, A. and Flewitt, P., In Proceedings of the 15th European Conference on Fracture, CD-ROM, KTH. Stockholm, 2004.

4.

Smith, G., Hughes, G., Flewitt, P., and Crocker, A., In Proceedings of the 2nd International Conference on Multiscale Materials Modeling, Naser M. Ghoniem ed., UCLA, 2004, 282-4.

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ANTI-WING CRACK GROWTH FROM SURFACE FLAW IN REAL ROCK UNDER UNIAXIAL COMPRESSION Robina H. C. Wong1, Y. S. H. Guo2 , L. Y. Li3, K. T. Chau1 , W. S. Zhu2 and S. C. Li2 1Civil and Structural Engineering Depart., The Hong Kong Polytechnic University, Hong Kong 2Geotechnical & Structural Engineering Research Center, Shandong University, 250061,China 3The China University of Mining and Technology, Beijing, China [email protected] According to unofficial estimation, within the 20th century 3.5millions people die in natural disaster, of which over 40% was by earthquakes. Earthquakes remain one of the worst natural disasters posing threats to human civilization. For example on 21 September 1999, an earthquake of magnitude of 7.6 occurred near Chi-Chi Taiwan, causing about 2317 death, 8722 injured, and 51761 buildings collapses [1]. A surface rupture, which is more than 100 km long is associated with the earthquake. The first 90 km surface rupture running roughly followed the known Chelungpu fault in north-south direction, then the surface rupture turned east creating a new fracture zone going through the Shihkang Dam, at where waterfall was formed from a flat riverbed, and the maximum surface displacement of the surface rupture was about 7 m in both vertical and horizontal directions. This newly formed fault arouse much international attention regarding its formation mechanism and many studies are still ongoing. The fault rupture mechanism is still not fully understood. The rupture mechanisms from pre-existing 3-D fault is worth to investigate for it has both academic merit and of societal need. A series of experiments have been conducted on 3-D opened surface fault (or flaw) in both artificial (PMMA) and real rocks (marble, gabbro and sandstone) under uniaxial compression [23]. It was found that the mechanisms of fracture propagation in homogeneous (PMMA) material may not be the same as in inhomogeneous materials (real rock). Under the uniaxial compression, wing crack (tensile crack) and petal crack are very common observed in the PMMA specimen (Fig. 1a) and in some of marble specimens (Fig. 1b). However it was observed in other real rock specimens, tensile cracks induced along the opposite direction of the wing crack first (Fig. 1c to 1e). This is the so called anti-wing crack while the wing crack or compressive crack induced at the later stage (Fig. 1c & 1d). This phenomenon has not been reported before. According to the stress field around the flaw tip on the homogeneous material [4-5], the maximum tangential stress VTmax is near the position of T S/2(90q). The definitions of I and T are given in Fig. 2. It is further supported by the observation form the PMMA specimen where the wing crack propagates upward while the lower one propagates downward. However, it is not clear why anti-wing tensile cracks induced in most of the real rocks first. According to the acoustic emission (AE) measurements (see Fig. 1e), the AE signals supported the observation from the real rock specimen where anti-wing crack would induce first. This interest phenomenon is worth to further investigate.

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FIGURE 1 Crack growth form flaw tip (1a to 1e). Acoustic essmision (AE) sensors were mounted on the surface of specimen to detact the AE signal (1e). The AE signle induced around the flaw area (1f). The surface of real rock specimens is painted to produce a big contrast for crack observation.

FIGURE 2 The stress field around a partially circular crack as a function of orientation I and location angle T. The curves shows the maximum normalized stress VT/Vcr various angle T at different orientation I Acknowledgements: The study was supported by the Hong Kong Polytechnic University (APG46) and the National Natural Science Foundation of China to Zhu-WS (40272120, 50229901).

Reference 5.

Lin, C.W., Lee, Y.L., Huang, M.L. Lai, W.C., Yuan , B.D. and Huang, C.Y., Eng. Geology, 71, 13-30, 2003

6.

Wong, R.H.C., Huang, M.L., Jiao, M.R., Tang, C.A. and Zhu, W., Key Eng. Materials, 261263, 219-224, 2004

7.

Wong, R.H.C., Law, C.M., Chau, K.T. and Zhu, W.S., Int. J. of Rock Mech. & Min. Sci., 41(3), 360, 2004.

8.

Murakami, Y. and Natsume, H., JSME Int. J. A-Solid Mech., 45(2), 161-169, 2002

9.

Chau, K.T., Wong, R.H.C., Wong, Y.L., Lai, K.W., Third Int. Conf. Continental Earthquake, Beijing, China, July 12-14, 60, 2004

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MECHANICAL BEHAVIOR MODELING IN THE PRESENCE OF STRAIN AGING J. Belotteau1,3, C. Berdin1, S. Forest2, A. Parrot3 and C. Prioul1 1MSSMat, Ecole Centrale Paris, Grande voie des Vignes, 92295 Châtenay Malabry Cedex, France. 2Centre des Materiaux P.M. Fourt, Ecole des Mines de Paris, BP87, 91003 Evry Cedex, France. 3EDF R&D/MMC, Site des Renardieres, 77818 Moret s/ Loing Cedex, France. [email protected], [email protected], [email protected], [email protected], [email protected] In many fields some structural materials are subjected to strain aging, which gives rise to inhomogeneous yielding such as Piobert–Lüders’ bands and Portevin – Le Châtelier instabilities. These phenomena occur in steels containing interstitial elements in solid solution such as carbon or nitrogen which segregate to dislocations during aging and pin them. Strain aging in ferritic steels induces a loss in ductility and fracture toughness at mild temperatures [1]. To study the influence of strain aging on ductile tearing, it is possible to simulate plastic strain instabilities using a local constitutive equation [2] taking into account the interaction between solute atoms and dislocations responsible for strain aging [3]. This study first requires the identification of the model parameters, which needs to correlate the experimental values obtained from tensile tests to the intrinsic behavior of the material and then requires a good interpretation of the upper and lower yield stresses in the presence of static strain aging. So we have performed a numerical study of the Lüders’ plateau featuring the influence of several parameters such as meshing, boundary conditions or behavior law on the nucleation and growth of Lüders’ bands. The influence of the local band development on the plateau has been investigated. Correlations between the plateau stress level and the local behavior will be discussed. As proposed by Tsukahara and Iung and for the sake of simplicity the aging process is introduced in the local constitutive equation by an overstress necessary to the unlocking mechanism [4]: at yield point (V0) the stress drops down to V1 and then follows a linear isotropic strain hardening behavior, as shown in Fig. 1. During the simulation of a tensile test, the specimen exhibits a strain localization band oriented around 50° from the tensile direction, growing from an “artificial” defect until filling the whole specimen. The band spread is related to a plateau at nearly constant stress on the V–H macroscopic curve. In a first part we have investigated the shape of the Lüders’ peak and plateau. Correlations can be made between the stress variations and the band spreading along the specimen (Fig. 2). Several structure effects are examined: boundary conditions, type and location of the initial defect, meshing. In a second part the notions of upper and lower yield stresses, usually used in industry are questioned. A correlation has been checked between the lower yield stress, i.e. the plateau stress level, and the intrinsic parameters of the local behavior law V0 and V1. Different forms of constitutive equations have been tested. The respective effect of structure and local material behavior on the stress-strain curve can then be clearly separated. This offers the possibility of further modeling of ductile tearing in the presence of strain aging.

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FIGURE 1. Local behavior to simulate Lüders’ bands. Introducing local softening allows strain to localize.

FIGURE 2. Simulation of Lüders’ bands: relation between plateau singularities and the progression of the strain band. Dependence of lower yield stress on prescribed load conditions.

References 1.

D. Wagner, J.C. Moreno, C. Prioul, J. M. Frund and B. Houssin, J. Nucl. Mater., vol. 300 Issue 2-3, 178-191, 2002.

2.

S. Graff, S. Forest, J. -L. Strudel, C. Prioul, P. Pilvin and J. -L. Béchade, Mater. Sci. Eng A., vol. 387-389, 181-185, 2004.

3.

Y. Estrin and L.P. Kubin, J. Phys. III, vol. 1, 929-943, 1991.

4.

H. Tsukahara and T. Iung , Mater. Sci. Eng. A, vol. 248, 304-308, 1998.

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ON THE LOCAL CONDITIONS FOR CLEAVAGE INITIATION IN FERRITIC STEELS Jorg Hohe, Valerie Friedmann and Dieter Siegele Fraunhofer Institut fur Werkstoffmechanik Wohlerstr. 11, 79108 Freiburg, Germany [email protected] [email protected] [email protected] The present study is concerned with an investigation of the local conditions for initiation of cleavage fracture in ferritic steels which have been analyzed in the context of a research program directed to different methods of cleavage fracture assessment (Hohe et al. [Swindeman, R.W. et al., Pressure Vessels and Piping, 507-512, 2004.]). The investigations are performed experimentally and numerically using a German nuclear grade 22NiMoCr3-7 (A 508 class 2) pressure vessel steel as a material example under forged conditions. The heat treatment of the material consists of an austenization at 900°C, quenching in water, tempering at 650°C for 7.5 hours and subsequent air cooling. Following the basic characterization of the material, a variety of fracture mechanics specimens is tested. In the experimental investigation, specimens with different geometries including SE(B)-, C(T)- and CC(T)-specimens, different thicknesses ranging from 10 mm to 50 mm and different crack depths ranging from a/w = 0.13 to a/w = 0.52 are tested. The test temperatures are ranging from -120°C to 0°C. The tests are performed and evaluated according to ASTM standard E 1921 [ASTM E 1921, Standard Test Method for Determination of the Reference Temperature T0 in the Transition Range, ASTM, West Conshohocken, PA, 2002.] or similar, where the standard is not applicable. In this context, significant constraint effects are observed, resulting in a strong specimen geometry dependence of the measured fracture toughness KJc. In order to assess this effect, the local mechanical conditions at the cleavage initiation sites are investigated. To determine the fracture mechanism, all specimens tested are analyzed by fractographic methods. It is observed that all specimens fail by pure transgranular cleavage. Nevertheless, at higher test temperatures (T -30°C), some ductile tearing precedes the cleavage failure. The cleavage triggering sites in all cases are situated in the interior of the ligament at a distance of approximately 20 to 170 m (depending on the load level at failure) ahead of the crack front. Larger distances are found at higher test temperatures due to the higher failure loads. Subsequently, the fracture mechanics tests are simulated numerically using the finite element method. Full three-dimensional, geometrically nonlinear analyses with extremely fine meshes are performed for an accurate determination of the local stress and strain fields in the cleavage fracture process zone directly ahead of the crack front. Special interest is directed to the maximum principal stress I which is assumed to control the propagation of a freshly initiated micro-crack (Ritchie et al. [])Ritchie, R.D., Knott, J.F. and Rice, J.R., J. Mech. Phys. Solids, vol. 21 (1973) 395.. At the cleavage origin, approximately constant values of this quantity are found irrespectively of the specimen geometry and the test temperature and thus the failure load level (see Fig. 1). Nevertheless, a deterministic criterion based on the level of the maximum principal stress I alone does not form a sufficient criterion for cleavage initiation since the critical value f is already reached for rather small load levels at some positions rather close to the crack front. As an extended concept, Chen et al. [Chen, J.H., Wang, Q., Wang, G.Z. and Li, Z., Acta. Mat., vol. 51, 1841-1855, 2003.] have proposed an alternative three-parameter criterion. This criterion

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takes the equivalent plastic strain e as well as the stress triaxiality coefficient e/kk into account. The equivalent plastic strain is assumed to control the nucleation of micro-cracks which might serve as cleavage initiation sites whereas the stress triaxiality coefficient controls the possibility of blunting and thus the criticality of freshly nucleated micro-cracks for triggering of cleavage fracture. For the specimens in the present experimental database, a large scatter of both quantities at the cleavage origin is observed when the failure load is reached. On the other hand, it can be shown that the levels of both quantities at cleavage initiation are coupled rather than being independent. Based on these results, a framework for the assessment of cleavage fracture in ferritic steels based on the local mechanical fields is proposed.

FIGURE 1. Local cleavage stress for different specimen geometries and failure loads.

References 1.

ASTM E 1921, Standard Test Method for Determination of the Reference Temperature T0 in the Transition Range, ASTM, West Conshohocken, PA, 2002.

2.

Chen, J.H., Wang, Q., Wang, G.Z. and Li, Z., Acta. Mat., vol. 51, 1841-1855, 2003.

3.

Hohe, J., Tanguy, B., Friedmann, V., Stöckl, H., Böhme, W., Vafolomeyeva, V., Hebel, J., Burdack, M., Fehrenbach, C., Schüler, J., Sguaizer, Y., Siegele, D., Kritische Überprüfung des Mastercurve-Ansatzes im Hinblick auf die Anwendung bei deutschen Kernkraftwerken, Fraunhofer Institut für Werkstoffmechanik, Report No. S8/2004, 2005.

4.

Ritchie, R.D., Knott, J.F. and Rice, J.R., J. Mech. Phys. Solids, vol. 21 (1973) 395.

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UNIFIED CONSTITUTIVE EQUATIONS TO DESCRIBE ELASTOPLASTIC AND DAMAGE BEHAVIOR OF X100 PIPELINE STEEL T. T. Luu1,2, B. Tanguy1, J. Besson1, A. Pineau1 and G. Perrin2 1Ecole des Mines de Paris, Centre des Materiaux, Evry Cedex, France 2Applied Mechanics Division, Institut Francais du Petrole, Rueil-Malmaison, France [email protected], [email protected] Economic gas transportation over long distances requires the use of high pressure and consequently the use of high strength steels such as grade API X100 which is investigated in this study. This steel is produced using Thermo-Mechanical Controlled Process (TMCP) as thick plates which can be rolled into large diameter tubes. The resistance to ductile crack propagation of these new steels must be determined to access the integrity of pipelines. This is done using Charpy tests, for which the upper shelf energy (USE) is determined, or drop weight tear tests. The purpose of this study is to establish unified constitutive equations able to represent the plastic and rupture behaviour of plates and tubes ; the model must account for plastic anisotropy (induced by the production process) and for the pre-strain resulting from rolling plates into tubes (about 2% [1]). To illustrate the pre-strain effect [2], load-displacement curves issued from instrumented Charpy tests for the plate and the tube for two configurations (L-T and T-L) are reported on Fig. 1 where the value of corresponding USE are given. The maximum load is obtained for the tube (Fig. 1a TL direction) due to pre-strain. However, for the T-L solicitation a sharp drop of the load in the case of the tube is observed once the ductile crack has initiated. This results in a strong decrease of the USE for the tube.

FIGURE 1. Load-displacement curves for the dynamic Charpy test at 20°C. (a) L-T direction, (b) T-L direction Material behavior was investigated using several specimen geometries: smooth tensile, notched tensile (NT) with different radii, compact tension. Oligocyclic tests were used to access isotropic and kinematic hardening contributions to the overall plastic behavior. Tensile tests were conducted along long (L), transverse (T) and short (S) directions to characterize the anisotropy of the material. Tensile properties (yield strength (YS), ultimate yield strength (UTS) and uniformed elongation (UE) for plate and tube along three directions are reported on table 1.

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832

TABLE 1. X100 steel plate and tube mechanical properties

The strategy to describe the elastoplastic and damage behavior was the same than the one used in [3]. The Gurson ductile damage model was used to describe the initiation and the propagation of ductile damage; the anisotropic elastoplastic behavior was described using the model proposed in [4]. For plastic strain less than UE, the parameters of the elastoplastic model were identified on smooth tensile tests for the three directions (L, T, S). For larger plastic strains, inverse identification using notched tensile tests was used. Comparisons between experiments, the anisotropic model and von Mises criterion are reported on Fig. 2 for the plate. Moreover, considering a pre-strain of 2%, the constitutive equations well describe the behavior of notched specimens cut off from the tube. The parameters of the Gurson model were identified using the notched tensile tests and used to simulate Charpy and compact tension tests.

FIGURE 2. Normalized load (F/S0) vs radial displacement (')s/) along the short direction in the notch. Experiments (symbols), von Mises simulations (dashed lines) and simulations with the anisotropic model (solid lines)

References 1.

Qui, H., Enoki, M., Hiraoka, K., Kishi, T., Eng. Frac. Mech., Vol. 72, 1624-1633, 2005.

2.

Hagiwara, N., Masuda, T., Oguchi, N., J. of Pressure Vessel Tech., Vol. 123, 355-361, 2001.

3.

Rivalin, F., Besson, J., Di Fant, M., Pineau, A., Eng. Frac. Mech., Vol. 68, 347-364, 2001

4.

Bron, F., Besson, J., International Journal of Plasticity, Vol. 20, 937-963, 2004

8. Modelling of Material Property Data and Fracture Mechanisms

833

ESTIMATION OF LOWER BOUND ENGINEERING FRACTURE TOUGHNESS IN THE DUCTILE TO BRITTLE TRANSITION REGIME R. Moskovic and R. A. Ainsworth British Nuclear Group, Berkeley, Gloucestershire GL 13 9PB, United Kingdom. British Energy, Barnett Way, Barnwood, Gloucester GL4 3RS, United Kingdom. [email protected], [email protected] Ferritic steels are used for the manufacture of components that form pressure boundaries of nuclear power plant. The mechanism of fracture of ferritic steels changes with increasing temperature and reducing specimen thickness from brittle, cleavage fracture to ductile. In order to assess the structural integrity of a component, fracture toughness properties are measured in a laboratory on specimens that are smaller than the component. In order to use fracture toughness results measured on small specimens in fracture mechanics assessments of plant components, it is necessary to apply thickness or size correction to cleavage fracture toughness values. These thickness corrections can be derived either from statistical analyses of cleavage fracture toughness databases or by adopting a framework based on the Master Curve. In this approach, the cleavage fracture toughness, K25, of a reference thickness B = 25mm is related to fracture toughness, KB, for a thickness B by an equation: K25 = Kmin + (KB – Kmin)(B/25)1/4

(1)

where Kmin is a minimum toughness, usually taken as 20MPam. This equation implies that if section thickness of a component to be assessed is significantly greater than the thickness of the specimens used to measure the cleavage fracture toughness then the resulting estimates of the lower bound values will be substantially lower. In the Master Curve approach, the thickness correction is the same for all ferritic steels independently of the microstructure and tensile properties of the steel. However, where cleavage fracture toughness data are available for several different sizes of specimen over a range of temperatures, it is possible to use statistical techniques to determine the specimen size dependence of cleavage fracture toughness. This paper illustrates application of this approach to the Euro fracture toughness database obtained from tests performed on quenched and tempered pressure vessel steel DIN 22NiMoCr37. There are data sets consisting entirely of cleavage initiation fracture toughness values for several specimen sizes at three different temperatures: -154ºC, -91ºC and -60ºC. In addition, there is a data set of cleavage initiation fracture toughness values for a single specimen size at –110ºC. These data were analysed in two different ways. First, the data for each test temperature were analysed to estimate the thickness dependence of cleavage fracture toughness for specific temperatures. The random scatter in the data was modelled by a Weibull probability distribution and the Weibull shape parameter at each temperature was assumed to be the same for all specimen sizes. The analyses showed that the Weibull shape parameter varied with temperature in the range from 3.08 to 5.85. The thickness dependence of cleavage fracture toughness also varied with temperature. At two temperatures, -154ºC and -60ºC, the coefficient for thickness dependence was of the order of 1/15. At –60ºC, this value was approximately 1/6. A further analysis at –60ºC in which the Weibull shape parameter was allowed to vary with specimen size yielded a different shape parameter for each specimen thickness and the coefficient for thickness dependence was approximately 1/33.

R. Moskovic and R. A. Ainsworth

834

The statistical analyses have shown that the specimen thickness correction may be smaller than assumed in the Master Curve. In this approach, the effect of thickness on cleavage fracture toughness is rationalised by the weakest link concept. With an increase in the thickness and the associated crack length there is an increasing likelihood of sampling the weakest microstructure. Hence, it should be possible to sample the weakest link either by testing a thick specimen or a set of small specimens with the same aggregate crack length as the thick specimen. In the EURO fracture toughness database, there are at least 30 values of fracture toughness for each specimen thickness at each temperature. These data can also be used to assess the effect of specimen thickness on the lower bound values of cleavage fracture toughness. For the purpose of these analyses, it was assumed that the lowest eleven values, comprising approximately 10% of the data, are in the lower tail of the distribution. In these analyses, the data were re-arranged as follows: •

The data obtained at the same temperature for different specimen thicknesses were arranged in ascending order and the lowest eleven values were extracted.

•

Data obtained at the same temperature for different specimen thicknesses were statistically analysed as a function of thickness. Standardised residuals were computed and arranged in ascending order and the lowest eleven values were extracted.

•

Values of cleavage fracture toughness for different specimen thicknesses were adjusted using the size correction K25 = KB(B/25)¼. The calculated values of K25 were arranged in ascending order and the lowest eleven values were extracted.

Percentages of values in the lower tails of the distribution for different specimen thicknesses were compared. At –154ºC and –91ºC there was a weak trend in percentage to increase with specimen thickness consistent with a small effect of specimen thickness on the lower bound cleavage fracture toughness. At -60°C, there was no trend. In addition to the above statistical analyses, the cleavage fracture toughness values were examined graphically. The values for each specimen thickness were ordered, ranked and cumulative values of failure probability for each data point calculated. The cumulative failure probabilities were plotted against measured values of J. Examination of the plots showed that the curves for different specimen thicknesses converged below approximately 0.1 cumulative probability consistent with no thickness effect on cleavage fracture toughness in the tails of the distribution. At higher cumulative probability values, the curves diverged with increasing J consistent with specimen thickness effect on cleavage fracture toughness in the main body of the data.

8. Modelling of Material Property Data and Fracture Mechanisms

835

CLEAVAGE FRACTURE MICROMECHANISMS RELATED TO WPS EFFECT IN RPV STEEL S. R. Bordet1, B. Tanguy1, S. Bugat2, D. Moinereau2 and A. Pineau1 1Centre des Materiaux, Ecole des Mines de Paris, UMR CNRS 7633, BP 87, 91003 Evry Cedex, France 2EDF R&D, Dept. MMC, Les Renardieres, 77818 Moret-sur-Loing Cedex [email protected], [email protected], [email protected], [email protected], [email protected] Since the first investigations four decades ago, a large number of experiments on ferritic steels has confirmed the existence of a warm pre-stress (WPS) effect, which describes the effective enhancement of the cleavage fracture toughness at low temperature following the application, at a higher temperature, of a stress intensity factor (SIF) which exceeds the fracture toughness of the virgin material at low temperature. These experiments allowed for the establishment of the socalled ‘conservative principle’, which states that no fracture will occur if the applied SIF decreases (or is held constant) while the temperature at the crack-tip decreases, even if the fracture toughness of the virgin material is exceeded. In structural integrity assessments involving a prior overload or a thermal transient, such as that of a nuclear pressure vessel subjected to a pressurized thermal shock (PTS) consecutive to a loss of coolant accident (LOCA), such a principle is of great importance in the evaluation of the safety margins. Three main reasons have been advanced to explain the WPS effect: the blunting of the crack tip at high temperature, the formation of high compressive stresses on elastic unloading, and a change in the cleavage fracture micromechanisms induced by plastic deformation. While all these factors certainly contribute to the effective toughness enhancement following WPS, their relative incidence on the fracture risk is not easily established. In this paper, we choose to mainly focus on the cleavage fracture micromechanisms following WPS, as a first step towards better quantifying the individual contributions of crack tip blunting and residual stresses. This paper presents different WPS fracture test results obtained on 18MND5 (A533B) RPV steel, supplemented by isothermal tests on the virgin material for comparison: •

toughness tests in compact tensile (CT) geometry following different thermo-mechanical cycles between 20 and –150°C: LCF (Load-Cool-Fracture), LUCF (Load-Unload-CoolFracture) and LCIKF (Load-Cool-Increasing applied K- Fracture).

•

notched tensile (NT) tests (notch radius = 2.4 mm) plastically deformed in traction, compression, and traction followed by compression, at room temperature, and then broken in liquid nitrogen.

Extensive fractographic investigations using electron microscopy revealed two competing particles for triggering macroscopic cleavage: •

titanium nitride (TiN) particles, often bound or clustered with other particles such as manganese sulfides (MnS) and oxides (CaO, MgO, Al2O3 etc.).

•

grain-boundary carbides.

In the fracture toughness tests, the particles responsible for global cleavage fracture are almost exclusively TiN particles, whether the specimen was pre-stressed or not. This is also the case for the notched tensile tests on the virgin material at liquid nitrogen temperature. Significant changes, however, were observed in the pre-deformed NT specimens. While the TiN particles are still the

836

S. R. Bordet et al.

main critical particles in the NT specimens pre-deformed in compression alone, these particles are replaced by carbides in specimens tested in traction-compression or traction alone. More specifically, for specimens pre-strained above 20% deformation in traction, global cleavage initiates at grain boundaries (the presence of carbides is not easily observed) in vicinity of holes formed around cracked (TiN, oxides) or detached (MnS) particles, which serve as stress concentrators. A material aspect of the WPS effect in 18MND5 steel is therefore the deactivation of brittle TiN particles at high temperature: matrix straining under low stress enables breaking the particle without causing unstable propagation. Because the yield stress increases as the temperature is decreased, there exists, for a given geometry, a transition temperature below which the breaking of a sufficiently large TiN particle will systematically trigger global instability. This assertion is confirmed by tensile tests performed on the virgin material at –150°C: arrested ferrite microcracks, originating from broken TiN particles and a few grains long, were observed on the specimens. All arrested cracks were surrounded by a region of extensive ductile crack growth, which is indicative of crack formation at an early stage, characterised by low stress level. The experimental observation that the TiN particles are still the main initiators for global cleavage in the CT geometry, despite relatively large pre-loads, is explained by the fact that the large strain region remains very localized at the crack tip. At a blunted, yet highly constrained, crack tip, the peak stress occurs at some distance from the crack tip (about twice the CTOD), and keeps approximately constant while moving away from the crack tip under increasing load. Reloading at low temperature not only globally raises the stress level, which favours cleavage propagation, but also, for a sufficiently large applied SIF, causes the peak stress to sample material little affected by the WPS at high temperature, hence the continued participation of the TiN particles in cleavage initiation. A material effect of WPS is therefore also present in the CT geometry, through a more or less complete exhaustion of the potentiality to nucleate cleavage microcracks (i.e. through TiN particle cracking) in the WPS affected region. These findings are useful for understanding some of the difficulties with cleavage toughness modelling, notably in the ductile-to-brittle (DBT) transition, of steels of similar composition. Recent attempts to model the transition using local approach (Beremin type) cleavage models had to allow for an apparent temperature dependence of the parameter Vu, to take into account a possible change of micromechanisms. For 18MND5 steel, this apparent temperature dependence can be attributed to a modification of the cleavage initiation micromechanisms, from cleavage initiated by TiN particle breaking at low temperature to cleavage started at grain boundary carbides in the transition, possibly helped by ductile damage (holes around inclusions).

8. Modelling of Material Property Data and Fracture Mechanisms

837

MODELLING OF FATIGUE DAMAGE IN ALUMINUM CYLINDER HEADS R. Salapete1,2, B. Barlas3, E. Nicouleau2, D. Massinon3, G. Cailletaud1 and A. Pineau1 1Centre des Materiaux, Ecole des Mines de Paris, UMR CNRS 7633, B.P.87, F-91003 Evry cedex 2RENAULT, 67 Rue des Bons Raisins, 92508, Rueil Malmaison, France 3Fonderie Montupet, 67 rue J. de la Fontaine, 60181 Nogent-sur-Oise, France [email protected] Because of the regular increase in specific power, automotive cylinder heads, in particular those used in Diesel direct injection engines, are exposed to increasing thermomechanical loadings. Those cylinder heads are usually made of cast aluminum alloys. Cyclic loads corresponding to the alternative heating and cooling of the operative engine generate fatigue cracks, initiating from the fire deck (the inter valve bridge region) which can lead ultimately to engine failure (Fig. 1). Beyond a limit level of crack propagation, some essential functions of the cylinder heads, in particular the separation between the different fluids circuits (intake, exhaust, water cooling, and oil) are no longer fulfilled. The failure assessment in the design stage of an engine is therefore of crucial importance. In the present study, a failure assessment method for cylinder heads made of A319 type aluminum alloy is presented. The method includes three stages: structural analysis using an elastoviscoplasticity model, crack initiation model and, finally, crack propagation assessment. Elastoviscoplasticity model A cyclic viscoplastic constitutive equation including kinematic and isotropic hardening laws and taking also into account the progressive ageing of the A319 type aluminum alloy, is used [1-3]. Structural computations are made thanks to finite element codes, Zebulon or Abaqus / Zebulon interface (Zmat) in order to represent the cyclic behavior of the material during thermomechanical loadings. Fatigue crack initiation model A fatigue crack initiation model based on continuum damage mechanics was developed. This model was established from a large number of isothermal and anisothermal tests carried out on fully machined specimens. The formulation uses a Wohler type curve and accounts for ageing and temperature effects. It is implemented as a post-processor of the Zebulon code and can be used on an Abaqus data base. It provides a fairly reasonable estimation for the appearance of 0.1 –1mm class cracks. Fatigue crack propagation model The prediction of the life spent in crack propagation from 0.1 –1mm defect up to failure is derived from fracture mechanics concepts. A modified stress intensity factor is introduced to account for plasticity on fatigue crack propagation [4]. Isothermal fatigue crack growth tests were performed on specimens containing an artificial short crack (0.150 mm < a < 1 mm). A “master” curve giving the variation of crack growth rate, da dN , with the amplitude of the effective stress intensity factor 'K eff was thus derived. This curve includes the temperature and crack closure effects. A weight function method was used to calculate the stress intensity factor corresponding to corner cracks initiated either from the ports counter borings or to cracks crossing the region

R. Salapete et al.

838

between them, as observed in Fig. 1. The number of cycles corresponding to crack propagation was determined by integrating the “master” curve. Having in hand such an approach, the life prediction can now be obtained as the result of initiation and propagation of a crack. This last point is crucial, since one can discriminate between dangerous propagating cracks, and cracks which will stop before gaz from combustion reaches the water jacket. Several significant examples are shown in the paper.

FIGURE 1 : inter valve bridge failure

References 1.

Nicouleau-Bourles, E., In Etude expérimentale et numérique du vieillissement d’un alliage d’aluminium. Application aux culasses automobiles, PhD thesis, Ecole des Mines de Paris – (1999).

2.

Barlas, B., In Etude du comportement et de l’endommagement en fatigue d’alliages d’aluminium de fonderie, PhD thesis, Ecole des Mines de Paris – (2004).

3.

Salapete, R., Barlas, B., Nicouleau, E., Massinon, D., Cailletaud, G., Pineau, A., In Fatigue life predictions of aluminum cylinder heads. Fatigue Design, Senlis, November 2005, to appear

4.

Haigh, J.R., Skelton R.P., A strain intensity study of type 304 and 316 stainless steels. Fatigue crack growth and failure. Materials and Science Engineering, Vol 36, pp 133-137 (1978).

8. Modelling of Material Property Data and Fracture Mechanisms

839

LOCAL APPROACH TO HIGH TEMPERATURE DUCTILITY MODELING IN 6XXX ALUMINIUM ALLOYS D. Lassance, D. Fabregue, F. Delannay and T. Pardoen Universite catholique de louvain, Materials Science and Processes Department Unité IMAP, Reaumur, Place Sainte Barbe 2, B1348 Louvain-La-Neuve, Belgium Tel : +32 10 472417, Fax : +32 10 474028, [email protected] Low and medium strength AlMgSi alloys are commonly used for hot extrusion. For high productivity it is necessary to obtain the alloy in a soft condition so that the extrusion rate can be increased without overloading the press. Such AlMgSi alloys can be considered as two phase alloys in which one phase is the Al matrix and the second one is constituted by different particles among which the Fe rich intermetallics. The second phase particles may have important consequences on the deformation process, because not only they affect the flow stress of the material, but also they are likely to influence the ductility and change the final microstructure. In the case of commercial aluminium extrusion alloys, a homogenisation heat treatment of the as-cast material is required to improve ductility and enable efficient extrusion. The optimisation of such extrusion processes depends on a thorough understanding of the homogenisation kinetics and, in particular, of the morphological evolution of the intermetallic inclusions during the homogenisation process. Moreover damage initiation occurs in such alloys by decohesion or fracture of inclusions as referred by Toda and Kobayashi [1]. By performing a long homogenisation heat treatment at a sufficiently high temperature, during which the -Al5FeSi phase transforms to the more rounded meta-stable cubic -Al12(FeMn)3Si phase or equilibrium hexagonal phase, this unfavourable effect can be improved. The aim of this work is to improve the understanding and the control of the damage resistance during hot extrusion. To achieve this goal, the link between hot deformation behaviour and microstructural evolution during the homogenisation treatment of the 6xxx aluminum alloys serie is studied and compared with the behavior at room temperature. Experiments show that during deformation, different void populations are nucleated by different particle groups. The first type of void come from the AlFeSi particle/matrix decohesion, the second one corresponds to the AlFeMnSi particle/matrix decohesion whereas the third one corresponds to pennyshape voids initiated by the multiple fractures of elongated AlFeSi particles, which accelerates the damage progression. In the case where two (or more) populations of voids are present, the strain at the onset of coalescence (and thus the ductility) tends to decrease. Such an influence of multiple void populations on the deformation process has already been observed experimentally [2]. In order to take this into account and to relate quantitatively microstructure and ductility, FE simulations based on an enhanced micromechanics-based model are used. The model used is a Gurson type constitutive model considering several populations of cavities. The model consists in using a Gologanu type model for the matrix including the first population. Then the local strains close to the cavity are extracted from the results of the solved equations. These strains are used to solve the Gurson equation locally giving the evolution of the second population of voids close to the first cavity . Using a modified Thomason model, one can predict the onset of coalescence [3]. This model is well suited for the present case as it incorporates void shape effects which is key to capture the impact of the / transformation on ductility. The results of ductility calculations show that the model correlate correctly the experimental values at room temperature and high temperature. The evolution of ductility with the AlFeMnSi particles content evolution is properly predicted.

D. Lassance et al.

840

References 1.

Toda, H., and Kobayashi, H., Materials Science Forum, vol. 426-432, 393-398, 2003.

2.

Marini, B., Mudry, F, Pineau, A., Engng. Fracture Mech., vol.22, 989-996, 1985.

3.

Fabregue, D., and Pardoen, T., to be published

9. Micromechanisms in Fracture and Fatigue

841

SMALL FATIGUE CRACK GROWTH IN STEEL -COMPRESSOR DISKS OF AIRCRAFT ENGINES. A. A. Shanyavskiy and A. Yu. Potapenko State Centre for Safety Flight of Civil Aviation, Moscow, Russia 124340, Moscow, Airport Sheremetievo, P.O. Box 54, SCSFCA [email protected] It was the problem for in-service fatigue crack growth from the steel-disk base of the high-pressure engine compressor. The fractographic analysis have been performed to examine the crack growth mechanism and to reproduce crack growth period in term of number of engine flights. It was shown that the crack growth performs in low-cycle-fatigue area because of cascade of the interacting small cracks, Fig.1.

FIGURE 1. Fatigue fracture surface on the in-service fatigued steel- disk. The statistic analysis of in-service fatigue cracks detection in disks in time, simulation of the crack growth in disks on the basis of the well known kinetic curve for the disk-material have shown that the crack growth period on the distance 4.0mm can be performed in service without disk in-flight failure, Fig.2.

842

A. A. Shanyavskiy and A. Yu. Potapenko

FIGURE 2. Fatigue striation spacing, G, against crack growth depth, a, for (1) tested specimens, (2) reproduced from the striation spacing measurements in-service fatigued disks and modeled as striation spacing dependence on the 'K2. Results are shown for two critical crack length 4.0 mm and 4.5 mm. The inspection interval for disks non-destructive testing was recommended. The new disk design for stress level diminishing has been discussed.

9. Micromechanisms in Fracture and Fatigue

843

MICROMECHANISMS OF DAMAGE IN MULTIAXIAL FATIGUE OF AN AUSTENITIC-FERRITIC STAINLESS STEEL Ahmed El Bartali, Véronique Aubin, Suzanne Degallaix and Laurent Sabatier Laboratoire de Mécanique de Lille (UMR CNRS 8107) Ecole Centrale de Lille 59651 Villeneuve d’Ascq Cedex, France [email protected] Austenitic-ferritic stainless steels, also called duplex stainless steels, are designed to combine the properties of both ferritic and austenitic phases in order to optimize mechanical strength, ductility and corrosion resistance. They are therefore used for components submitted to corrosive environments as for instance in the chemical, petrochemical or nuclear industry or for the transport of chemical products. Increasing safety requirements together with tighter economic restrictions lead to harder industrial requirements towards significant weight reduction by simultaneous improvement of the mechanical properties. In order to achieve this goal, a thorough understanding of the mechanical behaviour of these materials under complex mechanical loading is necessary. This knowledge bases upon understanding of the strain physical mechanisms at a microstructural level. Specifically, the identification of constitutive laws under complex cyclic loadings requires a multiaxial fatigue experimental data base. Low cycle fatigue tests with the continuous observation of the surface phenomena and the quantitative analysis of the strain fields allow identifying physical mechanisms of strain distribution, crack initiation and damage evolution in fatigue. One purpose of the present work is to complete the data base of fatigue results available in our laboratory (Aubin [1]). Tension-compression fatigue tests were carried out using cylindrical specimens and tension-compression/torsion fatigue tests were performed with tubular specimens. All the specimens were obtained from the same rod of a X2 Cr Ni Mo 25 7 duplex stainless steel containing 40 vol.% austenite and 60 vol.% ferrite. An optical method was developed in order to register online the strain field and the damage on the surface of the specimens during the fatigue tests. By using a digital image correlation technique the method identifies and extracts correspondent small zones in the deformed and in the reference images (Hild et al [2]). The displacement vector field is determined, its gradient delivers the strain field. Figure 1c shows the calculated longitudinal strain obtained from the image of a specimen after 0.27% total strain in simple tension (fig. 1b) and from the reference image (fig. 1a) of the undeformed specimen.

FIGURE 1. Strain fields measurement by digital image correlation

A. El Bartali et al.

844

For the optical strain analysis a very smooth cylindrical notch was machined on the specimen surface. In order to follow the strain evolution and the surface damage, each specimen was polished and etched. The observations were carried out at the scale of the grain size (about 10 Pm). An in-situ observation device composed from CCD camera equipped with macro objective was conceived and mounted on the frame of the testing system. It allows the observation of the specimen during testing and the acquisition of images for the strain field analysis (Fig. 2). The observation zone (about 100 Pm x 100 Pm) is large enough to be considered as a Representative Elementary Volume (REV) of the macroscopic behaviour of the two-phase material.

FIGURE 2. In-situ observation device Strain fields were calculated with an image correlation software. Analysis of the strain fields and their evolution during the cyclic loading shows a heterogeneous strain distribution and the localization of the plastic strain at the grain scale. Moreover, it allows to identify the initiation sites of micro-cracks and to understand the micro-crack propagation process.

References 1.

Aubin, V., Quaegebeur, P. and Degallaix, S., Materials Science and Enginerring A, 346, 208-215, 2003

2.

Hild, F., Raka, B., Baudequin, M., Roux, S. and Cantelaube ,F., Applied Optics, Vol. 41, No 32, 2002

Vol

9. Micromechanisms in Fracture and Fatigue

845

MULTISCALE MODELING OF FRACTURE AND PLASTICITY IN LAYERED STRUCTURES Alexander Hartmaier, Nils Brodling and Huajian Gao Max Planck Institute for Metals Research Heisenbergstr. 3, 70569 Stuttgart, Germany [email protected] Plasticity in the geometrical confinement of a multilayered composite material is studied with a dislocation-based model, where the mutual interaction of dislocations in the elastically inhomogeneous layered structure is defined within the theory of elasticity on the continuum level. The interface between two different layers is described as a cohesive zone, which allows crack initiation and delamination to be studied on a rather fundamental level, taking into account information on atomic binding energies across the interface. With this combined dislocation dynamics-cohesive zone model we investigate whether a pre-existing crack in a ductile layer of the composite structure will blunt or rather propagate in a brittle fashion. It is seen that the length scale defined by the geometrical confinement of the plastic zone in the layered structure plays a critical role in determining the behaviour of the entire structure. In the two-dimensional model underlying this work, the stress and strain fields of straight edge dislocations are calculated according to Mura's solution of the dislocation eigenstress in an infinite bi-material [1]. The correct elastic boundary conditions for a plastic layer embedded in an elastic material are established by dividing the problem into calculating stresses in an infinite elastic medium and then correcting the tractions across the crack plane and the cohesive zone by appropriate counter forces. In this work, these counter forces are produced by a surface layer of virtual dislocations with continuous (non-lattice) Burgers vectors. The distribution of these virtual dislocations that establishes the correct tractions across surface plane and cohesive zone is calculated with a boundary integral method. The Green's function for the boundary integral is constructed following the approach of Gutkin and Romanov [2]. Once the surface distribution of the virtual dislocations is known, the corresponding stress and strain fields within the medium can again be calculated using Mura's equations. The boundary conditions along the cohesive zone comprise a region where the crack is fully open and where consequently the tractions across the crack plane vanish. Ahead of this crack the cohesive zone is located, where the atomic bonds are strained, but not yet completely separated. The surface tractions in this region are defined by the elastic displacements across the cohesive zone, which are given by the displacement fields of the dislocations and the boundary conditions, and the force-separation characteristics of the atomic bonds. With this model the complex interplay between dislocation mediated plasticity and crack opening, crack blunting and, finally, crack advancement is studied. Fig. 1 shows a sketch of the combined dislocation dynamics-cohesive zone model. The first applications of this model have been aimed at determining whether there exists a critical thickness of the ductile layer below which crack advancement within this layer occurs and above which the layer shows bulk-like behaviour. Our simulations have shown that the fracture toughness of such layered structures increases continuously with the thickness of the ductile layer until the bulk limit is met. The results are in good qualitative agreement with the simple analytical model by Hsia, Suo and Yang [3]. The dependence of this transition thickness on material parameters like dislocation density and distribution, dislocation mobility, and the relative stiffnesses of elastic and plastic layers are investigated as well as the influence of the external loading conditions and the temperature. Further studies will include initiation of secondary cracks as a consequence of slip localization and subsequent dislocation pile-ups at interfaces (see Fig. 1).

A. Hartmaier et al.

846

FIGURE 1. Sketch of the combined dislocation dynamics-cohesive zone model. A primary crack (cohesive zone 1) in the ductile layer (material 1) is loaded which causes yielding of the surrounding material. Depending on the geometry and material properties it is possible that either crack advancement occurs or ductile blunting of the crack tip. In the latter case slip localization and stress concentrations from dislocation pile-ups against the elastic layer (material 2) may cause opening of a secondary crack (cohesive zone 2).

References 1.

Mura, T., In Advances in Materials Research, vol. 3, chap 1, edited by H. Herman, Interscience Publishers New York, 1968, 164-201.

2.

Gutkin, M.Yu. and Romanov, A.E. , physica status solidi, vol. 125, 107-125, 1991.

3.

Hsia, K.J., Suo, Z. and Yang, W., J. Mech. Phys. Solids, vol. 42, 877-896, 1994.

9. Micromechanisms in Fracture and Fatigue

847

CRITICAL AND FRACTURE PLANES OF 18G2A STEEL UNDER NONPROPORTIONAL COMBINED BENDING AND TORSION A. Karolczuk and E. Macha Technical University of Opole, Department of Mechanics and Machine Design ul. Mikolajczyka 5, 45-271 Opole, Poland [email protected], [email protected] Many multiaxial fatigue failure criteria of materials are based on the critical plane approach [1-3]. In these criteria, it is assumed that the fatigue failure of material is caused by stresses and/or strains acting in one plane (called critical) within the material. The proper orientation of that plane in fatigue failure criteria based on the critical plane concept must be established for fatigue life calculation. In the paper the damage accumulation method was used to determine the critical plane orientations. In this method, the critical plane is the plane where the maximum damage degree, computed according to the selected fatigue failure criterion, is the highest. The critical plane orientations are often compared to the experimental fatigue fracture plane orientations. Fatigue tests were performed in the high cycle fatigue regime (HCF). Round cross-section specimens made of 18G2A (Fig.1, a)) steel were subjected to different combinations of constant and variable amplitude bending Mg,a and torsion Ms,a. The fatigue tests were performed under bending and torsion moments control system. Two approaches were used to calculate stress courses from histories of moments. In the first approach, stresses and strains were computed using simple elastic beam theory (nominal stresses). In the second approach, time courses of moments were used to calculate stresses and strains histories taking into account plastic strains and nonlinear stresses distribution along cross-section of specimen on the basis of the algorithm described in the paper. The computed, by two approaches, histories of loading were used to calculate critical plane orientations. It was assumed that the orientation of the critical plane is controlled only by shear or tensile fatigue mechanism. Additionally, the theoretical critical plane positions were compared to the experimental fatigue fracture plane orientations. It was assumed that fatigue fracture plane orientation can be determined from the crack line position detected on the free surface of the specimen. Detection of the fatigue crack and measurement of its orientation were performed on the basis of photos of the specimen surface. The photos of specimens were taken using a microscope with magnification of 60 times, connected directly to a computer. The obtained picture of a surface segment was 1.8 x 1.8 mm (macroscopic scale) with a resolution 167x167 pixels per mm2. Points representing cracks have been approximated by a regression line using the least squares method. The slope coefficient of the regression line has been used to calculate the experimental value of the angle Dexp (Fig. 1).

A. Karolczuk and E. Macha

848

& FIGURE 1. Specimen geometry and scheme measurement of angle Dexp. (a) Shear s and normal & n directions in the plane defined by angle D (b) From the obtained results and analysis the following conclusions can be drawn: 1

For proportional constant and variable amplitude loading the influence of plastic strains on the critical plane orientation is negligible.

2

For non-proportional constant amplitude loading the plastic strains should be taken into account to determine the critical plane orientation.

3

Accumulated damage degrees according to analyzed fatigue failure criteria are much more higher in elastic model than they are in elasto-plastic model.

References 1.

Carpinteri A., Spagnoli A., International Journal of Fatigue, vol. 23, 135-145, 2001.

2.

Morel F., International Journal of Fatigue; vol. 22, 101–119, 2000.

3.

Das J., Sivakumar M., Engineering Failure Analysis, vol 7, 347-358, 2000.

9. Micromechanisms in Fracture and Fatigue

849

SLIP PROCESSES AND FRACTURE IN IRON CRYSTALS V. Pelikan, P. Hora, A. Machova1 and M. Landa1 CDM-Institute of Thermomechanics AS CR, Pilsen, 301 14 Veleslavínova 11 1Institute of Thermomechanics AS CR, Prague 8, 182 00 Dolejškova 5 [email protected], [email protected], [email protected], [email protected] The brittle-ductile behavior of cracks has long been an area of intensive study. In particular, body centered cubic (bcc) iron has been studied often in the recent past in the framework of continuum (e.g. Rice et al. [1-3]) and atomistic models (e.g. Mullins et al. [4-8]), and as well in experiments (e.g. Marsh et al. [9], Šmida and Bošanský [10]) due to the structural steels applications. The models consider usually plane strain conditions (2D) along the crack front and temperature of 0 K. However, free sample surface (where plane stress conditions are expected in the normal direction) may influence the ductile-brittle behavior, as well as the thermal atomic motion. Such studies require 3D atomistic simulations. This contribution is devoted to crack simulations by molecular dynamic (MD) technique in 3D bcc iron crystals. We use our new MD code for parallel processing in MPI. Interatomic interactions in bcc iron are described using N-body potentials of Finnis-Sinclair type (Ackland et al. [11, 12]). The 3D codes have been tested in perfect samples under simple uni-axial tension and in thermal simulations. The simulated thermal expansion in bcc iron agrees well with experimental data (see Machová [13]), as well as the phonon frequency spectra [11, 12]. In crack simulations we consider a central pre-existing Griffith (through) crack loaded in tension mode I. The relatively long crack is embedded in a thin bcc iron crystal having the basic cubic {100} orientation. The crack is introduced by removing part of atoms from the central plane, i.e. its initial blunting corresponds to the lattice parameter. Crack surface lies on a (001) plane, crack front is oriented along the [010] direction, and the direction of the potential crack extension is [100]. The interatomic interactions across the free crack faces are not allowed. Surface relaxation has been performed before a loading to avoid its influence on crack tip processes. We performed the 3D crack simulations at temperatures of 0 K and 300 K. At these temperatures, the samples were loaded symmetrically in the directions by prescribing external forces Fext distributed homogeneously at individual atoms lying in several surface layers, similar to [11]. The samples were loaded slowly, gradually in time. While at the temperature of 0 K brittle crack initiation has been observed, at 300 K dislocation emission and slip processes on {110} and {112} planes have been detected. The slip processes start at the free sample surfaces, which is in agreement with our stress analysis and MD simulations by Zhou et al. [14]. The process begins on {110} planes via emission of a curved dislocation (~ quarter circle loop) from the corners, where the crack penetrates the free sample surface. We further show that the slip processes on the inclined {110} planes cause crack tip blunting and hinders crack growth. The slip processes on the oblique {112} planes make jogs in the crack front and enable a slow plastic crack growth. Our results are in agreement with continuum predictions that the microscopic processes at the crack front generally depend also on the mutual orientation of the crack and accessible slip systems (see e.g. Pokluda and Šandera [15]).

V. Pelikan et al.

850

Acknowledgements The work was supported by the Grant Agency at Academy of Sciences of the Czech Republic under a grant IAA2076201. The authors thank Dr. F. Kroupa, Dr. V. Paidar and Alena Spielmannová for very helpful discussions.

References 1.

Rice, J.R., J. Mech. Phys. Solids, vol. 40, 239-271, 1992

2.

Beltz, G.E. and Fisher, L.L., In Multiscale deformation and fracture in materials and structures, edited by T.J. Chuang and J.W. Rudnicki, Kluwer, Boston, 2001, 237-242.

3.

Argon, A.S., Xu, G. and Ortiz, M., In Fracture-Instability, Dynamics, Scaling, and Ductile/ Brittle Behavior, edited by R.L.B. Selinger et al., Materials Research Society, vol. 409, Pittsburgh, 1996, 29-44

4.

Mullins, M. and Dokainish, M.A., Phil. Mag. A, vol.46, 771-787, 1982

5.

Kohlhoff, S., Gumbsh, P. and Fishmeister, H., Phil. Mag. A, vol. 64, 851-878, 1991

6.

Shastry, V. and Farkas, D., Modelling Simul. Mater. Sci., vol. 4, 473-492, 1996

7.

Machová, A., Beltz, G.E. and Chang, M., Modelling Simul. Mater. Sci. Eng., vol. 7, 949-974, 1999

8.

Beltz, G.E. and Machová, A., Scripta Materialia, vol. 50, 483-487, 2004

9.

Marsch, P.G., Zielinski, W., Huang, H. and Gerberich, W., Acta metall. mater., vol. 40, 28832894, 1992

10. Šmida, T. and Bošanský, J., Materials Sci. Eng. A, vol. 287, 107-115, 2000 11. Machová, A. and Ackland, G.J., Modelling Simul. Mater. Sci. Eng., vol. 6, 521-542, 1998 12. Ackland, G.J., Bacon, D.J., Calder, A.F. and Harry, T., Phil. Mag. A, vol. 75, 713-732, 1997 13. Machová, A., Computational Materials Science, vol. 24, 535-543, 2002 14. Zhou, S.J., Beazley, D.M., Lomdahl, P.S., Voter, A.F. and Hollian, B.L., In Advances in fracture research, edited by B.L. Karihaloo et al., Pergamon, New York, 1997, 3085-3094 15. Pokluda, J. and Šandera, P., Metall. Mater., vol. 33, 375-383, 1995

9. Micromechanisms in Fracture and Fatigue

851

A DISCUSSION OF THE APPLICABILITY OF 'K-VALUES TO EXPLAIN THE FATIGUE CRACK GROWTH BEHAVIOUR OF SHORT CRACKS A. Tesch, H. Doker, K. H. Trautmann, R. Pippan1 and C. Escobedo2 German Aerospace Center, Institute of Materials Research; 51170 Köln; Germany 1Erich-Schmid-Institute for Materials Science of the Austrian Academy of Sciences; 8700 Leoben; Austria 2Airbus Deutschland GmbH; 21129 Hamburg; Germany [email protected] In a joint research project of AIRBUS Deutschland in Hamburg and the Institute of Materials Research of the German Aerospace Centre (DLR) in Köln short corner cracks emanating from holes were investigated. Fatigue crack growth thresholds and fatigue crack growth rates (da/dN) of long cracks were determined at different R ratios for Al 2524-T351 and Al 6013-T6.

FIGURE 1. Short crack growth results for different stress ratios R, compared with long cracks growth data for 6013-T6. For the short crack tests a very small edge notch was cut into one edge of the hole of M(T) specimens (Fig.1) with the Focused Ion Beam (FIB) Technology. From these FIB-notches short corner cracks were introduced by compression loads (R=20). The lengths of these initial cracks varied between 30µm and 100µm. Fatigue crack growth tests were performed with R = 0,1 and R = 0,7. In Fig. 1, the experimentally determined da/dN-'K curves of short corner cracks are compared with the long crack test data for the alloy 6013-T6. In this graph the stress intensity factor solutions were taken from Murakami’s stress intensity handbook [1].

A. Tesch et al.

852 It seems that:

At the same R-values short cracks grow below the threshold of the stress intensity factor range of long cracks. At R = 0,7 short cracks propagate approximately 10 times faster than long cracks at the same 'K-values. The difference in the crack propagation rate between the long crack data and the short crack data becomes bigger at lower R-ratios (e.g. R = 0,1). The short crack growth rate is not influenced by the stress ratio R. It is well known, that short cracks don’t fulfil the rules of linear elastic fracture mechanics (LEFM) [e.g. 2-5]. If one takes an effective stress intensity factor derived from the Dugdale model pertaining to perfect plastic materials [6], most of the short crack characteristics in Fig.1 vanish: At R = 0,7 short cracks propagate with the same propagation rate as long cracks at the same 'K-values and the cracks don’t propagate below the threshold of long cracks. At R = 0,1 short cracks grow below the threshold of long cracks at the same stress ratio, but not below the threshold of long cracks at higher stress ratios (e.g. R = 0,7). The crack growth rates of short cracks are independent of R. This paper discusses the influence of the different solutions to calculate the stress intensity on the observed short crack behaviour. The formula of LEFM [1] as one limit, the aera concept of Murakami and Endo [7], considerations of Riemelmoser and Pippan [2], and an effective stress intensity factor derived from the Dugdale model pertaining to perfect plastic material [6] as the other limit are compared.

References 1.

Newman, J.C. and Raju, I.S., in Stress Intensity Factors Handbook, Editor-in-Chief Y. Murakami, Pergamon Press, Oxford, England, 1987, 712-722.

2.

Riemelmoser, F.O. and Pippan R., International Journal of Fracture, vol. 118, 251-270, 2002.

3.

Suresh, S., Fatigue of Materials, second edition, Cambridge University Press, Cambridge, United Kingdom, 2001

4.

Newman, J.C., Jr., in Small-Crack Test Methods, ASTM STP 1149, edited by J. Larsen and J.E. Allison, American Society for Testing and Materials, Philadelphia, 1992, pp. 6-33.

5.

Taylor, D., in The Behaviour of Short Fatigue Cracks, EGF Pub.1, edited by K.J. Miller and E.R. de los Rios, Mechanical Engineering Publications, London, pp. 479-490.

6.

Cioclov, D.D., in Fatigue Life Simulation-Equivalent Initial Flaw Approach-EIFSIM Version 3.2d/2004 User’s Manual, Saarbrücken, Germany, 2005.

7.

Murakami, Y. and Endo, M., Engineering Fracture Mechanics, vol. 17, 1-15, 1983.

9. Micromechanisms in Fracture and Fatigue

853

SIMULATION OF CRACK GROWTH UNDER LOW CYCLE FATIGUE AT HIGH TEMPERATURE IN A SINGLE CRYSTAL SUPERALLOY B. Fedelich, Y. Kiyak, T. May and A. Pfennig Bundesanstalt für Materialforschung und -prüfung (BAM) Unter den Eichen 87, 12205 Germany [email protected] Blades in gas turbines or aero-engines undergo a combination of creep and cyclic thermomechanical loading corresponding to start up, steady state operation and shut-down. The blades of the first stages are nowadays usually made of single crystal Ni-base superalloys due to their higher creep resistance. Film cooling allows for even higher service temperatures but the stress concentrations at the cooling holes and the local damage induced by drilling the holes are known to promote cracking. The prediction of the crack behaviour under high temperature cyclic loading is thus an essential element of any blade lifing procedure. Crack growth tests have been performed at 950°C with Single Edge Notch specimens of a Nibase single crystal superalloy. In particular, several cycle shapes, frequencies and orientations have been used, thus allowing the assessment of the influence of these parameters on the crack growth rate. The crack growth is monitored by the electric potential method. The formula of Johnson [1] has been used to relate the electric potential to the crack length. The distance between the leads and the crack plane has been treated as an adjustable parameter and identified from several marker bands on the fracture surface. In addition, oxidation experiments have been carried out to characterise the kinetics of the oxide scale growth at the same temperature. On the other side, crack growth has been simulated with the FE program Abaqus in real test conditions by the node release technique. The FE nodes are released on the basis of the measured crack growth rate. To limit the computational time, the simulations have been performed in either plane strain or stress with a 2D sub-model. The appropriate boundary conditions for the sub-model have been identified from computations with a 3D model of the whole specimen. The mesh of the 3D specimen is showed in Fig. 1a and an example of the predicted crack opening profile after 20 cycles can be seen in Fig1b. The simulation results are compared with the test results on the basis of the computed crack tip opening displacement (CTOD). The CTOD is evaluated by the 45° rule, which yield values that are remarkably insensitive to mesh refinement in contrast to the opening of individual nodes, as can be observed on Fig. 2. The crack is propagated until a stabilized value of the CTOD is obtained. This is usually the case when the crack has crossed the initial plastic zone, as already reported by several authors, e.g., González-Herrera and Zapatero [2]. The oxidation of the crack flanks has been also taken into account, using the oxide scale measurements. The procedure provides a direct evaluation of the effects of cycle form, crystal orientation, plasticity and oxide induced crack closure.

B. Fedelich et al.

854

FIGURE 1. a) 3D mesh used to identify the boundary conditions on the 2D sub-model. b) Equivalent plastic strain distribution at maximum load after 20 cycles.

FIGURE 2. First node opening displacement and CTOD evaluated by the 45° rule for two mesh refinements. A constitutive law for Ni-base single crystal superalloys has been developed and implemented in the UMAT user-subroutine of Abaqus. It corresponds to a simplified version of a micromechanical model previously developed by Fedelich [3]. The model is based on the slip system theory and accounts for octahedral and cubic slip, for dislocation multiplication as well as kinematical hardening. Furthermore, the effects of rafting during long duration tests can be predicted.

References 1.

Johnson, H. H., Materials Research & Standards, vol. 5, 442-445, 1965.

2.

González-Herrera, A. and Zapatero, J., Engng. Fract. Mech., vol. 72, 337-355, 2005.

3.

Fedelich, B., Int. J. Plasticity, vol. 18, 1-49, 2002.

9. Micromechanisms in Fracture and Fatigue

855

FATIGUE CRACK GROWTH FOR DIFFERENT RATIOS OF BENDING TO TORSION IN ALCU4MG1 D. Rozumek and E. Macha Technical University of Opole ul. Mikoajczyka 5, 45-271 Opole, Poland [email protected] and [email protected] The paper contains the fatigue crack growth test results obtained under proportional bending with torsion in AlCu4Mg1 aluminium alloy [1]. Specimens with rectangular cross sections and dimensions: length l = 90 mm, height w = 10 mm and thickness g = 8 mm were tested [2]. Each specimen had an external unilateral notch with depth 2 mm and radius U = 0.2 mm. The tests were performed under the stress ratio R = -1. The notches in the specimens were cut with a milling cutter and their surfaces were polished after grinding. The tests were realized on a fatigue test stand MZGS-100 where the ratio of torsion moment to bending moment was MT(t)/MB(t) = tgD = 3 / 3, 1 and M t

(Fig. 1) and loading frequency was 29 Hz. The total moment

3

M T2 t  M

2 B

t was generated by force on the arm 0.2 m in length.

FIGURE 1. Loading of the specimen. Unilaterally restrained specimens were subjected to cyclic bending with torsion with the constant amplitude of moment Ma = 7.92 N˜m. Crack development was observed on the specimen surface with the optical method. The fatigue crack increments were measured with a digital micrometer located in the portable microscope with magnification of 25 times and accuracy 0.01 mm. At the same time, a number of loading cycles N was written down. J-integrals were calculated with the finite element method (FEM) using the computer program FRANC3D and FRANC2D. The test results were shown as graphs of the crack length a versus the number of cycles N, and crack growth rate da/dN versus the 'J integral range. 'JI was compared with the 'JIII for different ratios of bending to torsion (Fig. 2). The experimental results for elasto-plastic range at the constant rate value da/dN shown in Fig. 2 were described with the following formula § 'J I ¨ ¨ J © Ic

2

· § ' J III ¸ cos D  ¨ ¸ ¨ J ¹ © IIIc

where JIc = 0.68JIIIc.

2

· ¸ sin D ¸ ¹

1

(1)

D. Rozumek and E. Macha

856

The graphs in Fig. 2 present the experimental results for stress ratio R = - 1. In Fig. 2 it can be noticed that together with an increase in plasticity there occurs a deflection of experimental points in direction of mode I. The bigger plasticity, the greater deflection of points is.

FIGURE 2. Experimental data for different ratios of bending to torsion for R = - 1. The test results (Fig. 2) fatigue crack growth rate da/dN = 7.6˜10-8 m/cycle and da/dN = 1.4˜10-7 m/cycle were described with graphs 1 and 2, respectively.

References 1.

Rozumek D., Proc. of the 7th Int. Conf. on Biaxial/Multiaxial Fatigue and Fracture, DVM Berlin, Germany, 2004, 489-494.

2.

Macha E., Rozumek D., Proc. of the 15th European Conference of Fracture, Advanced Fracture Mechanics for Life and Safety Assessments, Stockholm, KTH, 2004, CD-ROM, 8ps

Acknowledgements: This work was supported by the Commission of the European Communities under the FP5, GROWTH Programme, contract No. G1MA-CT-2002-04058 (CESTI)

9. Micromechanisms in Fracture and Fatigue

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DUCTILE DAMAGE MODELS APPLIED TO ANISOTROPIC FRACTURE OF AL2024 T351 D. Steglich, W. Brocks and T. Pardoen1 Helmholtz Association of National Research Centres (GKSS), D-21502 Geesthacht, Germany, [email protected] 1Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium, [email protected] Al2024-T351 is an aluminium alloy renowned for its good mechanical properties, damage tolerance and resistance against corrosion. Therefore it has been used for decades in aircraft applications, especially in fuselage skins. Airplane designers estimate the fracture resistance of fuselage components by ductile crack growth resistance tests, which have to be performed on different specimen geometries and sizes. These test campaigns are time consuming and expensive. The development of predictive models for ductile crack extension is thus essential in order to improve structural design and maintenance and accelerate the insertion of new materials or assembling methods. Micro-mechanically based damage models accounting for both void nucleation and void growth such as the Tvergaard or Rousselier models allow for the description of size and geometry effects. These are often encountered when trying to transfer rupture parameters from small to large test specimen. The models are commonly restricted to isotropic material behaviour with respect to both deformation and damage. Metal alloys which have undergone extensive plastic deformation by rolling, extrusion, etc. exhibit a significant anisotropy of mechanical properties, however. Predictions of fracture resistance for rolled panels loaded in longitudinal and transverse direction have been performed by accounting for the plastic anisotropy and assuming a scalar damage variable. Due to the cubic symmetry of fcc and bcc metals, the yielding behaviour may still be considered as almost isotropic, while ductility shows a significant reduction, if loading is applied in the thickness direction. This effect is considered by orientation dependent damage parameters. Generally, the identification of model parameters is a crucial point. It can be done phenomenologically by fitting numerical simulations to respective results of mechanical tests. The specific feature of micro-mechanical models is, however, that the damage parameters can be directly identified from microstructural investigations. Optical microscopy (OM), scanning electron microscopy (SEM) and synchrotron-radiation based X-ray microtomography (XTM) have been used to obtain quantitative information. Figure 1 shows a reconstructed view of the investigated volume. The particle clusters appear white, while the surrounding matrix is grey. It is obvious that the particles are aligned in a network-like structure. These particle clusters separate the matrix into “matrix domains”. The domains have a disc-like shape, with the S-direction as the shortest axis and almost identical dimensions in L- and T-direction, see figure 2. In the present contribution, the model developed by Pardoen and Hutchinson based on the growth and coalescence of axisymmetric voids embedded in a work hardening matrix material is chosen to simulate the failure of round notched bars. The effect of varying model parameters is studied by cell model calculations. Special emphasis is laid on a careful characterisation of the precipitate and particle morphology. From this microstructural information, a simplified model is derived, which allows to directly evaluate model parameters for loading in S-direction. In a second step, these parameters are modified based on simple geometrical assumptions and used to predict failure in L-direction.

858

D. Steglich et al.

FIGURE 1. Particle clusters (white) in the investigated material in an XDM analysis.

FIGURE 2. Model of the microstructure accounting for direction-dependent failure mechanisms

9. Micromechanisms in Fracture and Fatigue

859

FATIGUE AND FRACTURE PROCESSES IN SEVERE PLASTIC DEFORMED RAIL STEELS F. Wetscher, R. Pippan and R. Stock1 Erich Schmid Institute of Material Sciences, Austrian Academy of Sciences, Jahnstraße 12, A8700 Leoben, Austria CD-Laboratory for Local Analysis of Deformation and Fracture, Jahnstraße 12, A-8700 Leoben 1Voestalpine Schienen GmbH, Kerpelystraße 199, A-8700 Leoben, Austria [email protected] On the surface of rails a severely deformed layer is formed during the application due to the permanent loading of a rail-wheel contact [1]. In this deformed layer cracks are formed and may grow to a critical length. Therefore, it is of great importance to determine the fracture properties of these plastically deformed regions to enhance finite element calculations for live time predictions and define service intervals. In this study, the rail steel UIC 900A has been severely deformed by Equal Channel Angular Pressing (ECAP) [2] with a tool angle of 120° using Route A. The samples for ECAP had a size of 10x10x70mm and were deformed at room temperature. From these deformed samples, CTspecimens for fracture toughness tests and fatigue tests were machined. The investigation of the microstructure of this fully pearlitic steel subjected to severe plastic deformation has shown that a nanostructured lamellar structure parallel to the shear plane evolves and the mechanical strengths increases markedly [3, 4]. Hence, two critical directions for the crack were defined as shown in Fig. 1.

Figure 1 Sketch of the ECAP deformed sample and the machined CT specimens It can be expected that the crack cannot easily grow through the lamellae in the case of specimen “A” whereas in specimen “B” almost no obstacles will hinder the progress of the crack. Figure 2 shows that already after three ECAP passes the crack does no longer follow the original direction in a fracture toughness experiment in the case of the sample orientation “A”. If the sample orientation is “B”, the crack goes almost perfectly straight through the sample.

F. Wetscher et al.

860

Figure 2 Tested CT-Specimens after 3 ECAP passes with different orientation Fatigue crack propagation curves were measured for different values of R using a direct current potential drop technique. All experiments were performed for different numbers of ECAP passes and therefore for different shear strains. The results as a function of the direction and the strain are explained in terms of the developing microstructure.

References 1.

Wang, L., Pyzalla, A., Stadlbauer, W. and Werner, E.A., Mat. Sci. Eng. A., vol. 359, 31-43, 2003

2.

Segal, V.M., Mat. Sci. Eng. A., vol. 197, 157-164, 1995

3.

Wetscher, F., Vorhauer, A., Stock, R. and Pippan, R., Mat. Sci. Eng. A., vol 387-389, 809816, 2004

4.

Wetscher, F., Tian, B., Stock, R. and Pippan, R., to be published in Mat. Sci. Forum

9. Micromechanisms in Fracture and Fatigue

861

DAMAGE EVOLUTION IN TORSION SPECIMENS DEFORMED AT FORGING TEMPERATURES Gernot Trattnig, Reinhard Pippan and Siegfried Kleber1 Erich Schmid Institut of Material Science of the Academy of Sciences, CD Laboratory for the local Analysis of Deformation and Fracture, Austria, Leoben 1Böhler Edelstahl, Kapfenberg, Austria [email protected], [email protected], [email protected] Torsion experiments at forging temperatures were carried out in order to analyse the dependency of the damage evolution on forming parameters like testing temperature, strain, strain rate and prior heat treatment. The testing material was the nickel-based superalloy NiCr20TiAl (Böhler L306 VMR). Experiments were carried out with a high temperature torsion testing machine at forging temperatures between 900 and 1100 °C. In this way shear strains up to 3000 percent were achieved. Flow curves for certain testing temperatures and strain rates are gained, furthermore the influence of prior heat treatment was examined.

FIGURE 1. (a) Used torsion specimen geometry; (b) ruptured specimen after 25 revolutions at 1000 °C testing temperature with prior heat treatment; (c) SEM image of a cut through the symmetry axis of specimen (b) with apparent voids. The deformation of the torsion specimen (Fig. 1.a) leads to void nucleation, void growth and void coalescence and subsequently to rupture of the torsion specimen (Fig. 1.b). The shear strain in the specimen increases from cero in the centre to the maximum value at the surface. By analysing a cut through the symmetry axis of a deformed specimen different deformation stages can be examined with a single specimen. Fig. 1.c shows a scanning electron microscope (SEM) image of a cut through the symmetry axis of the specimen in Fig. 1.b. This specimen was deformed at a testing temperature of

G. Trattnig et al.

862

1000 °C to a shear strain of approx. 1200 % with prior heat treatment. By digital image analysis the void area fraction and the number of voids were gained. The void area fraction was taken as an indicator for the accumulated damage. By varying experimental parameters like testing temperature, strain rate, prior heat treatment and shear strain, their influence on the damage could be evaluated. In this way it is possible to evaluate different damage respectively fracture criteria, e.g. presented by Clift et al. [1], Wifi et al. [2], VenugopalRao et al. [3]. In addition circumferential notches were induced in torsion specimens with a lathe and sharpened by razor blade polishing. The void density in un-notched torsion specimens was compared to the void density in front of the growing crack in these notched torsion specimens.

References 1.

Clift, S.E., Hartley, P., Sturgess, C.E.N., and Rowe, G.W., Int. J. of Mechanical Sciences, vol. 32, 1-17, 1990.

2.

Wifi, A.S., Abdel-Hamid, A., and El-Abbasi, N., J. of Materials Processing Technology, vol. 77, 285-293, 1998.

3.

Venugopal-Rao, A., Ramakrishnan, N., and Krishna-kumar, R., J. of Materials Processing Technology, vol. 142, 29-42, 2003.

9. Micromechanisms in Fracture and Fatigue

863

MICROSTRUCTURAL EFFECTS ON SHORT FATIGUE CRACK PROPAGATION AND THEIR MODELLING H. J. Christ, O. Duber, W. Floer, U. Krupp, C. P. Fritzen1, B. Kunkler1 and A. Schick1 Universität Siegen, Institut für Werkstofftechnik, 1Institut für Mechanik und Regelungstechnik 57068 Siegen, Germany [email protected] Cyclically loaded components in structural applications often undergo a stress amplitude which is close to the fatigue limit of the material used. Under such conditions, crack initiation and short crack propagation is considered to play an important role. It is well established that in high cycle fatigue (HCF) cracks propagate as stage I cracks during a rather large fraction of fatigue life (up to 90% of the number of cycles until failure, Nf). The propagation behaviour of these so-called microstructurally short fatigue cracks is strongly affected by microstructural properties, such as the grain size and the presence of phase boundaries, and cannot be described using linear-elastic fracture mechanics. Because of the significance of crack initiation and early crack propagation for cyclic life, new concepts and experimental methods have to be applied in order to provide a robust and reliable fatigue life assessment. Results from two interdisciplinary research projects are reported in this presentation, which were carried out by the authors during the past seven years, in order to shed light on the relevant mechanisms and to illustrate the implementation of these findings in a life prediction model. In order to study the effect of grain boundaries as obstacles to short crack propagation, a metastable beta titanium alloy (TIMETAL®LCB) in the solution annealed single-phase condition was used. Push-pull fatigue tests were conducted at room temperature in laboratory air at various stress amplitudes and stress ratios on electrolytically polished, cylindrical specimens. A shallow notch was used to predefine the crack initiation sites. Crack growth was monitored and evaluated using optical and scanning electron microscopy (in combination with EBSD/OIM). Furthermore, crack closure was determined by means of laser interferometry (ISDG). It was found that crack initiation occurs mainly at grain boundaries on the surface and can be attributed to the elastic anisotropy of the material [1]. Crack growth is strongly affected by the microstructure of the material, in the sense that grain boundaries act as microstructural barriers which decelerate or even stop propagating cracks. The barrier strength of a grain boundary depends on the crystallographic misorientation of the adjacent grains, as shown by orientation measurements using EBSD. Since stage I crack growth takes place on slip planes, the misorientation between the slip planes in the grains involved is the decisive factor and not the orientation difference between the lattices of the grains. Furthermore, crack closure measurements showed that for low stress amplitudes roughness-induced crack closure is predominant, whereas at higher stress amplitudes plasticity-induced crack closure prevails [2]. A duplex stainless steel (X2 CrNiMoN 22-5-3) with a two phase austenitic-ferritic microstructure was applied to characterize the role of phase boundaries. Major differences in the propagation behaviour of short cracks were noticed as compared to LCB, which can be related mainly to the presence of two phases in the duplex steel. Crack initiation in the duplex steel occurs primarily because of the interaction of slip bands, which develop in the softer austenitic phase, with JD-phase boundaries. The crack propagation is determined not only by the crystallographic misorientation between adjacent grains but also by the spacial arrangement of the constituent phases. Also the phase of the grain that contains the crack tip is an important factor, since this phase determines the plastic zone at the crack tip. At low stress amplitudes, crack growth takes

H. J. Christ et al.

864

place in the harder D-phase in single slip at 45° to the stress axis, whereas in the softer J-phase, crack advance occurs in double slip and perpendicular to the stress axis. Therefore, the crack can alternate between stage I and stage II crack growth depending on the yield strength of the current grain [3]. On the basis of the results obtained for the titanium alloy a numerical model was developed, which is capable to describe the strong interaction of the propagating short fatigue crack with grain boundaries. Crack closure is implemented as well. The model calculates the crack growth in stage I and hence predicts fatigue life on a physical basis. It also allows to simulate the short crack growth phenomena found in the duplex steel. The influence of the spacial arrangement of the two phases as well as the impact of the different yield strength is correctly reproduced [3,4]. A comparison between experimentally observed data and the results of the simulation calculation is given in Fig. 1.

FIGURE 1: Experimentally observed and simulated crack growth in a duplex steel [4]

References 1.

Hu, Y.M., Floer, W., Krupp, U., Christ, H.-J., Materials Science and Engineering, vol. A278, 170-180, 2000.

2.

Krupp, U., Floer, W., Lei, J., Hu, Y.M., Christ, H.-J., Phil. Mag A, vol. 82, 3321-3332, 2002.

3.

Düber, O., Künkler, B., Krupp, U., Christ, H.-J., Fritzen, C.-P., Journal of Fatigue, in print.

4.

Künkler, B., Düber, O., Krupp, U., Christ, H.-J., Fritzen, C.-P., in 11th International Conference on Fracture 2005, CD-ROM.

9. Micromechanisms in Fracture and Fatigue

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MICROMECHANICAL ASPECTS OF TRANSGRANULAR AND INTERGRANULAR FAILURE COMPETITION I. Dlouhy and M. Holzmann INSTITUTE of Physics of Materials, Academy of Sciences of the Czech Republic, Zizkova 22, 61662 Brno, Czech Republic [email protected] Occurrence of intergranular initiation of brittle fracture could be taken as significant simple measure of the negative influence of impurities content. This micromechanism of failure has been usually responsible for strong decrease of mechanical properties, anomalous fracture behaviour or, at least, comparably larger and in structural applications unacceptable data scatter. The intergranular fracture initiation itself has to be taken as result of competition between two stress-controlled fracture micromechanisms: cleavage and intergranular. For action of these micromechanisms a criterion of some local fracture stress acting over some microstructurally susceptible distance (volume) has to be reached. What is the cause that forces the metal grain boundary to fail in intergranular manner rather than transgranular? As known, it is a cohesion strength that decreases at the same time as the cleavage fracture stress is kept on the same level. But a number of questions are connected with relation of microscopic cohesion strength and local fracture stress, with effect of pre-strain due to cold deformation or constraint phenomena etc. An interconnection of fractographic methods with analysis of data from simple suitable specimen (e.g. Charpy type) seems to be the effective tool for solution of these problems. The aim of paper can be seen in analysis of micromechanical aspects of brittle fracture initiation connected with intergranular decohesion as micromechanism that is well susceptible to metallurgic cleanliness and cumulative degradation of material. Causes and characteristics governing the intergranular fracture initiation and occurrence of this fracture micromechanism in competition with cleavage one should be also addressed.

FIGURE 1.Comparison of FTTD for both steel melts after and step cooling treatment A CrNi steel of commercial quality and the same steel with increased content of impurity elements have been used for investigation. Step cooling treatment has been applied in order to induce intergranular embrittlement and brittle fracture initiation in both steel melts. Except for standard specimen geometry for three-point bending the pre-cracked Charpy type specimens were applied for determination of fracture mechanical properties. Fractal analysis was applied in order

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to characterise the quantitative morphological differences in fracture surfaces. Relation of cleavage fracture stress and critical stress for intergranular failure has been followed. Fracture behaviour of the steel. The typical temperature dependences of fracture toughness are shown in Fig. 1 for the steel A and R after step-cooling treatment. The as received state is here represented by thin dashed lines only. It follows from comparison of main trends that except for the scatter in fracture toughness values a very limited embrittlement occurred and only slight shift of transition region was observed for melt A.

Quantitave characterisation of fracture surfaces. Change of fractal dimension, DF, is shown in Fig. 2 for the investigated states. The separate points represent data for steel A in initial state and in embrittled state. The scatter bands are shown for initial state represented by full lines only, for the state after embrittling ageing by shaded field. It follows from comparison that practically the same DF values appears to be the main characteristics of brittle failure for both microstructures. Based on this finding and based on knowledge shown in previous part, the “embrittled” state of steel A posses “still acceptable properties” and embrittlement process is just in stage of conversion to intergranular initiation. Evident differences have been found when comparing both embrittled microstructures of the steel melt A and R, the higher value of fractal dimension corresponds to higher fracture roughness due to intergranular failure mechanism.

Figure 2.Change of fractal dimension, DF, with distance from crack tip, x, – steel A with initial microstructure and after ageing, steel R after step cooling Critical (fracture) stress quantification. To determine the local fracture stress experimentally two procedures were used in the paper some quantitative results will be described in more detail. It has been found that the (local) fracture stress is lower for steel with intergranular initiation when compared to the steel with pure cleavage failure mechanism. Fractal dimension corresponded well to brittle fracture morphology reflecting, on quite susceptible level, the changes from pure cleave to intergranular fracture. The fracture stress may be used as local criterion of fracture and as one of parameters for identification of critical impurity levels causing intergranular embrittlement. Authors gratefully acknowledge to Grant Agency of the Academy of Sciences (GAAV 200410502) for the financial support.

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DEFECT IN ULTRA-FINE GRAINED MG-BASED ALLOYS DEFORMED BY HIGH-PRESSURE TORSION J. Cizek, I. Prochazka, B. Smola, I. Stulikova, R. Kuzel, Z. Matej and V. Cherkaska Faculty of Mathematics and Physics, Charles University in Prague, Czech Republic V Holešovikách 2, CZ-180 00 Praha 8 Czech Republics R.K. Islamgaliev, O. Kulyasova Ufa State Aviation Technical University, Russia Ufa 450 000, Russia [email protected] Applications of Mg-based alloys at elevated temperatures are limited by the low melting point of Mg. This difficulty can be overcome by an addition of rare earth elements. A number of novel promising Mg-based hardenable alloys with high creep resistance at elevated temperatures have been developed, e.g. Mg-Gd, Mg-Mn-Sc etc. Despite the favorable strength and thermal stability, a disadvantage of these alloys consists in a low ductility, which is not sufficient for industrial applications. Grain refinement is known as a way how to improve ductility. It has been demonstrated that an extreme grain size reduction can be achieved by methods based on severe plastic deformation (SPD). In the present work we used high pressure torsion (HPT), which is the most efficient in grain size reduction among the SPD-based techniques, for preparation of selected Mg-based alloys with ultra fine grained (UFG) structure. Microstructure investigations and defect studies of HPT deformed UFG Mg-based alloys are presented in this paper. The extraordinary properties of UFG materials are closely related with defects (grain boundaries, dislocations) introduced by HPT. Positron lifetime (PL) spectroscopy [1] is a well-established non-destructive technique with high sensitivity to open volume defects. It enables identification of the defect types present in the material studied and determination of defect densities. Thus, PL spectroscopy represents an ideal tool for defect studies of UFG materials. In the present work PL spectroscopy was combined with X-ray diffraction (XRD), microhardness measurements, and direct observations of microstructure by TEM. Typical TEM image of HPT deformed Mg-10wt.%Gd alloy is shown in Fig. 1 as an example. It exhibits homogeneous UFG structure with grain size around 100 nm, mainly high-angle type grain boundaries, and high dislocation density. High number of dislocations leads to a significant broadening of XRD profiles. Two components were resolved in PL spectrum of HPT deformed Mg-10wt.%Gd alloy. Namely the free-positron component and a contribution of positrons trapped at dislocations, which represent dominant positron trapping sites. Spatial distribution of dislocations was investigated.

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FIGURE 1. A TEM image of Mg-10wt.%Gd alloy deformed by HPT.

References 1.

Hautojärvi, P., Corbel, C., In Proceedings of the International School of Physics “Enrico Fermi”, Course CXXV, edited by A. Dupasquier, A.P. Mills, IOS Press, Varena 1995, 491532.

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MODELLING CRACK-TIP SHIELDING EFFECTS IN PARTICLE REINFORCED COMPOSITES Jana Hornikova, Pavel Sandera and Jaroslav Pokluda Brno University of Technology, Technická 2, Brno, Czech Republic [email protected] When a crack propagates in particle reinforced composites, the particles induce various shielding effects at its tip. These effects can either increase or decrease the crack driving force which is reflected in the change of fracture toughness of a composite. The increase in this value is particularly important in case of brittle-matrix composites [1]. The paper is focused on the calculation of selected local shielding effects caused by rigid particles and holes at the tip of a crack under remote mode I loading conditions. A numerical two-dimensional analysis based on the finite-element code ANSYS was employed to investigate a superposition of influences of both the modulus difference and the crack tip tilting, induced by a local mode II component. The influence of size and spacing of particles distributed in a regular network around the crack tip was also considered in the numerical analysis. The effective stress intensity factor Keff was calculated for many crack tip positions in an appropriately chosen area between two particles of the network. Then, by assuming the translation symmetry, the results were generalized for all possible positions within the network. The presence of inclusions generally induces the mixed mode I + II at the tip of the straight crack and, in this case, the crack tilting appears to minimize the mode II loading. The ratio between the averaged stress intensity factors (SIFs) at deflected and straight crack fronts expresses a relative amount of toughening [2]. Spherical particles of the same interparticle spacing l

60 µm , of different

diameters d  6, 180 µm and of 20-times higher Young moduli than the matrix (rigid inclusions) are considered in the model. Moreover, particles of negligibly small moduli (holes) are also studied for comparative reasons. A geometrical configuration of a standard CT specimen was modeled using a mesh of six-node triangular elements in the investigated region. The central nodes of elements at the pre-crack tip were shifted in order to simulate a singularity of the stress field. Several thousands possible positions of the crack tip were analyzed within an investigated area in between a pair of spherical particles, according to the scheme in Fig. 1. This area was chosen to be long enough to reproduce the translation symmetry and to generalize the results to a periodical square network of particles. This can be done by multiplication of normalized effective SIFs in the points lying within both the left-hand and the right-hand parts of the investigated region associated by the translational periodicity. To assess the crack driving force, the effective SIF [3] normalized to the remote K If was used as follows:

K eff

K

2 I

12

 K II2

K If

(1)

The tendency to the crack tip tilting by an angle at the onset of an unstable fracture was assesses by using the well-proved criterion [4] based on the minimization of the mode II affected crack growth:

§D · 4 tan ¨ ¸ © 2¹

KI  K II

2

§ KI · ¨ ¸ 8 © K II ¹

(2)

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The Keff - factor can be considered to be invariant, i.e. independent on the kink angle , when assuming only a formation of an elementary kink within the process zone during the KIc test. A further propagation of the kink causing an additional shielding is beyond the frame of this analysis.

FIGURE 1. CT specimen and the investigated region (hatched area) of crack tip positions between two particles. In spite of a significant crack tip tilting induced by spherical holes, the resulting effect is a slight increase in the crack driving force or the Keff factor (anti-shielding). However, a possible crack-tip trapping in the holes was not taken into account. On the other hand, the rigid particles cause a significant decrease in the Keff-value (shielding), while leaving the crack geometry practically unaffected. These results are in a qualitative agreement with previously published simple models [5] concerning the interaction of a crack with a single particle.

References 1.

M. Kotoul and R. Urbiš: Engng. Fract. Mech. 68 (2001), p. 89.

2.

K.T. Faber and A.G. Evans: Acta Met. 31 (1983), p. 565.

3.

J. Pokluda, P. Šandera and J. Horníková: Fat. Fract. Engng. Mat . Struct. 27 (2004), p. 141.

4.

D. Broek: Elementary Engineering Fracture mechanics (Martinus Nijhoff Publishers, The Hague 1984).

5.

F. Erdogan, G. D. Gupta and M. Ratwai: J. Appl. Mech. 12 (1974), p. 1007.

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EARLY STAGES OF FATIGUE DAMAGE IN 316L STEEL J. Man, K. Obrtlik, J. Polak and P. Klapetek1 Institute of Physics of Materials, Academy of Sciences of the Czech Republic Žižkova 22, 616 62 Brno, Czech republic 1Czech Metrology Institute Okružní 31, 638 00 Brno, Czech Republic [email protected], [email protected], [email protected], [email protected] The study of the nature and the physical mechanisms of fatigue damage evolution have started more than 100 years ago by Ewing and Humfrey [1]. These authors firstly performed the optical microscopic observations on flat specimens of polycrystalline Swedish iron fatigued in rotating bending. They observed the localized cyclic slip in surface grains and the formations of pronounced surface markings. Their most important finding – the identification of fatigue cracks within the rough surface relief – has activated hitherto persisting interest in mechanisms of fatigue damage. The localization of the cyclic plastic strain in so-called persistent slip bands (PSBs) and the formation of pronounced surface relief at the locations where PSBs intersect originally flat surface is a general and very important feature of early fatigue damage of crystalline materials. The sharp surface slip markings (called persistent slip markings – PSMs) consist of extrusions and intrusions. Fatigue cracks nucleate in these locations later in the fatigue life (for recent review see Polák [2]). Thus, for the understanding of fatigue crack initiation, knowledge of the PSMs topography and its evolution is essential. The purpose of the present work was to study growth and crystallographic pattern of intrusions and extrusions within individual grains of polycrystalline austenitic 316L stainless steel fatigued with constant plastic strain amplitude at room temperature. For this purpose two modern experimental techniques were employed: atomic force microscopy (AFM) and electron backscattering diffraction (EBSD). In agreement with our recent study by Polák et al. [3] and Man et al. [4], unambiguously documenting limitations of AFM technique in observation and quantitative evaluation of the surface relief topography, extrusion growth was systematically monitored by direct observation of the metallic surface and plastic replica technique has been used to reveal intrusions. Experimental details were similar to those described in our previous work [3, 4]. Experimental material was 316L steel supplied by Uddeholm with average grain size of 39 µm.

Experimental results and their discussion Inverse pole figure as obtained by the analysis of EBSD measurement for all 32 surface grains in 316L steel showed that no specific orientation of grains was preferred in this surface relief study. The comparison of the observed and calculated trace angles of PSMs revealed that in the majority of grains only 1 slip system (ss) was activated (primary ss in 20 grains, secondary ss in 7 grains). Only within 5 grains both the primary and the secondary ss were detected and in 1 grain no PSMs were developed at the moment of arrest of the fatigue test (after 6750 cycles ~ 15% Nf).

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FIGURE 1. Typical configurations of extrusion/ intrusions pairs observed in 316L steel. FIGURE 2. Growth of extrusions and intrusions in 316L steel. Statistical evaluation of results obtained by AFM systematic observations of identical areas within individual grains in 316L steel using both direct specimen observation and plastic replicas can be summarized as follows: (i) Intrusions developing at PSB/matrix interface are always preceded by extrusions regardless of the orientation of individual grains of a polycrystal. (ii) Four typical configurations of extrusion/intrusion pairs were detected (see Fig. 1). Intrusions denoted A and B are produced at the side of the extrusion where the emerging active slip plane is inclined to the surface at an obtuse and an acute angle respectively (see also Fig. 2). (iii) The first intrusions appear after 200–1000 cycles (~ 0.4–2.2% Nf) at the moment when the “static” extrusions develop (Fig. 2), predominantly but not exclusively at the side of an extrusion where the emerging active slip plane is inclined to the surface at an acute angle (position B denoted in Fig. 1). They grow faster in comparison with stage II of extrusion growth. (iv) Typical morphology of mature PSMs developed after 6 750 cycles (~ 15% Nf) consists of ribbon-like extrusions accompanying by two thin parallel intrusions going simultaneously along PSM/matrix interface. Experimental data on the morphology and growth of extrusions and intrusions are discussed and compared with the predictions of the recent theoretical models and computer simulations of surface relief evolution and fatigue crack initiation which are based on irreversibility judged from intra-bulk behaviour of entire PSBs.

References 1.

Ewing, J.A. and Humfrey, J.C.W., Phil. Trans. Roy. Soc. (London), A200, 241–250, 1903.

2.

Polák, J., In Comprehensive Structural Integrity, Vol. 4, edited by I. Milne, R. O. Ritchie and B. Karihallo, Elsevier, Amsterdam, 2003, 1–39.

3.

Polák, J., Man, J. and Obrtlík, K., Int. J. Fatigue, 25, 1027–1036, 2003.

4.

Man, J., Obrtlík, K. and Polák, J., Mater. Sci. Eng., A351, 123–132, 2003.

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AB INITIO STUDY OF ELASTICITY AND STRENGTH OF NANO-FIBRE REINFORCED COMPOSITES M. Cerny and J. Pokluda Faculty of Mechanical Engineering, Brno University of Technology Technická 2, Brno 616 69, Czech Republic [email protected] Ab initio calculations of elastic moduli and theoretical uniaxial strength of composite lamina having continuous nano-fibre reinforcements are performed using pseudo-potential plane-wave code of Kresse et al. [1]. Obtained results are used to verify validity of macro-scale empirical relations for composites (rules of mixtures) [2] on the nano-scale. All quantities are computed from the dependence of crystal energy on a suitable deformation parameter. Results for tungsten nano-fibres in niobium matrix will be presented as a particular example of the ab-initio analysis. A model of the nano-composite is built by periodic repeating of 4x4x1 bcc-based supercell displayed in Fig. 1.

FIGURE 1. The supercell The crystal basis of our supercell contains 32 atom in both A (solid circles) nad B (open circles) ¢001² planes. The gray solid circles belong to other (adjacent) supercells. The dashed contours define considered interfaces between tungsten (W) wire and niobium (Nb) matrix in investigated lamina models of different atomic concentration of W. Calculation procedure consists of following steps: first, computation of the equilibrium volume of each lamina model and determination of the lamina bulk modulus. Atomic positions within the cell were relaxed in order to minimize the interfacial stresses. Second, the elongation of the crystal system in ¢001² direction to simulate uniaxial loading applied in a direction parallel to the lamina fibres. The system energy is minimized at any elongation by varying lengths of lateral cell edges (the p1 and p2 translation vectors lengths). The dependence of total energy on the relative elongation yields the uniaxial stress applied on the system as well as the Young modulus value. The dependence of the computed composite bulk modulus B on the atomic concentration of W (nearly corresponding to the volume fraction Vf of tungsten fibres) is depicted in Fig. 2 by solid symbols. It seems to nicely follow the simple rule of mixture for an ideal composite

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B V f B f  (1  V f ) Bm

(1)

where Bf and Bm are bulk moduli of the fibre (W) and matrix (Nb), respectively [2]. The line in Fig. 2 follows eq. (1) for experimental values Bf = 310 GPa and Bm = 170 GPa.

FIGURE 2. The dependence of the bulk modulus on the atomic concentration of tungsten in the Nb-W composite. This result confirms on the atomistic level that deviations from eq. (1) observed for real composites are caused by their imperfections, particularly by reduced interface cohesion. Similarly, computed values of Young modulus as well as maximal values of uniaxial stress exhibit simple linear dependence on atomic concentration of W. On the other hand, atomic volume linearly decreases with W concentration.

References 1.

Kresse, G. and Hafner, J., Phys. Rev. B vol. 48 13115, 1993; Kresse, G. and Furthmller, J., Phys. Rev. B vol. 54 11169, 1996; Kresse, G. and Furthmller, J., Comput. Mat. Sci. vol. 6 15, 1996.

2.

Holiday, L., Composite materials, Elsevier, Amsterdam-London-NewYork, 1966.

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STRENGTH AND FRACTURE OF ULTRA-FINE GRAINED ALUMINUM 2024 ECAP METAL Kee Bong Yoon, Young Wha Ma1, Jeong Woo Choi1 and Seon Hwa Kim2 Professor, Department of Mechanical Engineering, Chung Ang University 221 Huksuk Dongjak, Seoul 156-756, Korea 1PhD Students, Graduate School, Chung Ang University 221 Huksuk Dongjak, Seoul 156-756, Korea 2Professor, Department of Materials Engineering, Soon Chun Hyang University 646 Eupnae Shinchang Asan, Chungnam 336-745, Korea [email protected], [email protected], [email protected] and [email protected] When subjected to severe shear deformation by ECAP (Equal Channel Angular Pressing), microstructure of Al2024 becomes extremely refined. To measure the strength of this ultra fine grained metal, the small punch (SP) testing method was employed as a substitute for the conventional uniaxial tensile testing since the size of metal bar processed by ECAP were limited to 12 mm in transverse direction as shown in Fig. 1. The small punch tests were performed with specimens in longitudinal and transverse directions of Al 2024 ECAP metal. For comparing the strength values with those assessed by SP tests, the uniaxial tensile tests were also conducted with specimens in longitudinal direction, in which specimen sampling is possible. Failure characteristics were investigated using scanning electron microscopy (Fig. 2). The surfaces of the tested SP specimens showed that failure mode was shear deformation (Fig. 3). Based on this observation it was argued that the conventional equations proposed for assessing the strength of the material by the SP test were improper to assess those of Al2024 ECAP metal. Using the geometry shown in Fig. 4, an equation for assessing the strength of Al 2024 ECAP metal was proposed and was proven to be accurate by comparing the strength measured by the SP test with that from the standard tensile test. Difference of the strength values between the SP test and the standard test was less than 4.5%. Hence using the equation proposed in this study the strength in T-direction was obtained with the same accuracy. Difference of microscopic fracture characteristics in L and T directions and its relationship to the strength values were also discussed.

FIGURE 1. Specimen machining and directions of small punch testing for L- and T-specimens.

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FIGURE 2. SEM observation of the tested SP specimen of Al 2024 ECAP metal.

FIGURE 3. Cross-section of the interrupted small punch test specimen of L-specimen of Al 2024 ECAP metal.

FIGURE 4. Measuring parameters for assessing the strength of the metal by SP tests.

References 1.

Choi, J.W., MS Thesis, School of Mechanical Engineering, Chung Ang University, 2005

2.

Kim, Y.S., Theory of Plasticity, Sigmapress, Korea, 2003

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FATIGUE LIFETIME OF BEARING STEEL IN ULTRA-HIGH-CYCLE REGION Ludvik Kunz, Petr Lukas, Marian Cincala1 and Gianni Nicoletto2 Institute of Physics of Materials, ASCR, Žižkova 22, 616 62 Brno, Czech Republic, e-mail: [email protected], [email protected] 1University of Zilina, Velky diel, 01026, Žilina, Slovak Republic, e-mail: [email protected] 2Dept. of Industrial Engineering, University of Parma, Parco Area delle Scienze 181/A, 43100 Parma, Italy, [email protected] Fatigue initiation mechanism in high-cycle and ultra-high-cycle region is a topic of increasing importance due to rising demands on lifetime of engineering components. Car engines, high-speed trains and turbines are typical examples of engineering systems loaded up to gigacycle region [Bathias, C., Paris, P.C., Gigacycle fatigue in mechanical practice, M. Dekker, New York, USA, 2005.]. According to the valid standards, e.g. [ISO Standard 12107:2003(E) Metallic materials – Fatigue testing – Statistical planning and analysis of data.], S-N curves are generally limited to 107 cycles. It is assumed, that the fatigue limit can be determined as a horizontal line below which no failure takes place. Stair case method is frequently applied to the experimental determination of fatigue limit on the basis of 107 cycles. In contrast to low-cycle and conventional high-cycle fatigue, where the mechanisms of fatigue damage, crack initiation and propagation are more explored, progress in ultra-high-cycle fatigue is highly desirable. The experimental fatigue lifetime data in the ultra-high-cycle region have been shown to exhibit sometimes a “two-stage” or “stepwise” S-N curve [Murakami, Y., Nomoto, T., Ueda, T., Murakami, Y., Fat. Fract. Engng Mater. Struct., vol.22, 581-590, 1999.,Wang, Q.Y., Baudry, G., Bathias, C., Berard, J.Y., In Proc. of the EUROMAT 2000, edited by Miannay, D. et. al, Elsevier 2000, 1083-1088.]. Majority of these observations has been performed on bearing steels by Japanese researchers using rotating bending loading, e.g. [Tanaka, K., Akiniwa, Y., Fat. Fract. Engng Mater. Struct., vol.25, 775-784, 2002.,]. It has been pointed out that the two-step S-N curves are related to two different types of crack initiation: surface or internal at inclusions. Twostep S-N curve was theoretically predicted even for one phase materials [Mughrabi, H., Fat. Fract. Engng Mater. Struct., vol.22, 633-641, 1999.]. Recently some authors expressed the opinion that the two-step S-N curve is related rather to the type of loading than to the material [Marines, I., Dominguez, G., Baudry, G., Vittori, J.-F., Rathery, S., Doucet, J.-P., Bathias, C., Int.J. of Fatigue, vol.25, 1037-1046, 2003.]. The aim of this contribution is to report on experimentally determined S-N curves of bear-ing steel in rotating bending and in tension-compression in region where a step is expected, to analyze the crack initiation and to throw more light on the two step S-N curve phenomenon. Hypereutectic bearing steel according to the Czech standard SN 14 109 and corresponding to the European 100Cr steel, E52100 or SUJ 2 steel was used for the study. Two types of mechanical cyclic loading were used. Tension-compression fatigue tests under controlled load were conducted in resonant machine Amsler. The cycling was characterized by sine load wave with a frequency of 190 Hz. The stress ratio R was chosen equal to -1. The second loading system was rotating bending one, operating at a frequency 50 Hz. Experiments were performed at room temperature in the ambient air atmosphere.

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Experimentally determined S-N curves in tension-compression and rotating bending are shown in Figs 1a and 1b. It can bee seen that there is a clear difference in the curve shape. Despite of considerable scatter of data, the experimental points corresponding to tension-compression test can be approximated by continuously decreasing dependence, full line in Fig.1a. All specimens failed by internal initiation. Data generated by rotating bending exhibit typical two-step curve and clear separation of groups of points corresponding to the surface and internal initiation.

FIGURE 1a. S-N curve, tension-com-pression loading. FIGURE 1b. S-N curve, rotating ben-ding.

FIGURE 2. S-N curve based on tension-com-pression and corrected rotating bending data. Fracto-grafic analysis including location of crack initiation made it possible to correct the rotating bending results in terms of the local stress amplitude at the initiation site. Fig.2 shows the corrected results for rotating bending together with tension-compression data. It can be seen that the number of cycles to fracture increases continuously with decreeing stress amplitude. In the discussion, details of crack initiation on inclusions of different type and the serious scatter of lifetime data, which is inherent to the very high strength bearing steels, will be addressed.

References 1.

Bathias, C., Paris, P.C., Gigacycle fatigue in mechanical practice, M. Dekker, New York, USA, 2005.

2.

ISO Standard 12107:2003(E) Metallic materials – Fatigue testing – Statistical planning and analysis of data.

3.

Murakami, Y., Nomoto, T., Ueda, T., Murakami, Y., Fat. Fract. Engng Mater. Struct., vol.22, 581-590, 1999.

4.

Wang, Q.Y., Baudry, G., Bathias, C., Berard, J.Y., In Proc. of the EUROMAT 2000, edited by Miannay, D. et. al, Elsevier 2000, 1083-1088.

5.

Tanaka, K., Akiniwa, Y., Fat. Fract. Engng Mater. Struct., vol.25, 775-784, 2002.

6.

Shiozawa, K., Lu, L., Ishihara, S., Fat. Fract. Engng Mater. Struct., vol.24, 781-790, 2001.

7.

Mughrabi, H., Fat. Fract. Engng Mater. Struct., vol.22, 633-641, 1999.

8.

Marines, I., Dominguez, G., Baudry, G., Vittori, J.-F., Rathery, S., Doucet, J.-P., Bathias, C., Int.J. of Fatigue, vol.25, 1037-1046, 2003.

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CALCULATION OF K-FACTOR AND T-STRESS FOR CRACK AT ANISOTROPIC BIMATERIALS Michal Kotoul, Tomas Profant and Oldrich Sevecek Brno University of Technology, Faculty of Mechanical Engineering Technická 2, CZ 616 69, Brno, Czech Republic [email protected] The increasing use of fibre-reinforced composites in high performance structures has brought a renewed interest in the analysis of cracks in anisotropic materials. Most matrices of the advanced composite material are brittle. They prone to cracking under very low applied stresses and failure frequently occurs in the form of multiple matrix cracking. The orientations of these cracks may vary depending on the relative position of the reinforcement in relation to the load. The stress field in the neighbourhood of crack is governed by the overall anisotropic material response. Therefore, first the overall anisotropic parameters must by obtained by some homogenisation technique to calculate the stress field, which drives the crack in the matrix material. The existence of material interfaces in composites, especially in laminates, brings another problems in the analysis of cracks – the problem of crack terminating at the interface of two anisotropic solids and the problem of interfacial crack in anisotropic solids. These problems are also encountered in the technology of protective coatings. For the assessment of crack behaviour in the aforementioned situations it is essential to investigate the stress field near the crack tip. Although the finite element (FE) analysis is capable of capturing the singular stress behaviour near a corner or a crack tip in homogeneous regions with a refined mesh of conventional elements, this traditional FE approach fails to accurately capture the appropriate singular behaviour near a corner or a crack tip at the junction of dissimilar materials. A very promising approach to an accurate calculation of the near crack tip fields consists in the application of so-called two-state (or mutual) conservation integrals. Among these two-state conservation laws, the two-state J-integral proposed by Chen and Shield [Chen, F.H.K.and Shield, R.T., Z. Angw. Math. Phys. (ZAMP), vol. 28,1-22, 1977.] has been widely employed for obtaining stress intensities and elastic T-stresses for cracks, as well for finding dislocation strength. The twostate conservation integrals, e.g. [Chen, F.H.K.and Shield, R.T., Z. Angw. Math. Phys. (ZAMP), vol. 28,1-22, 1977.]-[Choi, N.Y.and Earmme, Y.Y, Mech. Materials, vol. 14, 141-153, 1992.], in conjunction with a displacement-based FEM provide an efficient tool for calculating stress intensities and elastic T-stresses for crack, or for calculating dislocation strength. This method is capable of extracting the near-tip information directly from the far-field deformation where the numerical fields are more accurate. This is a major advantage over the singular finite elements, and other various special techniques such as the boundary collocation, the singular hybrid FEM or the enriched FEM. Basically, the two state conservation integral can be based upon the well-known Jintegral or upon the M-integral proposed by Budiansky and Rice [Budiansky, B. and Rice. J.R., ASME J. Appl. Mech., vol. 40, 201-203, 1973.] and Knowles and Sternberg [Knowles. J.K.and Sternberg, E., Arch. Rat. Mech. Anal., vol. 44, 187-211, 1978.]. Let ‘A’ and ‘B’ denote two independent elastic states for the plane problems. Another elastic state ‘C’ can be obtained by superposing ‘A’ and ‘B’. Then one can write the path-independent integrals

JC

J A  J B  J  AB , M C

M A  M B  M  AB

(1)

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The integrals J(A,B) and M(A,B) result from the mutual interaction between two elastic states ‘A’ and ‘B’. These are conservation integrals for two equilibrium states, since the area version of these contour integrals vanishes identically for the domains with no singularities. In applications, one of the elastic states ‘A’ and ‘B’ comes for example from FE computation and the second is called the auxiliary solution. The success of the mutual integral method is crucially linked to the existence of `the auxiliary solutions in the form of the complementary eigenfunction. The existence of these complementary solutions was proved with the aid of the eigenfunction series by Im and Kim [Im, S.and Kim, K.-S., J. Mech. Phys. Solids, vol. 48, 129-151, 2000.]. Once the mutual integral is computed from the far-field deformation together with appropriate auxiliary solution, the individual stress intensity factors and/or T-stresses may be determined. While the auxiliary solution was found for semi-infinite and finite (interfacial) crack for the general case of anisotropic medium, see e.g. Beom and Atluri [Beom, H.G.and Atluri,S.N., Int. J. Fract., vol. 75, 163–183, 1996.] and Kim et al. [Kim, J.H., Moon, H.J. and Earmme, Y.Y., Mech. Mater., vol. 33, 21–33, 2001.], it is still unknown for bi(multi)material wedge for the present. The paper will address the application of the concept of mutual two-state integrals to the calculation of stress intensities and T-stresses for crack arrested at an anisotropic/anisotropic material interface. Numerical procedures for estimation of general stress intensity factors based on finite element method will be suggested and tested. As a first step of the analysis a numerical procedure based upon the implicit method suggested by Papadakis and Babuska [Papadakis, J.P. and Babuska, I., Comput. Methods Appl. Mech. Eng., vol 122, 69-92, 1995.] will be used for the determination of eigenvalues and eigenvector in Williams-like asymptotic expansion. Implicit methods do not have a closed form for the eigenequation, they are slower but they can be used for anisotropic materials as well as multi-material wedges. They use the variational formulation of the problem which provides a functional of sesquilinear form. The classical FEM approximation is then used leading to a system of homogeneous algebraic equation for eigenvalues and eigenvectors. In second step, the construction of auxiliary solution for multi-material wedge will be attempted. Finally, the stress distribution in the vicinity of the singular stress concentrators will be obtained by combination of the developed asymptotic analytical and corresponding numerical computations based on finite element method.

References 1.

Chen, F.H.K.and Shield, R.T., Z. Angw. Math. Phys. (ZAMP), vol. 28,1-22, 1977.

2.

Yau, J.F., Wang, S.S. and Corten, H.T, ASME J. Appl. Mech., vol. 47, 335-341, 1980.

3.

Shih, C.F.and Asaro, R.J, ASME J. Appl. Mech., vol. 55, 299-316, 1980.

4.

Kfouri, A.P., Int. J. Fract., vol.30, 301-315, 1986.

5.

Choi, N.Y.and Earmme, Y.Y, Mech. Materials, vol. 14, 141-153, 1992.

6.

Budiansky, B. and Rice. J.R., ASME J. Appl. Mech., vol. 40, 201-203, 1973.

7.

Knowles. J.K.and Sternberg, E., Arch. Rat. Mech. Anal., vol. 44, 187-211, 1978.

8.

Im, S.and Kim, K.-S., J. Mech. Phys. Solids, vol. 48, 129-151, 2000.

9.

Beom, H.G.and Atluri,S.N., Int. J. Fract., vol. 75, 163–183, 1996.

10. Kim, J.H., Moon, H.J. and Earmme, Y.Y., Mech. Mater., vol. 33, 21–33, 2001. 11. Papadakis, J.P. and Babuska, I., Comput. Methods Appl. Mech. Eng., vol 122, 69-92, 1995.

Acknowledgement. The support through the grant GACR 101/05/0320 is gratefully acknowledged.

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INTERACTION OF MICROCRACKS WITH GRAIN BOUNDARIES: SYSTEMATICAL INVESTIGATION OF THE MECHANISMS M. Marx, W. Schaf and H. Vehoff Institute of Materials Science and Methods, Saarland University Building 43B, D-66041 Saarbrücken, Germany [email protected] Fatigue is based on the initiation and propagation of microcracks. This period can occupy up to 90% of the lifetime of a cyclic loaded structure. It is well known that short fatigue cracks propagate faster than long cracks at the same level of the stress intensity factor 'K [1,2,3]. Deshpande, Needleman and Van der Giessen showed that the behavior of short cracks is determined by the internal stresses under cyclic loading due to the dislocation structure in the vicinity of the crack tip [4]. However, in this investigation the influence of grain boundaries and phase boundaries was not included. Due to the emission and movement of dislocations during crack propagation grain boundaries influence the crack propagation rate, it is observed that short cracks may stop in the front of grain boundaries. Therefore the estimation of lifetime of a broad range of fatigued structures and components on the basis of the stress intensity factor is difficult.

FIGURE 1. Crack initiated by Focused Ion Beam (FIB) in front of a grain boundary The interaction between microcracks and micro structural elements like grain boundaries and phase boundaries is described qualitatively quite well by the models of Tanaka and Navarro and De Los Rios [5,6]. However, the influence of grain boundary parameters like the misorientation of the grains at the grain boundary or grain boundary segregation is missing in these models. To create a physically more fundamental model it is necessary to investigate the interaction of microcracks with different grain boundaries and different crack parameters systematically. These measurements are not possible by observing natural cracks. Therefore a new method was developed to initiate microcracks with a predicted crack length and distance from the grain boundary at grain boundaries with different misorientation angles. The grain boundaries were characterized completely by orientation imaging microscopy. Afterwards cracks were initiated near the grain boundaries of interest by focused ion beam (FIGURE 1). The crack growth during cyclic loading was investigated by replica technique and by in situ loading in SEM with a resolution of about 20 nm. The influence of the grain boundary on the crack tip opening displacement and crack propagation rate (da/dN) was measured quantitatively.

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FIGURE 2: Crack propagation rate as function of the distance from the grain boundary, sample 1: small angle boundary (13°), sample 2: large angle boundary (32°) A significant difference was found in the crack propagation rate for small angle and large angle boundaries (FIGURE 2). Additionally the Electron Channeling Contrast Imaging (ECCI)technique was used to get further information on the interaction of cracks and grain boundaries. By in situ loading the crack propagation mechanisms were investigated step by step. The further aim of these investigations is a better lifetime prediction and a prolongation of the lifetime by grain boundary engineering.

References 1.

Suresh, S., Ritchie, R.O., Int. Metals Rev., vol. 29, 445, 1984

2.

Ritchie, R.O., Peters, J.O. Mat. Trans., vol. 42, 58, 2001

3.

Suresh, S., Fatigue of materials, Cambridge University Press, Cambridge, UK, 1998

4.

Deshpande, V.S., Needleman, A., Van der Giessen, E., Cata Materialia, vol. 51, 1, 2003,

5.

Tanaka, K., et. al., Eng. Fracture Mech., vol 24, 803, 1986

6.

Navarro, A., De Los Rios, E.R., Phil. Mag. A, vol. 57, 15, 1988

9. Micromechanisms in Fracture and Fatigue

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DISLOCATION ARRANGEMENTS IN CYCLICALLY STRAINED INCONEL 713LC M. Petrenec, K. Obrtlik and J. Polak Institute of Physics of Materials, Academy of Sciences of the Czech Republic Zizkova 22, 616 62 Brno, Czech Republic [email protected], [email protected], [email protected] INCONEL 713 LC is a cast polycrystalline superalloy used to produce turbine wheels of small internal-combustion turbines [1]. The dislocation structure, which is formed in the material during cyclic loading, is closely connected with fatigue damage of the material. The fatigue processes of numerous structural materials in the initial stage are characterized by heterogeneous dislocation configuration that becomes unstable during cycling. Localized bands with a specific substructure are formed. Due to the localized deformation the characteristic surface relief is developed and subsequently fatigue cracks are initiated [2]. In the studies of the dislocation structures of CSMX4 single crystal the specific dislocation arrangement corresponding to cyclic strain localization was observed only recently [3]. The aim of this contribution is to study the dislocation arrangement of INCONEL 713 LC cyclically strained in symmetrical cycling at room and high temperatures. The work is a part of a complex project directed to the relationship between the internal structure, the stress-strain response and the fatigue life of polycrystalline nickel base superalloys [1,4].

Experimental, results and discussion Polycrystalline INCONEL 713 LC superalloy was supplied by PBS Velká Bíteš, a.s. in the form of cast rods. Chemical composition is 11.90 Cr, 5.75 Al, 4.57 Mo, 1.96 Nb, 0.7 Ti, 0.19 Fe, 0.10 Zr, 0.08 Co, 0.05 C, 0.013 B, the rest is Ni (all in wt %). The structure includes rough dendrites and shrinkage pores up to 0.4 mm in diameter. The average grain size was 4.2 mm [1,4]. The specimens were fatigued in electrohydraulic MTS 810 testing machine in symmetrical pushpull loading with constant total strain amplitude Ha to fracture. The tests were conducted at room temperature (300 K) and at 773 K, 973 K and 1073 K in the air [4]. Internal dislocation structures were observed in Philips CM-12 transmission electron microscope, operating at 120 kV with a double tilt holder using the technique of oriented foils [5]. Specimens were sectioned in the gauge area parallel to the loading axis. Bright field imaging conditions were mostly adopted and the diffraction patterns and Kikuchi lines were used to determine the grain orientation (stress axis S.A. and foil plane F.P.). Though the details of the dislocation structures slightly differed depending on the testing temperature, the general feature, i.e., the thin dislocation rich bands passing through the J channels and the J´ precipitates parallel to the primary slip plane (111), were common at all the temperatures. Contrary to room temperature cycling, where ladder-like structure of the bands developed (Fig. 1), only thin bands passing through the matrix and precipitates (Fig. 2) are present at 1073 K. In the previous studies [6,7], the arrangement of dislocations in the bands parallel to the primary slip plane was observed only exceptionally. Dislocation arrangements observed in the present work are consistent with surface relief study by AFM in IN 713LC at different temperatures [4]. Parallel slip markings are common feature of the surface relief produced by cyclic straining at all the temperatures. In the room temperature cycling, the localization of the cyclic slip into very thin bands results in building up the sharp surface relief in the form of persistent slip markings consisting of extrusions and intrusions. The sharp persistent slip markings are thus closely connected with the specific dislocation arrangements in the thin bands running

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parallel to the primary slip plane similarly as in case of single and polycrystals of simple f.c.c. and b.c.c. metals [2,8].

FIGURE 1. Detail of a slip band in a single-slip-oriented grain (300 K).

FIGURE 2. Detail of slip bands in a single-slip-oriented grain (1073 K).

References 1.

Obrtlík, K., Man, J., Polák, J., In Proceedings of 7th European Conference on Advanced Materials and Processes (EUROMAT 2001), Associazione Italiana di Metallurgia, Milano, 2001, No. 894.

2.

Polák, J., Cyclic Plasticity and Low Cycle Fatigue Life of Metals, Academia/Elsevier, Prague/ Amsterdam, 1991.

3.

Obrtlík, K., Lukáš, P., Polák, J., In Low Cycle Fatigue and Elasto-Plastic Behaviour of Materials, K.-T. Rie and P.D. Portella (Eds.), Elsevier, Amsterdam, 1998, 33–38.

4.

Obrtlík, K., Man, J., Petrenec, M., Polák, J., In Proceedings of the Eight International Fatigue Congress (FATIGUE 2002), edited by Blom, A. F., vol. 2/5, EMAS, West Midlands, UK, 963–970.

5.

Obrtlík, K., Polák, J., Komrka, J., Scripta Metall. Mater. 28, 495–499, 1993.

6.

Monier, C., Bertrand, C., Dallas, J. P., Trichet, M. F., Cornet, M., Mater. Sci. Eng. A188, 133139, 1994.

7.

Decamps, B., Brien, V., Morton, A.J., Scripta Metall. Mater. 31, 793-798, 1994.

8.

Polák, J., In Comprehensive Structural Integrity, edited by Milne, I., Ritchie, R. O., Karihaloo, B., vol. 4, Elsevier, Amsterdam, 2003, 1-39.

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CRACK INITIATION AND FRACTURE OF METAL MATRIX COMPOSITES K. Unterweger and O. Kolednik Erich Schmid Institute of Materials Science, Austrian Academy of Sciences Jahnstrasse 12, A-8700 Leoben, Austria [email protected] An experimental study is performed to investigate the role of the composite architecture on the mircomechanisms of crack initiation and fracture of particle reinforced metal matrix composites (MMCs) under monotonic loading. In-situ tensile tests are performed in the scanning electron microscope (SEM), and the SEM-micrographs of different deformation stages are analyzed by an automatic local deformation measurement system. The procedure, which is described in Tatschl and Kolednik [1], yields the local deformation and strain fields at the different stages with high accuracy and lateral resolution. In this way, the influence of the local composite architecture on the damage evolution in the material can be studied in great detail: the occurrence of first plasticity at particle corners, the formation of shear bands, particle fracture and decohesion, final fracture. The investigated material is a powder-metallurgically processed MMC with an Al6061 alloy as matrix and 10 or 20 vol. % SiC particles as the reinforcing phase. The particles have a mean diameter of 10 and 100µm, respectively. The specimens were solution annealed at 530°C for one hour, quenched and subsequently aged at 175°C for 15min, 8h, and 200h in order to yield an under-aged, a peak-aged, and an over-aged condition. For comparison, the un-reinforced matrix materials are also tested. As examples of the analyses, in Fig. 1 local strain maps are presented for the over-aged MMC with a volume fraction of 10% small and coarse particles at two different stages of deformation. Plotted are the local relative strains in loading direction Nxx, i.e., the local strains Hxx divided by the global strain. By comparing two stages of deformation, it becomes evident that for the MMC with small particles the pattern of the local relative strains remains constant during the deformation. Neither the local values of Nxx change significantly, nor an emergence of new shear bands can be found. It has been found that even in the pure matrix material the deformation is rather inhomogeneously distributed and shear bands develop which are orientated under approximately 45° to the tensile axis. The deformation pattern of the MMCs with small particles appears similar, but the deformation pattern is more diffuse than in the pure matrix material. Particle fracture happens very rarely and does not induce far-reaching shear bands in the matrix. Along with a good particle distribution and an obviously good interfacial bonding between matrix and reinforcements, the MMCs have therefore a high strength and a good ductility. The MMCs with coarse particles exhibit a much lower ductility than the MMCs with small particles. The reason is that they deform due to the development of particle-damage controlled shear bands in the matrix which take the main part of deformation. In the case of the peak-aged material only these damage controlled bands are observed, whereas in the under- and over-aged MMCs, additionally matrix shear bands develop independently from particle damage. This explains the poor mechanical properties of the peak-aged MMC with coarse particles.

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Figure 1. Local relative strains in loading direction (horizontal) for: MMC with 10µm particles at a global strain of 1.94% (a) and 5.07% (b); pixel-size = 0.04µm. MMC with 100µm particles at a global strain of 1.17% (c) and 2.72% (d); pixel-size = 0.232µm. Noticeable further improvements of the ductility and fracture toughness of MMCs can be only obtained if the local deformation and crack growth behavior is explored and related to the local composite architecture, see also Unterweger and Kolednik [2,3].

Acknowledgements The authors acknowledge gratefully the financial support of this work by the Fonds zur Förderung der wissenschaftlichen Forschung under the project number P14333-N02.

References 1.

Tatschl, A., Kolednik, O., Mat. Sci. Eng., vol. A339, 265-280, 2003.

2.

Unterweger, K., Kolednik, O., Materials Science Forum, vol. 482, 215-219, 2005.

3.

Unterweger, K., Kolednik, O., Z. Materialkde, in press.

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MECHANICAL BEHAVIOUR OF ULTRA-FINE GRAINED AUSTENITIC STAINLESS STEEL Stephanie Brochet, Angeline Poulon-Quintin, Jean-Bernard Vogt, Jean-Christophe Glez1 and Jean-Denis Mithieux1 Université de Lille I, LMPGM, UMR 8517, 59 655 Villeneuve d’Ascq, France 1UGINE&ALZ Research Center, BP 15, 62 330 Isbergues, France [email protected] There is an increasing interest in the development of fine grained materials because this could appear as a solution for providing higher mechanical strength alloys, allowing thus reduction in component mass and raw material saving. The origin in the improvement of yield stress is directly connected with the the Hall-Petch relationship: Re

Re0 

k d

(1)

Several processes are now available for the elaboration of ultra fine grained materials among which grain refinement reached by the recrystallisation of a highly cold rolled material. One interesting point of ferrous alloys is that they can exhibit phase transformation, either induced by temperature variations or by plastic deformation. Taking advantage of this last point, the tendency is to use metastable austenitic stainless steels for which microstructure undergoes to a partial martensitic transformation J Æ D’ during cold rolling resulting in a fine grained microstructure after recrystallization. With this aim in view, a new grade, type 316L modified, is developed by UGINE&ALZ. Successful thermo-mechanical processes give rise to microsize grained microstructures. These new grades have to satisfy a large panel of mechanical properties which must be investigated and connected with the microstructure as well as process parameters. The objective of the present work is to study the effect of the grain size and of the phase stability on the monotonic and cyclic response of a metastable austenitic stainless steel. Two austenitic microstructures, illustrated on the figure 1, are studied: the first one with a grain size of about 2µm and the second with a grain size of 20µm.

FIGURE 1. Optical micrograph of two studied microstructures tested in monotonic and cyclic experiments. Estimated grain size: a) 2µm b) 20µm.

888

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For tensile tests, the decrease of one decade of the grain size leads to an increase of 250MPa of the yield stress as well as the ultimate tensile strength values with keeping good value of elongation. Low cycle fatigue tests are carried out on thin sheet specimens (one millimetre in thickness) under total axial strain control ranging from 0,4% to 1,2% and using a fully push pull mode (RH=1). The study of the cyclic stress response shows an important influence of the grain size: - The cyclic accommodation, at the beginning of the test (less than 5% of the lifespan), consists of a cyclic softening for the fine grained microstructure whereas a cyclic hardening always precedes this stage on the coarse grained microstructure. The stress levels are 250MPa higher with the small grained microstructure. - A secondary cyclic hardening is observed for the higher strain levels. The intensity of this cyclic hardening increases with the strain amplitude, and is much significant with the coarse grained microstructure. The fatigue resistance is evaluated trying to take into account both the plastic strain and the stress amplitude. The mechanical behaviour is discussed from X-ray diffraction and TEM analyses of the microstructures before and after fatigue tests. Both small and large grained microstructures undergo phase transformation. The martensitic transformation is direct J Æ D’, H martensite is not observed. Nevertheless, even if the fatigue behaviour is function of the grain size, the amount of martensite formed due to the austenite instability during cyclic strain, seems to be nearly equivalent for both microstructures after fatigue tests for a same strain amplitude. This suggests that cyclic plasticity mechanisms differ between the fine and large grained steels.

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TRIBOLOGICAL PROPERTIES AND WEAR MECHANISMS OF WEAR RESISTANT THERMALLY SPRAYED COATINGS Sarka Houdkova, Frantisek Zahalka and Radek Enzl Škoda Research Ltd. Tylova 57, Plzeò, 316 00, Czech Republic [email protected] The tribological properties of parts surface, namely their wear resistance and friction properties, are in many cases determining for their proper function. To improve surface properties, it is possible to create hard, wear resistant coatings by thermal spray technologies. Using these versatile coatings it is possible to increase parts lifetime, reliability and safety. To predict their behavior, lifetime and application area of thermally sprayed coatings it is necessary to completely understand the relationships between technology, process parameters, microstructure and properties of the coatings. In the case of thermally sprayed coatings evaluation it is necessary to take into consideration their unique lamellar microstructure. Together with materials characteristics, such as hardness, Young modulus of elasticity or fracture toughness, the coatings porosity, cohesive strength, content of oxides and other microstructure defect also plays its role [1,2]. In the article, the set of thermally sprayed coatings were tested by tree different method to prove their wear resistance to various load conditions. The sliding wear conditions were represented by pin-on-disc wear test [ASTM G 99], the abrasion wear condition by dry sand rubber wheel test [ASTM G 65] and slurry wear test [ASTM G 75]. During the pin-on-disc test, the coefficient of friction between Al2O3 pin and grinded coatings surface wear recorded. After the test the wear tracks profiles were measured and wear rate for each coating was calculated according to [2]: K

V s.L

(1)

where K is wear rate V is volume loss L is load s is sliding distance In the case of dry sand rubber wheel test and slurry wear test, the coated samples were weighted periodically in pre-set intervals. It enables to construct a wear curves, representing coatings wear resistance. The results pin on disc measurement showed, that the lowest coefficient of friction were 0,365 for WC-Co coating, followed by 0,576 for NiCrSiB coating and 0,647 for Cr3C2-NiCr coating. The highest value of coefficient of friction, 0,857, was measured for steel coating AISI 316L. The wear rates, results from pin on disc test, can be seen from Table 1. The highest wear resistance were proved for both cermet coatings, WC-Co and Cr3C2-NiCr. The worst results showed AISI 316 L coating. Combined with the results of coefficient of friction measurements, the best, from tested coatings, for sliding wear is WC-Co coating, followed by Cr3C2-NiCr coating.

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TABLE 1. Pin on disc wear rates.

In the Fig. 1, the wear curves, based on the results of dry sand rubber wheel test can be seen.

FIGURE 1. Dry sand-rubber wheel abrasion wear test results. The slurry wear test showed very similar results to dry sand abrasion test. Again, as the best alternative for solution of abrasion wear are cermet coatings, based on hard particles in ductile matrix. The advantage of WC-CoCr and Cr2C3-NiCr coating is in their resistance to corrosion attacks.

References 1.

EricksonL. C.- Hawthorne H. M.- Troczynski, T.: Wear 250, 2001, p. 569-575

2.

Holmberg K.- Matthews A.: Coatings Tribology, Elsevier, Amsterdam, 1998

The article was prepared thanks to financial support of project no. MSM 4771868401.

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CRACK PROPAGATION RESISTANCE AND DAMAGE MECHANISMS IN NUCLEAR GRAPHITE A. Hodgkins, J. Marrow, P. Mummery, A. Fok1 and B. J. Marsden1 School of Materials, Materials Performance Centre, University of Manchester 1School of Mechanical and Civil Engineering, Nuclear Graphite Research Group, University of Manchester [email protected], [email protected] [email protected], [email protected], [email protected] Sharply rising resistance to crack propagation in polygranular nuclear graphite, immediately following crack initiation from a stress concentrator has been suggested to be due to bridging by filler particles in the wake of the crack. In other brittle materials in which such rising resistance (R-curve) is observed, the length of the bridging zone is linked to the crack extension over which rising resistance occurs. This is termed Stage I of the R-curve. Following this stage II of the Rcurve, a plateau, is commonly observed (Fig. 1). Tomography and optical strain mapping techniques have been used to monitor damage, and the permanent strains due to microstructure damage and crack propagation. The aim of this work is to develop a model for the effects of microstructure on resistance to crack propagation. Crack propagation tests have been carried out using optical microscopy and high resolution Xray tomography to determine the cause of the continued rise in resistance in stage II. The observations show that there is a physical bridging zone, characterised by small ‘pinning’ ligaments in the ‘binder’ phase in the first 5 to 6 mm from the crack tip. These, and microstructure damage ahead of the notch, are the likely cause of the stage I R-curve. The tomography observations have shown the effect of microstructure damage and have also indicated the existence of bridging regions up to 40mm behind the crack tip (Fig 2). Optical microscopy shows that the crack is actually continuous in these regions (Fig.3), however. It is suggested that frictional contact may occur between the two surfaces of the crack, and is the cause of the stage II R-curve. The crack opening displacement in these regions is below the resolution limit of tomography, thus apparent bridging is observed.

Fig 1: R-curve for compact tension specimens. Crack monitoring by compliance, surface strain mapping (ESPI) and 3D tomography (XRìT).

892

A. Hodgkins et al.

Fig 2: Tomography images of a propagating crack. Crack bridging is observed.

Fig 3: Frictional contact, 40mm behind the crack tip.

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ENVIRONMENT-ASSISTED CRACKING OF HIGH-STRENGTH MAGNESIUM ALLOYS WE43-T6 A. Ahmad and T. J. Marrow School of Materials, University of Manchester, M1 7HS, UK [email protected], [email protected] Some magnesium alloys experience environment assisted cracking (EAC) in ambient atmospheric air, and hydrogen embrittlement is the dominant mechanism [1-3]. The highest susceptibility has been found in aluminum-containing alloys (6% max) [4-5]. EAC has also been observed in pure magnesium [3]. The EAC sensitivity of aluminum-free rare earth-containing alloys, such as WE43 has not been previously investigated in detail. Previous work has shown that plastic strain nucleates EAC in WE43-T6 by cracking of the intergranular intermetallic [6]. This paper reports a quantitative study of the crack nucleation mechanism in WE43-T6. This is part of a project that aims to predict the probability of nucleation and propagation of cracks at notches and microshrinkage porosity in cast engineering materials. Notched specimens of WE43-T6 alloy (4.2 wt% Y, 2.3 wt% Nd, 0.7 wt% Zr, 0.8 wt% HRE, bal. Mg) were static-fatigue tested in ambient air. Static fatigue was only observed at stresses close to the dynamic tensile fracture stress, but stable cracks were observed at the notch root in run-out specimens, which did not fail within 100 hours (1). The statistical distributions of stable cracks initiated at the notch root below the failure stress and the clusters of intergranular intermetallic phase have been analysed, and compared. The strain at notch root, as a function of applied stress, was measured using Electronic Speckle Pattern Interferomery (ESPI) (2), and has been used to interpret the fracture behaviour of different notch geometries. The longest crack length in each surviving specimen was independent of the notch tip strain and was consistent with the longest intermetallic cluster size. At low notch strain, the cracks are shown to come from the same population, which is the same as the intermetallic cluster population. With increasing strain, the maximum crack length and crack density increases and the crack population distribution changes (3). The critical event that controls specimen failure in static fatigue is concluded to be coalescence of crack nuclei, rather than propagation of a single critical defect.

FIGURE 1: Cracks nucleated by brittle intermetallic clusters, a) metallographic section at notch tip, b) Scanning electron microscopy of notch tip.

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FIGURE 2: ESPI measurement of notch tip strain: a) strain map of the notch, b) the peak strain at the notch root as a function of stress.

FIGURE 3: (a) Effect of notch tip strain on maximum observed crack length at notch root, (b) maximum observed crack length compared to the intermetallic cluster population.

References 1.

Oryall, G. and Tromas, D., Corros. Sci., 27, 335-341, 1971.

2.

Chakrapani, D.G. and Pugh, E.N., Metal. Trans., 7A, 173-176, 1976.

3.

Stampella, R.S., Procter, R.P.M. and Ashworth, V., Corros. Sci., 24, 325-341, 1984.

4.

Makar, G.L., Kruger, J. and Sieradzki, K., Corros. Sci/, 34, 1311-1342, 1993.

5.

Emley, E.F., Principles of Magnesium Technology, London, 1966.

6.

Marrow, T.J., Bin Ahmad, A., Khan, I.N., Sim, S.M.A. and Torkamani, S., Mater. Sci. and Engng A, vol. 387-89, 419-423, 2004.

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EFFECTS OF SURFACE FINISH ON THE FATIGUE LIMIT IN AUSTENITIC STAINLESS STEELS (MODELLING AND EXPERIMENTAL OBSERVATIONS) M. Kuroda, T. J. Marrow and A. Sherry School of Materials, Materials Performance Centre, University of Manchester [email protected], [email protected], [email protected] The fatigue limit of austenitic stainless steels has been reported to be influenced by surface roughness, work hardening, microstructure and residual stresses induced by working. However, the available data in the literature is complicated by the interactions of these factors, which results in difficulty in obtaining a fundamental understanding of the mechanism. Therefore, models and experiments which can elucidate the contribution of each surface effect to the fatigue limit is required. Microstructure models for the effect of these factors on short fatigue cracks have been developed for aluminium alloys [E R de los Rios, M Trull, A Levers, “Modeling fatigue crack growth in shot-peened components of Al 2024-T351”, Fatigue Fract Engng Mater Struct, 23 (2000) 709-716. , C Vallellano, A Navarro, J Dominguez, “Fatigue crack growth threshold conditions at notches part I: theory”, Fatigue Fract Engng Mater Struct, 23 (2000) 113-121. ], but have not been sustantially verified by experiment, not demonstrated to be applicable to other alloys. This is the aim of this investigation, which has focussed on the parameters of surface roughness (i.e. stress concentration factor in terms of notch depth and root radius), residual stress (i.e. depth profiles) and microstructure (i.e. distribution of crack arresting/retarding boundaries). The response surface methodology (RSM) coupled with central composite design (CCD) was employed to prepare austenitic stainless steel fatigue specimens with a controlled range of surface characteristics. A wide range of conditions were produced by changing the final lathe cutting conditions of spindle speed, feed rate and cutting depth. The fitting of the response surface model for the data was statistically studied by analysis of variance (ANOVA). The response surface model (1) adequately represented the largest peak to valley height (roughness Ry) and the axial residual stress (determined by X-ray Diffraction), and was interpolated to design fatigue specimens of significantly different roughness and surface residual stress. The residual stress profiles below the surface were measured by X-ray Diffraction (2), and employed with surface profile measurements (3) and microstructure characterisation to predict the threshold fatigue stress for crack propagation as a function of short crack length. The staircase method was used to measure fatigue limit. This was used to test the model predictions, together with measurement of the stable crack nucleus population below the fatigue limit. Electron backscatter diffraction was used to characterise the microstructure and near surface plastic deformation. The effects of annealing, to remove plastic strain and residual stress effects, have also been investigated. The results show that the simple microstructure model does not necessarily apply to austenitic stainless steels, and the effects of additional factors such as the deformation structure must also be considered. E R de los Rios, M Trull, A Levers, “Modeling fatigue crack growth in shot-peened components of Al 2024-T351”, Fatigue Fract Engng Mater Struct, 23 (2000) 709-716. C Vallellano, A Navarro, J Dominguez, “Fatigue crack growth threshold conditions at notches part I: theory”, Fatigue Fract Engng Mater Struct, 23 (2000) 113-121.

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Fig. 1: Response surface of roughness and surface axial residual stress for the combined effects of feed rate and cut depth. Conditions 1 to 6 for fatigue study are identified.

Fig. 2: Variation of axial residual stress below the machined surface for various conditions.

Fig. 3: Surface roughness characterised by scanning electron microscopy stereo imaging.

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INTERGRANULAR STRESS CORROSION CRACK PROPAGATION IN SENSITISED AUSTENITIC STAINLESS STEEL (MICROSTRUCTURE MODELLING AND EXPERIMENTAL OBSERVATION). T.J. Marrow, L. Babout, A.P. Jivkov, P. Wood, D. Engelberg, N. Stevens, P.J. Withers and R.C. Newman School of Materials, University of Manchester, UK and Department of Chemical Engineering and Applied Chemistry, University of Toronto, Canada [email protected] Stress corrosion cracking is a life-limiting factor in many components of nuclear power plant in which failure of structural components presents a substantial hazard to both safety and economic performance. Uncertainties in the kinetics of short crack behaviour can have a strong influence on lifetime prediction, and arise due both to the complexity of the underlying mechanisms and to the difficulties of making experimental observations. This paper reports a research programme into the dynamics and morphology of intergranular stress corrosion cracking in austenitic stainless steels, which makes use of recent advances in high resolution X-ray microtomography. In particular in-situ, three dimensional X-ray tomographic images of intergranular stress corrosion crack nucleation and growth in sensitised austenitic stainless steel (FIGURE.1) provide evidence for the development of crack bridging ligaments, caused by the resistance of non-sensitised special grain boundaries. (FIGURE.2) A simple grain bridging model, introduced to quantify the effect of crack bridging on crack development, has been assessed for thermo-mechanically processed microstructures via statically loaded room temperature simulant solution tests and as well as high temperature/pressure autoclave studies. Thermo-mechanical treatments have been used to modify the grain size, grain boundary character and triple junction distributions, with a consequent effect on crack behaviour. Two and three-dimensional finite element models of intergranular crack propagation have been developed (FIGURE.3), with the aim of investigating the development of crack bridging and its effects on crack propagation and crack coalescence.

FIGURE. 1: Successive intervals during in-situ tomography observations of stress corrosion crack growth showing failure of crack bridging ligaments

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FIGURE. 2: Fractography of ductile crack bridging ligament due to low energy grain boundary segments, associated with annealing twins.

FIGURE. 3: Three dimensional intergranular stress corrosion crack model, predicting the development of crack bridging ligaments.

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IDEAL STRENGTH OF NANOSCALE THIN FILMS Takayuki Kitamura, Yoshitaka Umeno and Akihiro Kushima Department of Mechanical Engineering and Science, Kyoto University. Yoshidahonmachi Sakyo-ku Kyoto, Kyoto, Japan. [email protected] With the development of nano fabricating technology, we can now obtain materials with structures in nano scales, and there is increasing interest in understanding the mechanical properties of such materials from atomistic point of view. The ideal strength was originally defined as the stress or strain at which perfect crystal became mechanically unstable with respect to arbitrary homogeneous deformation[1]. There have been quite a few numbers of researches investigating the ideal strength of materials[2-7] since this is a fundamental mechanical property of the material. However, nano-structured materials do not have the three dimensional periodicity as perfect crystals, and investigating the ideal strength of perfect crystal is not sufficient for understanding the mechanical property of such materials. It is required to investigate the effect of structures on the mechanical property. As a first step, we can consider evaluating the ideal strength of the material with high symmetry which is a basic structure. Here we expanded the definition of ideal strength to include the strength of highly symmetric structured materials namely ideal structure. We conduct ab initio calculation for precise evaluation of ideal strength of the material with ideal structure to obtain the fundamental mechanical property of nano-structured materials. In this study, we evaluated ideal strength of Si nanoscale thin films with p(2×1) asymmetric (100) surface under tensile deformation to investigate the effect of surface structure on mechanical strength. We conducted tensile simulation for films with 6, 10, and 14 atomic layers. Fig. 1 shows relationships between tensile stress and the strain of Si nanofilms under [011] tension. The result of the bulk is also shown for comparison. At low strain region, where the strain is less than 0.1, you cannot observe significant difference in the curve between the results of nanofilms and the bulk.

FIGURE 1. Tensile stress-strain curve of Si nanofilms under [011] tension.

T. Kitamura et al.

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FIGURE 2. Change in charge density of Si nanofilms under [011] tension. The maximum stresses of Si nanofilms are lower than that of the bulk and decrease as the thickness of the film decreases. Fig. 2 shows change in electronic density of Si nanofilms during tension. The isosurfaces with the charge density of 0.425 X 103 nm-3 are drawn. In 14 layered film, charge densities of all bonds decrease equally at unstable deformation as in the bulk. In the case of 10 and 6 layered films, breakings of bonds propagate along dashed lines and lead to fracture. This difference in the fracture mechanism causes the thinner film to have lower ideal strength. However, the ideal strength of Si nanofilm with 14 atomic layers which is 1.8 nm thick is about 96% of that of the bulk. These results indicates that the effect of surface structure on the mechanical property can be observed when the thickness of the film is fairly small, less than 1.8 nm.

References 1.

Born, M. and Huang, K., Dynamical Theory of Crystal Lattices, Oxford UP, 1954.

2.

Ogata, S., Li, J. and Yip, S., Science, 298, 807-811, 2002.

3.

Sob, M., Wang, L. and Vitek, V., Mater. Sci. Eng., A 234-236, 1075-1078, 1997.

4.

Sandera, P., Pokluda, J., Wang, L and Sob, M., Mater. Sci. Eng.. A 234-236, 370-372, 1997

5.

Clatterbuck, D., Chrzan, D. and Sob, M., Acta. Mater., 51, 2271-2283, 2003.

6.

Roundy, D. and Cohen, M., Phys. Rev., B 64, 212103, 2001.

7.

Umeno, Y. and Kitamura, T., Mater. Sci. Eng., B 88(1), 79-84, 2002.

9. Micromechanisms in Fracture and Fatigue

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TOUGHNESS VARIABILITY R. Bouchard, G. Shen and W.R. Tyson Materials Technology Laboratory Natural Resources Canada 568 Booth St., Ottawa, Canada K1A 0G1 [email protected] The weakest-link model of brittle fracture initiation introduced by Beremin et al. [1] has had substantial success in describing the inherent variability (scatter) in fracture toughness values for steel samples failing by cleavage. A project was initiated at MTL/CANMET to explore the applicability of the weakest-link model to Charpy absorbed energy. In the course of this work, fracture toughness tests using standard three-point-bend bars were performed. The results of these tests were unexpected, and are reported here. The tests were performed using a carbon/manganese structural steel in the as-rolled condition. The microstructure was polygonal ferrite with slightly banded pearlite (volume fraction 19%), with average ferrite grain size 12:m (surface) and 14.5:m (centre) as shown in Fig. 1.

Fig. 1. Optical micrographs of plate microstructure. Fracture toughness tests were performed following ASTM E 1921 [2], which allows determination of a reference temperature T0 in the transition range at which the median toughness of 1T size specimens is 100 MPa—m. The test temperature (-110qC) was chosen to be close to T0, and a total of 26 tests were carried out. All results were valid according to E 1921. Data was ranked and cumulative probability calculated as described in E 1921. The results are shown in Fig. 2.

Fig. 2. Weibull plot of fracture toughness results

R. Bouchard et al.

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The weakest-link model predicts that results should fall on a straight line of slope four on a Weibull plot such as Fig. 2. However, the slope of the best-fit line through the data of Fig. 2 is 1.86, differing significantly from 4. Possible reasons for the discrepancy are discussed. The most likely reason is material inhomogeneity, although there is no microstructural evidence for this and samples were taken from a nominally uniform region of the plate.

References 1.

Beremin, F. M., “A Local Criterion for Cleavage Fracture of a Nuclear Pressure Vessel Steel”, Metallurgical Transaction A, Volume 14A, 1983, pp. 2277-2287.

2.

“E 1921-02: Standard Test Method for Determination of Reference Temperature, T0, for Ferritic Steels in the Transition Range”, Annual Book of ASTM Standards, Volume 3.01, America Society for Testing and Materials, PA, U.S.A., 2002.

9. Micromechanisms in Fracture and Fatigue

903

THERMO-MECHANICAL BEHAVIOUR OF NANOSTRUCTURED COPPER C. Duhamel, S. Guerin, M. J. Hytch and Y. Champion Centre d'Etudes de Chimie M?tallurgique - CNRS 15 rue Georges Urbain 94407 Vitry-sur-Seine, cedex, France [email protected], [email protected], [email protected], [email protected] A material is an “ultrafine grained material” when substantial deviation(s) of its behaviour is observed compared to the “standard” coarse grained materials properties. In plasticity, ultrafine grained metals and alloys exhibit at room temperature new behaviours such as near-perfect elastoplasticity, strain rate sensitivity and high mechanical performances. For copper, these features are detected for grain size below around 300 nm ; this threshold is connected to the length scale associated to the lattice dislocation of the metal, Champion et al [1]. Nanostructured metals and alloys open interesting perspectives of applications as far as their special mechanical behavior can be controlled by orientation of their nanostructure and chemistry. One of the main key-point that impedes the use of nanostructures, is the problem with ductility, which limits the shaping and the use when plastic deformation occurs. Ductility may happen in nanostructures in relation with an increase of the strain-rate sensitivity, m, which occurs at room temperature when grain size is below around 300 nm and at relatively low strain rate, H , below 10-4 s-1, Conrad and Jung [2]. However, as early shown by Woodford, [3] and in connection with the Hart criterion, Hart [4] significant elongation is obtained when the strain-rate sensitivity becomes sufficiently high: for example, 100% of elongation should be expected when m is around 0.2 and as well known as superplasticity behavior, few hundred per cents may be expected when m is larger than 0.3. Literature data show that significant values of m are obtained at extremely low stain rate H < 10-5 s-1, for nanostructured and this effect is enhanced with decreasing the grain size in the ultrafine domain, when lattice dislocations are still present. Some strategies to increase ductility have been already examined based on the fabrication of “complex” nano-architectures where regions are capable of stress relaxation, as for instance, bimodal nano-micro grained size metals, severe plastic deformed metals with dislocations saturated grain-boundaries and dentritic nanostructures which have the properties of limiting the propagation of shear bands and associated mechanical instabilities. On the other hand, direct use of strain-rate sensitivity promoting ductility may be also exploited at high temperature. Preliminary studies showed as expected that m increases with the temperature, with the main drawback that nanostructures exhibit a low thermal stability. Use of nanostructures at moderate temperatures would necessitate investigations of the mechanisms involved in the plastic deformation at various temperatures. Understanding of the mechanisms would lead to engineering strategies involving the control of the structure and the chemistry, to increase the stability combined with appropriate mechanical properties.

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FIGURE 1. strain-rate sensitivity m versus temperature for different strain rates.

To investigate the mechanisms of plasticity, measurements of the strain rate sensitivity were carried out on nanostructures copper prepared by powder metallurgy from nanocrystalline copper powders. Metals have grain size of 90 nm. Experiments were carried out between room temperature and 120°C and for strain rate ranging from H =1u10-5 s-1 and 2u10-3 s-1 (Fig. 1). Analysis of the data leads to parameters such as activation volume and energy which give an insight of the micromechanisms involved in the plastic deformation.

References 1.

Champion, Y., Langlois, C., Guérin, S., Lartigue-Korinek, S., Langlois, P. and Hÿtch, M.J., Mater. Sci. Forum vol. 482, 71-76, 2005.

2.

Conrad, H. and Jung, K., Scripta Mat. available online 2005.

3.

Woodford, D.A., Trans ASM, vol 62, 291-294, 1969.

4.

Hart, E.W., Acta Metal. vol. 15, 351-355, 1967.

9. Micromechanisms in Fracture and Fatigue

905

SOME INSIGHTS INTO FATIGUE CRACK INITIATION STAGE H. Alush and Y. Katz Negba, Beer Sheva 84230, Israel [email protected] Fatigue crack initiation stage is competitive and requires a full screening of potential initiation sites. In a more comprehensive view, the role of the mechanical driving force is generally broadened, thus, deformation/environment interactions become significant. Besides better fundamental understanding as related to the fatigue process other considerations emerged like the distinction between initiations or propagation controlled processes. This has direct implications on the fatigue life assessment. The current phenomenological study selected polycrystalline, pure copper of 99.98 %, a typical FCC model system in the intensive volume of fatigue investigation. The material with various impurity traces included at the most, aluminum of 100ppm. After heat treatment microstructure of 50-80 µm grain size was tested at ambient temperature. Standard mechanical properties were determined and strain controlled fatigue tests were performed. The latter in the range of about 10-4 to 10-3 plastic strain amplitudes. The specimens consisted of uniform and cylindrical geometry, 3mm in diameter and tension/compression cyclic tests of load ratio, R=-1 at 3Hz were conducted. Four fold interrelated information levels were searched namely, mechanical response, low energy dislocation structure development, slip upset and crack initiation tracking. These were achieved by closed loop strain controlled devices, Transmission Electron Microscopy (TEM), Scanning Electron Microscopy (SEM) and Micro Probe Microscopy (MPM). In addition crack on a micron scale resolution has been tracked by one stage replication technique. For some isolated cases crack initiation tracking was assisted by Acoustic Emission (AE) spectra. The slip upset was observed by centering on fine scale features that enabled a quantitative approach to be analyzed by defining the local strain. As addressed previously by Harvey et al [1], the local strain has been defined by the slip upset height and the slip spacing given for one cycle in equation (1):

f 'H p

h s

(1)

where h is the slip height or the displacement, s the slip spacing, p the imposed plastic strain amplitude and f the slip upset efficiency. The effective term f is introduced since only a fraction of the dislocations can emerge at the free surface. This due to forest dislocation interactions, dislocation annihilation in the bulk or orientation constraint. In this context, the study was extended also to residual stresses either thermal or by mechanical surface modification. The mechanical response clarified the saturation stress and the corresponding saturation cycles. Low energy dislocation structures caused by cyclic loading were substantiated by loop patch, veins and cells as well as Persistent Slip Bands (PSB). Higher strain amplitudes resulted in elongated cells, labyrinth and symmetrical cells. In the current specific system, crack initiation followed a sequence of events. The pre crack plastic deformation was confined to discreet zones highly related to crystal plasticity habits enhancing as such the crack onset. Consequently, micro crack coalescence occurred in the micro domain. The MPM findings indicated that the initiation life could be formulated with analogy to the total fatigue life based on a cumulative damage model. For the sake of consistency, the MPM results confirmed the role of compressive residuals on the local strain. Under the current imposed residuals in the order of 0.7y after 104 cycles the local strain reduced by 50%. Concerning the formulation form of the fatigue initiation life, damage

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accumulation efficiency factor was introduced beside the imposed cumulative plastic strain. Note that the present approach is geometrical, assisted by novel techniques. Finally, it seems advisable to compare the current approach to Muras School [2, 3] that utilized an energetic model. This comparative study actually supports the current quantitative approach that remains consistent with imposed residuals affecting the fatigue process. The notion that fatigue crack initiation stage is frequently less emphasized is mainly related to its complexity. In fine scale segments applications like thin films, structural integrity aspects can in fact be dominated by the crack initiation life. Accordingly, the following was concluded. Fine feature observations assisted by novel techniques promise further insights into the fatigue initiation stage. Even in highly smooth surfaces plastic dissipation is manifested by low energy dislocation structures and slips upset. Internal stored energy or geometrical changes at the free surface resulted in the initiation of discontinuities. Post crack initiation follows other level of considerations; crack tip shielding or micro crack coalescence might influence the propagation kinetics. Nevertheless, the current study facilitated beside experimental confirmation attempt in modeling, simulation or life predictions. At least the hierarchy of the critical parameters as related to the initiation stage can be evaluated by cause and further discussed.

References 1.

Harvey,S.E., Marsh,P.G and Gerberich,W.W.,Acta.Metall.Mater,vol.42,3493-3502,1994.

2.

Mura,T. and Nakasone,Y.,J.Appl.Mech.vol.57,1-6,1996.

3.

Vekataraman,G., Chung,Y.M.,Nakasone,Y. and Mura,T.,Acta.Metall et Mater.vol.39, 26312638,1991.

9. Micromechanisms in Fracture and Fatigue

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FATIGUE BEHAVIOUR OF METALLIC MATERIALS EXPOSED TO HIGH PRESSURE HYDROGEN ENVIRONMENTS Yoji Mine, Saburo Matsuoka, Yukitaka Murakami Chihiro Narazaki1 and Toshihiko Kanezaki1 Department of Mechanical Engineering Science, Kyushu University, Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan 1Graduate School of Engineering, Kyushu University, Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan [email protected] In order to solve the global warming problem, development and commercialisation of fuel cell (FC) systems are being promoted. In the FC systems, many stainless steels are used for the components such as the liners of ultra-high pressure vessels, piping, bearings, and springs. Such components are directly exposed to hydrogen environments under cyclic loading. It has been reported that hydrogen degrades the mechanical properties, especially ductility of metallic materials [1-3]. Moreover, the degradation of fatigue strength of metallic materials due to hydrogen intrusion is a matter of concern from a practical point of view. In our previous investigations [4-7], hydrogen was artificially (electro-chemically) charged into the specimens of several candidate materials, and it was revealed that hydrogen affects the slip band morphology and fatigue crack growth behaviour. In this study, hydrogen intrusion and fatigue crack growth behaviour in stainless steels exposed to high pressure hydrogen environments were investigated at room temperature and in laboratory air to clarify the effect of the intruded hydrogen on the fatigue crack growth. The materials used in this study were round bars made of austenitic (types 304, 316, 316L and 310S), ferritic (type 405) and martensitic (type 440C) stainless steels. The austenitic stainless steels were solution-treated, ferritic stainless steel was annealed, and the martensitic stainless steel was quenched and tempered. The Vickers hardness of type 304 and type 316L stainless steel was HV = 176 (SUS304) and HV = 157 (SUS316L). Hydrogen was charged into specimens by exposing them to high pressure hydrogen gas. The hydrogen exposure experiments were conducted at a pressure of 18, 25 and 40 MPa, at a temperature of 383 to 388 K and for a holding time of 100 to 115 h. Disks with a diameter of 7 mm and a thickness of 0.8 mm were used for the hydrogen exposure experiments. For the comparison, cathodically-charged specimen for fatigue test was prepared with platinum electrode at a current density of 27 A/m2 in a sulfuric acid solution (pH = 3.5) at 323 K for 672 h. The hydrogen content was measured by the thermal desorption spectrometry (TDS) at a heating rate of 0.33 K/s. The specimens for fatigue test were manufactured and were polished with #2000 emery paper and buff. A small artificial hole was drilled onto the specimen surface to limit the crack initiation sites. In the hydrogen-exposed and cathodically-charged specimens, a small artificial hole was introduced after hydrogen charge. Tension-compression fatigue tests were carried out at room temperature in laboratory air. All the fatigue tests were conducted at a stress ratio, R = -1 and at a frequency of 1.2 to 2 Hz to control a rise in the temperature. Crack growth behaviour was investigated by the replica method. The conclusions can be summerised as follows: (1) From the results of the hydrogen exposure experiments, the hydrogen content increased with an increase in the hydrogen exposure pressure up to 40 MPa. The increment in hydrogen content was dependent on the microstructure and chemical composition. Austenitic stainless steels contained more hydrogen compared with martensitic and ferritic steels by approximately an order of magnitude at the same hydrogen exposure conditions. Hydrogen thermal desorption spectra

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showed exposing the stainless steels to high pressure hydrogen environments raised the height of the lower-temperature peak of H2 ion intensity, i.e. diffusive hydrogen. (2) In SUS304, the fatigue crack growth rates of the hydrogen-exposed and cathodicallycharged specimens were approximately twice higher than those of the uncharged specimen; on the other hand, in SUS316L, acceleration in the fatigue crack growth of the hydrogen-exposed specimen was observed at a short crack length below ~400 Pm. The aspect ratio for the crack observed on the fracture surface, b/a significantly reduced in the hydrogen-exposed and cathodically-charged specimens in SUS304, while in SUS316L, the aspect ratio of the hydrogenexposed specimen was slightly smaller than that of the uncharged specimen. These results suggest that the concentrated hydrogen in the surface layer accelerates the fatigue crack growth in the austenitic stainless steels. The differences in the crack growth acceleration and the aspect ratio for the crack between SUS304 and SUS316L presumably arose from those in the content and distribution of the intruded hydrogen and/or the susceptibility to hydrogen. (3) A distinct difference in the appearance of slip bands was observed between the hydrogencharged (due to hydrogen exposure and cathodic charge) and uncharged specimens in both SUS304 and SUS316L. In particular, the difference was pronounced in SUS304. In the uncharged specimens, slip bands were densely and widely distributed; on the other hands, slip bands were discrete in the hydrogen-charged specimens. The crack growth morphology in the hydrogencharged specimens was also different from that in the uncharged specimens. The fatigue cracks in the hydrogen-charged specimens grew more straightly and were sharper compared with the uncharged specimens. These results imply that the intruded hydrogen into austenitic stainless steels influences the dislocation mobility to cause the slip localisation.

References 1.

Vennett, R. M. and Ansell, G. S., Trans. ASM, vol. 60, 242-251, 1967.

2.

Benson Jr., R. B., Dan, R. K. and Robert Jr., L. W., Trans. Metall. Soc. AIME, vol. 242, 21992205, 1968.

3.

Herms, E., Olive, J. M. and Puiggali, M., Mater. Sci. Engng. A, vol. 272, 279-283, 1999.

4.

Kanezaki, T., Mine, Y., Fukushima, Y. and Murakami, Y., Proceedings of the 15th European Conference of Fracture (ECF15), CD-ROM, 2004.

5.

Uyama, H., Mine, Y. and Murakami, Y., Proceedings of the 15th European Conference of Fracture (ECF15), CD-ROM, 2004.

6.

Murakami, Y. and Matsunaga, H., Proceedings of the Third International Conference on Very High Cycle Fatigue (VHCF-3), 322-333, 2004.

7.

Murakami, Y., Proceedings of the 11th International conference on fracture (ICF11), CDROM, 2005.

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IN-SITU INVESTIGATIONS OF THE FRACTURE MECHANISMS AT VARIOUS LENGTH SCALES Zbigniew Pakiela, Witold Zielinski and Krzysztof J. Kurzydlowski Faculty of Materials Science and Engineering, Warsaw University of Technology Woloska 141, 02-507 Warsaw, Poland [email protected] One of the main features of small crack growth are “slow-downs” observed when they approach microstructural barriers such as grain boundaries. In-situ observations of crack growth can deliver valuable information about fracture behaviour of the investigated materials. In this paper the authors present results of the in situ observation of the crack growth in various materials, at various length scales and under various modes of loading. In order to approach better understanding of the fracture behaviour light microscope (LM) with in-situ recording device, scanning electron microscope (SEM) equipped with a tensile test machine and transmission electron microscope (TEM) with a straining holder have been utilized.

In situ investigations by light microscopy Observations were carried on pure Cu of bimodal grain size with microcrystalline grains embedded in submicrocrystalline matrix. As mechanical properties of the materials with coarse and small grains are different, crack propagation should be different in the fine grained matrix and coarse grained islands, what is important from material design point of view. The crack growth in such materials is still not well described by classical fracture theory, so authors focused on this problem in this paper. For quantitative description of strain field the Digital Image Correlation method proposed by Peters and Ranson [1] was used.

FIGURE 1: a) experimental setup, b) strain field near a crack tip in nanostructureed Cu with bimodal microstructure.

In situ SEM fracture studies In situ SEM fracture studies were performed on the coarse grain Al sample directly in the vacuum chamber of SEM, equipped with tensile test machine. The sample with a thickness of 0.2 mm was pre-notched by means of dimple obtained by electro polishing. The processes of strain localization, crack initiation and propagation have been investigated with details showing distribution of slip bands.

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FIGURE 2. SEM images of the slip bands network evolution and the crack initiation in Al specimen during in situ SEM straining: a) arrangements of the slip bands at the very early stage of deformation; b) a nucleus of fracture.

In situ TEM deformation study 316 type stainless steel for the in situ TEM dislocation pile up against grain boundary studies as an appropite material having low stacking fault energy has been chosen. An increase of dislocation quantity in the pile up as well as slip of the dislocation in the opposite direction was registered and analyzed in detail.

FIGURE 3. Dislocation network evolution during stainless steel in situ straining: a) dislocation pile up against grain boundary: b) slip traces indicating dislocation motion

References 1.

Peters, W.H., Ranson, W.F., Opt. Eng. vol. 21, 427–432, 1982.

12. Interface Fracture and Behavior of Joints

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ENVIRONMENTAL ATTACK AT POLYMER/METAL INTERFACES A. J. Kinloch1, D. Bland1, K. T. Tan1 and J. F. Watts2 1Department of Mechanical Engineering, Imperial College London, Exhibition Road, London SW7 2BX, UK 2School of Mechanical and Materials Engineering, University of Surrey, Guildford, Surrey, GU2 5XH, UK. [email protected] There are many advantages that structural adhesives can offer compared to the more traditional joining methods such as welding, bolting, mechanical fastening, etc. However, there are some issues, which have so far limited the wider application of adhesives. The most important of these is the lack of knowledge concerning the durability of adhesive joints upon exposure to an adverse environment which invariably tends to lead to interfacial failure. This has led to extensive studies aimed at evaluating the effects of moisture, and developing a better understanding of the mechanisms of failure. Unfortunately, most of the laboratory test methods involve lengthy timescales and the results are often difficult to interpret quantitatively. Therefore, a most important challenge facing the adhesive community is to develop accelerated test methods that can assess quantitatively durability of adhesive joints in a relatively short-time scale and are able to predict accurate the service life of adhesive joints under such conditions.

Experimental The full details of the preparation of testing of the joints used for the fracture-mechanics tests are given elsewhere Korenberg et al. [1]. An adhesively-bonded joint using a tapered-double cantilever-beam (TDCB) specimen was employed. The substrates used throughout the present work were manufactured either from steel (British Standard 970 070M55) or aluminium alloy (British Standard 7075 (unclad)). The adhesive used was a hot-curing rubber-toughened epoxy adhesive, which was based upon a dicyandiamide-cured diglycidyl ether of bisphenol-A epoxy. Three types of joints were made: steel-steel, aluminium alloy-aluminium alloy and steelaluminium alloy joints. The last type will be denoted as ‘dissimilar-substrate’ joints. All substrates were first degreased in a liquid bath of boiling 1,1,1-trichloroehtylene before they were grit-blasted with 60Pm-78Pm mesh alumina particles. The specimens were tested under monotonic-loading conditions, with a displacement rate of the crosshead ranging from about 0.1Pm/min to 10mm/min. The tests were mainly conducted (a) in conditions of 21r1qC and approximately 55% relative humidity (RH), and (b) in ‘wet’ conditions of immersion in water at 21r1qC.

Results and Discussion The fracture energy, GC, of the various joints was measured in the two different environments as a function of the crack velocity, a . The results were plotted on a double-logarithmic scale. Three different regions of crack behaviour have been identified and have been labelled as ‘Region I’, ‘Region II’ and ‘Region III’. ‘Region I’ was observed at low crack velocities and the crack grew in a stable manner visually along the adhesive/substrate interface; and the data yielded linear relationships between GC and a . In contrast, ‘Region III’ occurred at high crack velocities and stick-slip crack propagation mode was observed, and the failure was mainly cohesive in the adhesive layer. ‘Region II’ was the transition region between ‘Region I’ and ‘Region III’. The reasons for these different regions, and the underlying mechanisms of failure which occurred, will be discussed in the presentation. However, clearly ‘Region I’, where interfacial failure is observed,

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is where attention must be focused in terms of measuring the effect that an aqueous environment may have upon the fracture performance of the joint. In ‘Region I’, the relationship between GC and a in the ‘55% RH’ tests was found to be controlled by the viscoelastic nature [3] of the epoxy adhesive, and was independent of the type of substrate used. Also, in such tests the application of a stress and the presence of water molecules at the crack tip was found to control the mechanism of failure of the joints. In the ‘wet’ environment of immersion in water, all the various types of joint showed an inferior behaviour compared to the tests undertaken in the ‘55% RH’ environment. It is also noteworthy that, in ‘Region I’, the dependence of GC upon a for tests in liquid water and water-saturated environments (i.e. the ‘RH’ environments) was very different. This implies that the relationship log GC  log a in the ‘wet’ immersion tests was not merely dependent on the concentration of water molecules. It is proposed that a subtle corrosion mechanism plays a crucial role in the tests conducted in liquid water, i.e. the ‘wet’ tests. Such corrosion processes lead to the production of hydroxyl ions at the crack tip which cause cathodic debonding to occur in the very alkaline environment created in this region. This results in the segregation of charge-carrying cations to the cathodic sites under the influence of the corrosion potential present in the system. Indeed, such a model has been supported by detailed surface-analysis studies, where relatively high concentrations of cations have been detected on the ‘wet’ fracture surfaces. Also, the physical appearance of joints after the immersion tests exhibited classical cathodic debonding features. The occurrence of corrosion was further supported by the good fit of the experimental data to the model of environmental crack growth proposed by Wiederhorn [3]. The durability of the steel/epoxy/aluminium-alloy dissimilar-substrate joints tested in the ‘wet’ environment was relatively even poorer, when compared to that of the similar-substrate joints. It is shown that this observation does not arise from residual stresses but from the occurrence of additional cathodic corrosion occurring in the dissimilar-substrate joints in water. Indeed, a relatively high concentration of hydroxyl ions was detected from the dissimilar-substrate joints compared to the similar-substrate joints. Finally, it is shown that the monotonically-loaded fracture-mechanics test methodology provides a good accelerated test method for evaluating the durability of adhesive joints. It allows an assessment of the environmental resistance of adhesive joints within a matter of days, as opposed to the more typical accelerated ageing tests which involve exposing the joint, unstressed in water, for many months.

References 1.

Korenberg, C.F., Kinloch, A.J. and Watts, J.F., J. Adhesion, vol. 80, 169-201, 2004

2.

Kinloch, A.J. and Young, R.J., Fracture Behaviour of Polymers, Applied Science Elsevier, London, 1983.

3.

Wiederhorn, S.S, J. Am. Ceramic Soc., vol. 50, 407-414,1969

12. Interface Fracture and Behavior of Joints

913

MODELLING OF ELASTIC-PLASTIC PEEL TESTS FOR STRUCTURAL ADHESIVES A. J. Kinloch, H. Hadavinia, L. Kawashita, D. R. Moore and J. G. Williams Department of Mechanical Engineering, Imperial College London, Exhibition Road, London SW7 2BX, UK [email protected] The adhesive fracture energy, Gc, of adhesive joints may be readily ascertained from linear-elastic fracture-mechanics (LEFM) methods, and indeed a British Standard (BS7991-2001) now exists for the LEFM Mode I value, GIc, largely as a result of the efforts of the European Structural Integrity Society (ESIS) TC4 Committee, as described by Blackman and Kinloch [1]. Notwithstanding, the LEFM test specimens are relatively complex and expensive to make and test, and many industries would far prefer to deduce the value of Gc from the very common and widely used ‘peel test’. The peel test is an attractive test method to assess the performance of a wide range of flexible laminates and adhesive joints. However, although it is a relatively simple test to undertake, it is often a complex test to analyse and thus obtain a characteristic measure of the toughness of the laminate, or adhesive joint. The most successful approach that has been adopted is one based upon applying a fracture-mechanics method using an energy-balance approach. A value of the adhesive fracture energy, Gc, is thereby ascertained, which is the energy needed to propagate a crack through unit area of the joint, either cohesively through the adhesive layer or along the bimaterial interface. The value of Gc may be obtained via an analytical or a numerical analysis of the peel test. However, the peel test invariably involves gross plastic deformation of the peeling arm, which may account for up to about 80% of the measured peeling energy. The value of Gc should be characteristic of the joint and, ideally, independent of geometric parameters such as the applied peel angle, the thickness of the flexible substrate arm(s) being peeled and the thickness of the adhesive layer. However, it is recognised that, since the value of Gc includes plastic and viscoelastic energy dissipation which occurs locally at the crack tip, it will be a function of the rate and temperature at which the peel test is conducted. (Only if such energy losses are reduced to virtually zero, and the locus of joint failure is exactly along the bimaterial interface, will the value of Gc be equivalent to the thermodynamic work of adhesion.) The present paper will describe the use of novel analytical and numerical methods to deduce the value of Gc from the elastic-plastic peel test.

Analytical Methods The first part of the presentation will concentrate upon analysing the mechanics of the peel test by applying a continuum fracture-mechanics method using an energy-balance approach. The theoretical analytical methods from Kinloch et al. [2] and Georgiou et al. [3], which describe models to ascertain values of the adhesive fracture energy, Gc, will be outlined and employd. As will be seen, the current challenge is to model accurately any extensive plastic deformation which may occur in the flexible peeling arm, since if this is not accurately modelled then the value of Gc deduced may suffer a high degree of error.

Numerical Methods Secondly, the paper will describe the use of a novel numerical method, based upon a finiteelement analysis (FEA) model, to deduce the value of Gc from the elastic-plastic peel test. A major

A. J. Kinloch et al.

914

feature of such a method would be its ready applicability to analysing more complex adhesivelybonded components where gross plastic deformation of the substrates accompanies fracture. For example, crush tests on adhesively-bonded aluminium-alloy tubes and box beams, as employed in the front-end section of the new Aston Martin ‘Vanquish’ sports car. The technique eventually chosen for numerically modelling the peel test was a FEA approach employing the node-release method to simulate crack growth along a pre-defined crack path. The main novel feature of this approach is that the critical equivalent plastic strain was chosen as the criterion for releasing the node. However, this parameter is a strong function of the degree of triaxiality at the crack tip. This was accounted for by using the FEA results to also obtain the stress field at the crack tip, and then employing the Rice-Tracy [4] model to allow for the different degrees of triaxiality found in the various types of peel test that were considered. The FEA model is then used to compute the energy dissipated by the plastic deformation of the peel arm during steady-state crack growth, and hence so deduce the value of Gc. The values of Gc so determined are shown to represent a ‘material characteristic’ parameter, independent of such factors as the peel angle, thickness of peel arm, etc.

Conclusions The advantages and disadvantages of the different methods will be reviewed and a major conclusion is that the values of Gc from the different modelling methods are found to be in very good agreement, and are also in excellent agreement with values from standard LEFM test methods.

References 1.

Blackman, B.R.K. and Kinloch, A.J., in ‘Fracture Mechanics Testing Methods for Polymers, Adhesives and Composites’ edited by D.R. Moore, A. Pavan and J.G. Williams, (Elsevier Science, Amsterdam, 2001) 225-270.

2.

Kinloch, A.J., Lau, C.C. and Williams, J.G., Int. J. Fracture, vol. 66, 45-70, 1994.

3.

Georgiou, I., Ivankovic, I., Kinloch, A.J. and Tropsa, V., J. Adhesion, vol. 79, 239-265, 2003.

4.

Rice, J.R. and Tracy, D.M., J. Mech. Phys. Solids, vol. 17, 201-217, 1969.

12. Interface Fracture and Behavior of Joints

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AN ALTERNATING CRACK GROWTH IN ADHESIVELY BONDED JOINTS A. R. Akisanya Engineering Department, School of Engineering and Physical Sciences King’s College, University of Aberdeen, Aberdeen AB24 3UE, UK. [email protected] Adhesive joints are increasingly used in the assembly of components in electronic, automobile and aerospace industries. A standard joint design is of sandwich type where two parts made from the same or different material are bonded by a thin layer of adhesive. The reliability and fracture characteristics of the joints under mechanical and thermal stresses during processing and service constitute a major technical problem. Cracks and flaws are inevitable in the manufacture of adhesive joints. The joint geometry, material combination and service loads must be chosen to prevent crack growth; this is sometimes difficult if not impossible. Hence, these parameters must be selected such that when crack growth does occur the chosen crack path is that which maximises the macroscopic toughness (or strength) of the joint. A sandwiched joint consisting of a brittle adhesive can fail in a variety of ways. The crack may grow along one of the interfaces, within the adhesive, alternate between the adhesive and the adjacent material or alternate between the two interfaces of the joint. The effect of remote loading on interfacial fracture toughness has been extensively studied, see for example Chai [1], Cao and Evans [2], Akisanya and Fleck [2], Banks-Sills and Schwartz [4]; the interfacial toughness increases with increasing magnitude of the remotely applied shear. Further, the directional stability of crack paths in adhesive joints has been related to the magnitude of the non-singular stress (usually called the T-stress) near the crack tip, e.g. Fleck et al. [5], Chen et al. [6]. In this paper we examine the effect of material combination and the remote mixed mode loading on the likelihood of occurrence of the alternating crack in an adhesive joint. Alternating crack trajectory has been observed by several authors during experimental testing of sandwiched joints with a brittle adhesive [1, 3, 6]. A detailed understanding of this failure mechanism is important since it significantly enhances the macroscopic toughness of the joint [3]. In a previous study (Akisanya and Fleck [7]) the effects of remote tension and thermal residual stress in the adhesive layer on the wavelength of the alternating crack were examined for a sandwiched joint subjected to a remote mode I loading. For a given material combination, the wavelength of the alternating crack increases with increasing magnitude of the thermal residual stress [7]. In the current paper we consider the effects of remote shear load on the alternating crack trajectory. The near-tip region of the alternating crack is replaced by a circular domain loaded f remotely by the crack tip stress intensity factor K



K If  iK IIf

for the homogeneous base

specimen neglecting the presence of the layer, as shown in Fig. 1. K f is related to the remotely applied loads and the geometry, see Tada et al. [8]. Loading is achieved by imposing the asymptotic crack tip displacement field for homogeneous body on the circular boundary of the idealised geometry shown in Fig. 1b. The numerical solutions of the interfacial crack-tip stress intensity factor are obtained. These solutions are combined with the well-established interfacial fracture mechanics to explore the necessary and sufficient conditions for the interfacial crack to kink into the adhesive layer in the presence of a pre-existing kink-type flaw. We find that for a

A. R. Akisanya

916

given size of flaw and material combination there is a range of K IIf / K If for which the alternating crack is likely to occur. The lengths "1 and " 2 of the interfacial crack prior to kinking into the adhesive (see Fig. 1a) are different for the two interfaces. An increasing magnitude of K IIf / K If results in an increase in one of the lengths and a decrease of the other.

Figure 1. (a) An alternating crack in a sandwiched joint subjected to remote mixed mode loading. (b) An idealised geometry of the alternating crack.

References 1.

Chai, H., Int. J. Fract., vol. 32, 211-213, 1987.

2.

Cao, H.C. and Evans, A.G., Mechanics of Materials, vol. 7, 295-304, 1989.

3.

Akisanya, A.R. and Fleck, N.A., Int. J. Fract., vol. 58, 93-114, 1992.

4.

Banks-Sills, L. and Schwartz, J., Int. J. Fract., vol. 118, 191-209, 2002.

5.

Fleck, N.A., Hutchinson, J.W. and Suo, Z., Int. J. Solids Struct., vol. 27, 1683-1703, 1991.

6.

Chen, B., Dillard, D.A., Dillard, J.G. and Clark Jr., R.L., Int. J. Fract., vol. 114, 167-190, 2002.

7.

Akisanya, A.R. and Fleck, N.A., Int. J. Fract., vol. 55, 29 – 45, 1992.

8.

Tada, H., Paris, P.C. and Irwin, G.R., Stress Analysis of Cracks Handbook, Del Research, St. Lious, MO, 1985.

12. Interface Fracture and Behavior of Joints

917

MEASUREMENTS OF INTERFACE FRACTURE AND MECHANICAL PROPERTIES OF LOW-K DIELECTRIC THIN FILMS F. Atrash and D. Sherman Department of Materials Engineering Technion-Israel Institute of Technology Haifa, 32000 Israel [email protected] The residual stresses and the biaxial elastic modulus of low-k dielectric thin films, and in particular the interfacial fracture energy of these films on a silicon substrate were all measured using a single method. The method consists of depositing a thin metallic 'super layer' on top of cantilever beam structures [1] of the low-k dielectric thin films, manufactured using the conventional micro machining processes. The 'super layer' generates tensile stresses in the investigated thin layers. When these beams are either released from the substrate or separated by spontaneous crack propagation initiated from a natural precrack, a curvature of the bilayer beam structures is formed and used to evaluate the above properties of the thin films and of the interface. The low-k dielectric thin films in this investigation is 0.5, 1, and 1.5 Pm thick Novelus CORAL© having a composition of 30at%C-20at%O-50at%Si. The CORAL© thin films were deposited on top of nearly 1 Pm thick Cu and 50 nm thick Ta thin films (the latter serves as a barrier layer), all on top of 725 Pm thick 6" (100) Silicon wafers. The metallic 'super layer' is highly stresses e-beam evaporated Ti layers, having thicknesses of 150, 200, and 250 nm. This constituted nine different bilayers, enabled to develop a comprehensive methodology to measure the mechanical properties and to provide valuable information regarding the evaluation of these properties. We use Timoshenko Equation [2] for the curvature of bilayer thermostats:

1 R

6( h1  h2 ) ' H res E2 h E1 h13 2 2 2 h1    h2  3( h1  h2 ) E1 h1 E 2 h2 3 2

(1)

res H 2res  H1res . where the index 1 designates the investigated layer, 2 the metallic super layer, 'H The thicknesses of the constituents, Eq. (1), were measured using alfa-step profilometer. The average radius of curvature, R, for each of the nine cases of the released or of the delaminated bilayers was calculated based on about 60 test results for each case. The elastic modulus of the Ti thin films was taken from the literature as 100±10 GPa. The residual stresses in the Ti thin films res

(required to calculate the residual strains in that layer, H 2 ) on top of the above multilayered structure was evaluated by means of Sotney Equation [3]; they are 677±66MPa, independent of the layers' thickness (in the range of 150-250nm). Eq. (1) has, therefore, two unknowns: 'Hres (since

H1res is unknown) and [ 1 R

E2 / E1 (since E1 is unknown). It can be rewritten as:

A1 A2[  A3 / [  A4

(2)

F. Atrash and D. Sherman

918

where the Ai's are functions of the thicknesses. Selecting a range of [ yields a curve of 'H vs. [for each set of specimens. Plotting 'H vs. [. for a group of specimens with same CORAL thickness (h1) generates three intersections which yield the range of values for 'Hres and for [. Fig. 1 shows the curves and the intersections obtained for the group with h1=1.5 Pm.

FIGURE 1. 'Hres vs. [for bilayers having 1.5 Pm thick CORAL film.

This group yields ECORAL

17.5 r 0.5 GPa and V res

45 r 5 MPa.

Knowing the material properties, it is now possible to calculate the interfacial fracture energy of the (weak) interface between the CORAL and the copper. Using the decohesion-no-decohesion criterion [1] of the nine bilayers it was evaluated to be 0.6-0.7 Jm-2, Fig. 2. More details of the calculations, the effect of layer thickness, and details of the evaluation of the interfacial fracture energy will be presented.

FIGURE 2. The decohesion-no-decohesion plot to evaluate the interfacial fracture energy.

References 1.

Bagchi A., Lucas G., Suo Z. and Evans A., J. Mater. Res., 9, 1734, 1994.

2.

Timoshenko S., Journal of the optical society of America, 11, 233-255, 1925.

3.

Stoney G., Proceedings of the royal society, A82, 172-175, 1909.

12. Interface Fracture and Behavior of Joints

919

INITIATION OF FRACTURE MECHANISMS AT THE FIBRE/MATRIX INTERFACE E. Martin1, B. Poitou1 and D. Leguillon 2 1LCTS, CNRS UMR 5801 Université Bordeaux 1, Pessac, France. 2LMM, CNRS UMR7607, Université P. et M. Curie, Paris, France. LCTS, 3 Allée de la Boetie, 33600 Pessac, France, Phone : (33)556 844 700, Fax : (33) 556 841 22, [email protected] Interface is the key region which determines the fracture properties of a composite material. Modelling of fracture mechanisms in the vicinity of the fibre/matrix interface must provide a better comprehension of the role of the interface properties in order to design the adequate fibre coating (Kerans et al.) [1]. For example, promoting the fracture of the interface under the influence of an approaching matrix crack allows to protect the fibre from stress concentration. The control of this fracture mechanism at the fibre/matrix interface leads to composites made with brittle matrices and reinforced with brittle fibres which exhibit high toughness. The aim of this paper is to provide conditions for the initiation of interfacial debonding in the vicinity of a matrix crack in brittle composites. Previous authors focus on the competition between crack penetration and crack deflection with the crack tip located at the bimaterial interface (He and Hutchinson) [2]. However, experimental observations have shown that interfacial debonding may occur ahead of the crack tip before the matrix crack reaches the interface (Xu et al.) [3].

FIGURE 1. a) Nucleation of a fibre crack in the vicinity of the matrix crack, b) Nucleation of an interfacial crack in the vicinity of the matrix crack. The fracture mechanism analysed is depicted in Fig. 1. An annular matrix crack is introduced in a representative cell (composite cylinder with a fibre radius Rf and a volume fraction Vf ). The distance between the crack tip and the fibre/matrix interface is denoted l. Upon axial loading and as a result of the stress concentration induced by the matrix crack, an interfacial crack of length 2d or a fibre crack of length p may nucleate. To evaluate the initiation stress of these nucleation mechanisms, standard approaches of fracture mechanics are ineffective but use is made of an initiation criterion (Leguillon) [4] which reveals efficient in such situations (Martin and Leguillon) [5] : i) an energy balance provides an incremental condition in which the infinitesimal energy rates of the classical Griffith's condition are replaced by finite energy increments, ii) an additional strength condition (which states that the opening normal stress along the anticipated path of crack nucleation is greater than the relevant strength) is imposed. Applying such approach provides the * initiation stress V i* (respectively V f ) of the deflection (respectively penetration) mechanism :

E. Martin et al.

920









V i*

g l , R f , V f , E f , E m ,Q f ,Q m , V ic , G cf V ic

V *f

g l , R f , V f , E f , E m ,Q f ,Q m , V cf , G cf V cf

, (1)

where ( E ,Q ) are the Young’s modulus and the Poisson ratio, ( V c , G c ) are the strength and the toughness. A finite element procedure determines the value of (f,g) in order to analyse the * * competition between the two nucleation mechanisms which is given by the condition V i  V f . Results show that the deflection criterion is expressed as :

G

c i

C

 C G C

c f

l , R

 D f

,V

V c f

f

, E

f

2

, E

w ith m

,Q

f

,Q

m

, D

D

l , R

f

,V

f

, E

f

, E

m

,Q

f

,Q

m



(2)

As illustrated by Fig. 2, it is interesting to note that a high value of the interfacial toughness c

G i can promote debonding provided the value of the fibre strength V cf is high enough.

FIGURE 2. Debonding criterion (the decohesion is predicted if the interfacial toughness

Gic is

lower than the plotted lines)

REFERENCES 1.

Kerans R.J., Hay R.S., Parthasarathy T.A., Cinilbulk M.K, J. Am. Ceram. Soc., 85, 25992632, 2002.

2.

He M.Y., Hutchinson J.W., Int. J. Solids Structures, 25, 1053-1067, 1989.

3.

Xu L.R., Huang Y.Y., Rosakis A.J., J. Mech. Phys. Solids, 51, 461-486, 2003.

4.

Leguillon D., Eur. J. of Mechanics – A/Solids, 21, 61-72, 2002.

5.

Martin E., Leguillon D., Int. J. Solids Structures, 41, 6937-6948, 2004.

12. Interface Fracture and Behavior of Joints

921

EFFECTS OF PLASTICITY AND RESIDUAL STRESS FOR CRACKS NEAR INTERFACES Ivar Reimanis, Keith Rozenburg, Matthew Tilbrook1 and Mark Hoffmann1 Metallurgical and Materials Enginering, Colorado School of Mines, Golden, CO 80401, USA 1School of Materials Science and Engineering, University of New South Wales, Sydney 2052, New South Wales, Australia [email protected] Cracks situated parallel to, and very near, the interface in layered, ductile-brittle composite specimens were investigated with finite element analysis. Elastic, plastic and thermal properties of Cu-W composites previously obtained from experiments were utilized in the model. A finiteelement model for simulating mixed-mode crack propagation in linear elastic materials was modified to incorporate yielding. A routine for automatic crack extension and remeshing enabled simulation of incremental crack propagation. Particular issues, including calculation of fracture parameters, crack propagation direction under mixed-mode loading and retention of plastic strain history, are addressed. The geometry and an example mesh close-up are shown in Fig. 1. Crack propagation was simulated in homogeneous and layered Cu-W composites, employing thermal and mechanical properties previously obtained from experiments. Two effects of plasticity on crack-tip stresses are predicted: (i) compliance mismatch leads to stress intensity factor amplification or ‘anti-shielding’, and (ii) accumulation of plastic strains leads to increases in effective toughness. Competition between these determines the structural reliability of the interface region. Influences of thermal, elastic and plastic mismatch on critical load and crack-tip mode-mixity were examined and reasonable predictions were obtained for crack-tip stresses and critical loads for cracks near interfaces in the presence of plastic yielding. The following conclusions were reached: 1

While the Irwin relation between crack-opening displacements and stress intensity factors cannot be used when plastic deformation occurs at the crack tip, a non-linear relationship may be obtained and used to calculate stress intensity factors.

2

Deflection of cracks near interfaces can occur due to mismatch in any one or more of elastic, plastic and thermal properties. Plasticity tends to mitigate the effects of residual stress on crack path.

3

The occurrence of plastic flow in the more ductile region increases stress intensity factors, due to the enhanced compliance, and rotates crack-tip stresses toward the ductile region.

4

For cracks close to the interface, a decrease in crack-tip stress intensity factors may be observed with crack extension, due to accumulation of plastic strain. This corresponds to an increase in effective toughness due to the work absorbed during plastic deformation.

Plasticity has an important influence on crack-tip stresses and propagation paths for cracks near interfaces. Accordingly, it is important to incorporate plastic deformation into models of failure near interfaces and to consider the effects of prior strain history on crack-tip stresses during simulations.

922

I. Reimanis et al.

FIGURE 1. (a) Layered copper-tungsten composite specimen configuration, showing dimensions and positive deflection direction. Material 1 is the stiffer, more brittle composition while Material 2 is the more ductile. (b) Close-up of crack-tip, showing the path used for J-integral calculation in simulations of homogeneous specimens.

12. Interface Fracture and Behavior of Joints

923

TOUGHNESS OF A ±450 INTERFACE L. Banks-Sills, Y. Freed, R. Eliasi and V. Fourman Dreszer Fracture Mechanics Laboratory Tel Aviv University Ramat Aviv, 69978 Israel [email protected] Experiments are carried out to determine the delamination toughness for a crack along the interface between two transversely isotropic materials. The material chosen for study consists of carbon fibers embedded within an epoxy matrix. A crack is introduced between two layers of this material, with fibers in the upper layer along the +450-direction and those in the lower layer along the –450-direction both with respect to the crack plane. The Brazilian disk specimen is employed in the testing.

FIGURE 1. Brazilian disk specimen. This specimen shown in Fig. 1 allows for a wide range of mode mixities. A crack (or thin notch) is placed along an interface between two layers with fibers on one side in the +450-direction and on the other side in the –450-direction. The two layers are within a composite laminate strip which was made from graphite/epoxy (AS4/3502) prepregs cured in an autoclave at a high temperature and pressure. A plate approximately 12.4 mm thick was fabricated by Israel Aircraft Industries with 15.4 mm wide and 25.4 µm thick Teflon (FEP fluorocarbon resin) strips introduced periodically between two of the ±450 layers. The plate consists of an inner part of {0,-45,+45,0}s each of nominal thickness 0.54 mm. Outer stiffening layers of ±450, 4.05 mm thick, were added to prevent plate bending. Strips were cut from the plate and glued to aluminium partial disks to form the specimen illustrated in Fig. 1. For details on specimen construction, see Banks-Sills et al. [1]. To calibrate the specimens, stress intensity factors are obtained which result from the applied load, as well as residual curing stresses. It may be noted that all three modes are coupled, leading to a three-dimensional problem. The finite element method and a mechanical M-integral are employed to determine the stress intensity factors arising from the applied load (Freed and BanksSills [2]). For the residual stresses, a three-dimensional thermal M-integral, together with the finite element method, is used for stress intensity factor determination (Banks-Sills et al. [3]). The stress intensity factors found for the applied load and residual stresses are superposed to obtain a local interface energy release rate Gi , together with two phase angles \ and I .

L. Banks-Sills et al.

924

From the load at fracture, the critical interface energy release rate or interface toughness Gic is determined as a function of the phase angles. There were twenty-six specimens. For each specimen, the interface toughness is obtained at twenty-one stations along the crack front. These results are plotted as the points in Fig. 2. A fracture criterion has also been developed for this three-dimensional problem. It is the surface shown in Fig. 2. Points along the crack front for nineteen of the specimens intersect the surface. It may be postulated for these specimens that some of the points along the crack front have become critical and drag the rest of the crack front with them as the delamination expands. For two of the specimens, all of the points are above the surface; whereas for five of them, all of the points are below. This behavior is considered as experimental scatter.

FIGURE 2. Delamination toughness Gic .

References 1.

Banks-Sills, L., Boniface, V. and Eliasi, R., Int. J. Solids and Struct., vol. 42, 663-680, 2005.

2.

Freed, Y. and Banks-Sills, L., Int. J. Fract. Mech., vol. 133, 1-41, 2005.

3.

Banks-Sills, L., Freed, Y., Eliasi, R. and Fourman, V., Tel Aviv University Report 2005/1, 2005.

12. Interface Fracture and Behavior of Joints

925

RESIDUAL STRESS INFLUENCE ON DISSIMILAR MATERIAL WELD JUNCTION FRACTURE P. Gilles and M.-F. Cipiere Framatome-ANP Tour AREVA Paris la Défense 92084, France Josette DEVAUX ESI-France Le Discover, 84 Bd. Vivier Merle 69485 Lyon France [email protected] In most of nuclear reactors such as Pressurized Water Reactors (PWR) or Boiling Water Reactors (BWR), heavy section components made in low alloy steel are connected with stainless steel piping systems. The dissimilar material weld (DMW) junctions are performed between ferritic nozzle ends and austenitic stainless steel piping, following a special manufacturing procedure to ensure a good resistance of the joint. Post weld heat treatment (PWHT) is applied to reduce residual stresses in the heat affected zone (HAZ), but whatever the process is, the difference in thermal expansion coefficients induces residual stresses during the cooling stage. Furthermore, differences in tensile properties may cause strain concentration at the weld to ferritic steel interface which enhances the risk of crack initiation and extension. Several experiences from the field confirm sensitivity to fatigue, corrosion or low toughness areas in this type of junction. In the framework of the European Community Research and Development Programme a project (ADIMEW, C. Faidy [1]) has been sponsored on the fracture behaviour of cracked stainless steel/ferritic steel bimetallic welds. The objective was to contribute to the development and verification of analysis methods which describe the behaviour of an external circumferential defect in a DMW. The type of fracture is ductile, but the question of the influence of the residual stress fields on tearing initiation has been raised since the material resistance is lowered when the crack is close to the interface between the ferritic steel pipe and the weld. It has been shown (Devaux et al. [2], Gilles et al. [3]) that this lowering of the “local” toughness is due the high degree of stress triaxiality at the interface. In defect assessments tensile residual stress fields have to be taken into account, except if their influence may be proven as negligible. The present paper aims to estimate the influence of the residual stress field by numerical simulation of the ADIMEW mock-up fracture behaviour and to recommend a simplified procedure for including residual stress field in a J estimation scheme. For the ADIMEW project, two DMW specimens have been manufactured of which one has been tested in 4-point bending and one being utilised for the experimental determination of welding residual stresses and for the generation of material property data for input to the analysis procedures. The cracked section of the ADIMEW mock-up is shown in Fig. 1. To guarantee the quality of the DMW's, a considerable experience and high degree of quality control has been required within the weld manufacturing process, in accordance with FRAMATOME-ANP basic nuclear specification.

P. Gilles and M.-F. Cipiere

926

FIGURE 1. Crack shape and location in the ADIMEW Dissimilar Weld Metal Junction The analysis is conducted in three steps as explained below: A refined numerical simulation of the welding process, which simulates each elementary step of the mock-up manufacturing procedure by modelling each of the passes, has been conducted and validated by comparison with the residual stress measurements using the neutron diffraction technique (C. Ohms [4]). This simulation assumes axisymmetry. The residual stress field is then transferred to a three dimensional mesh of the cracked DMW, the crack being closed. Then crack is opened progressively simulating crack manufacturing. Two finite element simulations of the fracture behaviour of the cracked mock-up under bending are conducted with and without considering residual stress fields. Two methods are used: one based on the crack driving force J and the other one using Rice and Tracey local approach criterion for ductile tearing initiation. The paper compares the predictions with the experiment and analyses the influence of the residual stress field on the crack opening behaviour and the stress redistribution due to yielding.

References 1.

Faidy C., “Structural integrity of dissimilar welds – ADIMEW project overview” In Proceedings of PVP 2004, ASME Pressure Vessel and Piping Conference, 2004, USA.

2.

Devaux, J., Mottet, G., Bergheau J.-M., Bhandari S. and Faidy C.: ‘Evaluation of the Integrity of PWR Bimetallic Welds’, Jour. of Pressure Vessel Technology, 2000, ASME, 122, 386373.

3.

Gilles Ph., Devaux J., Faidy C. – “ADIMEW project: Prediction of the ductile tearing of a cracked 16” dissimilar welded junction” Proc. of PVP2004, ASME Pressure Vessel and Piping Conference, 2004, USA.

4.

Ohms C., Katsareas D. E., Wimpory R. C., Hornak P., Youtsos, A. G., “Residual stress analysis in a thick dissimilar metal weld based on neutron diffraction”, PVP Vol. 479, ASME Pressure Vessel and Piping Conference, July 2004, USA.

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FRACTURE MECHANISMS OF A THIN ELASTIC PLASTIC LAMINATE C. Bjerken, S. Kao-Walter and P. Stahle Malmö University, Lund Institute of Technology Dept. Solid Mechanics [email protected] Packaging laminate has received much interest recently because of its use in liquid foor containers, cf. [1-3]. This study considers a crack in a laminate consisting of a soft and a hard layer. The layers are assumed to be thin so that the only significant fracture process is cross sectional necking in a region ahead of the crack tip. The necking proceeds until the cross sectional area is very small making any potential fracture of a remaining ligament insignificant to the macroscopic behaviour of the structure. An experimental and numerical investigation of a laminate consisting of a 25 Pm thick polymer sheet and a 9 Pm thick aluminium sheet demonstrates a remarkable increase of the fracture toughness and the fracture strength as compared with that of the individual layers.

FIGURE 1. a) Geometry of the CCP test specimen. b) Results for aluminium and LDPE tested separately and as a laminate. Tensile tests were performed on the laminate, an aluminium sheet and a low-density polyethylene (LDPE) sheet. The aluminium sheet and the LDPE sheet were identical to the two layers of the laminate. All specimens had the same length h = 230mm and width b = 95mm. A through thickness crack with the length a = 45mm was cut in the centre of the sheet and perpendicular to the direction of the load. The tests were performed according to the ASTM standard [4] Figure 1 that the maximum load, 13N, carried by the aluminium sheet is at somewhat less than 1mm. At that extension the LDPE sheet carries around 1N. Thus one may expect that laminate would carry a load of around 14N. However, the loading of the laminate is roughly 20N when it is extended 1mm. It is here assumed that, as the load is increased, crack growth is initiated in the aluminium fracture first. It is further assumed that this compel the strains to localize in the LDPE layer at the crack tip parallel with the necking region in the aluminium. Therefore the maximum load carrying capacity of the LDPE is reached at continued crack growth in the laminate. The maximum load a separate LDPE layer can carry is around 15N.

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To explore the features of this phenomenon elastic plastic FE analyses have been performed. The necking region that develops ahead of the crack tip neck is assumed to be in a state of approximately plane strain in a plane perpendicular to the direction of the crack. Therefore the fracture process is viewed as a two dimensional problem of plane strain for a cross section perpendicular to the crack ahead of the crack tip. Some de-cohesion between the two layers of the laminate is assumed. The role of the interface toughness is studied. The plastic deformation is simulated to the point when the cross section almost has vanished, i.e. almost to complete fracture. The following observations were made: - Onset of crack growth was observed to occur approximately at peak load. In the laminate fracture of LDPE occurred after completed failure of the Al-foil. -Peak load for the laminate is almost the same as the sum of the peak load for the Al-foil and the peak load for the LDPE layer. This suggests that both materials reach peak stress in a small region in the vicinity of the crack tip. -The energy required before onset of fracture is unexpectedly large and around three times larger than for the separate Al-foil layer. From the result the fracture toughness at onset of crack growth

References 1.

Kao-Walter, S. and Ståhle, P., In the Proceedings of SPIE, Third International Conference on Experimental Mechanics, Xiaoping Wu, Yuwen Qin, Jing Fang, Jingtang Ke, Editors, Volume 4537, Beijing, 2002, 253-256.

2.

Lau, C. C., A Fracture Mechanics Approach to the Adhesion of Packaging Laminates, Doctoral Thesis, Imperial College of Science, UK, 1993.

3.

Tryding, J., In Plane Fracture of Paper, Doctoral Thesis, Division of Structural Mechanics, Lund Institute of Technology , Sweden, 1996.

4.

ASTM International, Standard Test Methods for Tensile Properties of Thin Plastic Sheeting, D882-91, 1991.

12. Interface Fracture and Behavior of Joints

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CRACK-TIP PARAMETERS IN POLYCRYSTALLINE PLATES WITH COMPLIANT GRAIN BOUNDARIES R. Ballarini and Y. Wang Department of Civil Engineering Case Western Reserve University Cleveland, Ohio 44106-7201 [email protected] This paper presents two micromechanical models to study the statistics of the local stress intensity factor of a cracked polycrystalline plate. The first is a finite element model based Monte Carlo procedure where the plate's microstructure, which includes a finite number of crystals (or grains) separated by a finite thickness interphase, is approximated as a Poisson-Voronoi tessellation (Fig. 1). The statistics of the effective elastic moduli of the uncracked plate are calculated as well as the local stress intensity factors of the corresponding cracked plate (Fig. 2). This is done for selected values of the parameters that quantify the ratio of elastic mismatch between the crystals and the grain boundaries, and the expected number of grains in the plate. The results indicate that the average values and standard deviations of the local stress intensity factors are independent of the number of grains in the plate. The results of the Monte Carlo model suggest that the crack tip parameters of cracked polycrystalline plates could be calculated using an efficient alternative analytical model involving a long crack penetrating a circular inhomogeneity (Fig. 3). This problem is solved using the method of continuously distributed dislocations and by expressing the traction-free condition along the crack surfaces as a system of singular integral equations, which are solved numerically. The results demonstrate that as long as the elastic mismatch between the inhomogeneity and the surrounding material is interpreted correctly, then the approximate analytical model is associated with averaged stress intensity factors that are in excellent agreement with those of the polycrystalline microstructure. An attempt is made to apply the developed models to interpret experimental data obtained from warm lake ice. It is concluded that proper interpretation of data obtained from polycrystalline plates with compliant grain boundaries necessitates stress analyses that incorporate explicitly the stochastic microstructure. However, additional experimental data is required to resolve the issue that motivated the present study.

R. Ballarini and Y. Wang

930

References 1.

Y. Wang and R. Ballarini, Meccanica, vol. 38, 579-593, 2003.

2.

Y. Wang, “Crack-tip parameters in polycrystalline plates with compliant grain boundaries,” Ph.D. thesis, Department of Civil Engineering, Case Western Reserve University, 2003.

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EXTENDED FE SIMULATIONS OF CRACK GROWTH IN LAYERED AND FUNCTIONALLY GRADED MATERIALS C. Comi and S. Mariani Dipartimento di Ingegneria Strutturale, Politecnico di Milano Piazza Leonardo da Vinci 32, 20133 – Milano, Italy [email protected] , [email protected] In this work we address some computational issues concerning failure analysis of layered and functionally graded materials (FGMs). The gradual variation of the mechanical properties of FGMs, unlike the abrupt change encountered in layered ones, is known to improve the failure performance. We focus on quasi-brittle materials subject to quasi-static loadings. As in Zhang and Paulino [1], a cohesive model is used to simulate crack propagation in a linear elastic bulk. The relevant traction-displacement discontinuity law is implemented within the context of the extended finite element method (see, e.g., Sukumar et al. [2] and Mariani and Perego [3]). The approach allows to follow the crack path independently of the background finite element mesh; this feature is especially important for FGMs, since the gradation of the mechanical properties may lead to complex crack paths also in a simple symmetric test set-up, Rousseau and Tippur [4].

FIGURE 1. 4PB test on a FG SEN specimen. (a): specimen geometry and sketch of the material gradation; (b): adopted (coarse) spatial discretization.

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FIGURE 2. 4PB test on a FG SEN specimen: final crack path and relevant level sets of the in-plane maximum principal stress. Results concerning crack growth in functionally graded and layered glass-filled epoxy beams, Rousseau and Tippur [5], are presented in order to assess the effects of mechanical gradation on the failure mechanism. As for a single edge notched (SEN) specimen featuring a material gradation parallel to the expected propagation direction and subject to four-point bending (4PB) (see Fig. 1), first outcomes are shown in Fig. 2.

References 1.

Z. Zhang and G.H. Paulino. International Journal of Plasticity, vol. 21, 1195 1254, 2005.

2.

N. Sukumar, N. Mo?s, B. Moran and T. Belytschko. International Journal for Numerical Methods in Engineering, vol. 48, 1549-1570, 2000.

3.

S. Mariani and U. Perego. International Journal for Numerical Methods in Engineering, vol. 58, 103-126, 2003.

4.

C.-E Rousseau and H.V. Tippur. Acta Materialia, vol. 48, 4021-4033, 2000.

5.

C.-E Rousseau and H.V. Tippur. Engineering Fracture Mechanics, vol. 69, 1679-1693, 2002.

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SIMULATION OF PLASTIC FATIGUE CRACK GROWTH BY A TWO SCALE EXTENDED FINITE ELEMENT METHOD A. Gravouil, T. Elguedj and A. Combescure LaMCoS, Laboratoire de Mecanique des Contacts et des Solides UMR 5514, INSA Lyon Bat. Jean d’Alembert, 18,20 rue des Sciences 69621 Villeurbanne France [email protected] A new technique for the finite element modelling of elastic-plastic fatigue crack growth with frictional contact on the crack faces is presented. The eXtended Finite Element Method (X-FEM) is used to discretize the equations, allowing for the modelling of arbitrary cracks whose geometry are independent of the finite element mesh. This paper presents an augmented Lagrangian formulation in the X-FEM framework in order to simulate elastic-plastic crack growth with treatment of contact and friction. The original formulation, which takes advantages of a coarse and a fine mesh close to the crack tip, is presented. In a second time the numerical issues such as contact treatment and numerical integration are adressed, and finally numerical examples are shown to validate the method. The X-FEM uses the partition of unity in two ways: first to take into account the displacement jump across the discontinuity far from the crack tip, and second to enrich the approximation close to the front by considering the appropriate asymptotic fields [3] [4]. Several LEFM issues were treated with the X-FEM such as elastic fatigue crack growth, crack growth with friction, arbitrary 3D fatigue crack growth with level set methods and dynamic crack growth. In recent works the method has been applied to non-linear issues such as phase transformation, large strain analysis of rubber like materials, and finally it has been modified by the authors to deal with plasticity [1] [2] [7]. The main purpose of this contribution is, in the framework of the eXtended Finite Element Method, to treat the case of multiple non-linearities with a two scale approach : a coarse description of the structure is assumed (the X-FEM approach allows us to obtain an accurate solution without meshing the crack) and a fine discretization close to the crack tip in order to accurately describe the plastic zone. The presented method will focus on the case of plasticity combined with frictional contact and is applied to fatigue crack growth analysis [9]. In the case of material non-linearities, several issues have to be addressed. In a previous paper of the authors [8] an appropriate elastic-plastic enrichment basis was developed to allow the X-FEM to deal with plasticity [5]. ª ¬«

BD

º ¼»

1 T T T T T T ª º r n 1 « sin  cos  sin sin T  cos sin T  sin sin 3T  cos sin 3T » 2 2 2 2 2 2 ¬ ¼ (1)

In the present paper this approach is coupled with the treatment of frictional contact, and the problems associated with plastic crack propagation are explored. The formulation is presented by coupling an augmented Lagrangian method with the X-FEM, and the integration issues are studied [6]. Several numerical examples are given to show the possibilities and the efficiency of the method, and finally one concludes and presents possible future work.

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Figure 1.Crack propagation accross subdivided elements and evolution of the subelements between the two configurations.

References 1.

Hutchinson JW. Singular behaviour at the end of a tensile crack in a hardening material. Journal of the Mechanics and Physics of Solids 1968; 16:13–31.

2.

Rice JR, Rosengren GF. Plane strain deformation near a crack tip in a power-law hardening material, Journal of the Mechanics and Physics of Solids, 1968; 16:1–12.

3.

Moës N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing, International Journal for Numerical Methods in Engineering 1999; 46(1):133– 150.

4.

Babuska I, Melenk JM. The Partition of unity method, International Journal for Numerical Methods in Engineering 1997; 40:727–758.

5.

Fleming M, Chu YU, Moran B, Belytschko T. Enriched Element-free Galerkin methods for crack tip fields. International Journal for Numerical Methods in Engineering 1997; 40:1483– 1504.

6.

Simo JC, Laursen TA. An augmented lagrangian treatment of contact problems involving friction. Computers and Structures 1992; 42(1):97–116.

7.

Pan J, Shih CF. Elastic-plastic analysis of combined mode I, II and III crack-tip fields under small-scale yielding conditions, International Journal of Solids and Structures 1992;29(22):2795–2814.

8.

Elguedj T, Gravouil A, Combescure A. Appropriate extended functions for X-FEM simulation of plastic fracture mechanics. Computer Methods in Applied Mechanics and Engineering, accepted, 2005.

9.

Combescure A, Gravouil A, Baietto-Dubourg MC, Elguedj T, Ribeaucourt R, Ferrié E. Extended finite element method for numerical simulation of 3D fatigue crack growth. Proceedings of the 31st Leeds-Lyon Symposium on Tribology 2004

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ACCURATE DETERMINATION OF COHESIVE CRACK TIP FIELDS USING XFEM AND ADMISSIBLE STRESS RECOVERY B. L. Karihaloo1, Q. Z. Xiao1 and X. Y. Liu2 1Cardiff School of Engineering, Queen’s Buildings, The Parade, Newport Road, Cardiff CF24 3AA, U.K. 2Division of Engineering Sciences, Institute of Mechanics, Chinese Academy of Sciences, No.15 Beisihuanxi Road, Beijing 100080, China [email protected] (B L Karihaloo), [email protected] (Q Z Xiao), [email protected] (X Y Liu) Cohesive zone (or crack) models have been extensively used in the study of localisation and failure in engineering structures. Elices et al. [1] have discussed the advantages and limitations of these models. De Borst et al. [2] have given a concise overview of the various ways in which the cohesive zone methodology can be numerically implemented. The recently developed extended/ generalized finite element method (XFEM) (see, e.g., Daux et al. [3], Strouboulis et al. [4], and Karihaloo and Xiao [5]) provides a proper representation of the discrete character of cohesive zone formulations avoiding any mesh bias. Moes and Belytschko [6] and Wells and Sluys [7] analysed a continuous cohesive crack that runs through an existing finite element mesh without mesh bias. Remmers et al. [8] further studied the possibility of defining cohesive segments that can arise at arbitrary locations and in arbitrary directions and thus allow for the resolution of complex crack patterns including crack nucleation at multiple locations, followed by growth and coalescence. Rubinstein [9] has shown that relatively small errors in the determination of the crack path deflection angle can lead to a significant cumulative deviation of the crack path over a finite crack length. Therefore a reliable analysis of crack propagation requires not only a suitable criterion of crack growth but also an accurate evaluation of the crack tip field. The latter will be addressed in this contribution. We will first make a detailed analysis of the asymptotic field at the tip of a cohesive crack in quasi-brittle materials for typical cohesive laws. This analysis will help us understand the structure of the crack tip field, and at the same time, provide us with suitable crack tip enrichment functions for the corresponding cohesive cracks. For traction free cracks, it has been shown that the implementation of the accurate crack tip field as enrichment functions gives most the accurate crack tip field using the XFEM (Liu et al. [10]). We will then consider general cohesive cracks for which asymptotic fields are difficult to obtain, and enrichment functions at the crack tip can only be chosen to meet the local displacement conditions adjacent to the tip. In order to obtain accurate stresses, the statically admissible stress recovery (SAR) scheme of Xiao and Karihaloo [11, 12] will be extended to cohesive cracks. SAR uses basis functions, which meet the equilibrium equations within the domain and the local traction conditions on the boundary, and moving least squares (MLS) to fit the stresses at sampling points (e.g., quadrature points) obtained by the XFEM. It has been shown to be very powerful for traditional FEM as well as XFEM for linear elastic problems with traction-free boundary segments. Typical cohesive crack problems with linear and nonlinear cohesive laws will be analysed and compared with available results in the literature to illustrate the accuracy and applicability of the methodology developed in this paper.

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References 1.

Elices, M., Guinea, G.V., Gómez, J. and Planas, J., The cohesive zone model: advantages, limitations and challenges, Engng. Fract. Mech., 69, 137-163, 2002

2.

De Borst, R., Gutierrez, M.A., Wells, G.N., Remmers, J.J.C. and Askes, H., Cohesive-zone models, higher-order continuum theories and reliability methods for computational failure analysis, Int. J. Numer. Meth. Eng., 60, 289-315, 2004

3.

Daux, C., Moes, N., Dolbow, J., Sukumar, N. and Belytschko, T., Arbitrary branched and intersecting cracks with the extended finite element method, Int. J. Numer. Meth. Eng., 48, 1741-1760, 2000

4.

Strouboulis, T., Copps, K. and Babuska, I., The generalized finite element method, Comput. Meth. Appl. Mech. Eng., 190, 4081-4193, 2001

5.

Karihaloo, B.L. and Xiao, Q.Z., Modelling of stationary and growing cracks in FE framework without remeshing: a state-of-the-art review, Comput. Struct., 81, 119-129, 2003

6.

Moes, N. and Belytschko, T., Extended finite element method for cohesive crack growth, Engng. Fract. Mech., 69, 813–833, 2002

7.

Wells, G.N. and Sluys, L.J., A new method for modeling cohesive cracks using finite elements, Int. J. Numer. Meth. Eng., 50, 2667-2682, 2001

8.

Remmers, J.J.C., de Borst, R. and Needleman, A., A cohesive segments method for the simulation of crack growth, Comput. Mech., 31, 69-77, 2003

9.

Rubinstein, A.A., Computational aspects of crack path development simulation in materials with nonlinear process zone, Int. J. Fract., 119, L15-L20, 2003

10. Liu, X.Y., Xiao, Q.Z. and Karihaloo, B.L., XFEM for direct evaluation of mixed mode SIFs in homogeneous and bi-materials, Int. J. Numer. Meth. Engng., 59, 1103-1118, 2004 11. Xiao, Q.Z. and Karihaloo, B.L., Statically admissible stress recovery using the moving least squares technique, In Progress in Computational Structures Technology, edited by B.H.V. Topping and C.A. Mota Soares, Saxe-Coburg Publications, Stirling, Scotland, 2004, 111-138 12. Xiao, Q.Z. and Karihaloo, B.L., Statically admissible stress recovery for crack problems, In Proc. ICF11, Turin, Italy, March 20 - 25, 2005.

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A NEW GENERATION OF BOUNDARY ELEMENT METHOD FOR DAMAGE TOLERANCE ASSESSMENT OF AEROSTRUCTURES M. H. Aliabadi Department of Aeronautics, Imperial College London, Prince Consort Road, London, UK. [email protected] This paper presents a brief review of recent progress in development of dual boundary element formulations for damage tolerance assessment of aerostrucutres. A new generation of boundary element formulations known as the Dual Boundary Element Method was developed by Aliabadi and his students in 1992. for modeling crack growth in twoand three-dimenional linear elastic problems. The formulation was subsequently extended to nonlinear and transient problems. More recently, a new formulations have been developed which allow the application of the BEM to thin walled strucutres widely used in engineering, for example aircraft wings and fuselage panels, pressure vessels etc. The extension of the dual boundary element method to thin-walled problems has provided for the first time a comprehensive modeling tool suing BEM. In this paper application of the BEM to linear and nonlinear stiffened panels are reviewed. A flat square panel reinforced with three Z-stringers from the wing box of the B-52 Stratofortress is subjected to the transverse load. The panel and the stringers are modelled with 13 thin plates in total. Each plate is divided into 32 quadratic elements

Figure 1: BEM results a) stiffened flat panel, b) stiffnened curved panel, c) buckling of thin craked panel. Dirgantara and Aliabadi carried out a nonlinear fracture mechanics analysis of stiffened curved panel. In the analysis, BEM shell mesh has 64 boundary elements and the stiffener is modeled with 5 nodal points each. Recently Purbolaksono and Aliabadi presented a dual boundary element formulation for buckling analysis of plates with cracks. They presented the problem of a rectangular plate with longitudinal central crack subjected to compression. Fig. 1 presents the changes in the buckling mode of rectangular plate with aspect ratio 2. Recently Di Pisa and Aliabadi presented the application of the DBEM to modeling a wing section reinforced with stiffenerers which are riveted to the skin. In this paper a brief review of the recent advances in the application of the boundary element method to Damage Tolerance Assessment of Aerostructures structures was presented. The method is shown to be capable of analyzing linear and nonlinear problems with boundary only discretization.

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References 1.

Portela,A., Aliabadi,M.H. and Rooke,D.P. The dual boundary element method: efficient implementation for cracked problems, Int. J. Numer. Methods in Engng, 32, 1269-1287, 1992.

2.

Mi,Y and Aliabadi,M.H. Dual boundary element method for three-dimensional fracture mechanics analysis, Engineering Analysis, 10, 161-171, 1992.

3.

M.H.Aliabadi A new generation of boundary elements in fracture mechanics, Int. J. Fracture, 86, 91-125, 1997.

4.

Cissilino,A.P. and Aliabadi,M.H. Three-dimensional BEM analysis for fatigue crack growth in welded components, Int. J.Pressure Vessel and Pipping, 70, 135-144, 1997.

5.

Aliabadi,M.H. The Boundary Element Method, applications in solids and structures, Wiley, Chichester, 2002

6.

Dirgantara,T and Aliabadi,M.H. Numerical simulation of fatigue crack growth in pressurized shells, International Journal of Fatigue, 24, 725-738, 2002.

7.

DiPisa,C, Aliabadi,M.H. and Alaimo,A. Nonlinear Analysis of a reinforced panel undegoing large deformation, Proceeding of the 5th International Conference on Boundary Element Techniques, edited by Leitao,V and Alaiabdi,M.H., EC Publications, 2004.

8.

Purbolaksono,J and Aliabadi,M.H., Dual boundary element analysis of cracked plates under buckling loads, Int.J.Numer. Meth. Engng., 62, 537-563 2005

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ROBUST STRESS INTENSITY FACTORS EVALUATION FOR 3D FRACTURE MECHANICS WITH X-FEM Hans Minnebo, Eric Bechet and Nicolas Moes GeM - Institut de Recherche en Genie Civil et Mecanique, UMR CNRS 6183 Ecole Centrale de Nantes / Universite de Nantes 1, rue de la Noe, BP 92101 44321 Nantes CEDEX3 [email protected] Fatigue life prediction for cracked parts with the classical finite element method is not an obvious task for industrial structures. Indeed, it is necessary to take the crack geometry into account (its surfaces and front) with enough accuracy. The stress intensity factors (SIFs) are then computed and the crack can be propagated. Consequently, a remeshing step is necessary for the next time step's mechanical problem. These remeshing procedures are difficult in 3D and are very timeconsuming. The X-FEM (eXtended Finite Element Method) (Moes et al. [1]) allows to embed physical surfaces of discontinuity into a mesh without modifying it, thanks to the use of two combined level-sets (Stolarska et al [2]), the partition of unity method (Babuska and Melenk [3]) and an enrichment with compact support. This method fits particularly well to crack analysis. The use of specific enrichment functions for cracks, singular at the crack tip and discontinuous on the surfaces enables one to carry a complete analysis of the crack without having to change the mesh. Nevertheless, the enrichment functions are singular and thus difficult to integrate. So, it is necessary to use a non-standard integration scheme in order to improve the accuracy of the weak form's integration. We propose a modified integration scheme based upon a classical GaussLegendre scheme to solve this problem (Bechet et al [4]). This scheme combines a coordinates change with two variables changes adapted to the singular functions that are used for the crack tip. For the 3D case, the cylindrical property of the singular problem is used to extend the 2D integration method. We show increased convergence for both 2D and 3D cases. The conditionning of the stiffness matrix is degraded, due to the use of these singular enrichment functions. This brings into trouble conventional iterative solvers. In order to improve the condition number, we use a preconditionning step based upon a Cholesky decomposition, that makes a local orthogonalisation on the whole set of regular and enriched shape functions for each node. Although local, this pre-conditionner improves greatly the conditionning. The size of the enrichment zone is also discussed. On the one hand, the enrichment of too many nodes will lead to a huge matrix with a high condition number. On the other hand, with the enrichment of too few nodes, the representation of the problem will not be sufficient. So, an intermediate size has to be chosen. We propose a robust computation of the stress intensity factors, based on the X-FEM method, which takes into account all the real boundary conditions : thermal, centrigugal... The robustness of the SIFs evaluation is of primary importance for the estimation of the propagation path. The improvements over standard FEM will affect the computation in that way : an initial mesh is generated, not necessarily respecting the crack configuration, but with a sufficient refinement around the crack tip ; •

several steps of propagation are made, with an update of the crack representation (using level-sets) ;

H. Minnebo et al.

940 •

when the crack tip is in a region where the refinement is non longer sufficient or if the configuration is not suited for post-processing, a new mesh should be generated in the same way as the initial one.

So, we hope to save CPU time for computational fatigue analysis, as we reduce the number of remeshing steps. Those are also simpler to implement due to the lack of geometrical constraints on the mesh.

Acknowledgements The authors greatfully acknowledge the support of Snecma Moteurs.

References 1.

Moes, N., Dolbow, J., Belytschko, T., A finite element method for crack growth without remeshing., International Journal for Numerical Methods in Engineering, 46:131-150, 1999.

2.

Stolarska, M., Chopp, D. L., Moës, N., and Belytschko, T., Modelling crack growth by level sets and the extended finite element method, International Journal for Numerical Methods in Engineering, 51(8):943-960, 2001.

3.

Babuska, I., Melenk, J.M., The partition of unity method, International Journal for Numerical Methods in Engineering, 40:727-758, 1997.

4.

Bechet, E., Minnebo, H., Moes, N., Burgardt, B., Improved implementation and robustness study of the X-FEM method for stress analysis around cracks, International Journal for Numerical Methods in Engineering, accepted.

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A MICRO-MACRO PARTITION OF UNITY METHOD FOR CRACK PROPAGATION P. A. Guidault1, O. Allix1, L. Champaney1 and C. Cornuault2 1LMT-Cachan (ENS Cachan/CNRS/University Paris) 61 avenue du President Wilson, F-94235 Cachan Cedex, France 2Dassault Aviation 78 quai Marcel Dassault, cedex 300, F-92552 Saint-Cloud Cedex, France [email protected], {guidault,allix,champaney}@lmt.ens-cachan.fr In the last decade, two types of approaches have been designed to deal with effects which occur at different scales. The first class of approaches is the class of multiscale strategies. The second one is based on the Partition of Unity Method (PUM) first introduced by Melenk and Babuska [1] and all its applications. By enabling one to enrich the kinematics of continuous media, the PUM makes possible the introduction of discontinuities into the displacement field using a relatively small number of additional degrees of freedom. One of the main advantages in this case is that the mesh does not have to conform to the geometry of the crack. This technique greatly simplifies the meshing and remeshing processes which, despite the improvement of meshing tools, remain tedious tasks for engineers confronted with crack propagation situations. However, it does not completely incorporate the multiscale aspect induced by the localization of strains in the cracked zone. Generally, it requires further remeshing around the crack: thus, the remeshing problem is only partially resolved. Furthermore, conditioning difficulties remain because of the treatment of multiscale phenomena without separation. To overcome these two difficulties, the goal of our work in cooperation with Dassault Aviation is to combine both types of approaches, a multiscale one and a PUM-based one, in order to deal with crack propagation situations in an efficient way.

FIGURE 1. Three-point-bend specimen: microdisplacements (modeling of the crack by the XFEM) and macrodisplacements (thick lines). The process involved is a combination of two techniques. The first technique consists in applying the recently developed micro-macro approach [2] based on a homogenization technique. The microscale is associated with local phenomena which occur around the crack. This scale is much smaller than the macroscale which corresponds to the whole structure. This multiscale approach ensures a correct global-local dialog between the macroscale and the microscale. The second technique, based on the PUM, is used to define a proper representation of the local solution, in terms of discontinuity and solution at the crack tip, on the microscale. The integration of enrichment functions is obtained by the X-FEM, a PUM-based enrichment method introduced by Belytschko and Black [3]. With this scale separation, the macroproblem keeps the same structure throughout the calculation while the whole numerical effort is directed towards the microlevel [5].

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In a technical point of view, the meshing and remeshing difficulties are thus resolved not only at the global level but also at the local level. In the micro-macro approach, the fact that a crack affects both the local level and the global level raises the question of the kinematics and the description of the forces on the two scales. Consequently, the choice of the macroscale and its associated discretization in order to include the macroeffect of a crack is discussed. Moreover, in order to limit the use of the refined scale only to where it is required, a decomposition of the domain into substructures and interfaces is proposed to link two finite element descriptions. Finally, the integration of the X-FEM [4] as a local enrichment method in such a multiscale frame is presented. Simulations of fatigue crack growth will be shown in the field of linear elastic rupture. Our work in progress consists in applying the strategy to ductile fracture mechanics and, more widely to damage.

References 1.

Melenk, J. M. and Babuska, I., Computer Methods in Applied Mechanics and Engineering, vol. 139, 289-314, 1996.

2.

Ladeveze, P., Loiseau, O. and Dureisseix, D., International Journal for Numerical Methods in Engineering, vol. 52(1-2), 121-138, 2001.

3.

Belytschko, T. and Black, T., International Journal for Numerical Methods in Engineering, vol. 45(5), 601-620, 1999.

4.

Stolarska, M., Chopp, D. L., Moës, N. and Belytschko, T., International Journal for Numerical Methods in Engineering, vol. 51(8), 943-960, 2001.

5.

Guidault, P.-A., Allix, O., Champaney, L. and Navarro, J.-P., In Proceedings of the Seventh International Conference on Computational Structures Technology, edited by B.H.V. Topping and C.A. Mota Soares, Civil-Comp Press, Stirling, 2004, 443-444.

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A DYNAMIC CRACK PROPAGATION CRITERIA FOR XFEM, BASED ON PATH-INDEPENDENT INTEGRAL EVALUATION Ionel Nistor, Serge Caperaa and Olivier Pantale Ecole Nationale d’Ingenieurs de Tarbes 47, Avenue d’Azereix, TARBES, 65016, FRANCE [email protected], [email protected], [email protected] The eXtended Finite Element Method (XFEM) has been successfully used for several years for the numerical analysis of cracked structures under statically and later under dynamically loadings. Based on Partition of Unity Method, the XFEM was developed at Northwestern University (Moes et al. [1]) firstly as a method for analysing crack growth without remeshing, using special enrichment functions to model discontinuous displacement fields. Since, the method was continuously improved and applied to various domains of fracture mechanics. The dynamic crack propagation is one of them and an important contribution for its modelling by XFEM was given by Belytschko et al. [2]. In this paper we propose a crack evolution model for XFEM, based on dynamic energy release rate computation using a path-independent integral. The numerical implementation of this model was achieved in the home-made code DynaCrack (Nistor et al. [3]). Developped using OrientedObject programming framework, this code allows an explicit analysis of bi-dimensional structures under dynamic loads, using XFEM. A particular approach concerning the enrichment functions was adopted in order to obtain easily time-dependant solution. Only the Heaviside step function was used and the crack-tip was restricted to cut one element at a time, passing from edge to edge. So, the discontinuous displacement field for a N-nodes mesh, including NÃ enriched nodes, is approximated, using the classical shape functions ) u

h

X

¦

I N

where by

uI

I I  X u I 

I I  X H

¦

I N

I

and the enrichment one H , by:

 X a I

*

(1)

are denoted the classical degrees of freedom and by a I the enriched ones.

A cohesive model is also incorporated in DynaCrack in order to model the material behaviour in the cohesive zone between the mathematical crack-tip (i.e. the point where the crack opening displacement is zero) and the physical crack-tip (i.e. the point of the complete separation of crack faces). The introduction of the numerical crack-tip by this enrichment approach, gives us the possibility to handle with cohesive model parameters in function of the considered material. Adapted to our implementation of XFEM, the dynamic crack evolution model must provide the crack advancing criteria, the propation direction and the crack speed. To answer these questions, the crack evolution model implemented in DynaCrack is based on physical quantities, analytically developed by Freund [4] and used by many authors for various finite-elements based methods for computational fracture. The crack will propagate if at the crack-tip the current energy release rate exceeds a critical limit, given as a material property. For computing the current dynamic energy release rate, the path-independent integral derived by Nishioka and Atluri [5], will be numerically evaluated:

J'

,

I. Nistor et al.

944

J k'

³ >W

@

 U n k  V ij u i , k n j d * 

*  *c

³ U u u i

i ,k

 U u i u i , k dS

S

(3)

where W and U are the strain and kinetic energy densities, surrounding contour * directed away from the crack-tip, *c

n

is the unit normal vector to

*c  *c represents the crack

edges inside of considered contour and S is the area inside of * . The most important feature of the path-independent integral is the invariance of its value with the chosen contour and this allows us to avoid the effects of the non-accurate solution for the closely crack-tip field in XFEM using the far fields for integrating quantities from (3). Another important feature of

J ' -integral

is given by its property to be related to the dynamic stress

intensity factors. The dynamic stress intensity factors are directely extracted from components, using the equations system:

J 1'

A I a K I2  A II a K II2 ; 2P

J 2'



A IV a

P

J'

K I K II (4)

where A I , II , IV a are coefficients depending on the propagation speed crack a and P is the shear modulus. The ratio between K I and K II values, computed at each time step, used in the critical hoop stress criterion relation, gives the crack propagation direction. The crack speed is provided by the numerical propagation algorithm, since the crack-tip advances one edge at a time. Several numerical examples demonstrating the main features of DynaCrack and the computational efficiency of the proposed crack evolution model are presented in the last section of the paper.

References 1.

Moes N., Dolbow J., Belytschko T., A finite element method for crack growth without remeshing, Int. J. Numer. Meth. Engng, vol. 46 (1), 133-150, 1999

2.

Belytschko T., Chen H., Xu J., Zi G., Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment, Int. J. Numer. Meth. Engng, vol. 58, 1873-1905, 2003

3.

Nistor I., Pantale O., Caperaa S. On the modelling of the dynamic crack propagation by Extended Finite Element Method: Numerical implementation in DynELA code, COMPLAS VIII, Barcelona, 2005 (to appear)

4.

Freund L.B., Dynamic Fracture Mechanics, Cambridge University Press, 1998

5.

Nishioka T. and Atluri S.N., On the computation of mixed-mode K-factors for a dynamically propagating crack, using path-independent integrals J’, Engineering Fracture Mechanics, Vol. 20, 193-208, 1984

13. Computational Fracture Mechanics

945

TRUSS MODEL AS SIMPLE COMPUTATIONAL TOOL IN FRACTURE MECHANICS P. G. Papadopoulos, D. Plasatis and P. Lambrou Department of Civil Engineering Aristotle University of Thessaloniki, Greece

[email protected] The usual finite elements have complicated stiffness matrices and present particular difficulties in handling nonlinear problems (Argyris [1]). The bar of a truss is the finite element with the simplest possible local stiffness matrix (Absi [2], Fraternali et al.[3], Papadopoulos and Xenidis [4], Slaich and Schäfer [5]), which can be written, in 2D, as:

(1) where

elastic stiffness,

geometric stiffness, E elasticity modulus, A cross-section area and

undeformed length of the bar. The c = {cx cy} are direction cosines of bar axis, N axial force, present length of the bar and I2 is the unit matrix in 2D. Whereas, the simple global stiffness matrix of a truss can be written: (2) where B = (Bik) i : 1 … n, k : 1 … b is the Boolean linkage matrix of a truss and n, b are the numbers of nodes and bars of the truss, respectively. Bik = -1 if node i is left end of bar k, Bik = +1 if node i is right end of bar k and Bik = 0 if there is no connection between node i and bar k. The cross-section areas A of the bars are determined by considering the correspondence between the stress-strain relations of Elasticity theory and the force-deformation relations of a truss element [2-5]. The bars of the truss model obey nonlinear uniaxial stress-strain – laws [4]. Thus, the whole truss can, in a simply way, describe material nonlinearities. On the other hand, by writing equilibrium equations with respect to the deformed truss and updating the simple stiffness matrix of the truss, within each step of an incremental loading procedure [4], we can, in a simple way, take into account geometric nonlinearities. A short, thus transparent, computer program with only about 250 Fortran instructions has been developed for the nonlinear static analysis of a truss model in 2D, as well as in 3D. The truss model can be proved a simple and useful computational tool in Fracture Mechanics. Applications, by a truss model in 2D, are presented (Fig. 1). A plate with a crack is subjected to uniaxial tension. And the following are clearly observed, in accordance with theory: 1) Stress concentration at the crack, 2) Stress relief above the crack tip, and 3) Far from the crack, the stress field approximates the uniform field of a plate without crack. The formation of plastic zone at the crack tip and the crack propagation are also studied by the truss model, and comparisons are made with other published experimental and computational results.

P. G. Papadopoulos et al.

946

Figure 1. a. A plate, with a crack, subject to uniaxial tension. b. A truss model of one quarter of the plate. c. One quarter of a plate without crack. Deformations, reactions and stresses of the bars in kN/cm2. Uniform stress field. d. One quarter of a plate with crack. Deformations, reactions and stresses of the bars in kN/cm2 near the crack (+tension, -compression).

References 1.

Argyris, J.H., Editor. Fe.No.Mech. (Finite Elements in Nonlinear Mechanics). International Conferences. Institute for Statics and Dynamics. University of Stuttgart, I. 1978, II. 1981, III. 1984.

2.

Absi, E., Calcul Numerique en Elasticite. Eyrolles, Paris, 1978.

3.

Fraternali, F., Angelilo, M., Fortunato, A., A lumped stress method for plane elastic problems and the discrete-continuum approximation. International Journal of Solids and Structures, vol. 39, 6211-6240, 2002.

4.

Papadopoulos, P.G., Xenidis, H.C., A truss model with structural instability for the confinement of concrete columns. Journal of EEE (European Earthquake Engineering), No 2, 57-80, 1999.

5.

Schlaich, J., Schäfer, K., Design and detailing of structural concrete using strut-and-tie models. Structural Engineering, 113-125, 1991.

13. Computational Fracture Mechanics

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FINITE ELEMENT MODELING OF COHESIVE CRACKS BY NITSCHE’S METHOD P. Hansbo and P. Heintz Department of Applied Mechanics Chalmers University of Technology, SE-412 96 Göteborg, Sweden [email protected], [email protected] In [1,2] a new finite element method, based on Nitsche’s method [5], was introduced, allowing for discontinuities, internal to the elements, in the approximation across the interface; a method that can handle both perfectly and imperfectly bonded interfaces without modifications of the code. For the problem of linear elasticity, the case of an internal boundary * over which there was continuity in traction but not necessarily in the displacement field, was studied in [2]. The problem was formulated as seeking the displacement field u and the stress tensor V such that in : 1 ‰ : 2 , in : 1 ‰ : 2 , u

0 on w : ,

 K V ˜ n on

(1) (3)

on * ,

>u @

(1)

(4)

*.

(5)

Here, [u] denotes the jump in the displacement field, n is a unit normal to the interface (its direction being tied to the definition of the jump), and K is a compliancy tensor. The last condition, which is a linear spring-type condition, clearly requires allowing for discontinuities in the displacement field. For this simple model, it can be shown that our method enjoys the usual stability and convergence properties of standard finite element methods. Numerical examples also demonstrated the ability to simulate crack propagation using an oversimplified maximum tensile stress model for deciding the crack propagation direction. In [3], Nitsche’s method was instead combined with the use of material forces for performing more realistic brittle crack propagation simulations. A typical example of brittle crack propagation using the Nitsche approach is given in Figure 1. Notice the refinement at the crack tip, which is necessary for resolving the stresses close to the tip. In this contribution, we extend the method of [2] to the case of cohesive cracks with a softening behavior under loading. The discontinuities are introduced when a failure criterion is met, so that the softening behavior is displayed only by the interface while the continuum is assumed to remain elastic. This is achieved by a cohesive law letting the compliances be functions of the jumps, K=K([u]).

P. Hansbo and P. Heintz

948

FIGURE 1. Brittle crack passing a stiff inclusion. We remark that a similar approach was taken by Mergheim and Steinmann [4], i.e., using elements with internal discontinuities in the spirit of [1,2]. However, in [4] the standard finite element formulation for handling interface springs were used, and the Nitsche framework was avoided. This standard formulation will be badly conditioned in case the springs are extremely stiff (which typically can lead to oscillations in the tractions [5]), and it also enforces a type of on/off behaviour: either an element has cracked or it has not. In contrast, we will use the combined Nitsche/spring formulation of [2] which in one single formulation encompasses the complete scale from full continuity to full discontinuity. This allows us, in a sense, to use elements which are only partially cracked since we can apply the full Nitsche method for the continuous part and the cohesive law for the cracked part of a given element. We will give a background to the method, the formulation for small elastic deformations, and some numerical examples showing the performance of the method.

References 1.

Hansbo A. and Hansbo P., Comput. Methods Appl. Mech. Eng., vol. 191, 5537-5552, 2002.

2.

Hansbo A. and Hansbo P., Comput. Methods Appl. Mech. Eng., vol. 193, 3523-3540, 2004.

3.

Heintz P., Chalmers Finite Element Center Preprint 2005-2.

4.

Mergheim J. and Steinmann P., Int. J. Numer. Methods Eng., vol. 63, 276-289, 2005.

5.

Nitsche J., Abh. Math. Sem. Univ. Hamburg, vol. 36, 9-15, 1971.

6.

Simone A., Comm. Numer. Methods Eng., vol. 20, 465-478, 2004.

13. Computational Fracture Mechanics

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COMPUTING CRACK GROWTH IN QUASIPERIODIC ALLOYS P. M. Mariano and F. L. Stazi Dipartimento di Ingegneria Strutturale e Geotecnica, Universita di Roma "La Sapienza", [email protected], [email protected] A standard crystalline lattice is characterized by periodicity and symmetries described by crystallographic groups. However, there exist strange alloys for which periodicity is violated by their own structure. They are characterized by a prominent influence at a gross level of atomic effects. We may classify three classes of aperiodic - or quasiperiodic - crystalline alloys: (i) The first class is the one of incommensurate modulated crystals (IMC) that can be obtained by primary periodic structures by ‘displacing’ ideal locations of atoms in a way in which the original period of the translational symmetry is incommensurate with respect to the ‘period’ of the modulation. (ii) Incommensurate intergrowth compounds (IIC called also composite crystals) are characterized by the presence of two or more (sub)lattices with periods mutually incommensurate. These sublattices shift reciprocally to try to match one another. (iii) Finally, quasicrystals are intrinsically quasiperiodic and satisfy symmetries forbidden by the classification of crystallographic groups: they may display five-fold, eight-fold, ten-fold symmetries. Let us think of a planar quasicrystal with pentagonal symmetry. From elementary geometry we know that we cannot fill the plane by using only pentagons. So that we are forced to insert here and there topological alterations - i.e. structures different from pentagons - called ‘worms’. Of course, the presence of worms alters periodicity. For all these classes, local rearrangements of atomic clusters occur within each crystalline cell. Such substructural rearrangements have influence on the gross mechanical behavior and the interactions power conjugated with them cannot be neglected. To describe substructural interactions, we follow the general format of multifield theories for complex bodies, so that we start by assigning to each material element a morphological descriptor of the substructural changes within the element itself and call such changes phason activity. For the substructural events occurring in quasiperiodic alloys, a natural descriptor is a vector w attached at each point. Substructural interactions are associated with w and its gradient and satisfy appropriate balance equations. The energetic landscape is different for the three classes of quasiperiodic alloys listed above. IIC and IMC may admit phason kinetics unless structural defects generate a ‘pinning’ effect that bars phason inertia and allows just phason modes of diffusive nature. On the contrary, for quasicrystals, only diffusion phason modes are allowed. The elastic energy depends for IIC and IMC not only on the macroscopic measures of deformation but also on w and its spatial gradient ’ w. The dependence on w is justified because it represents a relative displacement in IIC and IMC. On the contrary, in the case of quasicrystals, the elastic energy does not depend on w but only on ’ w. A unified description of the mechanics of quasiperiodic alloys is available [1]. It is based on a parametrized variational principle of Lagrange-d'Alambert type including dissipative effects due to phason friction always present in quasicrystals and in IMC and IIC when pinning effects occur. When we analyze the behavior of cracks in quasiperiodic alloys, we get modiefied expressions of the J-integral that account for the contribution of substructural interactions due to phason activity and altering the energetic landscape around the tip of the crack as in general occur for microstructures in all cases of complex bodies [2]. Preliminary numerical experiments on quasicrystals, developed in the theoretical limit of vanishing phason friction display unusual phenomena of clustering and self-organization of phonon (the standard deformative ones) and phason modes around the tip of a crack. They influence the crack propagation.

P. M. Mariano and F. L. Stazi

950

Here we develop the issue and analyze the influence of phason modes on the growth of a macroscopic crack. To investigate numerically the topic we cannot make use of standard numerical procedures for crack growth because they are based in part on the knowledge of exact solution for special cases. Here we develop a general procedure that allow us to evaluate directly the vector driving force at the tip of the crack without making use of stress intensity factors. We also find the direction of propagation by means of a maximum dissipation principle. The procedure has general interest for the mechanics of complex bodies but it is also non-standard for simple bodies.

References 1.

Mariano, P. M., Mechanics of quasiperiodic alloys, submitted, 2005.

2.

Mariano, P. M., Proc. Royal Soc. London A, vol. 461, 371-395, 2005.

3.

Mariano, P. M., Stazi, F. L., Augusti, G., Comp. Str., vol. 82, 971-983, 2004.

4.

Mariano, P. M. and Stazi, F. L., Crack growth in periodic and quasiperiodic alloys: computing directly the driving force, in preparation, 2005.

13. Computational Fracture Mechanics

951

X-FEM FOR 3D CRACKS IN SHAFT WITH CONTACT S. Geniaut1,2, P. Massin1 and N. Moes2 1LaMSID, EDF R&D, UMR CNRS-EDF 2832 1, avenue du General de Gaulle, 92141 Clamart, France. 2GeM, ECN/universite de Nantes, UMR CNRS 6183 1, rue de la Noe, 44321 Nantes Cedex 3, France. [email protected], {samuel.geniaut, patrick.massin}@edf.fr Meshing issues in the context of the finite element method (FEM) are often difficult ones to deal with, as in the case of modelling helix-shaped cracks in rotor shafts (Andrier et al. [1]). As a matter of fact, 3D automatic meshing programs often generate a large number of badly-shaped elements which are not reliable and imply ill-conditioned stiffness matrix. Creating an adequate mesh requires a considerable amount of user-time compared to the total computing time and these meshing procedures are relatively costly. Besides, remeshing is necessary at each propagation step. To avoid these difficulties, a recent method named eXtended Finite Element Method (X-FEM) allows one to consider a crack in a unique and simple mesh within the classical framework of the FEM (Moës et al. [2]). The crack, represented explicitly, is independent of the mesh, so the mesh does not need to follow the geometry of the crack faces and remeshing is therefore avoided. Based on the Partition of Unity Method (Melenk and Babuška [3]), X-FEM uses an enrichment of the classical shape functions. To represent displacement discontinuities through the interface, a generalized Heaviside function is introduced. Moreover, adding singular asymptotic fields at the crack tip gives accurate results in linear elastic fracture mechanics. In addition, the level set method (Osher and Sethian [4]) is a convenient way to describe a crack in 3D and propagating a level set is well documented in the literature (Sukumar et al. [5]). As the general framework of finite elements is kept, X-FEM can be easily extended to treat many problems such as cracks with plasticity or hyper-elasticity, which explains the recent wide interest for this new approach. However, to take into account the possible re-closing of the crack, interpenetrability must be prevented. Indeed, surveys of real industrial cases have shown that contact between the crack faces should not be neglected. Mixed method such as the Augmented Lagrangian Method (Alart and Curnier [6]) using both Lagrange multipliers and regularization are well suited to solve that problems. We propose in this paper an X-FEM approach with frictional contact. Few works deal with contact and X-FEM. Among them, Belytschko et al. [7] use Lagrange multipliers to treat a circular inclusion problem in 2D with X-FEM and frictionless contact. Dolbow et al. [8] propose a formulation of the problem of a crack with frictional contact in 2D sharing similar features with the Augmented Lagrangian Method [6] and satisfying alternatively the equilibrium and contact conditions using an iterative scheme. In our extension to small displacements in 3D, we have chosen a framework close to the Augmented Lagrangian Method using an hybrid (displacementpressure) and continuous formulation between two deformable solids for large displacements (Ben Dhia and Zarroug [9]), adapted to X-FEM. To adapt the mixed formulation of the contact problem, the following methodology has been used. From the Lagrangian form of the virtual work principle for two solids in contact, introducing the action-reaction principle, we obtain a simplified expression of the virtual work of contact forces. The hybrid formulation for the contact problem based on pressure unknowns is directly derived, incorporating weak forms of the contact laws. This formulation is well suited for a discretization by the FEM leading to an assembly of elementary terms for contact and friction. Appropriate choices of approximation spaces for the Lagrange multipliers are discussed in terms of

S. Geniaut et al.

952

convergence of the error. The Ladyshenskaja-Babushka-Brezzi (LBB) condition is verified by a numerical test (Chapelle and Bathe [10]). The integration aspects are also studied. Indeed, with XFEM, the crack faces are viewed as a single surface which may cut a finite element. The integration of contact terms on that non-meshed surface calls upon quantities related to the nodes belonging to the elements that are cut by the crack. Besides, one of the main features of contact with X-FEM is that under small displacements assumptions, no contact-nodes searching algorithm is needed, because a geometrical point of the surface can be seen as two physical points, one on each side of the surface. Therefore the displacement jump is expressed in terms of enriched degrees of freedom introduced by X-FEM. An extension of the formulation when large sliding occurs is under investigation. As the FEM framework is preserved, the implementation within the industrial finite elements software Code_Aster developed by EDF did not raise major difficulties linked to the architecture. To date, this method has managed to deal with problem of cracks involving structures with relatively simple geometries, when re-closing of the crack occurs. Once the validation process is satisfied, real industrial cases such as rotors under rotative bending will be investigated. Taking into account large displacements and plasticity at the crack tip is one of the future aims.

References 5.

Andrier B., Garbay E., Hasnaoui F. and Massin P., In Proceedings of the Seventh International Conference on Biaxial/Multiaxial Fatigue and Fracture, Berlin, Germany, 2004, 675-680.

6.

Moes N., Dolbow J. and Belytschko T., Int. J. Numer. Meth. Engng., vol. 46, 131-150, 1999.

7.

Melenk J.M. and Babuska I., Comp. Meth. Appl. Meth. Engng., vol. 139, 286-314, 1996.

8.

Osher S. and Sethian J.A., J. Comput. Phys., vol. 79, 12-49, 1988.

9.

Sukumar N., Chopp D.L., and Moran B., Engng. Frac. Mech., vol. 70, 29-48, 2003.

10. Alart P. and Curnier A., Comp. Meth. Appl. Meth. Engng., vol. 92, 353-375, 1991. 11. Belytschko T., Moës N., Usui S. and Parimi C., Int. J. Numer. Meth. Engng., vol. 50, 9931013, 2001. 12. Dolbow J., Moes N. and Belytschko T., Comp. Meth. Appl. Meth. Engng., vol. 190, 68256846, 2001. 13. Ben Dhia H. and Zarroug M., Revue Européenne des Elements Finis, vol. 9, 417-430, 2002 14. Chapelle D. and Bathe K.J., Comput. & Struct., vol. 47, 537-545, 1993.

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SOME IMPROVEMENTS FOR EXTENDED FINITE ELEMENT METHODS IN FRACTURE MECHANICS Patrick Laborde1, Julien Pommier2, Yves Renard2 and Michel Salaun3 1MIP, UPS Toulouse 3, 118 route de Narbonne, 31062 TOULOUSE cedex 4, France 2MIP, CNRS UMR 5640, INSA de Toulouse, 31077 Toulouse, France 3ENSICA, 1 pl. Emile Blouin, 31056 Toulouse cedex 5 [email protected], [email protected], [email protected], [email protected] Computer simulation of fracture processes remains a challenge for many industrial modelling problems. In a classical finite element method, the non-smooth displacement near the crack tip is captured by refining the mesh locally. The number of degrees of freedom may drastically increase, especially in three dimensional applications. Moreover, the incremental computation of a crack growth needs frequent remeshings. Reprojecting the solution on the updated mesh is not only a costly operation but also it may have a troublesome impact on the quality of results. In the last few years, Moës, Dolbow and Belytschko [1] introduced a numerical methodology which has been developed by the name of XFEM - eXtended Finite Element Method. Not only finite elements are enriched with the asymptotic crack tip displacement solutions, but also with a step function which takes into account the jump of the displacement across the crack. Then, the finite element mesh can be defined independently of the crack geometry. The partition of unity chosen to localize the enrichment functions is linked to the mesh and is generally defined using linear shape functions. An advantage of the XFEM method is to obtain more accurate numerical results than classical finite element one. However, the rate of convergence is not optimal with respect to the mesh parameter h and is independent of the degree of the finite element method (see Fig. 1, and [2]).

In the classical XFEM method, only the nodes the nearest to the crack tip are enriched; consequently the support of the additional basis functions vanishes when h goes to zero. So we propose to enrich a whole fixed area around the crack tip independently of h. The expected optimal rate of convergence is nearly reached. But the condition number of the linear system and the number of unknowns increase. A bonding condition is introduced on the enrichment area around the crack tip: for each singular shape function, the equality of the corresponding degrees of freedom is prescribed. Doing

P. Laborde et al.

954

so, the numerical tests show an important lake of optimality. A simple analysis shows that this is due to the transition layer between the enriched area and the rest of domain (see [3]). To overcome it, we propose a nodal matching condition at the interface. Numerical tests show that the optimal convergence rate is then obtained (see Fig. 2) even for high-order polynomial functions. These tests concern bidimensional plate using degree one, two and three polynomial finite element methods on triangular meshes with the Getfem++ [4] library.

References 1.

Moes, N, Dolbow, J, and Belytschko, T., A finite element method for crack growth without remeshing, Int. J. Numer. Meth. Engng., 46:131--150, 1999.

2.

Stazi, F.L., Budyn, E, Chessa, J, Belytschko, T, An extended finite element method with higher-order elements for curved cracks, Computational Mechanics, 31:38--48, 2003.

3.

Laborde, P, Pommier, J, Renard, Y, Salaün, M, High order extended finite element method for cracked domains, to appear in Int. J. Numer. Meth. Engng.

4.

Pommier, J, Renard, Y, Getfem++, An open source generic C++ library for finite element methods. http://www-gmm.insa-toulouse.fr/getfem

14. Cohesive Models of Fracture

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FAILURE PREDICTION OF ADHESIVELY BONDED T-PEEL JOINTS A. Pirondi Department of Industrial Engineering, University of Parma Parco Area delle Scienze, 181/A - 43100 Parma, Italy [email protected] Adhesive joining can offer significant advantages over traditional joining methods such as welding or mechanical fastening in structural applications. Automotive and aerospace industries are important examples. Joint fabrication procedures and component service loads may introduce or initiate defects, whose evolution will control the performance and the reliability of the bonded joint. In those cases, Fracture Mechanics (FM) can be used to assess the structural integrity of a bonded joint [1]. The FM approach consists in the comparison of a parameter, function of load and geometry of the cracked body (for example the strain energy release rate, G), with the fracture resistance (Gc). The simulation of fracture therefore requires to implement a criterion that triggers propagation when G=Gc. An attractive way to simulate the effect of a defect on joint strength is to incorporate a model of the rupture process (i.e. the criterion to trigger propagation). In particular, the fracture of bonded joints has been successfully simulated using the Cohesive Zone Model (CZM) in [2-7]. In this work, CZM was used to simulate failure of T-peel bonded joints (Fig. 1) with 1.5 and 3mm thick adherends, respectively, bonded toghether with Loctite Multibond 330 adhesive [8]. The fracture toughness and load-opening behaviour recorded in previous experiments on bonded DCB specimens [9] were taken as reference to calibrate CZM parameters.

FIGURE 1. Outline of half of the 1,5mm-thick T-peel joint tested in [8]. Two-dimensional and three-dimensional models were analysed using the FE code ABAQUS. The failing interface was modeled with the cohesive elements available in this software. The influence of: i) different cohesive law shapes, ii) elasto-plastic adherend behaviour, iii) modeling the presence of the adhesive layer explicitly, was studied. The results obtained with cohesive elements were initially compared with the corresponding ones obtained in a previous work [10] where the adhesive layer was modeled with a series of non-linear springs attached to the interface nodes of the cantilever (Fig. 2).

A. Pirondi

956

FIGURE 2. Comparison between load-displacement plots obtained modelling the adhesive layer with nonlinear springs [10] and with cohesive elements.

References 1.

Kinloch, A.J., Adhesion and Adhesives, Chapman and Hall, London, UK, 1986.

2.

Hutchinson, J.W., Evans, A.G., Acta Mater., 48, 125-135, 2000.

3.

Mohammed, I., Liechti, K.M., J. Mech. Phys. Solids, Vol. 48, 735-764, 2000.

4.

Yang, Q.D., Thouless, M.D., Ward, S.M., J. Mech. Phys. Solids, Vol. 47, 1337-1353, 1999.

5.

Knauss, W.G., Losi, G.U., J. Appl. Mech., Vol. 60, 793-801, 1993.

6.

Hadavinia, H., Kinloch, A.J., Williams, J.G., In Adv. in Fract. and Damage Mech. II, M. Guagliano and M.H. Aliabadi eds., Hoggar, Geneva, 2001, 445-450.

7.

Sorensen, B.F., Acta Mater., 50, 1053-1061, 2002.

8.

Rossetto, M., Private communication, Polytechnic of Turin, Turin, Italy, 2003.

9.

Pirondi, A., Nicoletto, G., In Proc. IGF 2000, Bari, Italy, 2000.

10. Pirondi, A., In Proc. ECF 15, Stockolm, Sweden, 2004.

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AN APPROACH FOR THE DETERMINATION OF MIXED MODE COHESIVE LAWS B. F. Sorensen and T. K. Jacobsen Materials Research Department, Riso National Laboratory 4000 Roskilde, Denmark, [email protected] R & D Department, LM Glasfiber A/S Rolles Møllevej 1 ,6640 Lunderskov, Denmark, [email protected] Prediction of failure of structures and materials remains an important topic in engineering design. In that respect, cohesive laws, describing the mechanical behaviour of a failure process zone, have shown to be useful tools in numerical simulation of crack growth [1], in particular in structures in which large-scale bridging develops [2]. The modelling has been rather advanced and is now reasonably well established. However, the determination of cohesive laws, which in most case can be regarded as material properties [3], still remains an unresolved issue. This is particular true for mixed mode cracking. Mixed mode cohesive laws are sometimes interpolated from measurements of pure mode I and pure mode II tests [4]. Furthermore, the normal stress is often assumed to depend on the normal crack opening, but not on the tangential crack opening displacements. It is difficult to evaluate the validity of such assumptions. The present study aims at the development of an approach for the determination of mixed mode cohesive laws. Special attention is devoted to large-scale bridging, since for such problems, linear-elastic fracture mechanics solutions are invalid. The suggested approach is therefore based on the path-independent J integral. A special test specimen, a double cantilever beam specimen loaded with pure bending moments (DCB-UBM) is used, since, the J integral can be determined in closed analytical form also under large-scale bridging for this test configuration:

J

1  Q 21M 2

2 1



 M 22  6 M 1 M 2 4B 2 H 3 E ,

(1)

here M1 and M2 denote the applied bending moments (positive signs are shown in Fig. 1), E and Q denotes the Young's modulus and the Poisson's ratio, B is the specimen width and H is the beam height. For plane stress, the terms 1-Q2 should be replaced by unity. The DCB-UBM specimen is shown schematically in Fig. 1.

FIGURE 1. Double cantilever beam specimen loaded with uneven bending moments.

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Assuming that the cohesive stresses are derivable from a displacement potential [5], mixed mode cohesive laws can be determined:

V n G n* , G t*



wJ R G n* , G t* wG n*



V t G n* , G t*



wJ R G n* , G t* wG t*

(2)

* * are the normal and shear stress, respectively, while JR, G n and G t are the fracture resistance (the value of the J integral), the normal and tangential opening at the end of the cohesive zone, see Fig. 1. It follows from (2) that mixed mode cohesive laws can be derived by

where

Vn

and

Vt

* simultaneous measurements of JR, G n* and G t . That is the key idea.

Here we present theoretical basic for the approach. Furthermore, the practical implementation of a DCB-UBM test fixture will be described. The approach will be illustrated for the problem of delamination of unidirectional fibre composites. This is a mixed mode cracking problem involving large-scale bridging. It is found, that the normal stress and shear stress both depend on both the normal and the tangential crack opening displacements.

References 1.

Tvergaard, V., and Hutchinson, J. W., J. Mech. Phys. Solids., vol. 41, 1119-35, 1993.

2.

Bao, G. and Suo, Z., 1992, Applied Mech. Rev., vol. 45, 355-61, 1992.

3.

Cox, B. N., and Marshall, D. B., Int. J. Fracture, Vol. 49, 59-76, 1991.

4.

Yang, Q. D. and Thouless, M. D., Int. J. Fracture, vol. 110, 175-87, 2001.

5.

Suo, Z., Bao, G., and Fan, B., J. Mech. Phys. Solids., Vol. 40, pp. 1-16, 1992.

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THE USE OF CZM FOR COUPLED FATIGUE/PLASTICITY CRACK PROPAGATION SIMULATION Jl. Bouvard, F. Feyel and Jl. Chaboche ONERA, DMSE-LCME 29 av de la Division Leclerc, BP72,92322 CHATILLON cedex France [email protected] In blading components, a large proportion of service life is taken up in initiating and growing surface or near surface short cracks through the Stage I fatigue regime, that is when the crack length is small compared to the scale of the crack tip plasticity. Such fatigue cracks driven by mechanical and thermal stresses can lead to the catastrophic failure of a component. This is why short cracks growth in Ni-base superalloys has received considerable attention. The main objective of this work is to develop refined mechanistic modelling techniques for the coupling between oxidation, local inelastic behaviour and fatigue crack propagation, using cohesive law formulations. A cohesive zone method is a numerical tool developed for the mechanics of interfaces, that was initially proposed to model crack initiation and growth. This method treats fracture as a gradual process in which separation between incipient material surfaces is resisted by cohesive traction. Its constitutive behaviour is specified through a relation between the relative opening displacement U and a corresponding traction T at the same location, with being either the local normal (n) or tangential (t) direction in the cohesive zone plane for 2D example. We focused here to present a cohesive zone model that incorporates the energy released at the crack tip, as well as closure effects induced by oxidation and cyclic plasticity/creep. We developed there an hybrid formulation that incorporates the traditional fracture mechanics approach in the framework of advanced damage mechanics concept. Many cohesive models have been proposed under monotonic loading but these cohesive laws are not able to model crack growth under cyclic loading. Consequently, for a structure, subjected to constant amplitude loading, shake down and crack arrest would be automatically predicted due to the stress fields redistribution and accommodation. A specific damage law with time dependency will be then developed to simulate the crack growth and to account for the different phenomena induced by the plasticity at crack tip[1-3]. The response of the analytical model under cyclic loading can be observed in Fig. 1. We can notice that the damage increases during loading and remains constant during unloading. We give in Fig. 2. the results concerning the use of this damage law in the case of a structure (a smooth specimen with a precracking) considering a single crystal material.

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FIGURE 1. description of the damage law.

FIGURE 2. : plastic strain and Von Mises fields at crack tip.

References 1.

De-Andres and al., “Elastoplastic finite element analysis of three-dimensional fatigue crack growth in aluminium shaft subjected to axial loading”, Int. J. Of Solids And Struct., pp. 22312258,1999.

2.

Nguyen and al., “A cohesive model of fatigue crack growth”, Int. J. Of Fract., pp. 351-369, 2001.

3.

Yang and al., “A cohesive zone model for fatigue crack growth in quasibrittle materials”, Int. J. Of Solids And Struct., pp. 3927-3944, 2001.

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DYNAMIC CRACK GROWTH : ANALYTICAL AND NUMERICAL CZM APPROACHES G. Debruyne, J. Laverne and P.E. Dumouchel1 EDF R&D LaMSID, 1 av du Général de Gaulle 92141 CLAMART, France 1LMM-UPMC, Paris VI University , 4 place Jussieu case 162, 75252 PARIS Cedex 5, France [email protected], [email protected], [email protected] I. Industrial motivations. Service life extension of PWR vessels is an important issue for a number of nuclear operators. This aim is partially subjected to improvement of safety margins. These margins may be enhanced by acceptance of a limited amount of crack growth, starting from an initial flaw. It is therefore necessary to predict not only the crack initiation but also the crack arrest. It is also of great interest to compare dynamic and static analysis and to know if quasi-static prediction is a conservative way or not. Analytical investigations for actual structures are rather complex to carry on. An academic problem theoretical analysis is therefore useful, in a first step, to understand the different features of dynamic crack propagation and arrest. Moreover, numerical investigations may usefully complete the analysis. II. Problem statement. The peeling of a thin film bonded on a rigid surface (cf fig 1.a) is a good example to check such features. This problem has been analyzed in a dynamic way by Freund (1989) with a Griffith criterion. It is revisited here with some slightly different conditions, where the film exhibits some weak toughness zones and activates, during the peeling process, a surface energy described by a Griffith or a Dugdale-Barenblatt model (cf fig 1.b). The analytical results are compared with a finite element model using cohesive zones.

The inextensible film is initially completely bonded and tighted by a tension force. A small deflection is then performed (with prescribed force or displacement) to one boundary, which leads to the film debonding. The toughness all along the bonded surface is uniform, except on a weak zone where a toughness jump arises. III. Analytical investigation. The 1D peeling problem is analytically performed with several configurations : displacement or force control, Griffith or Dugdale debonding criterion, and several toughness zones distributions. Dynamic and static investigations are both carried on (cf Fig 2.a and 2.b). Theoretical

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backgrounds to settle the main problem equations, starting from Hamiltonian principle, are briefly outlined. Fields solutions are completely described and waves fronts (including debonding zone) are exhibited.

IV. Numerical approach with CZM. Following the ideas presented in Francfort and Marigo [1], we assume that the fracture of a brittle body is governed by a principle of least energy. The total energy of a loaded structure is the sum of its (elastic) strain energy and its surface energy defined on its discontinuity surface, minus the potential of the dead loads (when forces are prescribed). The CZM relation between the density of the surface energy and the jumps displacement is taken as a exponential (Barenblatt-type) or a linear (Dugdale-type) function of the jump displacement. Two specifics finite element are used, lying on a know crack path (cf Laverne [3]). The first one is an interface element where the jumps are defined as linear functions of the nodal displacements. The second one is a finite element with an embedded discontinuity, taken into account by enhanced terms for displacements and strains. The previous academic 1D problem is now extended to a most realistic plane strain configuration simulating the Double Cantilever Beam test. The initial flaw is blunted so that the crack onset velocity is controlled by the bluntness parameter. Wave absorbing conditions are prescribed on longitudinal boundaries to roughly fit in with the film problem. In order to analyze the effects of wave reflections to crack kinematics, these conditions are released and a numerical investigation is carried out. The infuence of the following parameters is considered : cohesive law shape, including or not loading rate dependence, crack bluntness, interface or embedded discontinuity element, weak toughness zones.

References 1.

Francfort, G.A. & Marigo, J. -J., J. Mech. Phys. Solids, vol. 46(2), 1319-1342, 1998.

2.

Freund L. B., Dynamic Fracture mechanics, Cambridge Monographs on Mechanics and Applied Mathematics.

3.

Laverne J. Thèse de l’université Paris 13, 2004.

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SIMULATION OF PRE-CRITICAL CRACKING IN CONCRETE USING 3D LATTICE MODEL H.-K. Man and J. G. M. van Mier Swiss Federal Institute of Technology (ETH) Zurich, Institute for Building Materials ETH Hönggerberg, CH-8093 Zürich, Switzerland [email protected], [email protected] In this paper a discrete three-dimensional computational model of plain concrete structures at meso-level is used to simulate fracture experiments and to analyse cracking in the pre-critical stage. In the past and the present many different computational approaches at meso-level have been developed with the goal to study the mechanical behaviour of concrete, i.e. to simulate and to understand fracture, either using the discrete or the continuum modelling approach, mostly done in two-dimensions. In the used lattice model, the continuum is replaced by a network of beam elements. Derived from the statistical physics, it is a simple and efficient tool for understanding the fracture behaviour of brittle heterogeneous solids such as concrete. Fracture is simulated by a sequential removal of elements in each loading step, and gives insight and understanding into the fracture behaviour. In the past these kinds of simulations have been conducted in two dimensions, but recently the model has been successfully generalized to three dimensions which, in terms of fracture processes, is more realistic, see Lilliu and van Mier [1], Lingen [2]. As case study prisms subjected to displacement-controlled three-point bending fracture experiments will be simulated and analysed. For this purpose three-dimensional (triangular regular and random) lattice models are developed. For constructing 3D lattices, an alternative method will be introduced. This approach is a simple, but an efficient way to generate random 3D lattices. For simulating fracture experiments at the meso-level the material properties of concrete as a three-phase material (matrix, aggregate and interfacial transition zone) have to be considered and they are included into the lattice. In the present study various numerical experiments are concucted and the following parameter variations are studied; •

scaling of specimen size by maintaining the same particle structure and

•

the variation of thickness (full 3D-scaling).

A new method is introduced to find out where cracks preferably emerge. Analyses are conducted mainly during microcracking stage (on a typical load-displacement diagram of concrete it is the stage between the linear response and maximum load). Based on these investigations and the analysis of several parameters and distributions, it is possible to make predictions and explains where cracks nucleates, and how (why) fracture propagates.

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FIGURE 1. Boundary conditions and crack patterns of a three-point bend specimen, generated with a 3D random lattice (the green color indicates cracking).

References 1.

Lilliu, G., van Mier, J.G.M., Engineering Fracture Mechanics, vol. 70, 927-941, 2003.

2.

Lingen, F.J., Design of an Object Oriented Finite Element Package for Parallel Computers, PhD Thesis, Delft University of Technology, The Netherlands, 2000.

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EFFECT OF COHESIVE LAW AND TRIAXIALITY DEPENDENCE OF COHESIVE PARAMETERS IN DUCTILE TEARING I. Scheider1, F. Hachez2 and W. Brocks1 1GKSS Research Centre Geesthacht, Max-Planck-St. 1, D-21502 Geesthacht 2PCIM, Université Catholique de Louvain, Place Saint Barbe 2, B-1348 Louvain-la-neuve [email protected] The cohesive model has been introduced for numerical crack propagation analyses of ductile materials almost thirty years ago [1]. The two parameters of the cohesive model, the cohesive stress, 0, and the cohesive energy, 0, can be explained on a physical basis and determined by experiments [2]. However, up to now almost no literature exist about a metallurgical or micromechanical basis for the shape of the constitutive law c(), called traction-separation law (TSL) with being the material separation, and therefore many different shape functions are given in literature instead [3]. On the other hand, it has been proven that the shape of the TSL may have a significant effect on the result of the crack propagation analysis [4]. The present paper addresses the effect of the shape of the TSL without considering micromechanical phenomena. For an illustration of the problem, two different fracture specimens, namely a C(T) and an M(T) specimen, are simulated using two different traction-separation laws. One is a widely used cubic polynomial shape (e.g. [1]), the other obeys a function with a high initial stiffness and a wide region with constant stress [5]. Both functions are shown in Fig. 1.

FIGURE 1. Functions of two different traction-separation laws. The cohesive energy, *0, is equal for both functions. The material under consideration has the following elastic-plastic parameters: E = 210000 MPa, Q = 0.3, Y = 300 MPa, n = 10 (power hardening material law). The cohesive parameters are 0 = 1000 MPa and 0 = 100 kJ/m². The decreasing part of the TSL with constant stress starts at a separation of 75% of the critical separation 0. The results of the crack propagation analyses are displayed in Fig. 2, showing that the crack resistance is highest with the constant stress function for both the C(T) and the M(T) specimen. Obviously, the cohesive parameters cannot be chosen independently of the TSL. If the given parameter set is assigned to the polynomial law, then the corresponding parameters for any other function must be fitted in order to give the same global response for the C(T) specimen. Consequently, simulations of the behaviour of an M(T) specimen using both TSLs with the respective parameters are expected to result in an identical load-displacement curve. It turns out that the parameters for the constant stress function have to be modified significantly to reproduce the load-displacement curve, namely 0 = 824 MPa and *0 = 120 kJ/m². The results are also shown

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in Fig. 2a. In a second step, the M(T) specimen behaviour has been simulated with this parameter set to check whether the load-displacement curve obtained by applying the polynomial law is reproduced by the constant stress function with the modified parameters. As can be seen in Fig. 2b, this is not possible. The load-deformation curve calculated with the constant stress function is significantly below the results obtained by the polynomial function.

FIGURE 2. Reproduction of the results achieved by the polynomial law with modified parameters of the constant stress function. a) Parameter fitting using the C(T) specimen, b) Results of the M(T) specimen with the fitted parameters. As this result puts the transferability of the cohesive parameters into question, experimental validations are necessary, since no decision can be made about the “correct” traction-separation law. Additional improvements are expected, if the local triaxiality is taken into account and the cohesive parameters made dependent on this value, as studied in [6].

References 1.

Needleman, A., J. Appl. Mech., vol. 54, 525-531, 1987

2.

Cornec, A., Scheider, I. and Schwalbe, K.-H., Eng. Fract. Mech., 70, 1963-1987, 2003

3.

Brocks, W., Cornec, A. and Scheider, I., In: Comprehensive Structural Integrity. Edited by I. Milne, R.O. Ritchie, B. Karihaloo, 2003, Elsevier, Amsterdam, 127-209.

4.

Scheider, I. and Brocks, W., Key Eng. Mat., vols. 251-252, 313-318, 2003

5.

Scheider, I., In First M.I.T. Conf. on Comp. Fluid and Solid Mech., edited by K.J. Bathe, Elsevier, Amsterdam, 2001, 460-462

6.

Brocks, W. and Siegmund, T., Int. J. Fract., vol. 99, 97-116, 1999

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MODELING QUASIBRITTLE MATERIAL CRACKING WITH COHESIVE CRACKS: EXPERIMENTAL AND COMPUTATIONAL ADVANCES J. Planas, J. M. Sancho, A. M. Fathy, D. A. Cendon and J. C. Galvez Universidad Politécnica de Madrid ETS de Ingenieros de Caminos, Canales y Puertos, Profesor Aranguren sn, 28040 Madrid, Spain. [email protected], [email protected], [email protected], [email protected], [email protected]. Fracture processes in concrete and other quasibrittle materials can be realistically described by means of the cohesive crack model which, as introduced by Hillerborg in his celebrated fictitious crack model, can be viewed as a constitutive assumption for the fracturing behavior of the material [1]. The present paper discusses two important aspects concerning the application of the cohesive crack to practical problems. The first aspect is the experimental determination of the cohesive law, which is necessary to make accurate predictions; the second aspect is the computational procedure to use to carry out the predictions. Recent improvements of the test procedure developed in [2] for concrete are presented, which are currently being considered for standardization by ACI Committee 446, and an improved experimental setup is described together with various series of tests. The method relies on the combination of results from diagonal compression splitting tests and three-point bending tests on notched beams. Closed-form formulas are given to carry out the inverse analysis of the tests to compute a bilinear approximation of the cohesive law. The influence of the shape of the stress vs. crack opening curve on the test reliability is discussed in terms of the brittleness of the specimen, and limits on the specimen size for other quasibrittle materials are deduced. The paper next addresses the computational aspects of the practical application of the cohesive crack model. Recent improvements of the method developed in [3] are described that show that classical finite elements with embedded cohesive cracks can be formulated that provide a robust method for cohesive crack growth analysis while keeping the implementation simple (i.e. any finite element code accepting user-defined finite elements can be used). Contrary to other strong discontinuity approaches (SDA) the proposed method does not require enforcing crack path continuity (crack tracing or tracking) or defining exclusion zones. Such numerical resorts are required, respectively, to avoid crack locking and to prevent cracking of elements close to a main cohesive crack. The proposed method combines simple features such as 1

constant strain elements which incorporate a) strong discontinuity kinematics and b)local crack equilibrium (strong form of equilibrium condition),

which implies that the stiffness matrix is, in general, non symmetric (SKON formulation according to Jirásek’s classification [4]---static and kinematically optimal nonsymmetrical). 2

cohesive models with simple formulation based on a)central-force law (crack traction vector parallel to the relative displacement of crack

faces)

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b)damage-like behavior (unloading to the origin) and c)Rankine criterion for crack initiation and crack orientation. The approach further incorporates two basic ingredients that proved essential to avoid crack locking and spurious cracking: 3

the crack location in the finite element is selected to minimize the asymmetry of the tangent stiffness matrix of the element (the crack does not go through the centre of gravity of the element), and

4

the crack is allowed limited adaptability, which means that the crack is allowed to reorient itself according to rotation of the stress axes, but only as long as the cohesive crack opening is small: after a threshold crack opening is reached, the crack orientation is kept constant.

Evidence is provided that shows that the method leads to mesh insensitive results, free from mesh bias effects, and to robust behavior, both in 2D and in 3D cases. The effect of the various ingredients of the model are evaluated and it is shown that the combination of central forces and crack adaptation is essential for good performance.

References 1.

Planas, J., Elices, M., Guinea, G. V., Gómez, F. J., Cendón, D. A. and Arbilla, I. Engineering Fracture Mechanics, vol. 70(14), 1759-1776, 2003.

2.

Planas, J., Guinea, G.V., and Elices, M., International Journal of Fracture, vol. 95, 367-378, 1999.

3.

Sancho, J.M., Planas, J. and Cendón, D.A., In Fracture Mechanics of Concrete Structures, edited by V.C. Li et al., Ia-FraMCoS, 2004, 107-114.

4.

Jirásek, M. International Journal of Solids and Structures, 35, 4133-4145, 1998.

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PINWHEEL MESHES AND BRANCHING OF COHESIVE CRACKS P. Ganguly and K. D. Papoulia Department of Theoretical and Applied Mechanics and School of Civil and Environmental Engineering Cornell University Ithaca NY 14853, USA [email protected] We consider the use of cohesive interface models in a dynamic finite element setting to simulate crack branching under mode-I loading conditions as performed in an experiment by Sharon et al. [1] (Figure 1.)

Figure 1. Experimental setup We follow the approach of implementing the cohesive interface law in a zero thickness cohesive interface finite element positioned along bulk element edges. Since in this problem the crack pattern is not known in advance, the possibility of prepositioning cohesive surfaces is precluded and every edge of the bulk elements is considered as a potential fracture surface. The crack propagation path can then be resolved as part of the solution of the governing equations. We use an adaptive approach in which cohesive surfaces are only inserted when they are needed, i.e., the effective initial stiffness of the cohesive model is infinite. We denote this type of model as initially rigid. Special considerations in its finite element implementation are essential to its numerical behavior. It was pointed out by Papoulia et al. [4] and Sam et al. [5] that in explicit dynamics using a rigid model, the correct time convergence rate can be obtained only if the condition that the nodal forces be continuous at the moment of activation is satisfied. We use a scaled down version of the above experiment [2, 3] to reduce the number of degrees of freedom. A pinwheel mesh [6] is used to triangulate the domain with 8 mesh edges resolving the cohesive zone. The simulations are performed for various initial stretches as shown in Figure 2. A mesh-shape parameter was varied to measure the mesh dependence of the crack path. Dependence of crack path on this parameter should decrease for finer meshes. Our numerical simulations validate this result and further suggest that the crack path computed in the pinwheel mesh is more stable as the mesh is refined compared to a structured mesh which is used in [2].

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Figure 2. Crack branching simulations for different initial strains.

References 1.

Sharon, E. and Fineberg, J., Microbranching instability and the dynamic fracture of brittle materials, Physical Review B, 54(10):7128-7139, 1996.

2.

Zhang, Z. and Paulino G. H., Extrinsic cohesive modeling of dynamic fracture and microbranching instability in brittle materials. Unpublished.

3.

Miller, O., Freund, L. B. and Needleman, A., Energy dissipation in dynamic fracture of brittle materials. Modeling and Simulation in Material Science and Engineering, 7, 573-586, 1999.

4.

Papoulia, K. D., C.-H. Sam and S. A. Vavasis, Time continuity in cohesive finite element modeling, Int. J. Num. Methods. Eng., 58(5): 679-701, 2003.

5.

Sam, C.-H., K. D. Papoulia and S. A. Vavasis, Obtaining initially rigid cohesive finite element models that are temporally convergent, Eng Frac Mech, 72(14): 2247-2267, 2005.

6.

Ganguly, P., S. A. Vavasis and K. D. Papoulia, An algorithm for two-dimensional mesh generation based on the pinwheel tiling, SIAM J. Scientific Computing, in press.

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A DYNAMIC CRACK GROWTH SIMULATION USING COHESIVE ELEMENTS M. Anvari and C. Thaulow Department of Engineering Design and Materials, NTNU Richard Birkelandsvei 2B, 7491 Trondheim, Norway [email protected] [email protected] Rate sensitive and triaxiality dependent cohesive elements are used to simulate ductile crack growth under quasi static and dynamic loading conditions. A number of finite element analyses are performed for a center-cracked specimen made of aluminum alloy (6XXX-series). Loaddisplacement curves for different cases and considerations are presented and the results are discussed. The analyses show that, for a cracked specimen, ignoring material rate dependency can consequence to quite high energy absorption predictions. When the speed of loading on a structure is high, four additional influences on ductility compared to quasi-static cases have to be taken into consideration as addresses by El-Magd and Brodmann [1]: rate dependent plasticity, adiabatic heating, mass inertia, and decrease of local failure strain. In finite element representation of cohesive zone modeling (CZM), failure happens in cohesive elements which are defined as interface elements between undamaged continuum elements. The stress in the cohesive elements is controlled by a separation dependent law, named traction separation law (TSL). The TSL used in simulating ductile fracture is meant to represent the process of void initiation, growth and coalescence. The idea of the present contribution is to obtain it by studying the stress-elongation response of a single element obeying Gurson type constitutive equation [2]. TSL generally consists of cohesion and decohesion parts. The opening at which a cohesive element fails totally is called critical separation, G0, and is one of the fracture parameters. The other parameter is the maximum traction or cohesive strength, S. The area under the TSL is the energy absorbed by the cohesive element, *0 and is known as the cohesive energy: *0

³

G0

0

T G dG

(1)

Among the aforementioned phenomena that are important in dynamic fracture, the effect of strain rate on damage has been considered in the present article. To consider the effect of strain rate on cohesive element properties, a single plane strain Gurson type element (unit cell) has been loaded under variety of strain rates. A rate dependent version of the model known as “complete Gurson model” developed by Zhang et al. [3] has been used. It has been mentioned by variety of authors, e.g. Hancock and Mackenzie [4] and Brocks et al. [5], that stress state, for example stress triaxiality, influences the mechanical response of ductile materials. Therefore, the effect of stress triaxiality on TSL has been examined by applying different values of constant stress biaxialities on the unit cell, too. In all the cases, the variation of maximum traction and the energy absorbed are investigated. These values are considered as cohesive strength and cohesive energy as functions of stress triaxiality and strain rate. The results are then used for crack growth simulations of the aluminum M(T) specimen. Since the measures of strain rate and stress triaxiality are not available in the cohesive elements, they are calculated automatically from the adjacent continuum elements and transferred to them. In the beginning of each calculation, the cohesive parameters are adjusted to the values transferred. Both quasi-static and transient dynamic analyses are performed and the load-displacement curves are obtained in different cases.

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It is shown that cohesive elements have the potential of performing ductile crack growth simulation not only in static cases, but also in high speed dynamic loading. The cohesive model presented can be used for both small and large scale yielding and takes effects of different strain rates and triaxialities into account. Unloading at the crack tip, which happens because of stress waves, has been implemented by irreversible separation behaviour of the cohesive elements. The results of the analyses show that generally, ignoring constraint or local strain rate on TSL makes the analysis underestimate the toughness. The toughness of the structure increases under dynamic loading because of the inertia and strain rate sensitivity, but for a cracked specimen, ignoring rate sensitivity of material in high speed of loadings can lead to quite high energy absorption predictions. Depending on the load speed, material properties, the structure dimensions and the crack length, the effect of phenomena like elastic waves, strain rate, adiabatic heating and inertia forces might be different.

References 1.

El-Magd, E. and Brodmann, M., Mat. Sci. Eng. A, vol. 307, 143-150, 2001

2.

Gurson, J., J. Eng. Mat. Tech., vol. 99, 2-15, 1977

3.

Zhang, Z.L., Thaulow, C. and Ødegård, J., Eng. Fract. Mech., vol. 67, 155-168, 2000

4.

Hancock, J.W. and Mackenzie, A.C., J. Mech. Phys. Solids, vol. 24, 147-169, 1976

5.

Brocks, W., Sun, D.Z. and Honig A., Int. J. Plast., vol. 11, 971-989, 1995

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A NEW COHESIVE ZONE MODEL FOR MIXED-MODE DECOHESION M. J. van den Bosch , P. J. G. Schreurs and M. G. D. Geers Netherlands Institute for Metals Research (NIMR), Delft, The Netherlands Eindhoven University of Technology, Eindhoven, The Netherlands Dep. of Mech. Eng., Eindhoven University of Technology, The Netherlands [email protected] This paper focuses on the frequently adopted exponential cohesive zone law of Xu and Needleman (Xu and Needleman [1]). In spite of its wide applicability, this cohesive zone law gives an unrealistic physical response under most mixed-mode loading conditions. This conclusion is based on investigations of the influence of the coupling parameters and the assessment of the dissipated energy under mixed-mode loading conditions. One of the assessment methods is to firstly load the cohesive zone in normal direction until 'n,max. At that time an energy Wn has been dissipated. The second step is to break it completely in tangential direction by shearing it until 't >> Gt. In the second step an energy Wt has been dissipated, resulting in a total dissipated energy of Wtot (= Wn + Wt). The loading sequence is shown in Fig. 1.

FIGURE 1. Loading sequence of a cohesive zone. Step 1: load the cohesive zone in normal direction until ' n  ' n, max and subsequently break it in shear: ' t !!G t .

Tn and Tt are the tractions in normal and tangential direction respectively. The tractions are a function of both the normalized normal and tangential opening displacements 'n/Gn and 't/Gt. Where Gn and Gt are characteristic lengths. The initial areas under the curves represent the normal and tangential work-of-separation: In and It. The shaded areas in Fig. 1 represent the energies dissipated after loading in normal and tangential direction: Wn and Wt. The total dissipated energy as a function of 'n,max is depicted in Fig. 2a for the exponential cohesive zone law of Xu and Needleman. The required energy to break the cohesive zone has a minimum, which is not likely to occur unless specific experimentally verified mechanisms in the interface have proven to lead to this kind of behavior. Remedies for this physical problem are not yet available in literature. Thus, a modified exponential cohesive zone law, based on the law of Xu and Needleman, is formulated. The total dissipated energy, in case of this modified cohesive zone

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law, is shown in Fig. 2b. The Wtot for the modified cohesive zone law shows a more realistic behavior for most practical cases: a smooth increase from It to In.

FIGURE 2. The total dissipated energy when the cohesive zone is first loaded in normal direction until n,max and then broken in shear (see also Fig. 1) for the exponential cohesive zone law of Xu and Needleman (a) and the modified exponential cohesive zone law (b). In both cases: In = 100 [Jm-2] and It = 80 [Jm-2]. It is shown that the dissipated energy, under mixed-mode loading conditions, can be predicted by an analytical expression. The mode-I parameters of the cohesive zone law, In and Gn, can be determined by double-cantilever beam experiments, as described by Sørensen and Jacobsen [2]. The mode-II parameters, It and Gt, might be determined by a similar approach. Results of experimental mixed-mode bending (MMB) tests (Benzeggagh and Kenane [3]) are used to verify the predictability of the modified cohesive zone law under mixed-mode loading conditions.

References 1.

Xu, X. P., Needleman, A., Mod. Sim. Mat. Sci. Eng., vol. 1, 111-132, 1993

2.

Sørensen, B. F., Jacobsen, T. K., Eng. Frac. Mech., vol 70, 1841-1858, 2003

3.

Benzeggagh, M.L., Kenane, M. Comp. Sci. and. Tech., vol 56, 439-449, 1996

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COHESIVE-ZONE MODELING OF CRACK GROWTH IN SPECIMENS WITH DIFFERENT CONSTRAINT CONDITIONS C. R. Chen1, O. Kolednik2 and F. D. Fischer3 1 Materials Center Leoben 2 Erich Schmid Institute of Materials Science, Austrian Academy of Sciences 3 Institute of Mechanics, University of Leoben and Erich Schmid Institute A-8700 Leoben, Austria [email protected] This paper deals with the tri-dimensional (3D) finite element modeling of ductile crack growth in smooth-sided compact tension (CT) and double edge notched tension (DENT) specimens with smooth side-surfaces using the cohesive zone model. The main problem is that the cohesive zone parameters, the separation energy, *, and the cohesive strength, Tmax, vary along the crack front and also with the crack extension. The purpose of the study is, therefore, to investigate how the cohesive zone parameters and the in-plane and out-of-plane crack tip constraint are interrelated. The material is a pressure vessel steel 20MnMoNi55, and the specimen thickness is 10 mm. The slant shear-lip fracture near the side-surfaces is modeled as a normal fracture along the symmetry plane of the specimen. The cohesive zone parameters are determined by fitting the simulated crack extensions found by the 2D and 3D computations to the experimental data of the multi-specimen tests. The effects of element size and load increment on the results of the simulations are also studied. The results show that * affects both the moment of fracture initiation and the crack growth rate, whereas Tmax strongly affects the crack growth rate, but has little effect on the fracture initiation. For the same cohesive zone parameters, the crack tip triaxiality near the midsection is lower in DENT specimens than in CT specimens. When the separation energy is set constant for CT and DENT specimens, the cohesive strength for the DENT specimens should be significantly lower than that for the CT specimens in order to make the simulated crack extensions near the midsection fit to the experimental data, see Fig. 1. For constant cohesive zone parameters, the simulated crack extension shows a strong tunneling effect, however for the CT-specimen the crack extension near the side surfaces is still too large (Fig. 1). For a better fit between simulated and experimental crack growth, both the cohesive strength and the separation energy near the side-surface should be considerably reduced compared to the values near the midsection (Fig. 2). When the same cohesive zone parameters are applied to the 3D model and a plane strain model, the stress triaxiality in the midsection of the 3D model is much lower and the von-Mises equivalent stress is distinctly higher than in the plane strain model.

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FIGURE 1. The cohesive zone parameters that make the simulated crack extensions near the midsection fit to the experimental data: (a) * = 180 kJ/m2 and Tmax = 3.14 Vy for CT; (b) * = 180 kJ/ m2 and Tmax = 2.58 Vy for DENT.

FIGURE 2. (a) Assumed variations of the cohesive strength and the separation energy in thickness direction of the CT-specimen; (b) Comparison of the simulated crack extension curves with the experimental data. Acknowledgements The authors acknowledge gratefully the financial support of this work by the Materials Center Leoben under the project numbers SP7 and SP14.

References 1.

Chen, C.R., Kolednik, O., Scheider, I., Siegmund, T., Tatschl, A., Fischer, F.D., Int. J. Fracture, vol. 120, 517-536, 2003.

2.

Chen, C.R., Kolednik, O., Heerens, J., Fischer, F.D., Eng. Fract. Mech., in press.

3.

Chen, C.R., Kolednik, O., Int. J. Fracture, in press.

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EFFECT OF ANISOTROPIC PLASTICITY ON MIXED MODE INTERFACE CRACK GROWTH V. Tvergaard and B. N. Legarth Department of Mechanical Engineering, Solid Mechanics Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark [email protected] Crack growth in metals gives rise to plastic work in the material surrounding the crack-tip, which contributes significantly to the fracture toughness, such that the macroscopic work of fracture is much larger than that of the local fracture process. For mode 1 crack growth with isotropic plasticity this has been studied numerically by Tvergaard and Hutchinson [1], modeling the local fracture process by a traction-separation law along the crack plane, with a specified work of separation per unit area. Subsequently, the same authors have used the method to account for the effect of a T-stress on crack growth [2]. Crack growth along an interface between an elastic-plastic solid and a rigid solid has been analysed by Tvergaard and Hutchinson [3], using a traction-separation law to represent the local fracture process, and Tvergaard [4] has extended this analysis to consider crack growth between dissimilar elastic-plastic solids. Due to the mismatch of elastic properties on either side of the interface the elastic crack-tip fields are characterized by an oscillating stress singularity, and the analyses under conditions of small scale yielding make use of these elastic fields as boundary conditions on the outer edge of the region analysed. Plastic anisotropy is often important in practice, due to texture development during large plastic straining in a metal forming process, or due to microstructure effects, as e.g. inclusions elongated in a particular direction (Legarth [5]). Several different models of anisotropic plasticity have been discussed by Kuroda and Tvergaard [6] in relation to studies of the forming limits for thin metal sheets with anisotropic properties. For crack-tip blunting one of these anisotropic yield surfaces (Hill [7]) has been used to the study the evolution of the crack-tip fields (Legarth et al. [8], [9]). Subsequently, two of the models (Hill [7], Barlat et al. [10]) have been used in numerical studies of crack growth (Tvergaard and Legarth [11]), with the local fracture process modeled by a traction-separation law, as in [1]-[4]. In these applications to fracture mechanics elasticviscoplastic versions of the anisotropic plasticity models have been applied, so that strain-rate sensitivity is accounted for. Recently, the crack growth analyses for anisotropic plasticity have been extended by Tvergaard and Legarth [12] to incorporate an anisotropic plasticity model with a vertex-type plastic flow rule, proposed by Kuroda and Tvergaard [13]. In the studies to be presented here, the effect of anisotropic plasticity is analysed for crack growth along an interface between a ductile material and an elastic material that does not yield plastically. While the crack growth analyses in [9] have considered only mode I loading conditions, the present analyses, with anisotropic plasticity only on one side of an interface, are carried out for various degrees of mixed mode loading. As in previous analyses for isotropic plasticity [3,4], it is found that plastic flow near the crack-tip results in much increased resistance to crack growth when mode II conditions dominate, but the main focus here is on differences resulting from anisotropy.

References 1.

Tvergaard, V. and Hutchinson, J.W., J. Mech. Phys. Solids, vol. 40, 1377-1397, 1992.

V. Tvergaard and B. N. Legarth

978 2.

2. Tvergaard, V. and Hutchinson, J.W., Int. J. Solids Structures, vol. 31, 823-833, 1994.

3.

Tvergaard, V. and Hutchinson, J.W., J. Mech. Phys. Solids, vol. 41, 1119-1135, 1993.

4.

Tvergaard, V., J. Mech. Phys. Solids, vol. 49, 2689-2703, 2001.

5.

Legarth, B.N., Int. J. Mech. Sci., vol. 45, 1119-1133, 2003.

6.

Kuroda, M. and Tvergaard, V., Int. J. Solids Structures, vol. 37, 5037-5059, 2000.

7.

Hill, R., Proceedings of the Royal Society of London A 193, 281-297, 1948.

8.

Legarth, B.N., Tvergaard, V. and Kuroda, M., Int. J. of Fracture, vol. 117, 297-312,

9.

2002.

10. Legarth, B.N., Tvergaard, V. and Kuroda, M., On-line publication of WCCM V – 11.

ISBN 3-9501554-0-6, 2002. http://wccm.tuwien.ac.at/

12. Barlat, F., Lege, D.J. and Brem, J.C., Int. Journal of Plasticity, vol. 7, 693-712, 1991. 13. Tvergaard, V. and Legarth, B.N., Int. J. of Fracture, vol. 130, 411-425, 2004. 14. Tvergaard, V. and Legarth, B.N., Int. J. Solids Structures (2005) (in print). 15. Kuroda, M. and Tvergaard, V., J. Mech. Phys. Solids, vol. 49, 1239-1263, 2001.

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CHARACTERISATION OF TG-SCC IN PURE MAGNESIUM AND AZ91 ALLOY N. Winzer1, G. Song1, A. Atrens1, W. Dietzel2 and C. Blawert2 1Materials Engineering, The University of Queensland, Brisbane, Qld Australia 4072 2GKSS-Forschungszentrum Geesthacht GmbH, Germany [email protected] [email protected] Our recent critical review [ ] of the stress corrosion cracking (SCC) of magnesium aims to provide a foundation for the safe and effective use of magnesium alloys, including practical guidelines for the service use of Mg alloys in the atmosphere and/or in contact with aqueous solutions. This is to provide support for the rapidly increasing use of Mg in industrial applications, particularly in the automobile industry. These guidelines should be firmly based on a critical analysis of our knowledge of SCC based on (1) service experience, (2) laboratory testing and (3) understanding of the mechanism of SCC, as well as based on an understanding of the Mg corrosion mechanism. Early reports have led to the perception of high SCC resistance for pure Mg and Mg-Mn alloys. Subsequent research on pure Mg, Mg-Al alloys and Zr containing alloys have shown that SCC is a significant issue, and that SCC can occur for loading equivalent to 50% of the yield stress for many combinations of alloy + (common) environment. The review [1] indicated that the following must be rationalised in any comprehensive mechanism of Mg SCC. •

"Pure Mg suffers transgranular stress corrosion cracking (TGSCC),

•

"Mg alloys suffer TGSCC in distilled water.

•

"TGSCC in Mg alloys is related to hydrogen,

•

"Small additions of sulphate and bromide ions to distilled water decrease significantly the threshold stress intensity and significantly increase the steady state crack velocity.

These observations may be rationalized in terms that the environment influence may be characterized in terms of an effective hydrogen fugacity, and it is the aim of our experimental program to quantify this approach. A number of recommendations are given [1] for the prevention of SCC of Mg alloys exposed to the atmosphere or aqueous solutions. One of the most important recommendations might be that the total stress in service (i.e. the stress from the service loading + the fabrication stress + the residual stress) should be below (and during service should remain below) a threshold level, which, in the absence of other data could be (conservatively) estimated to be ~ 50% of the tensile yield strength. On the basis on the critical review [1], a research program has been devised as illustrated in Fig. 1. The work reported in this paper is part of that research program. Transgranular Stress Corrosion Cracking (TG-SCC) of Mg and Mg-alloys has been investigated for ZE41 and AZ91 alloys in distilled water, NaCl solution and NaCl+K2CrO4 solution, using the linearly increasing stress test (LIST) [ ], Fig. 2. ZE41 and AZ91 represent the two principal classes of Mg alloys; zirconium-containing alloys and others respectively. Pure Mg was investigated to study the influence of second phases. The study investigated the influence of stressing rate on crack velocity, which was characterised using the DC potential drop (DCPD) technique. Fractography and surface composition analysis using X-Ray Photon Spectroscopy (XPS) was carried out comparing samples fractured in air, subject to TGSCC in solution and for specimens pre-exposed to SCC environments.

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FIGURE 1. Schematic of research program on environment influences for TGSCC of Mg Alloys.

FIGURE 2. Schematic drawing showing the principle of the LIST apparatus. The load on the specimen is increased linearly by means of a lever principle and a linearly moving load on the right hand side of the lever. The lever is maintained horizontal via a linear actuator and a servocontroller by means of a displacement signal from one end of the lever arm.

References 1.

N. Winzer, A. Atrens, G. Song, E. Ghali, W. Dietzel, K. U. Kainer, N. Hort and C. Blawert, Advanced Engineering Materials, 2005 to appear in August issue.

2.

A. Atrens, C. C. Brosnan, S. Ramamurthy, A. Oehlert and I. O. Smith, Meas Sci Technol vol 4, 1281-1292, 1993.

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HYDROGEN EMBRITTLEMENT AND CRACKING OF 18MN-4CR STEELS A. Balitskii Karpenko Physico-Mechanical Institute of National Academy of Sciences of Ukraine Naukova Street, Lviv, 79601, UKRAINE [email protected] The number of generators retaining ring failures caused by the fracture of these details increases with the power of electric machines. Since hydrogen is used as a cooling agent, these accidents leads to fires, cause damage of generators, or even result in their complete failure. Statistical data of this sort are mainly accumulated for 18Mn-4Cr-type steels [1-8]. The temperature dependence of the fracture toughness of 18Mn-4Cr-type steels is characterized by presence of the minimum at about 550 oC (Fig.1). After thermal treatment performed at 400 oC, fracture toughness abruptly drops to its minimum value and then somewhat increases but does not reach the original value. At temperatures higher than 600 oC, fracture toughness begins to decrease again. If tempering temperatures are not higher than 400 oC, we observe plastic fracture. At higher tempering temperatures (e.g. 600 oC), we have a mixed type of fracture, i.e., a combination of plastic (intragranular) and brittle (intergranular) types of fracture. The time to failure of 18Mn-4Cr-type steels is the same in dry hydrogen and in dry air (Fig.2).

FIGURE 1. Temperature dependences of fracture toughness and sub critical crack growth rates in specimens from18Mn-4Cr steel [9]. FIGURE 2. Long term strength of 18Mn-4Cr steel in dry hydrogen and in air (1), in distilled water without oxygen (2), in humid hydrogen (3), in water saturated with oxygen (4), and in a nitrate solution (5) [10]. Humid hydrogen is a much more aggressive medium than distilled water without oxygen. Saturation of water with oxygen and nitrated leads to asharp decrease in the time of specimes fracture. The diagrams of structural strength of the materials of a rotor retaining ring (traditional and promising) presented in Fig.3 illustrated the advantages of new 18Mn-18Cr steel.

A. Balitskii

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FIGURE 3. KIC – VVT diagrams ({ – KJC, z – KIC) (a) (in air), Kfc – VVT (b), Kth – VVT (c) (electrolytical hydrogenation with current density 100 /m2) of steels for rotor-retaining ring unit: 1 – 3,5NiCrMoV; 2 – 8Mn8Ni4Cr; 3 –18Mn-4Cr; 4 – 18Mn-18Cr. To increase the crack growth resistance of retaining ring materials in hydrogen environments admixtures of La (up to 0.05 vol. %), Ce (up to 0.1 vol. %) in N-containing 18Mn-4Cr have been introduced during experimental melting. They have a positive influence on quantuity, geometry and distribution regularity of non-metallic inclusions, improve the metal quality, and change its dislocation structure. Applying Ca (up to 0.05 vol. %) for deaccidation of steels significantly influences the geometry and composition of nonmetallic inclusions, observed on fracture surfaces of specimens. Experimental steels with high content of Cr, Cu and other alloying components demonstrated increasing resistance to corrosion-mechanical fracture and long-term stength in hydrogen-containing environments.

References 1.

Balitskii, A.I., Modern Materials for Powerful Turbogenerators, National Academy of Sciences of Ukraine, Lviv, 1999.

2.

Balitski A., Krohmalny O., Ripey I., Intern. J. of Hydr. Energy, vol.25, 2, 167-171, 2000.

3.

Balyts’kyi O.I., Mater. Sci. , vol.33, 4, 539-552, 1997.

4.

Balitskii A.I., Mater. Sci. , vol.34, 4, 113-120, 1998.

5.

Balitskii A.I., Mater. Sci. , vol.35, 4, 485-490, 1999.

6.

Balitskii A.I., Mater. Sci. , vol.36, 4, 541-545, 2000.

7.

Balitskii A.I., Makarenko V.G., Shved M.M., Shokov N.A. In Abstr. of IV Sem. on Hydrogen in Metals, vol.2, Moscow, 1984, 137.

8.

Balitskii A.I., Shokov N.A., In Abstr. of 2nd Symp. on Fracture Mechanics, vol.II, Zhytomir, 1985, 61.

9.

Scarlin R. B., Albrecht J., Speidel M. O., In Proc. 8th Int. Brown Boweri Symp., Plenum Press, New-York, London, 1984, 453–461.

10. Speidel M. O., VGB Kraftwerktechnik, vol.61, 5, 1981, 417–427. 11. Lukas P., Kunz L., Bartos J., Mat.Sci.Eng.,vol.56, 1982, 11-18. 12. Shuju H., Xiaofang L., Shufeng Z., Yuanchun H., Haicheng G., Corrosion, vol. 55, 12, 1999, 1182 – 1190.

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TRANSIENT STRESS AND EAC OF STEAM TURBINE DISC STEEL A. Turnbull and S. Zhou National Physical Laboratory Queens Road, Teddington, Middlesex, TW11 0LW, UK [email protected] For economic reasons, the power industry is now operating its 500 MW coal-fired plants on a twoshift cycle in which the turbines are on-load for 16 hours per day and off-load overnight and at weekends. The concern with ‘two-shifting’ is the impact on environment assisted cracking of the associated transients in stress, water chemistry and temperature. On-load, with well-controlled water chemistry, the condensate on the low-pressure turbines will be free of oxygen with chloride and sulphate levels both up to about 300 ppb. Off-load, the condensate would essentially be pure water but aerated unless there is nitrogen blanketing. The stress off-load would be zero. Ideally, to fully simulate two-shifting in laboratory testing, the combined influence of transient stress and water chemistry would be evaluated but there are technical difficulties in synchronising the changes in the stress, temperature, oxygen, and anion (chloride and sulphate) concentrations. For the purpose of assessing the impact of transient stress on crack propagation, the environment was held constant, viz. deaerated 300 ppb Cl- +300 ppb SO42- solution at 90 °C. Separate measurement to examine the effect of transient water chemistry at constant stress are underway. Fatigue precracked compact tensions specimens were contained in a environmental chamber and the test solution ciculated from a 22 L reservoir that was refreshed weekly to maintain good water chemistry. The oxygen concentation was monitored on-line and was typically 1 ppb. A trapezoidal load cycle was used to reflect service behaviour. It is desirable to sensibly accelerate the process to maximise the number of stress cycles per day. In this case, a 20 min period (a typical hot start period) was fixed for both the load rise and fall time and for zero load. The maximum load was set to give a K value of 40 MPa m1/2 for 100 mins. Later, this hold period was varied to assess the impact on crack growth. In parallel with the transient load tests, two tests at constant stress intensity factors of 30 MPa m1/2 and 40 MPa m1/2 were undertaken. A pulsed high resolution/high stability DCPD method was used to monitor crack length. Unusual behaviour was experienced in tests of the disc steel under constant load. No crack growth was observed for well-controlled conditions extending to 9 months. However, in one test an uncontrolled excursion in oxygen and chloride solution lasting just 1 hour, by which time the environmental conditions had been restored to normal, induced a crack growth rate of 9.0x10-12 m/ s that was sustained for a further 4 months, after which it decreased to 2.3x10-12 m/s. In another test, no cracking was observed after 9 month under constant load. To possibly activate the crack growth process, a single trapezoidal load was applied. No crack extension was detected in the next 2.8 months after the transient load application but the crack then started growing at a rate of 2.2x10-12 m/s. An example of the results from transient loading is shown in Fig. 1.

984

A. Turnbull and S. Zhou

FIGURE 1. Crack growth rates under trapezoidal loading for turbine disc steel in deaerated 300 ppb Cl- +300 ppb SO42- solution at 90 °C. Loading wave 1 has hold time of 100 mins and loading wave 2 has hold time of 300 min. There is no apparent static load contribution to the crack growth rate; the crack growth is not sustained under static load condition (the slight decay in apparent crack length is a reflection of corrosion product we believe) and there is no effect of hold time on the cylic crack growth rate. The cyclic crack growth rate is high, about 10-6 m/cycle. With typically one cycle per day in service except weekends, and accounting for any stress corrosion cracking component at maximum load (to allow for chemistry transients) a crack growth rate of 0.4 mm per year would be estimated. Crack inspection intervals should be adjusted accordingly under two-shifting operation. With proposals for four-shifting under consideration, life expectancy will be very significantly reduced.

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IRREVERSIBLE HYDROGEN TRAPPING IN WELDED BETA-21S TITANIUM ALLOY D. Eliezer1, 2, E. Tal-Gutelmacher1, C. E. Cross2 and Th. Boellinghaus2 Materials Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84501, Israel 2Federal Institute for Materials Testing and Processing (BAM), Berlin D-12200, Germany [email protected]

1Dept.

ȕ - 21S titanium alloy is ranked among the most important advanced materials for a variety of technological applications, due to its combination of a high strength/weight ratio, good corrosion behavior and oxidation resistance. However, in many of these technological applications, this alloy is exposed to environments which can act as sources of hydrogen, and consequently, hydrogeninduced cracking and property degradation, hydrogen-induced ductile-to-brittle transition associated with a change in the fracture mode from ductile, micro-void coalescence to brittle, cleavage have to be considered[1-4]. In the aged E-21S alloy, the susceptibility to hydrogen induced cracking and the decrease in the alloy's strength has been attributed to the E-phase precipitated during the aging and the hydrogen-induced stabilization of the E-phase[1, 2, 5]. Hydrogen-induced intergranular cracking in the cathodically pre-charged E-21S alloy was significantly influenced by the preferential Į precipitation at E grain boundaries[5]. Even without hydriding, the Į -E interfaces could provide trapping sites and the accumulation of hydrogen at these interfaces could result in fracture. Pound[6] revealed that in aged E-Ti alloys the relationships among the trapping constants, resistance to hydrogen embrittlement and grain boundary are critical in determining the role of trapping in hydrogen embrittlement of these alloys. Very few data are available in literature for intrinsic hydrogen effects in welded E-Ti alloys and almost no reports on trapping characteristics. Thus, in this work hydrogen was introduced to the alloy via the arc shielding gas (argon with pre-mixed amount of hydrogen (5% H2) at a flow rate of 20 L/mi), using a GTA welding process for full penetration, bead-on-plate welds on E-21S plate. GTAW allowed us to investigate the hydrogen evolution phenomenon from the welded E21S alloy and, in particular, to determine whether the trapping characteristics can change in correlation with the unique morphology induced in the alloy’s microstructure by the welding process. NDT analyses exposed no porosity or any other volumetric defects in the welds. The amount of hydrogen inside the welded specimens, measured by Leco, was 455 ± 29 wt. ppm, in comparison to 56 ± 6 wt. ppm in the as-received material. SEM microstructure investigations showed quite clearly the boundary between the dendritic microstructure in the fusion zone and the equiaxed grain microstructure in the HAZ with coarser quenched grains in comparison to the base metal. The microstructure developed in the weld metal varied noticeably from the edge to the centerline of the weld. EDS analysis revealed that enrichment of Mo and depletion of Ti takes place in the interdendritic regions. Hydrogen desorption and trapping characteristics were determined by means of thermal desorption spectroscopy (TDS) and were supported by other experimental techniques, such as LECO hydrogen determinator, XRD and SEM microstructure investigations. Detailed technical descriptions of the Leco and TDS system, as well as the quantification of several trapping parameters are given elsewhere[7]. TDS analyses are conducted on the welded E-21S titanium specimens using different temperature ramps of 3, 5 and 7 ºC/min. The results were summarized in Table 1.

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TABLE 1. Summary of TDS parameters for GTA welded -21S alloy.

The TDS plots were characterized by only one desorption peak, which occurs at very high temperatures (623-670ºC). The calculated energy for hydrogen desorption was found to be approximately 111 kJmole-1. This is a very high value, indicating that the residual hydrogen induced to the material from the gas shield during the welding process, is probably trapped at an irreversible, strong trapping site. Furthermore, even at a slow rate of 3 ºC/min, less than half of the absorbed amount of hydrogen is desorbed. XRD patterns of the weld metal revealed the existence of Į -phase in addition to the E-phase. Therefore, similar to aged E-Ti alloys, irreversible trapping might take place at the Į -E interface[8], resulting from possible misfit strain, or some other cause. Another assumption could be that the dendritic arms spacing might act as a possible irreversible trap site, for hydrogen accumulation at the interface might occur due to the high residual stresses induced by the welding process. Since hydrogen evolution and trapping can be affected by several factors, i.e., the unique microstructure; the shape, morphology and size of the dendrites, elements segregation and the change in the chemical composition, phase transitions that might occur, residual stresses induced by the welding process, the reasons for such deep trapping associated with welding have to be investigated further.

References 1.

Nelson, H.G., In Hydrogen Effects in Metals, edited by A.W. Thompson, N. R. Moody, TMS, Warrendale (PA), 1996, 699.

2.

Hardwick, D.A., In Hydrogen Effects in Metals, edited by A.W. Thompson, N. R. Moody, TMS, Warrendale (PA), 1996, 735.

3.

Teter, D.F., Robertson I.M. and Birnbaum, H.K., Acta Mater., vol. 49, 4313, 2001.

4.

Sofronis, P. et. al., In Hydrogen Effects on Material Behavior and Corrosion Deformation Interactions, edited by N.R. Moody, A.W. Thompson, E.E. Ricker, G.S. Was, R.H. Jones, TMS-AIME, Warrendale (PA), 2003, 537.

5.

Young, G.A. and Scully, J.R., Scripta Metall. Mater., vol. 28, 507, 1993.

6.

Pound, B.G., Acta Mater., vol. 45, 2059, 1997.

7.

Tal-Gutelmacher E., et. al., Mater. Sci. Eng. A, vol. 52(8), 230, 2004.

8.

Young, G.A. and Scully, J.R., Corrosion, vol. 50, 919, 1994.

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EAC IN HIGH STRENGTH STEELS FOR GAS TRANSPORTATION G. Gabetta and R. Bruschi 1 Eni S.p.A. Div.E&P, 5° Palazzo uffici, Via Emilia 1, 20097 San Donato Milanese (Mi) Italy [email protected] Snamprogetti, Via Toniolo 1, 61032 Fano (An) Italy [email protected] The use of high grade steels for pipelines (X80-X120 API 5L) gives the possibility of competitive gas transportation over long distance (3000-7000 km), with high capacity (15-30 Gsm3/year) and high pressure (10-15 MPa). Pipelines with those characteristics mast cross hostile environments, such as: permafrost, swamps, seismic activities, slopes, hydro-geo hazards. Long distance pipelines require large investment (of the order of 10 Billion US$), and 20-30 years of safe and efficient operation to have an adequate return of the investment. With the above requirements, materials risk must be minimal, in other words defect tolerance of the material becomes an important issue. Underground pipeline currently in operations are mainly made of low alloy steels of the API specifications (for instance, X65 and X52), showing a ferritic-pearlitic structure with elongated inclusions, mainly MnS. These materials have been proved susceptible to Transgranular Stress Corrosion Cracking (TGSCC) in diluted solutions of near neutral pH, with composition similar to the underground water. This cracking phenomenon has been firstly studied by Parkins [ 1,2 ] as a consequence of field observations [ 3 ]. Cracking was mainly observed under disbonded region of the pipeline coating, where cathodic protection is not effective. Hydrogen embrittlement due to the diffusion of atomic hydrogen produced in the cathodic reaction at the crack tip has been identified as the most probable active cracking mechanism, but the influence of the different variables (metallurgy, stress, environment) is not yet fully understood [ 4 ]. An important effect of time dependent stress variations, such as pressure fluctuation and/or land slide movements, was demonstrated [ 5,6 ]. To obtain steels with higher strength, suppliers act modifying microstructure and composition, so that the so-called micro-alloyed steels are produced. The goal of the producing process is to increase the strength, while decreasing (or not increasing) the toughness, taking into account the larger wall thickness, required for long distance transportation. In addition, there is a need for a transition temperature lower than -10°C (it can depend on external environmental: in artic conditions, this temperature can be lower), and of an adequate weldability. Due to differences in microstructure and composition, the comparison between old grades and new grades steels (and between new grades from different mills) is not immediate. Moreover, there is a lack of significant field experience, as Environmentally Assisted Cracking for pipelines often presents a long incubation time, difficult to predict and to handle. In particular, the damage can only be detected after many years of service and with only a short time interval remaining between the first detection and the final failure. In the frame of the TAP (High Pressure Gas Transportation) project, a first goal is to ensure that X100 steel will not "behave" worse than X65 steel in service. Experimental data obtained up to now are however somewhat contradictory concerning the effect of metallurgy: a coarse microstructure is definitely less resistant to EAC than a fine microstructure, but there is an effect of the different phases, as for instance that of interstitial elements, that could be quite important. To obtain data on the new material, a pilot section was built in Sardinia, in a military firing range. A 48" pipeline 750m long, designed for 15MPA, will be "operated" for about two years.

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The objective of the test is to verify the constructability of X100 pipeline, and to test the performance of X100 steels (joints will be provided by three different suppliers), under different working factors in realistic environments. Typical pipe defects will be simulated in the pilot section, to obtain field feedback on hydrogen embrittlement and EAC problems, at different levels of cathodic protection and mechanical damage. Pressure fluctuations will be applied to simulate about 25 years of operation of a trunk line for gas transportation. In the mean time, pipe samples from each pipe mill (having different microstructure) are tested in laboratory. Part of testing is dedicated to investigate the effect of crack nucleation and to compare the behaviour of X65 "old" steel to the behaviour of the new X100 steel. There is a need for additional efforts in order to validate specific test techniques and to develop procedures that can yield quantitative results ("figures"), and - most important - that can provide users with reliable figures. To pursue the goal for X100 steel, a deeper analysis of results and information will be necessary. Laboratory tests and literature results are important. The phenomenon of TGSCC was observed not only in pipeline steels, but in other components, such as for instance in nuclear pressure vessel steels [ 7 ]. Tests and discussion are underway since about 30 years on that subject. People involved in the design and building of large structure are facing new challenges and are looking for the application of the scientific findings.

References 1.

Parkins, R.N., "Mechanisms of Stress Corrosion Cracking" Cap.8.2, in "Corrosion" L.L.Sheir, Ed., Newness-Butterworths, London, 1963

2.

Parkins, R.N., Metals Performance, vol. 24, N°8, 1985.

3.

TransCanada Pipelines: "Report on 1987 Pipe Integrity Program, SCC Research Program and Planned 1988 SCC Research Program", 1988

4.

Zheng, W., Revie, R.V., Dinardo, O., MacLeod, F.A., Tyson, W.R., and Kiff, D.: "Pipeline SCC in Near-Neutral pH Environment: Effect of Environmental and Metallurgical Variables", EPRG 1996

5.

Gabetta, G., DiLiberto, S., Bennardo, A., "Laboratory tests reproduce transgranular stress corrosion cracking observed in field", paper N°00372, Corrosion 2000, Orlando, Fl, March 26-31, 2000

6.

Gabetta, G., Di Liberto, S., Bennardo, A., Mancini, N., "Strain rate induced stress corrosion cracking in buried pipelines", British Corrosion Journal, vol.36, n°1, 2001

7.

M.Elboujdaini and W.Revie, "Stress Corrosion Cracking on Canadian Pipelines", ICG-EAC 25th Anniversary celebration, May 11-16 2003, Ottawa, Canada

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HIGH TEMPERATURE FATIGUE CRACK GROWTH IN TITANIUM MICROSTRUCTURES H. Ghonem Department of Mechanical Engineering University of Rhode Island Kingston, Rhode Island 02881 (USA) [email protected] Titanium alloys are interesting to several industrial applications including transportation and biotechnology’s, aerospace designers having been particularly interested because of the combination of their fatigue and time-dependent mechanical properties, good formability, high specific properties due to a relatively low density, and high resistance to aggressive environmental and impact loads. Titanium based alloys represent 30% and 40% of the total mass in commercial and military engines, respectively, a considerable amount of this mass being devoted to high temperature rotating disc and blade components. The improvement of the engine performance being directly related to the increase of the operative temperature, Ti-rich Ti-Al alloys (Al < 12.4 wt %) which account for this goal are the most critically studied. These alloys are used under cyclic conditions in aggressive environments such as ambient air at elevated temperature, and can be submitted to the superposition of constant loading and large number of small amplitude perturbations. This paper examines the loading frequency effects on elevated temperature fatigue crack growth mechanisms in titanium alloys in two distinctive microstructures, Widmanstatten and fully lamellar. In this examination, the individual influences of environment and creep are identified in terms of both the macroscopic crack growth rates and detailed fractographic observations of the crack growth path as a finction of loading frequency and the applied '. . Results in both microstructures indicate the existence of two regions of microstructurally sensitive and insensitive transgranular crack growth. The transition between these two regions has been found to depend on the testing temperature. In the Widmanstatten microstructure, lower frequencies promoted an increase in cleavage fracture while an addition of hold time at maximum load resulted in prior-E grain boundary fracture attributed to creep damage. In addition, the transition to intergranular fracture at high '. has been found to take place at higher frequencies in vacuum, yielding a higher crack growth rate than in air which is indicative of a faster, more widespread viscoplastic flow without the presence of oxidation. The controlling feature in the fracture mechanism in this microstructure was identified as the intercolony boundaries. In fully lamellar microstructure, the crack growth rate is found to be insensitive to variations in lamella size. Furthermore, the presence of hold time within the loading cycle results in a fracture failure dominated by prior E intergranular fracture and DE interface decohesion. The role of the loading frequency is correlated in this microstructure to the associated crack tip shear activity and transmission at the DE interfaces. These interfaces are identified as the controlling fracture feature in fully lamellar microstructures. Experimental results as a function of

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temperature and frequency are detailed and a discussion focusing on the role of environment in observed fracture mechanisms is presented.

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CORROSION DAMAGING AND CORROSION FATIGUE ASSESSMENT IN THREE-LAYERED METALLIC MATERIAL I. M. Dmytrakh and V. V. Panasyuk Karpenko Physico-Mechanical Institute of National Academy of Sciences of Ukraine 5 Naukova Street, Lviv, 79601, UKRAINE [email protected], [email protected] The layer-like structures are widely used for corrosion protection of hull constructions in a power engineering and refinery industry. The work presents the corrosion and corrosion fatigue studies of three-layered metallic material with the aim to assess the possible corrosion damaging and corrosion fatigue crack growth behaviour under operating conditions. The subject of study consists of a basic (hull) material and two fused layers by thickness of 3.5mm each. The nominal chemical composition of each component is given in TABLE 1. The 1% solution of H3BO3 in distilled water with KOH additions (pH=8.0) was used as corrosive environment. TABLE 1. Chemical composition of three-layered material (% by wt).

FIGURE 1. Corrosion current density from the surface of cylindrical pit of variable radius r and constant depth h=25 mm in three-layered material. Based on the proposed methods of equivalent electrode for determination of electrochemical current in corrosion pits [1], the numerical procedure for the determination of a corrosion current density from the surface of deep cylindrical corrosion pit in three-layered material was developed. Using the standard electrochemical parameters for each material in the given environment, the corresponding values of the corrosion current density were calculated under different combinations of pit’s depth and radius. The sample of a calculation is given in Fig. 1. It has been shown that current density increases with increasing of pit’s radius and decreases under increasing of its depth. From received results also follows that the zones of fusion have

I. M. Dmytrakh and V. V. Panasyuk

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increased corrosion activity, especially it can be seen for zone of fusion between layer I and basic material (Fig. 1).

FIGURE 2. Diagrams of fatigue crack growth resistance for three-layered material in air (a) and in corrosive environment (b). Based on developed fracture mechanics experimental methods [2], fatigue crack growth behaviour in three-layered material was investigated both in air and corrosive environment. As result the diagrams of fatigue crack growth resistance (fatigue crack growth rate da/dN as function of stress intensity factor range 'K) were built (Fig. 2). These diagrams reflect an influence of corrosive environment and provide the data for quantitative assessment of fatigue strength of components and zones of fusion for given three-layered material.

References 1.

Dmytrakh, I. M., Kolodii, B. I. and Bilyi, O. L. Physicochemical Mechanics of Materials. International Scientific-Technical Journal, vol. 39, No 4, 14-18, 2003

2.

Dmytrakh, I. M. and Panasyuk, V. V., Influence of Corrosive Environments on Deformation and Fracture of Metals Near Stress Concentrators, National Academy of Sciences of Ukraine, Lviv, Ukraine, 1999

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SIMULATION OF HYDROGEN ASSISTED STRESS CORROSION CRACKING USING A TIME DEPENDENT COHESIVE MODEL I. Scheider, M. Pfuff and W. Dietzel GKSS Research Centre Geesthacht, Max-Planck-Str. 1, D – 21502 Geesthacht [email protected] Cohesive models are used for ductile tearing of metals since 1987 [1]. Nowadays, the numerical implementation using finite element technique is such that interfaces elements are introduced, which transfer cohesive stresses between continuum elements until they fail and form a crack. The constitutive law of the cohesive model, the so-called traction-separation law, which defines the dependence of the cohesive traction, V c, on the material separation, , contains two parameters, the cohesive strength, V 0, and the critical separation, G 0. The integral of the function V c( G ) gives the total energy dissipated by the cohesive element, called cohesive energy, * 0. During the last decade, the traction-separation law has been extended to cover time-dependent processes. In the case of stress corrosion cracking, the time dependence is caused by the differential equation of hydrogen diffusion, which in its simplest form is

wC wt

Deff ’ 2 C (1)

where C is the bulk hydrogen concentration and Deff the effective diffusivity. Implementations of such differential equations have been introduced in cohesive modelling recently [2, 3]. The approach in both investigations is based on the assumption that the hydrogen coverage of the interface reduces the cohesive energy and thus, the cohesive strength V c,0 of the material. The present paper addresses the development and implementation of a concentration dependent cohesive model in the commercial finite element package ABAQUS. Originally, the authors implemented interface elements for stable crack extension in ductile metals, [4]. This implementation is now extended to cover a linear dependence of the cohesive strength on the hydrogen concentration at the interface by

Vc

V c ,0 (1  P C )

(2)

where P is an additional parameter (between 0 and 1) that controls the effect of hydrogen on cohesive strength. The spatial hydrogen concentration gradient is considered in crack propagation direction only. The boundary condition for the hydrogen is such that an environmental concentration, Cenv, is defined at the moving crack tip; that is, when a cohesive element has failed, it gets the value of Cenv. The initial condition is that the concentration of the cohesive elements is zero, whereas Cenv is available at the crack flanks. In a numerical study the effect of hydrogen diffusion has been studied using the time dependent cohesive model. A C(T) specimen with W = 50 mm and an initial crack length a0/W = 0.5 has been analysed under different loading rates. The material is elastic-plastic with a yield strength of 200 MPa and a hardening exponent of n = 15. It is assumed that the yield strength itself does not depend on the hydrogen concentration, and the cohesive strength, which has an initial value of V

0

= 560 MPa, is affected by hydrogen according Eq. (2) and using P Cenv = 0.9. -The

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force load-line displacement curves for various loading rates are shown in Fig. 1. Of course, the residual strength decreases with loading speed as expected, since the hydrogen needs time to diffuse into the material. An experimental validation with a steel, which is already tested under various loading speeds, is to be performed in the near future.

FIGURE 1: Numerical simulation of fracture tests in a corrosive environment under various loading speeds.

References 1.

Needleman, A., J. Appl. Mech., vol. 54, 525-531, 1987

2.

Serebrinsky, S., Carter, E.A. and Ortiz, M., J. Mech. Phys. Solids, vol. 52, 2403-2430, 2004

3.

Liang, Y. and Sofronis, P., J. Mech. Phys. Solids, vol. 51, 1509-1531, 2003

4.

Scheider, I., In First M.I.T. Conf. on Comp. Fluid and Solid Mech., edited by K.J. Bathe, Elsevier, Amsterdam, 2001, 460-462

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ENVIRONMENTAL STRESS CRACKING OF POLYETHYLENE PIPES IN WATER DISTRIBUTION NETWORKS J. P. Dear, N. S. Mason and M. Poulton Imperial College London South Kensington Campus, London, SW7 2AZ [email protected] Water distribution networks are subject to both demanding operational and environmental stresses and these vary, for example, with the proximity of pipes to booster pumps, operating valves and other locations where the pipes are subjected to surge and other fluctuating stresses. Polyethylene water pipes are often used as they have good damage resistance to these stresses. A process that can shorten the life of polymer pipes is the removal of antioxidant from the material by chlorine present in the water. The result can be to reduce the life of the pipe by early exposure of weak features that can cause the pipe to fail. In assessing the average life of polymer water pipes, one need is failure data related to the loss of antioxidants for different concentrations of chlorine in the water. This study of the effects of chlorine in water pipes is part of researching the types and distribution of failures of a typical town’s water distribution network. For this study, laboratory experiments were performed using new polymer pipes subjected to accelerated life assessments. Pipes were subjected to different concentrations of chlorinated water and maintained at different pressures and for different elevated temperatures. Fig. 1(a) shows a plot of log10(hoop stress) versus log10(time to failure) for MDPE pipes which failed when internally pressurized with chlorinated water at 80oC for concentrations of 500 , 1000 , 3000 , 5000 , 10000 , 15000 , 30000 , 45000 and 120000 mg litre-1. A reference line is shown for Ductile and Brittle failures at 80oC when the pressurized water inside the pipe is not chlorinated. Fig 1(b) shows multiple cracking of the inner surface of a failed MDPE pipe exposed to chlorinated water.

FIGURE 1. MDPE pipe failure due to pressurized chlorinated water at 80oC: (a) Log10(hoop stress) versus log10(time to failure); (b) Axial crack formation on inner surface. Fig. 2 shows plots of antioxidant (OIT) profiles for failures in MDPE pipes (hoop stress of 4.6 MN m-2) versus distance from inner wall for a chlorine concentration of 15000 mg litre-1 and time to failure of 552 hours (Fig. 2(a)) and for a chlorine concentration of 5000 mg litre-1 and time to failure of 1176 hours (Fig. 2(b)). These are compared with concentration profiles from a model simulation (Figs 2(c) & (d)) obtained by numerical solution of coupled differential equations for antioxidant and chlorine diffusion/reaction. This modelling gives the normalised antioxidant

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concentration (CA/C0,A) and the normalised chlorine concentration (CCl/C0,Cl) as are shown across the thickness of the pipe wall (inner pipe radius = a and outer pipe radius = b). The dotted lines in Figs 2(a) and (b) are the initial antioxidant level prior to chlorine exposure. The effect of chlorine is: (1) Chlorine is absorbed in the polymer, diffusing and consuming antioxidant, (2) Oxidation of the polymer chains occurs leading to a reduction of molecular mass through chain scission, (3) Reduction in tensile properties of the polymer lead to a brittle layer forming and as the pipe expands due to creep, the brittle layer cracks and so provides an initiation site for slow crack growth.

FIGURE 2. Antioxidant profile through pipe thickness: (a) and (b) experimental data from failed MDPE pipes in chlorinated water at 80oC; (c) and (d) modelling data.

References 1.

Dear, J.P. and Mason, N.S., Polymers and Polymer Composites, vol. 9, 1-13, 2001.

2.

Smith G.D., Karlsson, K. and Gedde, U.W., Polymer Eng. and Science, vol. 32, 658-667, 1992.

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FATIGUE CRACK PROPAGATION IN 2XXX ALUMINIUM ALLOYS AT 223K C. Gasqueres1, C. Sarrazin-Baudoux1, D. Dumont2 and J. Petit1 1LMPM/ENSMA, UMR CNRS 6617, Chasseneuil-Futuroscope, France 2PECHINEY/ALCAN, Centre de Voreppe, France [email protected], [email protected], [email protected], [email protected] Aluminum alloys are widely used for constitutive parts of aircrafts and are consequently confronted with a wide range of temperature depending on altitude: from 300K (ambient temperature) on the ground down to 223K during a fly. Fatigue properties and particularly fatigue crack growth resistance at low temperature have been poorly studied. The literature provides results in cryogenic condition (77K) showing improved fatigue strength in Al-Li alloys [1,2]. This paper deals with a study of the fatigue crack propagation behavior of two high strength 2xxx Aluminum alloys elaborated in naturally-aged and peak-aged conditions. Tests were performed at 223K in an environmental chamber with a controlled dry atmosphere (dew point of 223K). Cooling of the specimen was performed by mean of two cooling blocks fixed on both sides of the specimen near the back face and own to the circulation of cooled silicon oil. Fatigue crack propagation tests were performed with an Instron servohydraulic testing machine under load control. The loading signal was a sinusoidal waveform one with a frequency of 35 Hz and a load ratio (R) of 0.1. The specimen used were of C.T. type (width W=50mm) with LT orientation. Each test began with a crack propagation in ambient air at K=12 MPa.m1/2. Then threshold tests were performed in cold environment using a load shedding technique. Finally, K was increased at constant load amplitude up to near-failure domain. Crack closure was detected using the compliance method, and the crack was optically tracked. The fatigue crack propagation mechanism in the naturally-aged alloys was shown strongly modified by the cold environment with an abrupt transition from a stage II propagation regime at room temperature to a highly retarded crystallographic stage-I like propagation regime at 223K. An illustration of this transition is given in figure 1. The main consequence is an improvement in fatigue crack growth resistance in cold environment as it can be seen in figure 2 for AA2024A T351 tested in air at room temperature and at 223K. But no change was observed on the peak-aged alloys and the fatigue crack propagation curves obtained in the cold environment are similar to those in ambient air. The propagation data after closure and Young modulus correction are analyzed in terms of a previous modelling established for fatigue crack propagation at room temperature [3]. The respective influence of microstructure, temperature and air dryness is discussed on the basis of scanning and transmission microscopy observations.

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FIGURE 1. Change in the fracture surface morphology of AA2024A T351 alloy induced by 223K dry environment.

FIGURE 2. AA2024A T351 fatigue crack propagation curves in ambient air and 223K dry environment.

References 1.

Park, K.J. and C.S. Lee, Scripta Materialia, vol. 34(2), 215-220, 1996

2.

Xu, Y.B., et al., Scripta Materialia, vol 33(2), 179-183, 1995

3.

Petit, J., G. Henaff, and C. Sarrazin-Baudoux, Fatigue crack growth threshold, endurance limits and design, Newman and Piascik, , American Society for testing and materials, West Conshohocken, 4-30, 2000

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HYDROGEN ASSISTED CRACKING PATHS IN ORIENTED PEARLITIC MICROSTRUCTURES J. Toribio and E. Ovejero Department of Materials Engineering, University of Salamanca E.P.S., Campus Viriato, Avda. Requejo 33, 49022 Zamora, Spain Tel: (34-980) 54 50 00; Fax: (34-980) 54 50 02, [email protected] Previous works [1-4] demonstrated that progressive cold drawing in eutectoid steels affects the microstructure of the material at the two basic microstructural levels. Firstly [1,3], it produces a preferential orientation and slenderising of the pearlitic colonies, so that they tend to become more slender and to align in a direction quasi-parallel to the drawing direction. In addition [2,4], cold drawing produces a preferential orientation and a densification of the pearlite lamellae, so that the latter tend to align in a direction parallel to the wire axis, with a reduction at the same time of the pearlitic interlamellar spacing. This paper deals with the consequences of the afore-said microstructural evolution on the posterior behaviour of the steels under hydrogen assisted cracking conditions. The experimental results show that cold drawing induces strength anisotropy in the steel, and thus the resistance to hydrogen embrittlement is a directional property that depends on the angle in relation to the drawing direction. As a consequence, an initial transverse crack changes its propagation direction to approach that of the wire axis, thus producing mixed mode propagation, the deflection angle (in relation to the initial crack propagation direction) being an increasing function of the cold drawing degree. This experimental result may be explained by micro-mechanical considerations on the basis of the lamellar microstructure of the steels. Special attention is paid to the hydrogen assisted cracking path as a function of the drawing degree, analysing the possible fracture of the pearlitic lamellae or the delamination between ferrite and cementite. While in the hot rolled steel (not cold drawn) the crack advances in a hydrogen environment by breaking the pearlitic lamellae, in heavily drawn steels the predominant mechanism of hydrogen assisted cracking is the delamination at the ferrirte/cementite interface (cf. Fig. 1) or the decohesion between two adjacent pearlitic colonies, thus permitting a micromechanical modelling as a micro-composite material.

FIGURE 1. Hydrogen assisted cracking path in heavily drawn steel.

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References 1.

Toribio, J. and Ovejero, E., Mater. Sci. Eng, vol. A234-236, 579, 1997.

2.

Toribio, J. and Ovejero, E., Scripta Mater., vol. 39, 323, 1998.

3.

Toribio, J. and Ovejero, E., J. Mater. Sci. Lett., vol. 17, 1037, 1998.

4.

Toribio, J. and Ovejero, E., Mech. Time-Dependent Mater., vol. 1, 307, 1998.

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EFFECT OF RESIDUAL STRESS-STRAIN PROFILE ON HYDROGEN EMBRITTLEMENT SUSCEPTIBILITY OF PRESTRESSING STEEL WIRES J. Toribio and V. Kharin Department of Materials Engineering, University of Salamanca E.P.S., Campus Viriato, Avda. Requejo 33, 49022 Zamora, Spain Tel: (34-980) 54 50 00, Fax: (34-980) 54 50 02, [email protected] Cold drawn wires of eutectoid pearlitic steel are widely used for prestressing concrete structures which usually work in hostile or aggressive environments, so that stress corrosion cracking of prestressing steel is a problem of major technological concern. In addition, there is general agreement that hydrogen embrittlement (HE) plays an important role in the environmental cracking of such a steel due to particular working conditions or to the local electrochemistry in the vicinity of a crack tip. In this framework, the Standard Test in Ammonium Thiocyanate was proposed by the International Federation of Prestressing (FIP) as a suitable experimental method for checking the susceptibility of high-strength prestressing steels to stress corrosion cracking in general, and particularly to hydrogen embrittlement. In spite of some objections to this standard corrosion test, it is the best suited for steel control and acceptance. However, the main disadvantage of the FIP test is the scattering of the results, which increases as the externally applied stress decreases. It can be caused by the distribution of residual stresses generated in the vicinity of the wire surface during the manufacturing (cold drawing) process. Previous research [1] established an important milestone by obtaining a quantitative relationship between the level of residual stress (represented by theoretical residual stress laws) and the fracture behaviour of prestressing steel wires under HE conditions, but a detailed analysis of the influence of real residual stress profiles caused by different regimes of surface rolling on the HE susceptibility of cold drawn prestressing steel wires has not been performed yet. This paper goes further in the analysis, so that the earlier developed computer model [1] is advanced and applied to analyze the influence of the residual stress-and-strain profiles after surface rolling on the hydrogen embrittlement susceptibility of cold drawn prestressing steel wires in FIP tests. To this end, a computer model was used to predict the wire life in the aggressive solution. The model is based on hydrogen transport by diffusion assisted by stress and strain [2-5]. It allows a detailed analysis of the influence on the wire life of the specific characteristics of the residual stress and strain distributions in the wires, and particularly of the residual stress at the surface, the profile of the residual stress law and the depth of the maximum hydrostatic stress point. Profiles of hydrostatic residual stresses and plastic strains are presented in Fig. 1. It is seen that a rolling process introduces severe inhomogeneity of residual stresses (samples C8 and C26) in contrast to relatively uniform distributions after drawing only (sample C0). In addition, Fig. 2 shows an excellent agreement between the theoretical predictions of the models and real experimental data obtained by means of the Ammonium Thiocyanate FIP test.

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FIGURE 1. Residual hydrostatic stress and plastic strain profiles in cold drawn wires.

FIGURE 2. Theoretical predictions of prestressing steel lifes and experimental data.

References 1.

Toribio, J and Elices, M., Int. J. Solids Structures, vol. 28, 791-803, 1991.

2.

Toribio, J. and Kharin, V., Fatigue Fract. Engng. Mater. Structures, vol. 20, 729-745, 1997.

3.

Toribio, J. and Kharin, V., Nuclear Engng. Design, vol. 182, 149-163, 1998.

4.

Toribio, J. and Kharin, V., Int. J. Fracture, vol. 88, 233-245, 1998.

5.

Toribio, J. and Kharin, V., Int. J. Fracture, vol. 88, 247-258, 1998.

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HYDROGEN EMBRITTLEMENT OF AUSTENITIC STAINLESS STEELS AT LOW TEMPERATURES L. Zhang, M. Wen, M. Imade, S. Fukuyama and K. Yokogawa National Institute of Advanced Industrial Science and Technology Central 5, 1-1-1 East, Tsukuba, 305-0046, JAPAN [email protected] Stainless steels suffer from hydrogen embrittlement (HE) at low temperatures, thus the improvement of the resistance to HE has been expected by alloying. The main elements of Ni and Cr improve resistance to HE by stabilizing austenite phase with respect to martensitic transformations and by increasing the stacking fault energy (SFE) to promote cross-slip. The addition of N also stabilizes austenite phase and improves resistance to HE. Although N does not change the SFE, N promotes planar-slip by inducing a short range order in the matrix [1,2]. Thus, N and Ni play distinct roles in improving resistance to HE. It provides a way to distinguish HE due to strain-induced alpha’ martensite from HE due to planar-slip. The degree of austenite phase stability against strain-induced alpha’ martensitic transformation and the tendency of forming austenite phase can be evaluated by an equation of Ni equivalent that is a modified form of Hirayama’s equation [2]: Nieq = Ni + 0.65Cr + 0.98Mo + 1.05Mn + 0.35Si + 12.6(C+N), (1) where all elements are in weight fraction. Thus, HE can be correlated with Nieq. However, the effect of Nieq on HE has not been studied until now. In the present study, Ni content of the austenitic stainless steels of Fe(10-20)Ni17Cr2Mo alloy and N content of those of Fe11Ni17Cr2Mo(0.001-0.25)N alloy, both based on type 316 stainless steel, were changed to study the effect of Nieq on hydrogen environment embrittlement (HEE). Tensile tests were conducted in hydrogen and helium at 1 MPa in the temperature range from 80 to 300 K to clarify the relation of HEE with Nieq. All tests were conducted with a strain rate of 4.2×10-5 /s. Alpha’ martensite content in austenite phase was measured as ferrite equivalent by the magnetic method. The fracture surface of the specimen was analyzed by scanning electron microscopy (SEM) after tensile tests. Martensitic transformation was analysed by transmission electron microscopy (TEM). HEE can be quantitatively described by the relative reduction of area (RRA) measured in hydrogen at 1 MPa relative to in helium at 1 MPa (reduction of area in hydrogen / reduction of area in helium). There is no HEE if RRA equals 1, and HEE increases with decreasing RRA. It was observed that the RRA decreases with decreasing temperature, reaches a minimum at around 200 K and then increases with further decrease in the temperature. The most serioue HEE occured at 200 K, thus the effects of Nieq on ferrite equivalent and the RRA at 200 K are shown in Fig. 1. It is clear that Nieq correctly predicts the austenite phase stability due to the same relation bewteen ferrite equivalent and Nieq of both N and Ni added steels. Both N and Ni can stabilize austenite phase by decreasing ferrite equivalent. However, these two kinds of steels have quite different RRAs. In the case that Nieq is above 27 %, no HEE of Ni added steels is observed, while HEE of N added steels is always shown although it decreases with increasing N.

L. Zhang et al.

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FIGURE 1. Effects of Nieq on alpha’ martensite content and the RRA at 200 K. Fracture surfaces in hydrogen of Ni added steels revealed that transgranular fracture occurs along alpha’ martensite laths and those of N added steels showed transgranular fracture togehter with slip plane fracture. Hydrogen induces slip planarity in fcc structure, thus the difference in RRA of N and Ni added steels is obviously due to planar-slip caused by N-induced a short range order. TEM observations indicated that strain-induced alpha’ martensite is formed at the intersections of the microscopic slip bands in the grains of both steels. The bcc structure is believed to be inherently more susceptible to hydrogen-induced cracking than the fcc structure and the bcc structure provides an effective short-circuit diffusion path for hydrogen due to the high diffusivity of hydrogen in it [3], thus alpha’ martensite increases hydrogen content in the matrix and promotes HEE. It is considered that strain-induced alpha’ martensite plays a key important role in hydrogen-induced crack propagation in these steels. It is thus concluded that in Ni added 316 series stainless steels HEE is completely controlled by alpha’ martensite content. In N added stainless steels, strain-induced alpha’ martensite also plays the primary role in HEE, but slip pnanarity plays more important role in inducing HEE when N is increased.

References 1.

Swann, P. R., Corrosion, vol. 19, 102, 1963.

2.

V. Gerold, H.P. Karnthaler, Acta Metall. vol. 37, 2177, 1989.

3.

Hirayama, T. and Ogirima, M., J. Jpn. Inst. Met., vol. 34, 507-510, 1970.

4.

Han G., He J., Fukuyama S. and Yokogawa K., Acta Metall., vol. 46, 4559-4570, 1998.

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HYDROGEN DIFFUSION AND EAC OF PIPELINE STEELS UNDER CATHODIC PROTECTION M. Cabrini and T. Pastore Università degli studi di Bergamo – Dipartimento di Progettazione e Tecnologie Viale Marconi, 5 24044 Dalmine (BG) Italy [email protected], [email protected] Pipeline steels can show Environmental Induced Cracking phenomena under slow straining with Hydrogen Embrittlement mechanism under cathodic protection. Hydrogen evolution can take place due to cathodic protection normally used in order to protect the pipeline against general corrosion. The steel is polarized at cathodic potentials in the range –0.8 to –1.1 V vs SCE, but very negative values could be reached in overprotected areas close to the impressed current anodes. The hydrogen ions reduction reaction takes place on the metal surface, forming adsorbed hydrogen. The adsorbed hydrogen diffuses into the metal owing its solubility in the metal lattice. Afterwards it can concentrate in plastic deformation areas, and promote brittle growth. Figure 1 shows the results of slow strain rate tests on a low alloyed steel. The loading curves obtained at –1050mV vs SCE is very different from the curve obtained in air. The differences are related to the presence of brittle areas on fracture surphace and secondary cracks (figure 1).

FIGURE 1. Stress vs strain curves obtained at 10–6 s–1 and different potentials and fracture surface of the SSR specimen after the test at –1050 mV vs SCE. Similar effect are also evident in Corrosion-Fatigue at low frequency: figure 2 shows da/dN vs 'K curves in air and in cathodic protection at –1050 and –900 mV vs SCE. The cathodic protection increases the fatigue cracks growth for intermediate values of 'K. In this range the crack propagation is dominated from hydrogen embrittlement. The EAC phenomena can take place at the cracks tip, after the hydrogen concentration reachs a critical value. The hydrogen diffusivity depends on microstructure of the steel. Table 1 summarizes the hydrogen diffusion coefficient of pipeline steels. The normalised reduction of area after SSR tests and the average fatigue cracks rate at 'K 20MPa—m at the same potential are also reported.

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FIGURE 2. a) da/dN vs 'K curves in air and in artificial sea water at different potentials, b) fracture surface of the specimens at the end of the CF tests in sea water at –1050 mV vs SCE

TABLE 1. Results of the hydrogen diffusion tests (transversal direction), SSR tests and CF tests at E = –1050 mV vs SCE

All steels show at –1050 mV vs SCE hydrogen embrittlement under slow straining. The steels with micrsotructures of bands of ferrite/pearlite have hydrogen diffusion coefficient higher than the steels with babded microstructures of fine ferrite with martensite or bainite and of the steels with temepred martensite. An increase of the hydrogen embrittlement susceptibility is observed as the hydrogen diffusion coefficient increases.

References 1.

Cabrini, M., Cogliati O., Maffi S., La metallurgia italiana, vol. 3, 13-20, 2003

2.

Zucchi F., Grassi V., Frignani A., Monticelli C., Trabanelli G., In Atti del Convegno Nazionale AIM, edited by AIM, Vicenza Novembre 17-19, 2004, CD-room .

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INITIATION OF ENVIRONMENTALLY ASSISTED CRACKING IN LINE PIPE STEEL M. Elboujdaini CANMET Materials Technology Laboratory - Natural Resources Canada, 568 Booth St., Ottawa, Ontario, Canada K1A OG1 [email protected]

Stress Corrosion Cracking Mechanism: Stress corrosion cracking (SCC) has been observed on the soil side of buried, natural gas pipelines since the early 1960s. Transgranular SCC has caused service as well as hydrotest failures, and cracks have been found associated with gouges and dents. Transgranular cracking occurs in environments with pH about 6.5, and is referred to as nearneutral pH cracking, as opposed to high pH cracking, which is intergranular in nature. The stress corrosion cracking (SCC) results from multiple metallurgical, mechanical, and environmental factors. Chemical composition of the steel, residual stress in the steel as well as applied stress, water chemistry in the field, including CO2, oxygen, and ionic concentrations in the groundwater near the pipe surface, may all have an effect on crack initiation and propagation [1,2]. Stress corrosion cracking in pipelines involves several steps: (i) The coating applied to the pipeline during installation becomes degraded, an electrolyte comes into contact with the surface, and the environment that causes SCC to develop; (ii) The initiation and growth of multiple cracks that form colonies; (iii) These cracks may continue to grow and coalesce; and (iv) In the final step, a dominant crack reaches a critical size for rapid growth to failure, producing either a leak or a rupture. The time to failure depends on a number of factors, including the pipe material, stress history, environment, and crack distribution. Nearly all studies of SCC have been carried out without distinguishing the characteristics of initiation from those of propagation. Many of the studies on propagation have focused on growth of long cracks in pre-cracked specimens. Initiation of SCC is, however, studied using specimens that are not pre-cracked. The definition of an initiated crack is not well defined, and there is no clear mechanistic interpretation of the events that lead to initiation. SCC has been observed to initiate from the base of localized corrosion sites (i.e. pits, crevices) for a variety of metal-environment combinations [1,3]. There remains debate on whether the stress intensification at the base of the pit or the enhanced electrochemical conditions within the pit is the controlling factor in SCC [2,4]. Several investigators believe it is the localized environment that plays the biggest role in crack initiation and not necessarily the stress concentration provided by the localized corrosion site, whereas others believe that crack initiation in smooth samples requires the presence of a stress raiser [3,4]. The most common way to establish such a stress raiser is either through corrosion or mechanical damage. Complexities in SCC Phenomena: SCC in steels for oil and gas pipelines is a very complex and challenging phenomenon. The complexity of SCC is reflected in the changes, with time, of the diverse parameters influencing the cracking phenomena, whereas the biggest challenge is in obtaining field-relevant reproducible laboratory data. SCC encompasses major effects from metallurgical, mechanical, and environmental parameters, all of which can be dominant under specific conditions. Adding to the complexity are the loading conditions in operating pipelines that define the mode of failure as SCC or corrosion fatigue (CF). While SCC and CF are sometimes regarded as different modes of failure, the distinctions between them in mechanistic or engineering terms are becoming less sharply defined [4].

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Figure 1: EDS spectra indicating chemical composition of three different inclusions as associated with the initiation of pits in X-65 steel sample (before and after test at Fmax=90%YS in NS-4 solution saturated with N2/5%CO2). Note the rapid dissolution of CaS inclusions and the formation of corrosion pits around the inclusions.

References 1.

National Energy Board, Calgary, Alberta, Stress Corrosion Cracking on Canadian Oil and Gas Pipelines, Report No. MH-2-95, 1996.

2.

Parkins, R.N., et al., Corrosion, 50, 394-408, 1994.

3.

Elboujdaini, M. et al,Corrosion/2000, Paper 00379, NACE, Houston, TX, 2000.

4.

Parkins, R.N., Metals Science and Engineering, A103, 143, 1988.

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FATIGUE CRACK GROWTH BEHAVIOUR DEPENDING ON ENVIRONMENT IN MAGNESIUM ALLOYS Masaki Nakajima1, Keiro Tokaji2, Yoshihiko Uematsu2 and Toshihiro Shimizu1 1Dept.

of Mech. Eng., Toyota National College of Technology, 2-1 Eisei-cho, Toyota 471-8525, Japan [email protected] 2Dept. of Mech. and Systems Eng., Gifu Univ., 1-1 Yanagido, Gifu 501-1193, Japan Recently, magnesium (Mg) alloys have become of major interest as a light-weight structural material because of their excellent specific strength. In extensive applications for structural components, fatigue properties such as fatigue strength and fatigue crack propagation (FCP) are critical, but studies on FCP behaviour are very limited. Kamakura et al. [1] have indicated that FCP behaviour in wrought Mg alloys was influenced significantly by humidity in laboratory air. This is due to very high electro-chemical activation resulting from poor corrosion resistance (Eliezer et al. [2]). Therefore, it is necessary to further study the FCP behaviour and mechanisms in corrosive environments. In the present paper, FCP tests have been performed using CT specimens of AZ31 and AZ61 in dry air, in laboratory air and in distilled water, and the effect of environment and mechanisms were discussed. The materials used are rolled AZ31 and extruded AZ61 plates from which CT specimens with L-T orientation were machined. FCP experiments were conducted at a stress ratio, R, of 0.05 in dry air, in laboratory air and in distilled water using electro-hydraulic fatigue testing machine operating at a frequency of 1 Hz. The dew point of dry air was –60qC. After experiment, fracture surfaces were examined using a scanning electron microscope (SEM).

FIGURE 1. Relationships between FCP rate and stress intensity factor range: a) AZ31, (b) AZ61. The relationships between FCP rate, da/dN, and stress intensity factor ranges, 'K, 'Keff in AZ31 and AZ61 are shown in Fig.1(a) and (b), respectively. It can be seen in Fig.1 that both alloys exhibits basically the similar FCP behaviour regardless of environment. FCP rates are nearly the same in laboratory air and in distilled water, while approximately an order of magnitude slower in dry air than in those environments. This indicates that humidity in laboratory air exerts a significant influence on FCP behaviour, which acts in the same manner as distilled water. Such

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M. Nakajima et al.

tendency of FCP behaviour is maintained after allowing for crack closure, indicating the intrinsic effect of environment on FCP behaviour. Microscopic appearance of fracture surfaces was similar in laboratory air and in distilled water, with many steps formed in each grain in high 'K region and extensive quasi-cleavage in low 'K region. In dry air, such appearances were not recognized and fracture surfaces were ductile in the entire 'K region.

FIGURE 2. Effect of cyclic frequency on FCP rate: (a) AZ31, (b) AZ61. In order to further understand the effect of environment, constant K tests were performed at K=3.5MPam1/2 in a wide range of frequencies of 0.01 Hz to 10 Hz. The obtained results are represented in Fig.2. As described previously, the FCP rates in dry air are an order of magnitude slower than those in laboratory air and in distilled water. It should be noted that the effect of cyclic frequency is less remarkable in laboratory air and in dry air, while the FCP rates in distilled water become faster with decreasing frequency, particularly remarkable in the low frequency region. From the observation of fracture surfaces, corrosion products were not seen in laboratory air, while extensively observed in distilled water. Therefore, it is believed that FCP rates would be enhanced by a mechanism such as hydrogen embrittlement in laboratory air and a further enhancement of FCP rate would result from anodic dissolution in distilled water.

References 1.

Kamakura, M., Tokaji, K., Ishiizumi, Y. and Hasegawa, N., J. Soc. Mat. Sci., Japan, 53, 1371-1377, 2004.

2.

Eliezer, A., Gutman, E.M., Abramov, E. and Aghion, E., Corrosion Review, 16, 1-26, 1998.

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ASSESSMENT OF HIGH-TEMPERATURE HYDROGEN DEGRADATION OF POWER EQUIPMENT STEELS H. M. Nykyforchyn and O. Z. Student Karpenko Physico-Mechanical Institute of National Academy of Sciences of Ukraine 5 Naukova Street, Lviv, 79601, Ukraine [email protected], [email protected] Long term service of power equipment in corrosion and hydrogenated environments causes a degradation of the physical, chemical and mechanical properties and correspondingly a decrease its lifetime. The method of the accelerated degradation of steels by thermocycling in the gaseous hydrogen is developed, which allows to realize during some weeks degradation of metal like in service during 10…20 years. The idea of the method has been based on the temperature dependence of hydrogen solubility and a decrease of hydrogen mobility at lower temperatures. Student [1] showed that this method causes changes of steel microstructures, similar to those that observed after long term exploitation. A relevancy of an usage of the effective range of stress intensity factor 'Kth eff as parameter which detects mechanical state of the degraded material, is proved. This finding has been also supported by relationship between the parameter Kth eff vs. the time of operation Wop and vs. the number of thermocycles n, cf. Fig. 1.

FIGURE 1. Effect of the operation time W (1) and number of thermocycles in hydrogen n (2) on the parameter 'Kth eff for the 12H1F (0.1% C; 1.1% Cr; 0.54% Mn; 0.26% Mo; 0.26% Si; 0.17% V; 0.019% S; 0.015% P) steel. The fractography and surface roughness examination by Student et al. [2] indicated a high probability of the premature contact of the corresponding fracture surfaces due to longitudinal shear in the prefracture zone (mode III of crack loading) for hydrogen degraded steel. The obtained results enabled to prove an existence of the fatigue crack closure mechanism due to mode III deformation and to develop the well known model of crack closure, caused by fracture surface roughness. An inversion of an effect of the absorbed by metal hydrogen on the 'Kth eff parameter in dependence of metal state caused by ageing is shown (Fig. 2). The higher Kth eff for the hydrogen charged metal in as received state (positive effect of hydrogen, which is typical for comparatively

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H. M. Nykyforchyn and O. Z. Student

low strength steels with high ductility, showed by Nykyforchyn [3]) changed to negative effect of hydrogen on this parameter after long term exploitation. Fractography investigation of fracture surfaces of the 12H1MF steel showed that the negative effect of hydrogen on the Kth eff level is accounted by the susceptibility of steel to hydrogen cracking due to the material degradation. The evidence of such hydrogen degradation is the fatigue striations situated perpendicular to the main crack direction and decorated by secondary microcracks. On this base the criterion of a definition of the limited state of metal as a result of its high temperature degradation is formulated: it is achieved when hydrogen starts to influence negatively on the 'Kth eff parameter and material becomes sensitive to hydrogen induced cracking.

FIGURE 2. Dependence 'Kth eff on- op for hydrogenated (1) and outgassed (2) 12H1MF steel. An approach to the residual life time evaluation of the power plant steam pipe lines is developed, which allows to take into account the negative hydrogen effect. It is based on the criterion of a definition of the limited state of metal and the correlation between a time of service and a number of cycles during the in-laboratory thermocycling in hydrogen.

References 1.

Student, O. Z. Materials Science, V.34, N4, 490-496,1998.

2.

Student, O.Z., Cichosz, P. and Szymkowski, J. Materials Science, N6, 1999.

3.

Nykyforchyn, H.M. Materials Science, N4, 2002.

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STRESS CORROSION CRACKING OF 18MN-4CR GENERATOR ROTOR END-RETAINING RING STEEL N. Mukhopadhyay and U. K. Chatterjee General Manager, BHEL, Hyderabad, and Professor, IIT Kharagpur Corporate R&D Division, BHEL, Hyderabad 500593, India, and Department of Metallurgical & Materials Engineering, IIT Kharagpur 721302, India [email protected], [email protected] 18Mn-4Cr austenitic steel has virtually been the standard material for the rotor end-retaining rings in power generation plants during the period of 1960-1980, before it was replaced by the 18Mn18Cr variety. A good number of cases of failure of the 18Mn-4Cr steel ring by stress corrosion cracking (SCC) led to the switchover to the higher chromium variety. The cases of failure have been documented in the report of EPRI Workshop on Retaining Rings for Electrical Generators (October 1982). SCC has been attributed to the presence of moisture, and though the sources of humidity have been identified as imperfectly dried hydrogen, leakages from water-fed stator winding, oil in the hydrogen-tightness circuit and moisture condensation during shut downs, storage and transportation of the rings, no light was thrown on the mechanism of SCC or any possible effect of the stress relieving temperature on SCC. The present study was undertaken with these considerations in view. A right circular cylindrical ring forging was used in the as-received and thermo-mechanically treated conditions. The chemical composition of the steel was:0.52 C, 0.01 S, 0.02 P, 18.98 Mn, 3.87 Cr, o.035 Al. 0.05 V, 0.15 Ni, 1.04 Si, balance Fe. The thermo-mechanical treatment route was in line with the fabrication and heat treatment method generally followed for the end-retaining rings viz. solution annealing at 10400 C, water quenching, cold working to 15% reduction in area, stress relieving at different temperatures, followed by furnace cooling. The temperatures for stress relieving were chosen as 3500 C, 4000C, 4500C and 5000C. Tensile specimens of 50 mm gage length and 3 mm diameter were prepared from both asreceived and thermo-mechanically treated steel. Stress corrosion tests were performed by constant load technique using a Mayes constant load SCC device in a 50 ppm chloride solution. The tests were carried out under free corroding as well as under polarization conditions using a Wenkin potentiostat. Supplementary electrochemical tests were performed to study the localized corrosion (pitting) behaviour under potentiostatic conditions. Stress corrosion cracking was encountered in all the specimens. The as-received material has shown predominantly intergranular cracking. The time to fracture has increased in specimens stress relieved at 3500 C (ca. 540 hr), 4000 C (ca. 430 hr) and 4500 C (ca. 300 hr), compared to that in the as-received specimens (ca. 150 hr), and the cracking mode is transgranular. The change in SCC susceptibility as well as the mode of cracking can be directly correlated to the extent of carbide precipitation. In the case of as-received specimens and specimens stress relieved at 5000 C, the precipitated carbides are massive and are aligned mostly along the grain boundaries. Potentiostatic etch tests were carried out by holding the sample potentiostatically at a series of potentials ( -370 mV to –720 mV, OCP being –590 mV SCE), for 2 hr for localized attack to initiate. Subsequent microscopic examination revealed localized attack at the sites of carbide precipitation. Even under large cathodic potentials, the attack was observed at grain boundary triple points indicating that the dissolution is chemically controlled. The corrosion product, observed as mounds at these sites, induces crevice corrosion leading to the formation of grooves as

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N. Mukhopadhyay and U. K. Chatterjee

stress corrosion crack nucleation sites. However, in SCC tests, the time to fracture has been found to be potential dependent, decreasing on anodic polarization and increasing on cathodic polarization, indicating the electrochemical nature of the cracking process. The soluble carbides that assist in pit initiation also help in crack propagation by providing an easy path for dissolution and also by the formation of occluded cells at these sites. The latter process is electrochemical in nature, and thus cathodic polarization has drastically slowed the process of crack propagation. Fractographic studies have revealed the evidence of corrosion tunneling and ‘saw-tooth’ type step formation in the transgranular fracture. Corrosion tunneling is a result of several slip steps intersecting the surface exposed to a cracking environment [1]. In the present alloy where the formation of a protective film is not indicated, the soluble carbides precipitated along the slip planes may be ascribed a role in tunnel formation. The fine ‘saw-tooth’ steps are indicative of fracture arising out of the joining of a number of microcracks in a single grain [2]. The formation of this transgranular feature can be attributed to the presence of a large number of carbide particles in the grain interior where microcracks will initiate through the process of dislocation build-up. The exclusively intergranular fracture in the specimens stress relieved at 5000 C is an indication of a shift in the heterogeneities from grain interior to grain boundaries, and the identifiable evidence of massive carbide precipitation along the grain boundaries supports this. Apart from the role of carbides and slip steps in providing paths for the ongoing crack front, strain induced martensite could also play a role in crack propagation. Evidence has been obtained that the present steel in as-received condition can be transformed to nonequillibrium bcc martensite by pneumatically peening with hardened steel shots. At the advancing crack tip, the stress concentration causes local plastic deformation, which is likely to produce martensite that promotes faster dissolution of the crack tip due to its anodic nature.

References 1.

Pickering, H.W. and Swann, P.R., Corrosion, vol. 19, 373-389, 1963

2.

Scully, J.C., In The Theory of Stress Corrosion Cracking in Alloys, edited by J.C. Scully, NATO Scientific Affairs Division, Brussels, 1971. 127-147

17. SIM, Philosophy, Instrumentation and Analysis

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NON CONTACTING STRESS MONITORING W. D. Dover, R. F. Kare and N. Stone TSC Inspection Systems 6 Mill Square, Featherstone Road Wolverton Mill, Milton Keynes, MK12 5RB [email protected] Key input data for SIM calculations are the service stresses and the defect size. For some applications only the service stresses are required. For well designed structures this could be for stresses that arise during construction and early service life. For other situations it may be necessary to monitor crack/defect size and the local stress. For the offshore industry the Alternating Current Field Measurement (ACFM) technique, TSC [1] was developed for subsea and topside inspection. ACFM has the capability to both detect and size cracks. A recent innovation for ACFM has been the introduction of array probes. These can collect crack depth information from various sites along the crack in one placement of the probe. The array probe is an area inspection and hence can also be used for crack size monitoring if left in place on the structure. An example of array probe monitoring is given in Karé and Tantbirojn [2]. More recently it has become possible to use a non contacting technique for measurement of the service stress. Recent developments of the alternating current field measurement system have now made non-contacting stress measurement and monitoring a possibility. It has been known for some time that mechanical stress can influence the magnetic domain distribution in ferrous metals. This feature, known as piezo-magnetism can be utilised to determine changes in the state of stress on the surface of a metal. Magnetic permeability changes of this sort can be measured using AC field measurement devices. These devices have been improved recently, by UCL and TSC Inspection Systems Ltd, to the point where very small changes in permeability and hence stress are detectable Zhou and Dover [3], Chen et al [4], Chen and Brennan [5], Brennan [6]. Thus changes in stress, of the order of a few percent of the zero to yield stress range, have been measured in the laboratory for structural steels. The very latest AC field measurement devices, known as the Stressprobe [1] can now be used for non-contacting induced field stress measurements in service. The Stressprobe has been used to monitor stress cycling from simple sine waves to broad band variable amplitude loading typical of that recorded on North Sea platform structures. The Stressprobe has a higher response for some materials, for example mild steels, and medium strength steels. With high strength steels the response is smaller and hence the gain needs to be larger. Despite this it is still possible to monitor the stress fluctuation and Fig. 1 shows a recent example of monitoring on drill collar material subjected to stress cycling at 3Hz. These tests were part of an attempt to use the Stressprobe to monitor the decay in residual stress during a fatigue test. As can be seen in Fig. 1 the Stressprobe is closely following the strain gauge output. Recent studies have included monitoring the loads in chains used in offshore mooring systems, offshore risers/tendons, and for pipelines. Some of this work was reported in Dover et al [7] and this ECF paper will report on more recent studies.

W. D. Dover et al.

1016

Figure 1 Monitoring with strain gauge and the Stressprobe on 4145H Drill collar steel

References 1.

TSC Inspection Systems Ltd, 6 Mill Square, Featherstone Road, Wolverton Mill, Milton Keynes MK12 5RB.

2.

Kare, R. F. and Tantbirojn, N., SIMoNET Inaugural Seminar March 2000, UCL.

3.

Zhou, J. and Dover, W. D., Journal of Applied Physics, Vol.83, No4, 1998, pp1694-1701.

4.

Chen, K., Brennan, F.P., and Dover, W.D NDT&E International, 33, 2000, pp 317-323.

5.

Chen, K. and Brennan, F.P., Journal of Strain Analysis, Vol 33, No 4, pp 291-303, 1998.

6.

Brennan, F.P., Proceedings of the First International Conference on Non-Destructive Evaluation in the Gulf, Doha, State of Qatar, November 1999, pp1-15.

7.

W D Dover, F P Brennan and B de Leeuw ACSM Stressprobe; a new non contacting stress measurement technique for the offshore industry

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RAPID CALCULATION OF STRESS INTENSITY FACTORS A. J. Love and F. P. Brennan NDE Centre, Department of Mechanical Engineering, University College London, Torrington Place London WC1E 7JE, UK [email protected] The demand to design evermore efficient, economic and safer structures continues and is set to only increase throughout the twenty-first century and beyond. Thus, the challenges confronting the engineer, concerned with ensuring a state of structural integrity prevails similarly grow evermore demanding. The SIF is widely recognised as the fundamental parameter vital for the assessment of defects, or cracks prone to linear elastic fracture behaviour. Difficulties in computing or measuring SIF are widely accepted especially when the crack is situated in a complex geometry or subject to a non-simple stress state. In addition, with the emergence of structural integrity monitoring systems there is likely to be an increased demand for the rapid availability of accurate SIF solutions for on-line defect assessment. This paper describes the development of a novel weight function methodology, which will potentially permit the determination of SIF solutions for such crack systems. Recent years have seen the advent of readily available and greatly enhanced computer processing ability leading to exciting developments in finite element and boundary element approaches to complex fracture problems. These require considerable skill and insight from the operator and are, therefore, likely to remain the preserve of specialists. Moreover, implementation by a non-specialist could yield dangerously erroneous solutions. If realised, the weight function methodology described below would present rapid, high quality solutions within the reach of design engineers in a format conducive for incorporation into standards and design codes. A general need exists in both industry and academia for SIF solutions for engineering components for which currently published solutions represent an idealised and often unrealistic approximation. Further to the limitations stated previously, solutions gained through numerical techniques are developed for specific applications and are generally applicable within restrictive limits of validity. Engineering optimisation and defect assessment of components in service however, often require broad ranging solutions, which can be rapidly calculated. A weight function approach meets these requirements and, while a specific application is cited in this paper and solutions tailored accordingly, the methodologies developed will be of significant relevance to the wider industrial and academic spheres. The SIF weight function, ‘h(a,x)’, as defined by Rice and Bueckner, is widely recognised as a powerful and efficient means of determining SIF solutions for cracks subject to complex loading configurations. In essence it permits the influence of component geometry, which it represents upon the SIF to be separated from that of applied loading. Once determined, it may be used in conjunction with a crack-line stress, ‘V(x)’, arising from any loading mode to yield new SIF solutions as shown below. a

K

³ V ( x ) h ( a , x ) dx 0

(1)

By virtue of the definition of the weight function as a unique property of geometry, the influence it represents can be isolated and combined. This characteristic is unique to the weight function. A number of researchers developed similar composition approaches after Impellizzeri

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A. J. Love and F. P. Brennan

and Rich used what they called Geometry Correction Factors for the influence of geometric anomalies on the weight function. These studies represented the beginning of the idea that geometric influences could be analytically separated. Recognition of this and advancements in weight function formulation led to the development of many subsequent engineering solutions by the building of complex geometry weight functions from more simple constitutive geometry weight functions. Brennan and Teh, who envisaged the ‘library’ of solutions for numerous notch types, conducted the most comprehensive study on the composition of weight functions. The ‘library’ refers to a generic set of constitutive solutions that systematically define a wide range of symmetric notch parameters. The weight function composition principle applied to symmetric notches proved the premise that geometric influences, described as weight functions, may be combined, or composed, via a suitable composition scheme to yield new SIF solutions. Extension of the principle to broaden the library database and incorporate symmetric notches, of extreme geometric form and asymmetric notches exposed limitations in the composition scheme in its presented form. Recent developments have addressed these limitations to allow formulation of a universal composition scheme applicable to all inter-related geometries shown above and application to the deepest point of surface cracks. SIF solutions obtained via the composition of weight functions have been shown to be of high accuracy, having wide ranging limits of validity in a manner that is both rapid and of relative mathematical simplicity. The composition of weight functions is therefore, ideally suited to numerous engineering applications including that cited here, for which full numerical modelling maybe unwarranted or inappropriate.

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VARIABLE AMPLITUDE CORROSION FATIGUE OF HIGH STRENGTH WELDABLE STEEL S. S. Ngiam and F. P. Brennan NDE Centre, Department of Mechanical Engineering, University College London, Torrington Place London WC1E 7JE, UK [email protected] In recent years there has been considerable interest in the offshore industry in using high strength weldable steels in the construction of offshore structures. This growing trend has seen high strength steel widely used in the fabrication of Jack-up platforms for production purposes, largely due to the optimisation of light weight design. This is particularly important due the competitive Oil & Gas industry, as considerable reduction in weight can lead to a significant saving in both manufacturing and operation costs. High strength weldable steels with nominal yield strength of circa 450 to 700MPa have been commonly used in the fabrication of jack ups, especially in the leg structures. Early realistic loading fatigue studies that were conducted on offshore structures in the North Sea, focused only on fixed platforms. For example, with the aid of the advancement of high-speed computer during the last two decades, several working group such as COLOS (Common Load Sequence for the European Coal and Steel Community Research Programme II), UKOSRP and Wave Action Standard Load History (WASH) were established to standardise realistic variable amplitude loading fatigue testing of offshore structures in the North Sea. These committees provided the foundation of standard load histories for variable amplitude fatigue testing. These load histories are not appropriate for Jack up structures as these are subjected to different loading conditions due to the different dynamic response of these structures. In this paper, the use of a Jack up Offshore Standard Load History (JOSH), which was developed under the framework of WASH, is reported. Although many models, including those mentioned above, are able to simulate realistic load sequences, the validity and suitability of the generated sequence are often overlooked. This paper gives an insight to a stationary standardised load sequence, generated using the JOSH model, for variable amplitude corrosion fatigue testing of jack-up structures. For clarity, the JOSH model, together with its major components is presented. Previous High Strength Steel projects have concentrated mainly on establishing the influence of cathodic protection, and overprotection, on the fatigue life of welded joints as the HSE Guidance has proposed the need for CP limiters when using High Strength Steels. A major finding from the early studies was that at least some of the newer steels were not very susceptible to overprotection (-1050mV) in a corrosive environment at modest lives. The impetus for this research programme stems from concerns over the lack of data for fatigue of high strength steels in the long life region. This study investigated the Long Life Corrosion Fatigue performance of SUPERELSO 702 (SE 702), a widely used weldable High Strength Steel (made by Creusot-Loire Industrie as a NiCrMo steel of similar strength). The main objective of the investigation was to study the effect of cathodic over-protection on the fatigue performance of high strength steel in the long life region. The corrosion tests were conducted under simulated seawater environment. Two cathodic protection (CP) levels, -800mV and -1050mV, were implemented by using CP limiters. Constant fatigue crack monitoring along the weld toe of the specimens enabled the study of the influence of CP during long life fatigue. The results obtained from this investigation are compared with previous Long Life Corrosion Fatigue of high strength steel research programmes. The results are also compared with the fatigue

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performance of conventional fixed platform steels such as BS EN 10025 Grade S355J2G3 (formerly known as BS4360 50D steel). Overall results have shown that there is a significant enhancement in long life fatigue performance of SE 702 over the conventional fixed platform steels. Although the cathodic over-protection specimens showed a significant reduction in fatigue performance, the fatigue lives are well above the S-N design curves and the effect of hydrogen embrittlement is less detrimental than expected.

17. SIM, Philosophy, Instrumentation and Analysis

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CRACK MONITORING USING ACFM R. F. Kare TSC Inspection Systems 6 Mill Square, Featherstone Road Wolverton Mill, Milton Keynes, MK12 5RB [email protected] Key input data for SIM calculations are the service stresses and the crack/defect size. For the offshore industry the Alternating Current Field Measurement (ACFM) technique [1] was initially developed for subsea and topside inspection but is now used universally. ACFM has the capability to both detect and size cracks. A recent innovation for ACFM has been the introduction of array probes. These can collect crack depth information from various sites along the crack in one placement of the probe. The array probe is an area inspection and hence can also be used for crack size monitoring if left in place on the structure. Previously, ACPD (Alternating Current Potential Drop), had been used for many years for monitoring crack shape evolution in welded connections. In these cases the ACPD contacts were usually spot-welded to the test component. The results from this work were of high quality and an example of early fatigue crack growth on a tubular welded T joint tested under variable amplitude corrosion fatigue [2] is shown in Figure 1. After the development of the non-contacting ACFM technique from ACPD it became possible to monitor cracks without the need to attach probes. In a recent series of fatigue tests [3] this new approach has been demonstrated using array probes for monitoring. The array probes consisted of eight Bx and Bz coils arranged in a row at 10mm spacing. Four array probes were used to cover an area 160x20mm. The fatigue tests were conducted on a high strength steel in four point bending at a frequency of 2Hz and a stress range of 200MPa. The specimen dimensions were 600 x 150 x 20mm and the weld had been ground to give a smooth finish. Some detail of one of the tests is given here as an illustration of monitoring. The test occupied a total of 1.1 million cycles and the majority of the crack data occurred over the last night of the test. Figure 2 shows the interpreted ACFM array data for crack depth growth rate for the latter part of the test. The test ended in a fast fracture from a crack which was 10mm deep and 50mm in length. It can be seen that the ACFM array probe showed a gradual increase in the crack growth rate prior to the final fracture. The final crack size was confirmed from visual inspection after the fracture event.

Figure 1: Early fatigue crack growth data, showing crack initiation in a tubular welded joint

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Figure 2: Interpreted ACFM array data for crack depth growth rate

References. 1.

TSC Inspection Systems, 6 Mill Square, Featherstone Road, Wolverton Mill, Milton Keynes MK12 5RB.

2.

Myers, P. T., Corrosion fatigue and fracture mechanics of high strength Jack-up steels, Ph D Thesis, London University, 1998.

3.

Kare, R. F. and Tantbirojn, N., Monitoring Crack size using ACFM, SIMoNET Inaugural Seminar March 2000, UCL.

18. Fracture of Biomaterials

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FATIGUE BEHAVIOUR OF FIBER REINFORCED BONE CEMENT B. Kumar and F. W. Cooke National Institute of Aviation Research, Wichita State University 1845 N .Fairmount St Wichita KS USA Othropaedic Research Institute Inc., Via Christi Regional Medical Center - St Francis Campus Wichita, KS, USA [email protected], [email protected] The use of poly methyl methacrylate (PMMA) based bone cement as a grouting agent for the invivo fixation of orthopaedic implants has been in practice for nearly fifty years. Fatigue failure of the bone cement has been identified as the primary cause of cement failure. Implant loosening due to the failure of the cement is one of the major reasons necessitating revision surgery. The need for a more fatigue resistant bone cement is well documented in the literature [1, 2, 3, 4]. One method of producing a more fatigue resistant bone cement is to reinforce it with short fibers [2]. In this investigation the impact of fiber reinforcement on the fatigue properties of the bone cement was studied. The mechanism of fatigue in brittle matrices and short fiber reinforced matrices is extremely complex. Therefore to during the course of this investigation only the following two types of fiber reinforcements: short flexible Polyethylene Terephalate (PET) fibers and stiff milled carbon fibers were used. To understand the mechanisms involved and their effect on the fatigue life of the composite, a three pronged approach has been used in this research. The key elements of the research can be summarized as follows: •

A test program was conducted to obtain fatigue data on fiber reinforced bone cement for a wide range of test conditions.

•

Rigorous statistical analyses of the fatigue data were performed.

•

A fractographic study of the fracture surfaces of the fatigue specimens was performed to develop a deeper insight into the micro-mechanics of the fatigue of reinforced bone cement.

To optimize the fiber reinforcement of the cement the effect of the following parameters was considered: (1) fiber types (stiff versus flexible), (2) fiber lengths, (3) fiber volume fraction and (4) fiber surface treatments was also conducted. Since S-N type of testing for all the specimen types would be very extremely time consuing, the comparison of all the specimen types was made by testing at a maximum stress of 15 MPa, since this is the most widely used stress level quoted in the literature on the subject [5]. The full S-N characterization of neat cement, one percent by volume scoured PET fiber reinforced, one percent by volume as received carbon fiber reinforced, one percent by volume treated carbon fiber reinforced, and two percent by volume as received carbon fiber reinforced bone cement was conducted. It is not possible to provide all the results of the testing conducted. Therefore only the S-N plot of different spedcimen types is shown on one plot in figure 1. From the overall observation of the fatigue test data, the statistical analyses and the fractographic analysis, it can be concluded that the reinforcement of the bone cement with the stiffer carbon fibers was moderately beneficial to its fatigue life. Further, the interface between the fiber and the bone cement matrix plays a crucial role in the energy dissipation process. The fractographic evidence shows the lack of interfacial bonding between the PET resulting in poorer reinforcement thus less positive influence on the fatigue resistance as compared to the carbon fiber reinforcement.

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FIGURE 1. S-N Plot of the testing

References 1.

Krause, W., and Mathis, R. S.," Fatigue Properties of Bone Cements: Review of the Literature," Journal of Biomedical Materials Research, Vol. 22, No. A1, 37-53, 1988.

2.

Reinforced Bone Cement in Orthopaedic Surgery," Journal of Biomedical Materials Research, vol. 10, 893-906, 1976.

3.

Topoleski, L. D. T., Ducheyne, P. and Cuckler, J. M., " Fracture Toughness of Titanium Fiber Reinforced Bone Cement," Journal of Biomedical Materials Research, Vol. 26, 1599-1617, 1992.

4.

Johnson, J. A., Provan, J.W., Krygier, J. J., Chan, K. H. and Miller, J., " Fatigue of Acrylic Bone Cement – Effect of Frequency and Environment," Journal of Biomedical Materials Research, Vol. 23, 819-831, 1989.

5.

Rydell, N., "Forces in Hip Joint, Part II Intravital Measurements," Biomechanics and Related Bio Engineering Topics, Ed. R. M. Kenedi, 351- 357, Pergammon Press 1965.

18. Fracture of Biomaterials

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FRACTURE AND FATIGUE OF BONE AND BONE CEMENT: THE CRITICAL DISTANCE APPROACH David Taylor, David Hoey, Lorena Sanz and Peter O’Reilly Trinity Centre for Bioengineering Mechanical Engineering Dept., Trinity College, Dublin 2, Ireland [email protected] This paper is concerned with the effect of stress concentrations on the failure of two materials of major importance in the field of biomechanics: bone and bone cement. Stress concentrations such as holes and notches are often introduced into our bones during orthopaedic surgery: examples are holes drilled to accommodate screws in fracture fixation, and pieces of bone removed for biopsies. Other workers have shown that the monotonic strength of whole bones is significantly reduced by the presence of circular holes: two interesting observations are that the size of the hole has a significant effect and that the size dependence is much greater for bones loaded in bending than those loaded in torsion [1,2]. The present work aimed to predict these effects. Bone cement, which is the polymeric material PMMA, is used widely in orthopaedic surgery to assist in the fixation of implants such as the artificial hip and knee joints. Fatigue cracking of this material is responsible for a large proportion of failures of these joint prostheses. Cement layers tend to contain defects, including small spherical pores of entrapped air and larger defects which are essentially casting defects. These features act as stress concentrations which can initiate fatigue cracking [3]. Much effort has been expended to try to reduce the amount of porosity in bone cement: the work described here attempted to quantify the effect of individual defect size and shape on high cycle fatigue strength. The theoretical model used in the work was the theory of critical distances (TCD). This approach has been the subject of much recent investigation in our research group (see, for example, [4,5]) and is also the subject of a special session at the present conference. The TCD can be used to predict the effect of stress concentration features on both fatigue and monotonic brittle fracture. The theory uses two material parameters: a critical stress and a critical distance. Failure is assumed to occur when some function of the elastic stress in the vicinity of the feature becomes equal to the critical stress. Various functions can be used, including the value of the stress at a fixed distance from the feature (we call this the Point Method (PM) because we consider only the stresses at a single point) and the average stress measured along a line drawn from the point of maximum stress (we call this the Line Method). The TCD has not previously been used to predict the behaviour of bone, though it has been extensively employed in studying fracture in fibre composite materials, since the 1970’s [6]. We have previously shown that the TCD can be used to predict brittle fracture in bone cement [5] and fatigue in metallic materials [4], but fatigue in bone cement has not previously been studied using this approach. Tests were conducted to measure the static strength (nominal stress to failure in monotonic loading) for samples of bovine bone. The loading axis was either parallel or perpendicular to the longitudinal axis of the bone. Some samples were plain (unnotched), others contained either a central circular hole or a pair of sharp edge notches. Stress analysis was carried out using FEA. Results showed that the TCD could be used, the critical stress being equal to the plain-specimen tensile strength: critical distance values were found to be almost the same for transverse loading as for longitudinal loading (L=1.5mm approx.), even though the tensile strengths in the two directions were quite different. Applying these data, and using a multiaxial criterion of the critical-plane type, we were able to predict other results on the effect of hole size; in particular we were able to

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demonstrate the much smaller effect of holes for bones loaded in torsion compared to bending [1,2]. Bone cement samples were moulded and tested in fatigue up to one million cycles to failure. Again we tested specimens which were either plain or contained holes or sharp notches, though in this case even the plain samples contained small spherical pores as a result of the casting process. Results showed that the TCD could be used also in this case, though it was found that the critical stress was significantly higher than the plain-specimen fatigue strength, by a factor of slightly more than 2. The consequence of this finding is that features having stress concentration factors less than 2 (such as spheres) are predicted to have no effect in reducing fatigue strength (except for any effect which they may have in reducing the load-bearing area). This prediction was confirmed by the observation that, whilst the plain specimens contained spherical pores up to 2mm in diameter, these pores were often not the source of failure: rather, cracks initiated from elsewhere in the specimens. In conclusion, the Theory of Critical Distances can be applied to both bone and bone cement, to predict fracture and fatigue, using FEA to obtain information on local stress fields around features and defects. The approach can usefully be employed to assess the likely reduction in strength of a bone as a result of removal of material during an operation, and so to optimise the size and shape of the removed portion. The theory can also be applied to analyse the effect of defects on the long-term integrity of bone cement layers in artificial hip joints and other implants. In this respect we showed that both the absolute size and the shape (especially the stress-concentration factor) of the pores need to be considered when assessing the potential benefits of any procedure for pore removal or reduction.

References 1.

Specht, T.E., Miller, G.J. and Colahan, P.T. Amer.J.Vet Res. 51 1242-1246 1990.

2.

Seltzer, K.L., Stover, S.M., Taylor, K.T. and Willits, N.H. Vet.Surg. 25 371-375 1996.

3.

Culleton, T., Prendergast, P.J. and Taylor, D. Clinical Mater. 12 95-102 1993.

4.

Taylor, D. Int.J.Fatigue 21 413-420 1999.

5.

Taylor, D., Merlo, M., Pegley, R. and Cavatorta, M.P. Mater.Sci.Engng A 382 288-294 2004.

6.

Whitney, J.M. and Nuismer, R.J. J.Comp.Mater. 8 253-265 1974.

18. Fracture of Biomaterials

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FATIGUE FAILURE IN RECONSTRACTED ACETABULA – A HIP SIMULATOR STUDY J. Tong, N. P. Zant and P. Heaton-Adegbile1 Department of Mechanical and Design Engineering University of Portsmouth, UK 1King Edward Hospital VII Hospital, UK [email protected] The long-term stability of total hip replacements (THRs) critically depends on the lasting integrity of the bond between the implant and the bone. Late failure in the absence of infection is known as “aseptic loosening”, a process characterised by the formation and progressive thickening of a continuous layer of fibrous tissue at the interface between the prosthesis and the bone. Aseptic loosening has been identified as the most common cause for long-term instability leading to gross migration of the implants and failure of the THRs. There is clearly a need to study the failure mechanisms in the acetabular fixation if the long-term stability of THRs is to be significantly improved. Retrieval studies based on revision operations at King Edward VII Hospital, UK, reveal that, although microcracks develop in the cement mantle, it is the debonding between cement and bone that often defines the final failure of cemented acetabular replacements. This was illustrated at the revision surgeries by the easy removal of the acetabular cups with cement mostly attached to the cup. It is felt that a fundamental understanding of the mechanisms that initiate and propagate the interfacial failure at the bone-cement interface is the key towards solving the problem. In this work, preliminary fatigue tests were carried out on cemented acetabular replacements using a servo-hydraulic testing machine (Si-Plan Electronics Research Ltd., UK). Thirdgeneration of composite pelvic bones were used to which Charnley cups were implanted using the bone cement, CMW, following the standard surgical procedures. The implanted hemi-pelvic bone model was then constrained at the sacro-iliac and pubic joints to represent the anatomic constraint conditions. To achieve the direction of the maximum hip contact force during gait, a milling vice with two rotational degrees of freedom was used. The hemi-pelvis was loaded to the peak hip contact force during normal walking (Bergmann et al., 2001), with a body weight of 70 kg assumed. Sinusoidal waveforms were applied and the load was fully compressive from -0.2 to -1.6 kN at a frequency of 5 Hz. Damage was monitored using CT scanning and pronounced interfacial fracture at the bone-cement interface was observed at 2 million cycles (Heaton-Adegbile et al., 2005) In vitro fatigue tests have been carried out utilising a new 4-station hip joint simulator (Simsol Ltd, UK), specially designed for testing of implanted acetabula. Hip contact force during gait, including both magnitude and direction (Bergmann et al., 2001), has been realised in the hip simulator so that the effects of physiological loading on the damage development in the acetabular replacement can be realistically assessed. Damage development in the joints is monitored using CT scanning at regular intervals. Permanent records are collected and the samples will be eventually sectioned and polished for microscopic studies. Results from the conventional fatigue tests will be compared with those from the hip simulator and recommendations with regard to pre- and post- clinical assessments of the fixation will be made based on the findings of this work.

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FIGURE 1. An implanted specimen under hip simulator testing.

References 1.

Bergmann, G.; Deuretzbacher, G.; Heller, M.; Graichen, F.; Rohlmann, A.; Strauss, J., and Duda, G. N. Hip contact forces and gait patterns from routine activities. Journal of Biomechanics. 2001; 34(7): 859-872.

2.

Heaton-Adegbile, P.; Zant, N. and Tong, J. In-vitro fatigue behaviour of a cemented acetabular reconstruction. Submitted to J Biomechanics.

18. Fracture of Biomaterials

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DEFORMATION AND FRACTURE OF BIOACTIVE PARTICULATE COMPOSITES DEVELOPED FOR HARD TISSUE REPAIR M. Wang Department of Mechanical Engineering, The University of Hong Kong Pokfulam Road, Hong Kong [email protected] Most human body tissues are composites in nature. Using natural tissues as templates, “designer” bioactive ceramic-polymer composites are developed for tissue replacement and regeneration [1]. This biomimicking concept has now been extended into developing bioactive composites with metals or ceramics as matrices. Furthermore, with the recent emergence of tissue engineering, bioactive composite scaffolding materials are under active development [2]. The composite approach is therefore being established as one of the most important and viable ways in developing new biomaterials. Hydroxyapatite (HA) reinforced polyethylene (PE) was the first bioactive ceramic-polymer composite developed for bone substitution [3]. Considering the loading conditions of this composite in its clinical applications situations, various types of mechanical testing have been conducted [4-9]. The deformation behaviour of this material was different under different deformation mode, which also depended on the HA content in the composite. In order to improve the mechanical performance of HA/PE composite, two methods were investigated: chemical coupling between HA particles and the polymer matrix [10], and hydrostatic extrusion [11]. The deformation process and fracture of the improved HA/PE composite showed significant differences from those of non-treated HA/PE composite [11, 12]. By carefully studying the deformation process and fracture behaviour of HA/PE composite of different HA contents, insights could be gained and lessons learnt for further developing various bioactive polymer-matrix composites for human body tissue repair.

(a) Tensile behaviour and deformation (b) Compressive behaviour and deformation FIGURE 1. Deformation and fracture of HA/PE composite (20vol.% of HA) Generally, composite having HA of smaller mean particle size possessed higher Young’s, compressive, torsional and flexural moduli. With an increase in HA amount in composite, modulus values of the composite increased, i.e., the incorporation of hard HA particles in the soft PE matrix stiffened the polymer. However, strength of the composite was not significantly increased by the addition of HA into the polymer. During tensile testing, all specimens fractured, and necking was noted before their fracture in composite having less than 20vol% of HA (Fig.1).

M. Wang

1030

2

3

4

FIGURE 2. HA/PE specimen during flexural testing FIGURE 3. Flexural fracture surface of HA/PE composite FIGURE 4. Deformation and fracture of HA/PE composite During flexural testing, composite containing more than 40vol% of HA fractured but composite of other HA volume percentages deformed without fracture after peak stresses had been passed (Fig.2). During compression testing, only with a few exceptions, even composite containing 45% of HA did not fracture when compression tests were stopped at 70% compressive strain. Composite specimens became barrel-shaped as compression tests proceeded and they went through three main stages of deformation (Fig.1). Debonding took place between HA particles and the polymer matrix during tensile and bending tests as gaps were observed at the HA-polymer interface (Fig.3). Under tension and bending loading conditions, the fracture mechanism of HA/PE composite was the same, which involved dewetting, cavitation, voids-coalescence, and tearing and fracture of polymer fibrils (Fig.4). Tensile deformation of hydrostatically extruded HA/PE composite was significantly affected by the polymer chain alignment [11]. Chemical coupling between HA particles and PE matrix delayed the dewetting and cavitation process [12]. The shear stress component of the biaxial fatigue stress could significantly shorten the fatigue life of HA/PE composite [9, 13].

References 1.

Wang, M., Biomaterials, vol. 24, 2133-2151, 2003

2.

Wang, M., et al., Journal of Materials Science: Materials in Medicine, vol.12, 855-860, 2001

3.

Bonfield, W., Journal of Biomedical Engineering, vol.10, 522-526, 1988

4.

Wang, M., et al., British Ceramic Transactions, vol.93, 91-95,1994

5.

Wang, M., et al., Journal of Materials Science: Materials in Medicine, vol.9, 621-624, 1998

6.

Wang, M., et al., Biomaterials, vol.19, 2357-2366, 1998

7.

Wang, M., et al., Key Engineering Materials, vol.284, 693-696, 2005

8.

Wang, M., et al., Key Engineering Materials, vol.254, 611-614, 2004

9.

Wang, M., et al., In Proc. 10th Intern’l Conf Biomed. Engg, Singapore, 2000, 219-220

10. Wang, M., et al., Materials Letters, vol.44, 119-124, 2000 11. Wang, M., et al., Journal of Materials Science, vol.35, 1023-1030, 2000 12. Wang, M., and Bonfield, W., Biomaterials, vol.22, 1311-1320, 2001 13. F.H.-L.Tang, MEng Thesis, Nanyang Technological University, Singapore, 2001

18. Fracture of Biomaterials

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FAILURE OF BIOMATERIALS IN IMPLANT FIXATION Patrick J. Prendergast, John R. Britton, Paul T. Scannell and Alexander B. Lennon Trinity Centre for Bioengineering Department of Mechanical Engineering, Trinity College, Dublin, Ireland [email protected] A surprisingly wide range of metals, polymers, and ceramics meet the requirements of biocompatibility for use in orthopaedic implants [1]. Three metals are by far the most commonly used: stainless steel, chromium cobalt alloys, and titanium and its alloys. Oxide ceramics (Al203, ZrO2) are used for bearing surfaces and calcium phosphate bioceramics and glass ceramics are used as coatings to invoke integration with host tissues. Regarding polymers, two are ubiquitous in orthopaedic implants: ultra-high molecular weight polyethylene (UHMWPE) for bearings and polymethylmethacrylate (PMMA) as a grouting to ‘cement’ implants into bones [2]. Unfortunately, in a very large number of cases, the biomaterials do not possess sufficient mechanical durability – in consequence the implant fixation does not outlive the patient. Revision operations are necessary in approximately 7% of hip and 5-10% of knee replacements at 10 years [see the Swedish National Hip Arthroplasty Register at www.jru.orthop.gu.se and the Swedish Knee Arthroplasty Register at www.ort.lu.se]. In the upper extremity, joint replacement has been bedevilled by the challenges of creating durable implant/bone fixation between implant and bone so that rather few operations are performed for these joints. Biomaterials can fail in their function by: •

insufficient mechanical durability; failure arises by fatigue, damage accumulation, and wear,

•

provoking adverse biological responses; failure arises by bone loss or bone death due to inappropriate stressing of the peri-prosthetic tissues, failure of bone ingrowth due to relative motion between implant and tissues, or osteolysis due to wear particles, etc…

Therefore, despite the undoubted success of orthopaedic implants [2], great challenges remain in improving the performance of the biomaterials if a satisfactory outcome for the individual patient is to be guaranteed. How can this be done? We believe an important challenge lies in an accurate understanding of how in-service loading regimes provoke various failure scenarios [3] in the implant/bone complex in the individual patient. In 1993, Huiskes [3] introduced this concept of ‘failure scenarios’. These scenarios are interlinkings of (i) and (ii) above – interlinkings that are empirical and based on clinical evidence. In this paper we will consider two failure scenarios for total hip replacement and we will present computational simulations of how the biomaterial affects the failure scenarios. The first is the damage accumulation failure scenario and the second is the failed ingrowth failure scenario. In simulating the damage accumulation failure scenario, stochastic effects are introduced by performing Monte Carlo simulations of damage accumulation in bone cement with randomly generated distributions of porosity. Microcrack initiation and growth are modelled using a multiaxial damage accumulation model based on bone cement fatigue strength data. This Monte Carlo approach can simulate the same variability and mean fatigue life of bone cement specimens as seen experimentally [4]. The algorithm can then be used to simulate the damage accumulation failure scenario in a cemented joint reconstruction; a unique failure will be predicted for each analysis – this is analogous therefore to the real situation. Data can then be combined from each of the simulations to give a statistical estimate of variability and mean damage accumulation. The

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failed ingrowth failure scenario occurs in non-cemented implants when bone fails to grow into the implant surface; instead fibrous tissue persists at the bone-implant interface and, in the end, the implant loosens. This process is simulated using finite element analysis in conjunction with an algorithm that relates the rate of change of density to the applied strain and the accumulated damage [5]. The influence of the Young’s modulus of the stem on the propensity for this failure scenario can then be tested in a simulation. To allow selection of the most appropriate implant for an individual patient, a model must be generated of the patients specific bone. This is a difficult objective because a patient-specific images and loading data must be imported - Fig. 1 gives an outline of the approach

FIGURE 1. A schematic diagram for the concept of patient-specific prosthetic analysis. Data from the patient’s electronic record is used to construct a patient-specific finite element model. The probability of failure (by damage accumulation or failed ingrowth) can then be computed.

References 1.

Park, J.B., Lakes, R.S., Biomaterials. An Introduction, 2nd Ed., Plenum, New York, 1992

2.

Prendergast, P.J., In Bone Mechanics Handbook, edited by S.C. Cowin, CRC Press, Boca Raton, 2001, Chapter 33

3.

Huiskes, R., Acta Orthop. Scand., vol. 64, 699-720, 1993

4.

Lennon, A.B., Prendergast, P.J., Math. Proc. R. I. A. (www.ria.ie) vol. 104A, 155-171, 2004

5.

Scannell, P.T., Prendergast, P.J., Engineer’s Journal, (in press) 2005

19. Structural Integrity Assessment in Theory and Practice

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STRESS ANALISYS OF HIGH PRESSURE STEAMLINES IN THERMAL POWER PLANTS A. Jakovljevic Electric Power Industry of Serbia, Head Department for Development and Investments, Belgrade, Serbia [email protected] Steamlines present statically undefined pipe structures allocating between connection points on the boiler and turbine; they consist of mutually welded elements connected to support structure by the support system. For this reason, it is necessary to bear in mind during all stress analyses of steam lines, an entire sequence of additional influences, which have considerable impact on the behavior of steamlines, and are not directly related to the operating parameters of the fluid: pressure and temperature. Overstressing by permanent, thermal and dynamic loads is primarily caused by inadequate configuration of the steam line, irregular operation of support system and loads in transintient states. High pressure steam pipelines are critical components of thermal power plants, which have significant influence on reliability and availability of plants as well as staff safety. Therefore, during operation, it is necessary to monitor their actual condition and also to provide preconditions for assessing high pressure steam pipeline’s behavior during further exploitation in order to perform residual life assessment. In operation conditions, high pressure steam pipelines are exposed to creep and low cyclic fatigue, which lead during the time, to microstructural degradation as well as appearance and development of steel damage. Methods for quantitative estimation of the remaining operation life are mainly based on the assumption that component is exposed only to the activity of internal pressure, which simplifies the problem. This is generally the reason why analyses are started with stress values, which do not represent stress to which the steamline component is exposed to during operation. Steamline has to be observed during the analysis as a complex structure, which is exposed, besides the action of internal pressure of the operation fluid, also to the action of additional external load. It greatly depends on configuration and support system of the steamline and it causes the appearance of stress conditions that greatly differ from design ones. Their negative impact on the operation life of the steamline and correct estimation of the remaining operation life require the consideration and quantification not only the impact of internal pressure and temperature but also all effecting loads. Due to that, usage of numerical methods for calculation and analisys of stress condition is neccesary. Most of numerical methods for the calculation of stress state are based on the application of finite elements method, which can be used in two ways, from the aspect of steamline analysis: for structural calculations of the complete structure, as well as for the calculation and analysis of individual components. The paper gives an example of the performed stress analysis of the main steamline at the unit A1 – TPP Nikola Tesla in Obrenovac, which is used to present the importance of stress analyses and the possibilities and restrictions of numerical methods for the performance of such analyses (Fig. 1). Considered steamlines were selected for the analysis because they with nearly 200.000 operation hours (designed for 100.000 hours) represent the oldest steamlines in Electric Power Industry of Serbia plants.

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FIGURE 1. Stress condition of the main steam line in hot state Structural analysis of stress state of these steamlines was performed according to ASME/ANSI B31.1 standard. Then, two pipe elbows of the same size were chosen from steamline. Selection is made so that one of them belongs to the group of pipe elbows with the highest load and the other to the group with the lowest load on the steamline and that there is sufficient date from previously performed investigations. Detailed analysis of the stress state of chosen elbows by the finite elements method was performed using linear-elastic analysis, for three different load cases. Application of finite elements method, although with some simplifications, enables to obtain the clearer picture and better consideration of the behavior of analyzed steamline components. Performed stress analyses enable the identification of critical points in which the stress is increased in the steamline and its components. These points have to be taken into consideration during the monitoring of steamline state. Impact of external load on the appearance of considerably different stress state in some components with nominally the same geometry, operating on the same pressure and temperature, as well as the possibility of appearance of the most unfavorable stress state outside the anticipated zones was clearly demonstrated.

19. Structural Integrity Assessment in Theory and Practice

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LAMINAR COMPOSITE MATERIALS DAMAGE MONITORING BY EMBEDDED OPTICAL FIBERS Aleksandar Kojovi, Irena Zivkovi1, Ljiljana Brajovi2, Dragan Mitrakovi and Radoslav Aleksi Faculty of Technology and Metallurgy 1Institute of Security 2Civil Engineering Faculty Karnegijeva 4, Belgrade, Serbia and Montenegro 1Kraljice Ane bb, Belgrade, Serbia and Montenegro 2Bul Kralja Aleksandra 73, Belgrade, Serbia and Montenegro [email protected], [email protected], [email protected], [email protected], [email protected] This article the describes procedure of embedding fiberoptic sensors in laminar thermoplastic composite material, as well as damage investigation after low energy impact, in real time. Experimental testing was carried out in order to observe and analyze the response of material under various load conditions. Different type of Kevlar® reinforced composite materials, and combination of Kevlar® and metal mesh (thermoplastic or thermoreactive matrix) were made. For that purpose intensity based optical fibers were built in specimens of composite materials. Main advantages of fiber optic sensors are their shape and structure which result in easy embedding while preserving mechanical properties of composite material, which make them a reliable automatic system for structure health monitoring.

FIGURE 1. Specimen placeholder. Impact toughness testing by Charpy impact pendulum with different loads was conducted in order to determine method for comparative measurement of resulting damage in material. Specimens were fixed in placeholder as shown in Fig. 1. Light from the light emitting diode (LED) was launched to the embedded optical fiber and was propagated to the phototransistor based photo detector. During each impact, level of signal, which is proportional to light intensity in optical fiber, drops, and then slowly recovers

1036

A. Kojovi et al.

FIGURE 2. Characteristic signal change during impact. Obtained signals were analyzed to find appropriate method for real time damage monitoring. Major part of damage occurs during the impact. Damage reflects in local, temporary release of strain in optical fiber, and raise of signal level as could be seen during the impact in Fig. 2. Mathematical method was developed and applied on signals to monitor development of damage in material and for analyzing quality of material. Results show that intensity based optical fibers could be used for measuring damage in laminar thermoplastic composite materials, and could be used as reliable automatic system for long-term structure health monitoring. Light signal intensity drops in an optical fiber in response to applied loading on composite material. Acquired optical fiber signals depend on type of material, but same set of rules (relatively different, depending on type of material) could be specified. Existing methods in most cases uses just intensity of signal before and after the impact, as measure of damage. In this case using real time measurement of signal during impact and appropriate analysis enables quantitative evaluation of impact damage in material and could be used to monitor damage in real time, giving warnings before the fatal damage occurs.

19. Structural Integrity Assessment in Theory and Practice

1037

SOL GEL SYNTHESIS AND STRUCTURE OF HYBRID NANOMATERIALS WITH STRONG CHEMICAL BONDS B. Samuneva, P. Djambaski, E. Kashchieva and G. Chernev Department of Silicate Technology, University of Chemical Technology and Metallurgy, Sofia, Bulgaria I.M. Miranda Salvado, M.H.V. Fernandes, A. Wu Department of Ceramic and Glass technology, CICECO, University of Aveiro, Portugal [email protected] Sol-gel synthesis at molecular level and low temperature gives us a possibility to obtain new materials with non-traditional physical and chemical properties of special interest, highly homogeneous and pure. Recently a great attention has been paid to this method because of synthesizing new hybrid (organic-inorganic) materials having nanoscaled structure. The newly synthesized hybrid coatings and bulk materials can be successfully applied in optics, electronics, technics, medicine, and biotechnology. The chemical composition of hybrids and the nature of chemical bonds between the organic and inorganic components in their structure are the most important parameters determining physico-chemical behavior of these materials. The different organic-inorganic hybrids can be classified into two broad families, according to the nature of chemical bond between their organic and inorganic components: Class I – hybrid systems in which one of components (organic, biologic or inorganic) is entrapped within a network of the other component and Van der Walls Hydrogen bonding or electrostatic interactions are found; Class II – hybrid materials in which the inorganic and organic parts are chemically bonded by a covalent or ionic-covalent bond. The hybrids belonging to Class II are more appropriate for obtaining of nanomaterials with high mechanical and corrosion resistance. The main purpose of this paper is to present a review of our recent research results in sol-gel synthesis and structure of multifunctional silica hybrid nanomaterials with strong chemical bonds between their organic and inorganic components. The silica hybrid materials have been synthesized via sol-gel technology at room temperature. Four different types of silicon precursors have been used - tetraethylortosilane (TEOS), tetramethylortosilane (TMOS), methyltriethoxysilane (MTES) and ethyltrimethoxysilane (ETMS). The hybrids were synthesized by replacing a different quantity of inorganic precursors with 5, 10, 15 and 20 mol % of the following organic compounds, respectively: polyethylene glycol (PEG), polyvinyl alcohol (PVA), acrilamide (AA), polyacrilamide gel (PAAG), methyl methacrylate (MMA), calcium alginate and agar-agar. The processes of sol-gel synthesis and structure evolution of gels have been studied by means of FT-IR (IR-MATSON 7000–FTIR spectrometer), XRD (Xray PW1730/10 diffractometer), BET-Analysis (Gemini 2370 V5.00), EDS (RONTEC EDS System), SEM (Philips-515) and AFM (NanoScope IIIA Tapping ModeTM). Thin transparent hybrid flakes and films have been obtained and no separation has been observed before and after gelation point. The results from the XRD - analysis prove that all the hybrids described in this study are in amorphous state, which is in good correlation with some other published works. The intensity of the XRD patterns depends on the type and quantity of the organic component. The data from BET - analysis show that the pore diameter is about 2 nm and that is connected with an increase of the organic component concentration; the surface area of such pores decreases from 587 m2/g to 125 m2/g.

1038

B. Samuneva et al.

FIGURE 1. AFM image of a hybrid sample (MTES) containing 20 % (MMA) To establish the existing chemical bonds in the hybrids synthesized, the FT-IR Spectroscopy has been used. It has been proved that the type of silica precursors influence significantly affects the formation of different in-nature chemical bonds. The absorption band at 2975 cm-1 , 1255 cm-1 and 694 cm-1 , due to the presence of Si-O-R (CH3 and C2H5) and Si-C bonds have been registrated in the IR spectra of the hybrids with ETMS. This fact directly proves the presence of strong chemical bonds between the inorganic and organic parts of the synthesized materials. At the same time it can be supposed that in the samples with TEOS only Van der Walls Hydrogen bonds or electrostatic interactions exist. The presence of well-defined nano units and their aggregates in the hybrid structure, formed by self-organizing processes, is clearly observed by AFM, Fig. 1. The average size of nanoparticles on the sample surface is from several nanometers up to 30 nm; the development of nanostructure evolution processes can be seen. The synthesized multifunctional hybrid nanomaterials could be successfully applied as carriers for cell immobilization and for corrosion and mechanical resistant coatings.

19. Structural Integrity Assessment in Theory and Practice

1039

AN ALTERNATIVE APPROACH TO CONVENTIONAL DATA PRESENTATION OF FATIGUE D. Angelova Donka Angelova – Professor, University of Chemical Technology and Metallurgy-Sofia (UCTM), 8 Kl. Ohridsky Blvd., 1756 Sofia, Bulgaria [email protected] Although major advances have been made in fatigue modelling, the application of fatigue concepts to different practical situations is highly individual and often involves empirical and semiempirical approaches including a large number of specifying constants. For most engineering alloys the plot of crack growth rate, log da / dN log ' K

against stress-intensity factor range,

exhibits a sigmoidal curve with three distinct regimes of crack growth, Suresh [1]: I of

threshold behaviour; II of Paris line log da / dN – log ' K ; and III of rapid increasing of da/ dN causing catastrophic failure. The Paris regime is described by an equation log da / dN



C log ' K , where C and m are scaling constants, and sometimes applied to all data obtained: M(K) in Fig. 1. At elastic-plastic conditions, [1] modelling based on m

da

/ dN



C log ' J

m

takes

FIGURE 1. Newly proposed alternative (Q) and conventional (M) data presentations of fatigue in a high-strength spring steel (C 0.56, Mn 0.81, Si 1.85, Cr 0.21, Ni 0.15, P 0.026, Mo 0.025, S 0.024) under fully reversed torsion, Murtaza [2] part: M(J) in Fig. 2. For the rest of ingineering materials the multitude of points M – M(K) or M(J) – may be expressed by different types of curves or just as a cloud of points. An alternative method is proposed comprising the fatigue testing of ingineering materials;

D. Angelova

1040

FIGURE 2. Alternative (Q) and conventional (M) presentations of fatigue in a E-Ti-6Al-4V alloy (Al 6.52, V 4.00, Fe 0.16, O 0.182) under axial and combined loading, Hoshide [3] measuring long-crack or main short-crack lengths a and the corresponding number of cycles

N ; calculating crack rates da / dN , stress-intensity factor range

'K

or J-integral range ( da / dN ) ' K or

'J, and a newly introduced energy fatigue-function in its 4 versions W W

( da / dN ) ' J ] or W

( da / dN ) a 1 / 2 or kW

normalizing constant from the type k

N

f

a f K

max

k ( da / dN ) ' K where k is a

a , a f f

and N

f

are respectively the

 is the stress

final length of fatigue crack and the number of cycles at failure, and K max a f intensity factor at V dimensional

max

from the applied stress range ' V

expression.

The

presentation

V

max

V

min

;

kW

is a non-

log da / dN  log W

or log da / dN  log kW is an almost straight line, Q(K) or Q(J) in Figs. 1 and 2, which may be termed the fatigue tendency of the material at a given stress range, mentioned for the first time and only for 'K in Angelova [4]. The two figures show the equation of this line in Q(K) and Q(J) as a thick line; each scatter band around such a line is indicated by two thin lines corresponding to ½ and 2 folds of da/dN.

A comparative analysis between M and Q presentations shows that at the same number of crack-size measurements, the precision of the proposed method is significantly higher, expressed quantitatively by the corresponding correlation coefficients fc shown in Figs. 1 and 2. This result suggests a possible decrease of fatigue measurements and is approved for another 11 materials.

References 1.

Suresh S., Fatigue of Materials, Cambridge University Press, Cambridge, UK, 1998.

2.

Murtaza G., Ph.D. Thesis, University of Sheffield, UK, 1992.

3.

Hoshide T., Hirota T., Inoue T., J. Materials Sci. Research Int.,Vol. 1, No 3, 169-174, 1995.

4.

Angelova, D." In Proceedings of ECF13 on CD, Abstracts Volume, San Sebastian, September 2000, 128.

19. Structural Integrity Assessment in Theory and Practice

1041

ABSORBERS OF SEISMIC ENERGY FOR DAMAGED MASONARY STRUCTURES D. Sumarac2, Z. Petraskovi1, S. Miladinovic1, M. Trajkovi3, M. Andjelkovic2 and N. Trisovic4 1system DC 90, Vele Negrinove 1,11000Belgrade, Serbia and Montenegro (SCG) 2Faculty of Civil Eng., Univ. of Belgrade, Bul. Kralja Aleksandra 73, 11000 Belgrade, (SCG) 3Faculty of Civil Eng. and Arch., Univ. of Nis, Aleksandra Medvedeva 14, 18000 Nis, SCG 4Faculty of Mechanical Eng. Univ. of Belgrade, Kraljice Marije 16, 11000 Belgrade, SCG [email protected], [email protected], [email protected], [email protected] In the present paper problem of damage of masonry structures due to earthquake is considered. It is known that masonry structures are very sensitive to earth shaking. Built from the bricks and bond by mortar, they cannot transmit large tensile stresses. Due to small earthquake of the magnitude 45 of the Richter scale those structures are usually damaged. Numerical calculation using FEM is applied on typical example of two store building ( Fig. 3). Also in the paper procedure of retrofit of damaged structures, using system DC 90, is shown. Results of laboratory testing of dampers of the system DC 90 due to dynamic loading with frequency 1-10 Hz are presented. Results are obtained in three institutes: IZIIS (Skopje), VTI (Belgrade) and IMS (Belgrade). Obtained results show high performances of dampers, which after embedment increase stiffness and ductility of structures up to 30% (Fig. 2). Besides that, results of model testing, obtained on vibro-platform for different type of masonry structures, which have been used in the areas of tectonic faults, are shown. Special attention have been made to testing in situ due to ambient vibrations (wind, earth shaking) and induced vibrations due to eccentric mass (Fig. 1). This testing was performed on damaged structures before and after embedment of dampers. Measurements are performed in Kolubara region by institute IZIIS and IMS. All investigations show high performances of embedded dampers (for which word prize was obtained on international exhibitions of patents and new technologies, Brussels Eureka 97). In the present paper process and methodology of transfer of technology for application of the system for large area heated by earthquakes is specially outlined. On examples of large number of objects reconstructed using system DC 90 in Kolubara region (Serbia), Algeria and Iran all advantages of the system DC 90 will be presented.

FIGURE 1. Equipment for generation of harmonic vibrations

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D. Sumarac et al.

FIGURE 2. Building before and after strengthening

FIGURE 3. FEM model of building

References 1.

Petraskovic, Z., Miladinovic, J.S., Technology of the Seismic Strengthening of Masonry Structures by Applying Vertical Ties and Diagonals with Seismic Energy Absorber, IMS Institute, Conference, Belgrade, Serbia and Montenegro, 2000

2.

Sumarac, D., Krajcinovic D., Elements of Fracture Mechanics, Naucna knjiga, Belgrade, Serbia and Montenegro, 1990 (in Serbian)

3.

Petrovic, B., Selected Topics of Seismic Engineering, Gradjevinska knjiga, Belgrade, Serbia and Montenegro, 1989 (in Serbian)

19. Structural Integrity Assessment in Theory and Practice

1043

NUMERICAL ANALYSIS OF TENSILE SPECIMEN FRACTURE WITH CRACK IN HAZ Gjorgji Adziev1, Aleksandar Sedmak2 and Todor Adziev1 1 Faculty of Mechanical Engineering - Skopje, FYROM 2 Mechanical Engineering Faculty, Belgrade, Serbia & Montenegro [email protected] The numerical solutions enable investigation of complex problems, including various effects, particularly in the cases where the experimental investigations and mathematical solutions are unappropriate due to high costs. This research deals with numerical modelling and behaviour analysis of tensile specimens, with crack located in the heat-affected-zone (HAZ), with respect to the effect of the weld strength mismatch on the stress-strain distribution around the crack tip and the causes leading to failure. ANSYS package for structural analysis was used for preprocesing, procesing and postprocesing. The welded joint is modeled as simplified multiregion material system, consisting the typical root, fill and surface layers, as well the HAZ region consisting the fine-grained (FG) HAZ and coarse-grained (CG) HAZ, Fig. 1. The crack tip with very small radius of 0.05 mm i.e. the crack front in the 3D (Fig. 2) analysis is modeled with great refinement of the mesh, thus enabling singularity of the stress-strain field around the crack tip. As material properties, in the input file the module of elasticity, the Poason's factor and the multilinear V-H curves are defined. Numerical analysis consisted of 3D and 2D modeling. The behavior of a specimen is 3D, but 2D analysis is also beneficial since the plane stress and plane strain conditions limit the structure behavior. Plane stress is dominant state on the free surface and is typical for structures of small width. Plane strain state is dominant in the middle of the specimen and is typical for structures of greater width. The three-dimensional condition is between these two extreme conditions, since the width of the tested specimens is between the definition of small and great width. Two cases are analysed, specimens with crack tip located in the fine-grained in the coarsegrained HAZ, both made of microalloyed high strength steel for pressurezed equipment. The both cases exhibited high fracture resistance, due to the barrier effect of the mismatching, shifting the initial crack towards the more ductile parent metal, thus decreasing the crack propagation rate. As proved both experimentally and numerically, the overmatching in welded joint has acted protective in respect to crack propagation, regardless of the position of crack tip (FG HAZ or CG HAZ), increasing significantly the fracture resistance. In both cases, after the initial propagation of the crack in FG HAZ or CG HAZ, relatively small overmatching has changed crack propagation direction toward weaker and more ductile parent metal. In the case of crack tip positioned in FG HAZ, being between stronger CG HAZ and weaker parent metal, the effect of overmatching is obvious. In the case of crack tip in CG HAZ, being between weaker FG HAZ and weaker weld metal, this effect is due to combined influence of slightly lower yield strength of FG HAZ and its significantly smaller size, and also due to the lower yield strength of the parent metal. Both pairs of curves, J vs. CMOD and F vs. CMOD exhibited good agreement between the experimental and 3D numerical results. Comparing with the 2D analysis, the experimental curves were between the two extreme conditions, as expected. The partial mis-agreement between the numerical and experimental results is due to: geometrical simplification of the welded joint, including its shape, dimensions, and its composition, material behavior simplification, having in mind the analytical determination - assessment of the V - H curves for the welded joint regions using the RambergOsgood law and, finally, the finite element analysis used here did not include crack extension.

1044

G. Adziev et al.

FIGURE 1. The simplified FEM model of the welded joint

FIGURE 2. The 3D model with enlarged crack tip region

19. Structural Integrity Assessment in Theory and Practice

1045

DETERMINATION OF JR-CURVE BY TWO POINTS METHOD I. Blacic and V. Grabulov Military Technical Institute, Belgrade, Serbia and Montenegro [email protected] Preliminary results of investigation on the application of new approach to determine resistance curve based on two pairs of known J- 'a values are presented in the paper. [1,2] Proposed procedure is based on the possibility to present the dependance of J-integral on crack extension 'a as a polynomial function [1]. This relation, given in ASTM 1737 standard, imvolved two constants:

J

C 1 ˜ ' a

C2

(1)

Constants C1 and C2 can be determined for two pairs of J integral and crack extension 'a, if 'a z 0, sincein that case J integral is zero for each value of C1 and C2. Statical conditions allow to break the test and by heat tinting to mark crack extenision 'a. The Ji follows from

Ji

2 ˜U i B ˜ b0

(2)

if no correction of J integral for crack extension is applied, or from recommendation ESIS P2

Ji

2 ˜U i B ˜ b0

§ 0 . 75 ˜ K  1 ˜ ' a ¨¨ 1  b0 ©

· ¸¸ ¹

(3)

which include correction of J integral for crack extension, with K = 2 for SENB type specimen. Equation for J integral from ASTM 1737 is not convenient since it is of incremental character for calculation of J integral plastic component (see A1.5.3. of this standard). New approach for resistance curve determination is based on Equ. (1), with constants C1 and C2 are defined based on the measurement of one pair values J- 'a at the end of the test and selection of point P1 from the plot load - load line displacement (Fig. 1), belonging to the blunting line, presented by relationship: J

M ˜V

y

˜ 'a

(4).

In this way, with two pairs values of crack extension 'a and J integral, constants C1 and C2 are defined. Anyhow, the practical application revealed that values of C1 and C2 strongly depends on position of P1 point on P- f0, Fig. 1, but also on blunting line defining procedure. For that, criterion of selection of point P1 must be defined. The paper suggests criterion for selection of point P1 via relation deflection – load for point P1 and maximum load Pmax, characteristic point on load – deflection plot.

1046

I. Blacic and V. Grabulov

Preliminary investigation for defining criterion for point P1 selection are made with high strength steels (seven strength levels in the range 700 to 1320 MPa). Based on found resistance curves selection of point P1 is performed by compliance method, enabling best agreement for new proposed method application. Obtained relationship load vs. displacement for load values corresponding to points P1 i Pmax in Fig. 1 is given in Fig. 2 for steels of different strength levels. The use of diagram from fig. 2 enables to define ratio f1/P1 from fmax/Pmax ratio, and thus the point P1 position. In this way the pair of J- 'a is determined by Equ. (2) to (4) , which with another pair, determined experimentally at the end of the test allows to determine constants C1 and C2 and resistance curve.

FIGURE 1. Chracteristic points on load- deflection plot

FIGURe 2. Dependance f1/P1 vs. fm

Performed preliminary investigation has shown that it is possible to define the criterion for selection of point P1 on the load – deflection curve, but it is only one criterion, further investigation is necessary.

Refferences 1.

ASTM E 1737–96 “Standard Test Method for J-integral Characterization of Fracture Toughnes”

2.

ESIS P2-92 “ESIS Procedure for Determining the Fracture Behaviour of Materials”

3.

Pod red V. Dalja, V. Antona “Statieskaja pronost i mehanika razrusenija stalej” Moskva Metalurgija 1986 god.

4.

M. Vnuk “Problemi stabilnosti zilavog loma” u monografiji “Uvod u mehaniku loma i konstruisanje sa sigurnosu od loma” str. 141-168 TMF Beograd 1980 god.

5.

G. A. Clarck i dr. “Single Specimen Test for JIc Determination” ASTM STP 590 ASTM Philadelphia 1976 god.

6.

G. Irwin “Fracture mechanics” u “Mechanical testing” ASM HANDBOOK vol. 8 ASM Metals park

7.

Dz. Dzojs “Ispitivanje J integrala i primena u elastoplastinoj mehanici loma” u monografiji “Perspektive razvoja i primene mehanike loma” str. 27-60 TMF Beograd 1987 god.

19. Structural Integrity Assessment in Theory and Practice

1047

MONITORING OF STRESS-STRAIN STATE OF BOILER DURING PESSURE TEST Jano Kurai, Zijah Burzic1, Nikola Garic, Milorad Zrilic2 and Bosko Aleksic CertLab, Pancevo, Serbia and Montenegro 1Military Technical Institute, Belgrade, Serbia and Montenegro 2University of Belgrade, Faculty of Tehnology and Metalurgy, Serbia and Montenegro [email protected] In order to extend power capacity a new boiler BF-9602, steam production110 t/h has been installed in Oil Refinery Panevo. Boiler producer is "Slovenske energetike strojarne A.S." Tlmae Slovakia. During the assembling of tube No 13, produced of St 35.8/I steel, missalignement occurred, e.g. in welding process the was not properly positioned in the axis (Fig. 1).

FIGURE 1. Zone of misalignment of tube No 3. During the assembling of tube No 52, also St 35.8/I steel, in the boiler upper part it has been destorded and plastically deformed, Fig. 2.

FIGURE 2. The region of plastic deformation on the tube No 52. In order to assess “fitness-for-purpose” of assembled tubes, Department of investment NIS Oil Refinery Panevo in Inspection procedure for boiler acceptance has specified additional testing in regions presented in Figs. 1 and 2, enabling to evaluate the stress and strain state of damaged zones during proof pressure test by cold water. This testing should be performed from outer side, applying appropriate methods, which will not affect the structural integrity of boiler. The final decision about damaged zones repairing will be made after the analysis of stress state, assessed by testing.

J. Kurai et al.

1048

Since new boiler has to be inspected after assembling, investor accepted the proposal to perform also the tests for stress assessment on water mantle of boiler. Additional aim of this testing was to define boiler state (so-called zero state) before service, only possible during first proof water pressure test. For accomplish this task, having in mind the location and orientation of damaged regions, as well as medium and operating condition, following methods have been applied: •

Acoustic emission method, and

•

Strain gauges measurement.

Obtained results and performed analysis allowed following conclusion: Measured microstrains on strain gauges and calculated normal stresses in measuring regions revealed that up to proof test of 78,8 bar all stresses have been in elastic range, indicating that no plastic deformation in tubes and in boiler mantle. This is confirmed by acoustic emission sensor, since during pressurizing no acoustic signal was monitored, e.g. no one activity was plotted. Based on performed testing and analysis it had been suggested to investor to accept the boiler as “fit for purpose”, with no further action.

19. Structural Integrity Assessment in Theory and Practice

1049

LOCAL VARIATION OF CRACK DRIVING FORCE IN A MISMATCHED WELD Jozef Predan, Nenad Gubeljak and Otmar Kolednik1 University of Maribor, Faculty of Mechanical Engineering, Smetanova 17, Maribor, Slovenia, [email protected] 1Erich Schmid Institute of Materials Science, Austrian Academy of Sciences, Jahnstr. 12, A-8700 Leoben, Austria [email protected] The paper deals with the assessment of the fracture resistance of an inhomogeneous welded joint. The material inhomogeneities create a difference between the near-tip crack driving force, Jtip, and the nominally applied far-field crack driving force, Jfar. This difference is quantified by the socalled material inhomogeneity term, Cinh, which can be evaluated by a post-processing procedure to a conventional finite element stress analysis. Figure 1 shows a welded joint, where the weld metal is in half overmatched (OM) and half undermatched (UM) configuration. Such welds are commonly used for repair welding or for welded joints where the possibility of hydrogen assisted cracking exists. The crack is perpendicular to the mismatch interface. The material properties have a jump at the mismatch interface, but are assumed constant in the regions above and below. In a preliminary study it has been shown that the slant interfaces to the HAZ have no noticeable effect. For this reason, the geometry is simplified to that of a CT specimen with a biomaterial interface between the OM and UM weld metal. The material inhomogeneity term is given by

C inh

 e˜³

6

>>I @@ I 

ı ˜ >>grad u @@ ˜ n ds

(1)

where V is the Cauchy stress, u the displacement, I the identity matrix, e the unit vector in the direction of crack growth, and n the unit normal to the mismatch interface 6.

FIGURE 1. Cross-section of the welded joint with notch position in under matched weld metal

A stationary crack is considered, but the distance between crack tip and interface is systematically varied. To assess the influence of several material parameters on Cinh and Jtip, analyses are performed for an inhomogeneity of the modulus of elasticity, the yield stress, and the stress hardening exponent separately, as well as for several combinations of the material parameters. The results demonstrate that the material inhomogeneity term is primarily determined by the magnitude of the yield stress inhomogeneity.

1050

J. Predan et al.

FIGURE 2. The dependence of the material inhomogeneity term Cinh according to distance between crack tip and interface L, is plotted, for different low values of Jfar and weld material properties. The material inhomogeneity term exhibits a singularity at the interface, (see Fig. 2), causing infinitely large crack driving force (for an OM/UM transition) or zero crack driving force (for an UM/OM transition), when the crack reaches the interface. This leads to an accelerated crack growth or a pop-in in the case of an OM/UM transition and a reduced crack growth rate, or even a crack arrest for an UM/OM transition. Alternatively, if the interface is not oriented perpendicularly to the nominal crack extension direction, a crack deflection may occur.

References 1.

Simha, N.K., Fischer, F. D., Kolednik, O. and Chen, C. R., J. Mech. Phys. Solids, vol. 51, 209-240, 2003.

2.

Simha, N.K., Predan, J., Kolednik, O., Fischer, F. D., and Shan, G.X., J. Mech. Phys. Solids, submitted.

3.

Kolednik, O., Predan, J., Shan, G.X., Simha, N.K. and Fischer, F. D., Int. J. Solids Struct, in press.

19. Structural Integrity Assessment in Theory and Practice

1051

STRENGTH RECOVERY OF MACHINED ALUMINA BY SELF CRACK HEALING Kotoji Ando1, Koji Takahashi1, Wataru Nakao1, Toshio Osada1 and Shinji Sato2 1Department of Safety & Engineering, Yokohama National University 79-5 Tokiwadai, Hodogaya-ku, Yokohama-shi, Kanagawa-ken, Japan [email protected] 2NHK spring Co. Ltd. , 3-10 Hukuura, Kanazawa-ku, Yokohama-shi, Kanagawa-ken, Japan In this study, the effect of crack-heal on cracks propagated during machining was studied systematically. From the obtained results, we proposed a new method for increase in reliability of machined alumina by using the crack-healing treatment. Ceramics have various excellent mechanical properties. Thus, they are expected to apply to various fields. However they have low fracture toughness, so that cracks propagated during machining reduce strength and reliability of machined components significantly. To overcome these problems, it is a good approach to heal the surface cracks completely. As an example, we investigated the crack-healing effect on the cracks on the bottom of semicircular groove, which initiated during machining, as shown in fig. 1. Machining operations were performed using a diamond drill with the cutting depth by a pass of 10 Pm. These machined specimens were crack-healed in air at 1100 oC- 1400 oC for 1-10 h. The bending tests of the asmachined and crack-healed specimens were also performed at R.T. Using stress concentration factor of 1.4, we evaluated the local fracture stress at the bottom of semicircular groove. Local fracture stress, which was reduced by machining, was found to be completely recovered by crack-healing at 1400oC for 10 h as shown in fig. 2. Moreover, as shown in Fig. 3, the characteristic strength of crack-healed specimens at 1400oC-10 h and the heat-treated smooth specimens were 1026 MPa and 1065 MPa, respectively, where the heat-treated smooth specimens was confirmed to have no defect on the surface by the previous study [1-2]. Thus, it was found that the fracture stress of crack-healed specimens at 1400oC-10 h became almost equal to that of heattreated smooth specimen and that the cracks were completely healed by these conditions. From the Weibull distribution, failure probability, F(x), of the crack-healed specimens at 1400 °C for 10 h was found to be less than 1% at the stress of 600 MPa which 90% as-machined specimens fractured. Therefore, it was concluded that the crack-healing was effective to improve the integrity of machined ceramics. Schematic diagrams of machined specimens

FIGURE 1. Schematic diagrams of machined specimens.

K. Ando et al.

1052

FIGURE 2. Effect of healing temperature on Local fracture stress

FIGURE 3. Effect of crack-healing on weibull distribution of local fracture stress

References 1.

K. Takahashi, M. Yokouchi, S.K. Lee, K. Ando, J. Am. Ceram. Soc., 86-12, 2003

2.

S.K. Lee, K. Takahashi, M. Yokouchi, H. Suenaga and K. Ando, J. Am. Ceram. Soc., 87-7, 2004

19. Structural Integrity Assessment in Theory and Practice

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CRACK INITIATION AND GROWTH IN HAZ OF MICROALLOYED STEEL K. Geric and S. Sedmak Faculty of Technical Sciences, Trg D.Obradovica 6, Novi Sad, S&CG, [email protected] Faculty of Technology and Metalurgy, Karnegieva 4, Beograd, S&CG [email protected] Due to welded joint microstructure heterogeneity it is very complex to perform a its toughness test, because it is difficult to position notch tip in the region of lowest toughness, and it is also difficult to control growing crack path. Microstructure of heat-affected-zone (HAZ) region in which fatigue crack tip in fracture toughness testing could be located depend on thermal cycle, defined by passes number and heat input. In order to get more insight in microstructure properties it is possible to simulate welding process by programmed heating and cooling of samples, and that test the specimens made from the samples. Failure behaviour of heat - affected - zone by simulated specimens and real welded joint is the subject of many papers, e.g. Chae et al. [1]. Low toughness in coarse grain HAZ region (CGHAZ) was attributed to local microstructure M-A constituent (high carbon martensite with some retained austenite), Davis and King [2]. Three microalloyed steels had been selected for the experimental analysis of crack-opening displacement (COD) as fracture mechanics parameter of simulated samples and real welded joints. The microstructure of HAZ of tested steels had been simulated on Smitweld LS1402 device. The samples 60 mm long, 11 mm wide and thick, were heated to different temperatures (1350, 1100, 950 and 850°C, selected as typical), and programmed cooled. Welded samples are produced by manual arc welding as multipass, without preheating due to small sample thickness. In performed 4 passes an average heat input was 1,5 kJ/mm. Three point bend specimen is used to measure COD at room temperature and at -30°C. Measured COD at -30°C on simulated samples is presented in Fig. 1.a, as depended on heating temperature of simulated samples, and in Fig. 1.b is presented COD obtained with specimens produced of real welded joint for different distances of notch tip from weld metal. Growing crack path in the specimen with clear pop-in in test diagram is presented in Fig. 2.a, and corresponding fracture surface, exhibiting ductile and cleavage regions is presented in Fig. 2.b. Obtained results, presented in other papers, Neves [3] showed that in similar steels HAZ toughness of simulated samples and of real welded joint differ. The explanation for high toughness level in real welded joint at small cooling time 't8/5, can be testing insensitivity on local heterogeneity region in multipass welded joint. One can suppose that that testing is more sensitive on microstructural effects in the case of simulated HAZ, compared to real welded joint. If this is the case, results can confirm that reduction in toughness is cause by brittle microphases (such as M-A constituents) in beinite microstructure of simulated coarse grain HAZ region , at short cooling time. This phenomenon is observed only in simulated HAZ, and not in HAZ of real welded joint, where total effect could be twofold. Due to overlapping of thermal cycles M-a constituent can be disolved, and no local brittle zone can occur.

K. Geric and S. Sedmak

1054

FIGURE 1. COD value in simulated (a) and real welded joints (b) on -30°C

FIGURE 2. The crack path, and SEM fractography

References 1.

Chae, D., Young C.J., Gotto D.M.and Koss, D.A., Materials Transaction A, vol. 32A, 20012229, 2001

2.

Davis L. and King J.E., Mater.Sci.Technology, vol. 3, 563-573, 1994

3.

Neves, J. and Loureiro A., J. Materials Processing Technology, vol. 32A, 1-7, 2004

19. Structural Integrity Assessment in Theory and Practice

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STRUCTURAL INTEGRITY AT ELEVATED TEMPERATURES - RESIDUAL SERVICE LIFE EVALUATION L. Milovic and S. Sedmak Faculty of Technology and Metallurgy Karnegijeva 4, 11000 Beograd, Serbia and Montenegro [email protected] Society for Structural Integrity and Life (DIVK) Bulevar vojvode Misica 43, room 258, 11000 Beograd, Serbia and Montenegro [email protected] The essence of creep deformation is that the plastic strain is time dependent and can occur at stresses which in an ordinary tensile test would be below the yield stress. The mechanism of creep relies on the thermally activated passage of atoms over an activation barrier which is characterized by an activation free energy. The mechanisms of creep are well established. However, practical creep-resistant materials tend to be extremely complex, because a large number and severe design criteria. It is important to understand the long-term creep and rupture behavior of such materials for their safe use in safetycritical applications such as power plant and aeroengines. For this reason there exist a large number of empirical or semi-empirical methods which will be consider in this paper, in order to understand well existing experimental methods for determining the creep parameters C(t) and Ct, and to analyze posibility the determine experimentally the parameter C*. Components in large-scale steam generating power plants are manufactured in thick section of creep resistant low alloy steels, being exposed to high temperature and high pressure. The design of high temperature pressure components is governed by national and international standards and allowable stresses are generally based upon mean 1x105 h creep rupture data with appropriate safety factors to take account of data scatter and departure from design conditions. Before predicting remnant creep life, laboratory generated creep rupture data are required. The experience has shown that in many cases components exposed to creep could successfully use well beyound the design life. Regarding weldments in thick walled components, as the most common location for creep failures, the life management has remained on regularly performed inspection regimes optimized through plant experience and through the analytical and experimental activities, despite the fact that the major advances have been achieved in the modelling of their behaviour under creep conditions. Thanks to the computer finite element analysis using continuum damage constitutive equations, it is possible now to predict the weld failure locations and even the times. However, valid formal design and assessment codes rely on more established procedures such as semi empirical weld strength reduction or efficiency factors, and reference stress techniques. The possibility of experimental determination of C* through J integral of weldments of steel produced for high temperatures application will be also considered in this paper.

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References 1.

Bhadeshia, H. K. D. H., Comprehensive Structural Integrity, vol. 5, 1-23, 2003

2.

Saxena, A., Comprehensive Structural Integrity, vol. 5, 201-240, 2003

3.

Gooch, D. J., Comprehensive Structural Integrity, vol. 5, 309-360, 2003

4.

Dogan, B. et al., In Abstract Book of the International Conference on Fracture ICF11, Turin (Italy), March 20-25, 2005, pp. 607 and 608, available also on the disc

5.

Saxena, A., et al., Fracture Mechanics, vol. 24, 510-526, 1995

6.

Saxena, A., et al., In Proceedings of the Life Extension and Assessment of fossil Power Plants, edited by B. Dooley, R. Viswanathan, EPRI, California, 1987, 575-605.

7.

Berkovic, M., et al., In Proceedings of the Fifth International Fracture Mechanics Summer School, edited by S.Sedmak, EMAS, United Kingdom, 1989, 71-88.

19. Structural Integrity Assessment in Theory and Practice

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THE ANALYSIS OF SUPPORTING STRUCTURE OF PLANETARY GEAR BOX SATELLITE M. Arsi, V. Aleksi and Z. Anelkovi1 Institute for Material Testing, Bulevar vojvode Misia 43, Belgrade, Serbia and Montenegro, 1Institute GOSA, Milana Rakia 35, Belgrade, Serbia and Montenegro [email protected] Existing dynamical models of supporting structure, mechanisms and gear driving of rotary excavator, with regard to models of external load caused by excavation reaction, do not allow complex introspection of their influence to dynamical behavior of rotary excavator. In addition to that, influence of own low-frequency oscillations and non-stationary loading regime to working strength of supporting structures and reliable assemblies can not entirely be perceived in phase of design and construction. Premature damages and fractures of gear box elements frequently occurs in praxis, which can be explained by application of inadequate design and construction methods, by the ignorance of basic material properties and welded joints and by mistakes in technology of elements manufacturing. Analysis of damaged and fractured parts supplies important informations for improvement of gear boxes design methods, existing material properties and technologies of their treatment and also for new materials and technologies development. Damage and fracture analysis enable also development of new technical solutions and examination methods in prototype phase. Review of performed theoretical and experimental analysis of satellite supporting welded structure of planetary gear box used for driving of excavator working wheel SRs 1300.26/ 5.0+VR±10, with fracture occurred, is presented through block-chart in Fig. 1. Satellite support on the planetary part of the gear box for driving of excavator working wheel is exposed to driving momentum and transversal bending forces. Theoretical stress state analysis of the satellite support is performed for different cases of loads: •

load of the satellite support caused by the operating force,

•

load of the satellite support caused by the own weight and alternating bending,

•

load of the satellite support caused by the alternating bending.

Safety factor to fatigue fracture of SD = 1.49 has been calculated by the application of TGL 19340 and stress spectrum has been obtained for the case of pure alternating variable bending taking into account influence of notch according Stiler’s method. Calculation of safety from fatigue fracture has been obtained on the basis of TGL 19340. Specific properties of cast materials have been taken into account according TGL 19341, and the influence of notch according TGL 14915. Taking into consideration that all mentioned regulations are related with stress concentration, correction of stresses obtained in the calculation of satellite support model has been performed. Calculation has been performed by using of software application called “AUTRA”.

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Figure 1. Review of performed theoretical and experimental analysis of satellite support Experimental assessment of stress spectrum has been performed by the tensometric measuring of strains on the driving shaft of excavator working wheel by using of four gauges of XY-120HBM type, which are suitable for measuring of strains caused by the torsion momentum on the shaft. Measuring results stated by normal strain H, have been recalculated to tangent stress W through elasticity modulus E and the Poisson’s coefficient Q, which together with polar resistance momentum of cross-section Wp determines torsion momentum T on the output shaft of transporter driving, which have been utilized for assessment of gear box operating life on the basis of experimentally determined stress spectrum. Comparison of stress spectrums determined by theoretical considerations and experimental examinations, in relation to carrying capacity of satellite support has shown that working stresses in critical sections have been close to yield point even without taking stress concentration into consideration. Design solution of satellite support elements and results of experimental examinations of parent materials and welded joints have shown that all significant parameters for the conditions of variable load have not been including during designing and manufacturing of welded structure and welded joints as critical points.

19. Structural Integrity Assessment in Theory and Practice

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FAILURE PROBABILITY OF GEAR TEETH WEAR M. Ognjanovic Faculty of Mechanical Engineering, University of Belgrade Kraljice Marije 16, 11120 Belgrade, Serbia [email protected], [email protected] Gear load capacity calculation is defined according to pitting of the teeth flanks. In service conditions, a failure process is combined of a number of damage processes. Which of them will be dominant depends on design parameters, technological and exploitation conditions. Periodically, for some of gears, extremely difficult service conditions exist, which creates a possibility for progressive teeth wear. Results of progressive wear are obtained by experiments. For these results, failure boundaries which can be used for parameters of Weibull's function definition, for different stress levels and for different stress cycles numbers (teeth mesh revolutions) have been defined. The first feature of a progressive wear process is stochastic behavior combined of a few elementary wear processes. The second one is that in service life these very strong working conditions are not continual. Periodical service conditions may be presented by the probability of these conditions p. By combining the failure probability PR of progressive teeth wear and the probability of service conditions p, it is possible to obtain the complex probability Fp=pPR which defines the probability of progressive wear in service life. The failure probability is the result of gear wear testing by using the FZG gear tester or another similar system for gear loading and long time testing. Figure 1 presents the results of gear testing in planetary gear drive tested in a back to back system similar to the FZG gear tester. The inferior boundary of failure probability distribution is defined by the visible flank failure beginning (10% failure). The superior boundary is defined by the thickness of the layer of teeth flank wear of 0,3 m (m – gear module ). Gear teeth is surface hardened and the hardened layer is eliminated by a progressive wear process. Some of the points are obtained by the testing and some of them are defined by approximation. For a more precise definition, it is necessary to perform a number of tests, which will be done in the future. The results presented are compared with the gear endurance limits available in the DIN 3990 for the surface hardened and not hardened steels. By using the lines of inferior and superior failure boundaries, it is possible to obtain Weibull's functions of the failure probability PR. The function of the stress cycles number (teeth mesh revolution) PR(N) can be defined for every level of the stress VHN . For every stress cycle number N (teeth mesh revolution) it is possible to define the following function PR(VHN)

PR  N 1  e

§N ·  ¨¨ ¸¸ ©K ¹

E

;

PR V HN



1 e

· §V  ¨¨ HN ¸¸ © K ¹

E

(1)

The parameters of the Weibull's function K and E are defined by using a coordinate of the points from the boundary lines which include the failure probability 0.1 and 0.9.

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References 1.

Floding A., Andersson S.: Simulation of Mild Wear in Spur Gears, Wear, Vol.207, pp 16-23., 1997.

2.

Hohn B.R.: Modern Gear Calculation, - Proceedings of the International Conference on Gears, VDI-Berichte 1665, pp 23-43., 2002

3.

Podgornik B., Vižintin J.: Wear Reaistance of Plasma and Pulse Plasma Nitrided Gears, Proceedings of the International Conference on Gears, VDI-Berichte 1665, pp 593-601, 2002

4.

Weck M., Hurachy-Schonwerth O., Bugiel Ch.: Service Behaviour of PVD-Coated Gearing Lubricated with Biodegradable Synthetic Ester Oils, - Proceedings of the International Conference on Gears, VDI-Berichte 1665, pp 677-690, 2002

5.

Bauer J., Andersson S.: Simulation of wear in gears with flank interference – a mixed FE and analytical approach, Wear, vol. 254, pp 1216-1232., 2003.

6.

Ding Y., Rieger F.N.: Spalling formation mechanism for gears, Wear, vol. 254, pp 13071317., 2003.

7.

Aslantas K., Tasgetiren S.: A study of spur gears pitting formation and life prediction, Wear, vol. 257, pp1167-1175, 2004.

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SOME ASPECTS OF ENGINEERING APPROACH TO STRUCTURAL INTEGRITY ASSESSMENT M. Kiric and A. Sedmak Ministry of science and environmental protection of Republic Serbia Mechanical engineering faculty Njegoseva 12, Belgrade, Kraljice Marije 16 [email protected] The structural integrity of nuclear steam supply systems in the U.S.A. was assured by designs that adhered to the ASME Boiler and Pressure Vessel Code and many other regulatory standards. The requirements of these codes and standards are based on linear elastic fracture mechanics (LEFM) concepts. In much or all of the working temperature regime of nuclear systems, power and chemical plants, as well aircraft propulsion, the material is being stressed above the transition temperature, where the fracture response is ductile and the material capable of considerable plastic deformation. The engineering approach, developed by EPRI, permits fracture analysis in the elastic-plastic regime by assuming the concept of J-controlled crack growth. When the conditions for J-controlled growth are satisfied, the JR curve will be independent of crack configuration and stable crack growth can be analyzed by the JR curve approach based on J. A rising JR curve is normally associated with growth and coalescence of microvoids. The initial part of JR curve, nearly vertical, can be analytically represented in various ways. The JR curve dependence on crack growth is approximated by the polynomial approximation in this paper. The engineering approach provides simple interpolation formulae for J integral and crack mouth opening displacement (CMOD) which superpose fully plastic solutions to linear elastic solutions. Fully plastic solutions and analyses are applied to cracked configurations which are completely yielded. In small-scale yielding, the plastic contribution is small compared to the elastic contribution and in other extreme in the fully plastic range, the plastic contribution is the dominant term >1@. In other words, the plastic component of J is negligible at low loads, but dominates at high loads >2@. It is considered a cracked cylinder with a long axial crack on internal surface. In this paper it is shown that some influencies should be taken into account. The contributions are calculated and their dependence on strain hardening exponent (n) and cylinder geometry are illustrated. The ratio of elastic J integral to the total J integral is less than 35% only at internal pressure equal to or greater than about 50 Mpa, dependent on relative crack depth for assumed cylinder corresponding to the size of a nuclear reactor pressure vessel. The ratio of crack depth to wall thickness (a/H) has a strong inluence on similar ratio of elastic CMOD and the total CMOD. The ratio of wall thickness to internal radius of cylinder (H/Ri) has opposite influences on the ratio of elastic component to total value: its increasing, causes decreasing of the J values ratio, while in the case of the ratio of CMOD values, it leads to their steep inrease. The partition of elastic and fully plastic components for cylinder, can be analyzed in terms of the internal pressure for which these components of J and CMOD are equal, Kiri >3@. The pressure value is dependent of crack depth, geometry and n. The paper gives the influencies of some geometric parameters, (a/H) and (H/Ri), on J and CMOD for assumed cylinder geometry, too. It is derived the parabolic relation between J and CMOD. The relation is dependent of crack depth, H/Ri and n. Only for a/H=1/8, H/ Ri=1/20 and n=3 the dependence is polynomial of the third order. Therefore it is concluded that it

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is possible, with some restrictions, to obtain J integral values from measurement of CMOD, as it was proposed for cracked tensile plate. The number of data pairs increases with polynomial order. To obtain predictions for crack initiation, stable growth and structure instability, the engineering approach compares the crack driving force (CDF) in terms of applied J to the JR curve in the CDF diagram. The J curve, tangent to the JR curve determines the point of instability given by the pressure and the amount of crack growth at instability. These values are solutions to two equations for the stable crack growth. They are found by numerical iterative calculation in this paper. It is a convenient procedure because it quickly provides the conditions for instability of various cylinder geometries and initial crack depths. As an example was considered a cracked pressure vessel made of HSLA steel with an internal axial crack. The analysis can be performed by using the formula for the hoop stress and the failure assessment diagram. The estimation of internal pressure boundary value by using the condition that the material begins to yield on inside surface of cylinder, provides too conservative value. It is assumed a conservative approach that the crack is open to the internal surface and being partthrough thickness. Thus the engineering approach was applied and an analysis was performed. The stable crack growth was calculated as well the full load carying cylinder´s capability.

References 1.

V. Kumar, M.D. German, C.F. Shih, An engineering approach for elastic-plastic fracture analysis, NP-1931, Research Project 1237-1, General Electric Company, New York 1981, p. 2-13.

2.

T. L. Anderson, Fracture mechanics - fundamentals and applications, CRC press Inc. 1995. Texas, p. 478.

3.

Kiric, B.M., The Ph.D. thesis, The Faculty for mechanical engineering, Belgrade, 2000., p. 109.

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STRUCTURAL INTEGRITY ASSESSMENT APPLYING ULTRASONIC TESTING M. Kiric Ministry of science and environmental protection of Republic Serbia, Belgrade [email protected] Nondestructive testing of materials and welded joints for detection and evaluation of cracks, as the most dangereous discontinuities, includes different methods, like : •

Liquid penetrant testing (PT),

•

Radiographic testing (RT),

•

Electromagnetic (eddy current) testing (ET)

•

Magnetic particle testing (MT)

•

Ultrasonic testing (UT).

Each testing method has its features, thus the selection depends on the scope and range of products and materials to be tested. Not all of them are suitable to evaluate cracks. This is the reason why the UT is the subject of the consideration, taking in mind that there are supplementary methods for detection of surface cracks like MT. The capabilities of UT for cracks detection are discussed. The experiences gained in pressure vessels testing have shown that UT by using pulse-echo technique is the best method for discontinuities characterization because of its versatility and possibility of quantification and memorization of results enabled by digital ultrasonic flaw detectors. The selection of UT should define the technique to be applied, also its sensitivity and reliability. The initial cracks and other discontinuities, made during fabrication, may be not detected before product use, but cracks can grow in time, dependent on service conditions, and be detected only after a period of product service life. If such discontinuities are detected, two further steps are possible, depending on crack size. The first is to leave them in the structure, but with their repeat evaluation after given time intervals. The determination of crack features may include: basic ultrasonic parameters, crack parameters and its proximity to the surface or to other discontinuities as well its basic shape and orientation. The second measure is the complex task to assess the structure integrity. For crack parameters evaluation by UT, estimated stress field and possible failure type (brittle or ductile fracture, fatigue and stress corrosion) are to be taken into account. The paper considers UT of welded joints in constructions, from the European standards point of view. It is a multitask UT because it is aimed at detection of discontinuities, their characterization and evaluation, by taking into account the geometry and welding technology. Characterization of discontinuities involves the determination of those features which are necessary for its evaluation with respect to known acceptable criteria. In order to correctly identify the discontinuity types specified in the acceptance criteria, or to make a correct fitness-for-purpose evaluation, it may be necessary to make a more detailed sizing and assessment of the shape of the discontinuity. The attention is given to the classification of discontinuities as planar or non-planar and criteria for the classification. One of the criteria considered are echodynamic patterns obtained as transient echo shapes during probe movement. The difference between the quality control concept and the fitness-for-purpose concept is made. Some examples are given to illustrate the standard approaches for UT.

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Evaluation of indications in accordance with standard, performed for detection by testings of welded joints, is based on reference levels, established by european standard EN 1712. For method 1, the setting of sensitivity may be performed by 3 mm diameter side drilled holes. The diameter is the same for different frequencies and parent material thickness, while for method 2, the distance gain size system, ultrasonic probe frequencies and reference levels depend on parent material thickness. On the other hand, evaluation level is determined by reference level. It is important from two reasons: all indications equal to or exceeding evaluation level shall be evaluated and the other is that the standard technique measures the lateral dimension of an indication over which the echo is equal to or greater than the evaluation level. Similar question can be put regarding the reference level for tandem examination. It is defined by 6 mm diameter side drilled hole for all thicknesses. The evaluation of indications by using method 3 of sensitivity setting is discussed, too. It is performed by using a rectangular notch with the depth of 1 mm if a probe angle is greater or equal to 70o and for the thickness range from 8 mm to 15 mm. Evaluation level is defined via the reference level regardless parent metal thickness and ultrasonic probe frequency. Because the resolution power of a probe depends on its ultrasonic frequency, the detection of the notch with the depth of 1 mm may be discutable. This question is considered from the point of double reflexion from the right corner and transverse waves transformation. The acceptance or rejection of welded joints with cracks is solved in two ways: crack are unacceptable, or they are conditionally acceptable. The acceptance levels given by standards are dependent on methods of sensitivity settings and thickness interval. They are analysed in respect to the fracture mechanics relations derived by using stress intensity factor for internal cracks. Acceptance levels allow greater relative echo amplitude for short indications, while for long indications relative echo aplitude is lowered, as expected. The level number is maximum three, while it could be greater, as it can be concluded from linear elastic fracture mechanics. As far as cracks are considered, it seems reasonable to apply small number of acceptance levels and linear elastic fracture mechanics, because UT is simplified in this way. Greater number of level would requires a softver for acceptance/rejection of discontinuities in welded joints. This softver will incorporate fracture mechanics criteria for evaluation of cracks and other discontinuities detected by UT.

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(CRACK-HEALING + PROOF-TEST): METHODOLOGY TO GUARANTEE THE RELIABILITY OF CERAMICS Masato Ono, Wataru Nakao, Koji Takahashi, Kotoji Ando and Masahiko Nakatani1 Department of Material science & Engineering, Yokohama National University 79-5 Tokiwadai, Hodogaya-ku, Yokohama, 240-8501, Japan Fax: 81-45-339-4024, [email protected] (Masato Ono) 1NHK SPRING Co., Ltd, Fukuura, Kanazawa-ku, Yokohama, 236-0004, Japan Structural ceramics have excellent heat corrosion and wear resistance. However, fracture toughness is low. Thus, they are brittle and sensitive to flaws. The flaws in ceramics are classified into propagated surface cracks in machining and embedded flaws. Ando et al. have progressed in development of the structural ceramics attached crack-healing ability by using oxidation of SiC. When ceramics admixed with SiC are kept in air at high temperature, SiC located on the crack surface reacts with O2 in air. Then, crack is completely restored by the products and the heat of the reaction. Moreover, the restored part is mechanically stronger than the other parts. However, the embedded flaws cannot be healed. Therefore, the present authors expect the combination of crack-healing and proof-test as a new methodology to guarantee of the reliability of a ceramics component. For this purpose, the minimum guarantee fracture, VGT, stress at high temperature for the specimens proof-tested at R.T. after crack-healing was estimated by using the measured temperature dependence of fracture stress and toughness. The fractures stress of the proof-tested specimens was also measured at elevated temperatures. From the obtained results, the validity of the estimated minimum fracture stress was discussed. The mixture of alumina powder and 20 mass% SiC powder was blended well in alcohol for 48 h. Then, the slurry was dried. Rectangular plates of 90 mm x 90 mm x 7 mm of alumina/SiC particle composite were sintered in N2 gas for 2 h via hot press under 35 MPa at 1923 K. The sintered plates were cut into the 3 mm x 4 mm x 36 mm rectangular specimens bar. This study includes investigation of effect of proof test on the embedded flaws as one of the purposes. Thus, many embedded flaws were consciously introduced to the test specimens. A semi-elliptical surface crack of 100 Pm in surface length was made at the center of the tensile surface of specimens with a Vickers indenter. The ratio of depth (a) to half the surface length (c) of the crack (aspect ratio) was a/c = 0.9. The specimens were crack-healed at 1573 K for 1 h in air. Crack-healed specimens, that are crack-healed above condition, were subjected to the proof-test at R.T. The proof test stress was 435 MPa. In the previous study, Ando et al. have proposed the estimation method of VGT [1]. In most ceramics, the fracture strength has negative temperature dependence. Thus, the minimum guarantee fracture stress at high temperature, VGT, can be lower than proof test stress at R.T. VGT can be expressed as following,

V

T G

2V 0T

S

­°§ K T arccos ®¨¨ ICR °¯© K IC

· ¸¸ ¹

2

§ V 0R ¨¨ T ©V0

· ¸¸ ¹

2

­° § SV pR ®sec ¨¨ R °¯ © 2V 0

· °½ ½° ¸  1¾  1¾ ¸ ° ¹ ¿ °¿

1

(1)

1066

M. Ono et al.

where KICT and V0T indicate the plane strain fracture toughness and the fracture stress of plane specimen at high temperature, respectively. For the estimation of VGT, it is necessary to obtain the temperature dependences of KICT and V0T. Figure 1 shows the comparison between VGT and experimental results as a function of test temperature. The open and closed diamonds indicate the fracture stress of the crack-healed specimens and the proof-tested specimens, respectively. The minimum values of the measured fracture stress of the proof-tested specimens at several temperatures are smaller than the proof test stress at R.T. In shorthand, one can observe the temperature dependence of the fracture stress of the proof-tested specimen. Double circle in Fig. 1 indicates the estimated value of the minimum guarantee fracture stress. All specimens except one tested at 1373 K fractured with higher strength than VGT at the same temperature. Thus, this estimation of VGT was accepted as correct. From the obtained results, it is concluded that the combination of crack-healing and proof-test is the effective techniques to guarantee of the fracture stress at high temperature of the ceramics component.

FIGURE 1. The comparison between minimum guarantee fracture stress and experimental results as a function of test temperature.

Reference 1.

K. Ando, Y. Shirai, M. Nakatani, Y. Kobayashi and S. Sato, J. Euro. Ceram. Soc., 22, 121128, 2002.

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RISK BASED INTEGRITY ASSESSMENT OF CONCRETE STRUCTURES M. Pavisic PM Lucas Enterprises Ltd. (Cyprus) Belgrade, Internacionalnih brigada 25a, Serbia and Montenegro [email protected] From the very beginning of its service life the concrete structure is exposed to the various loading conditions and excessive and adverse events – hazards (overloading, fire, explosions, floods, earthquakes and so on). As a consequence, the overall integrity of structure is jeopardized and some structural limit states could be reached. Risk is a probability that a particular adverse event (limit states) occurs during a stated period of time multiplied by the consequences. Damage initiation and development in concrete structures is time dependant process determined by the many factors as: aggressive environment, quality of the construction, loading history and the quality of maintenance. In the same time, damage progress affects the structural resistance, safety and reliability decreasing them during the time (Pavisic [1]). Having in mind mentioned, the right question concerning the concrete structure integrity assessment is: what degree of structural damage may be permitted and tolerable with no taking any protective actions to the structure or what is the limit of acceptable damage? The response to this question is very important not only from the point of view of the structural integrity assessment, but for making decision about the needs for structural repair and its remaining service life prediction (Fig. 1.).

FIGURE 1. Damage function Where is: D – damage (deterioration) T – time D0 ( t0 ) – damage (deterioration) acceptibility limit D1 ( t1 ) – limit state Ts – predicted structural service life TsTse – extended structure service life

M. Pavisic

1068

t0 – time when acceptable damage limit is overcome t1 – time when repair has to be carried out D0D1 – integrity assessment (inspecting, monitoring, testing) In fact, integrity assessment is an evaluation of the remaining structural resistance taking in account damage created and identified on the structure. The basic equation of the structure limit state is:

g

RS t0

(1)

where, R is structural resistance and S loading, both time dependant functions:

R

R(D,t) , S

S (t )

(2)

It is already well known that the parameters characterizing the structural properties and degree of structural damage are uncertain and random values by its nature and may be defined as the statistical variables having its probability density distribution (Hart [2]). Thus, we may count on the probability of some limit states to take place on the structure after some time being in service. The probability may be expressed by the following equation (Stewart and Rosowsky [3]):

Pf t Pr >R d S @ Pr [ R  S d 0] Pr [ g ( R, S ) d 0]

f

³f

R

(t ) f S (t )dt

0

(3)

where is: g(R,S)- limit state function fR(t) – probability density distribution of resistance fS(t) – probability density distribution of loading In the paper, the overall procedure, from integrity assessment and risk analysis, to the calculation of probability of limit state, is presented and the basic elements for decision making discussed.

References 1.

Pavisic, M., In Proceedings of 7th Internationl Conference on Mechanical Behaviour of Materials, Hague, The Netherlands, 1995.

2.

Hart, G.C., Uncertainty Analysis, Loads, and Safety in Structural Engineering, Prentice-Hall, Englewood Cliffs, New Jersey, 1982.

3.

Stewart, G.M, Rosowsky, V.D., J. Struct. Safety, vol. 20, 91-109, 1998.

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STRUCTURAL INTEGRITY ASSESSMENT BY LOCAL APPROACH TO FRACTURE M. Zrilic, M. Rakin, Z. Cvijovic, A. Sedmak1 and S. Sedmak2 Faculty of Technology and Metallurgy,Karnegijeva 4, 11000 Belgrade, Serbia & Montenegro 1Mechanical Engineering Faculty, Kraljice Marije 16, 11200 Belgrade, Serbia & Montenegro 2Society for Structural Integrity and Life (DIVK), Bulevar vojvode Misica 43, 11000 Belgrade, Serbia & Montenegro [email protected] Local approach to fracture has been developed for complete understanding of fracture mechanism [1,2], including the material degradation process. This approach combines theoretical, experimental and numerical solutions, enabling less conservative assessment of crack significance and residual stress. Steam lines, in service exposed to high temperature and high pressure, has been designed for a life of 100 000 hours. In order to assess residual life, extended experimental investigation of samples, taken from virgin 14MoV6 3 steel, Fig. 1 (left), not used for steam line construction, and an old steel of the same class, taken after exhausted nominal life, after 117 000 operating hours [3]. Five specimens of virgin and of used steel for three geometries (notch root radius 10 mm; 4 mm and 2 mm) and each geometry had been tested for determination of critical void growth rate R/ R0 values and void growth rate R/R0, corresponding to ultimate tensile strength. Critical value of void growth rate, corresponding to final fracture, is designed by subscript c, and the value of void growth rate, corresponding to maximum loading, e.g. to ultimate tensile strength, is designed by subscript m. Tearing fracture (ductile fracture, nucleation and coalescence of voids) have been analysed in local approach. For that, mechanical properties and fracture mechanics parameters are necessary. Substantial link in local approach is numerical simulation by finite elements method (FEM), applied through elastic-plastic analysis for ductile fracture solution using 3D elements of an axisymetric model. FEM calculation is performed by elastic-plastic analysis in NASTRAN software, using 3D elements [4]. Upper specimen half is modeled as a wedge element, with angle of 5o, corresponding to 1/72 part of upper specimen part, Fig. 2 (right). This affects the shape of finite elements mesh, producing wedge type elements around axes, and the other elements are of brick type. Calculated local criterion is material characteristic, representing local stress state, which corresponds to critical void growth and next unstable fracture. This material characteristic is a convenient form, directly applicable in FEM calculation. That means, when high stress level is found in a structure and void growth rate R/R0 is verified, at the critical (R/R0)c level, failure of structure can be expected. From engineering point of view this verification should be performed for maximum load, e.g. for ultimate tensile strength, (R/R0)m [5]. This should be the indication for critical behaviour of a structure.

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FIGURE 1. Notched tensile specimen (left), notched tensile specimen mesh (right).

References 1.

ESIS P1-92, Recommendations for Determining the Fracture Resistance of Ductile Materials, ESIS, 1992.

2.

Rakin, M., at al, Strength of Materials, Kluwer online, vol. 36, 1, 33-36, 2004.

3.

Zrilic, M., Aleksic, R., Thermal Science - International Journal, vol. 7, 1, 35-49, 2003.

4.

Zrilic, M., Burzic, Z., Cvijovic, Z., Strength of Materials, Kluwer online, vol. 36, 1, 47-58, 2004.

5.

Zrilic, M., Doctorate of Philosophy in Metallurgy Science, Belgrade, Serbia & Montenegro, 2004.

19. Structural Integrity Assessment in Theory and Practice

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BRITTLE AND DUCTILE FRACTURE IN SERVICE OF PRESSURE VESSELS N. Filipovic and K. Geric Zavod za zavarivanje – Beograd Fakultet tehnickih nauka –Novi Sad [email protected] Underground storage tank for liquefied natural gas, 9.96 m3 in volume, fractured during pressure proof test by liquid nitrogen (Fig. 1a). Cracks initiated in circumferential welded joints in lower part of the vessel mantle. Direction of crack growth is perpendicular to circumferential welded joints and parallel to vessel axis, in the direction of maximum tensile stress (Fig. 1b). The analysis of fractured surface on the left and on the right side along the heat-affected-zone (HAZ) of circumferential welded joint revealed that crack surface is typical for brittle fracture, normal to the plate, with coarse grains and typical V marks, directed to the initiation point. Vessel mantle was produced of structural steel S355J2G3 according to EN10025. Although microstructure shows expressed lamination and secondary structure, impact testing results in rolling and cross rolling direction at -20C, obtained from two plates have not exhibited significant difference (average energy values of 34 J and 39 J), with individual values greater for specimens in longitudinal direction. Impact energy for HAZ and weld metal is 20 to 25% lower compared to parent metal, but all of them are well above specified values in standard (13,5 J for KV150/5). Liquid nitrogen during pressurizing produced the temperature bellow nil ductility transition temperature of the steel and welded joint, which caused brittle fracture In the mobile storage tank for transportation of ammonia, due to overfilling for about 20 kg and steadily increasing temperature (month of July) the inner was completely filled by liquid phase, resulting in increase of pressure, which caused plastic deformation, bulging, wall thickness reduction in this position from 8 to 5.3 mm, and to final failure of tank (Fig. 2a). Crack initiated in the heat-affected-zone (HAZ) of fillet weld between mantle plate and support reinforcement, because plastic deformation was constrained in this position (Fig. 2b). Initial cause of cracking was the undercut 1 mm deep, at the beginning of fillet weld, which introduced local stress concentration Crack developed in brittle manner through HAZ, containing microstructural interphases of quenching with hardness of 320 HV10 up to 5 mm in depth, and then through reduced wall thickness of parent metal by shearing. Applied steel Nioval 470 MPa of nominal yield strength 470 MPa exhibited satisfactory impact toughness (120 J to 140 J at OC), what explains crack growth through HAZ of circumferential welded joint with coarse grain microstructure and increased hardness of 260HV10 /1/, and not through parent metal.

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1072

FIGURE 1. Brittle fracture of pessure vessel FIGURE 2. Plastic collapse of pressu

References 1.

Katarina Geric, Cracks in welded joints (in Serbian), Faculty of Technical Sciences, Novi Sad, 2005.

19. Structural Integrity Assessment in Theory and Practice

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MECHANISMS OF FRACTURE IN MEDIUM CARBON VANADIUM MICROALLOYED STEELS N. Radovic, Dj. Drobnjak and H. Hraam Department of Metallurgical Engineering, Faculty of Technology and Metallurgy, University of Belgrade, PO BOX 35-03, 11120 Belgrade, Serbia&Montenegro [email protected] The relationship between microstructural parameters and cleavage fracture has been studied in (950-1300°C) air cooled vanadium microalloyed steels by means of impact testing, light microscopy and scanning electron microscopy. Large variations in impact energy are obtained as a function of test temperature and microstructure. The results show that accicular ferrite (AF) and a multiphase structure consisting of ferrite-perlite (FP) and 30-70% AF posses room temperature toughness superior to that of classical bainitic sheaves (BS) as revealed by impact energy level. However, AF is superior to FP-AF in term of energy transition temperature. At liquid nitrogen temperature, all steel grades show similar behavior. Transgranular cleavage is exclusive mode of fracture. Primary brittle nuclei, which control the critical tensile strength for fracture, F, are found to be brittle TiN particles of diameter >2m. Large TiN particles are friendly, because the cracks are initiated by stress much smaller than that required for crack propagation. This means that cracks ill become blunted out, what will make them inactive before the stress for crack propagation is achieved. Carbides and martensite/austenite/carbide (MAC) constituent are tentatively identified as secondary brittle fracture nuclei, but they are of less significance. As the critical stage of brittle fracture is crack propagation through particle/matrix interface, the morphology and ferrite grain size play little role. Calculation of maximum tensile stress below the notch, max, and critical tensile strength for fracture, F, under the assumption that diameter of TiN particle, which are the primary nucli, are equal to penny shaped crack size, have shown that the requirements for crack propagation through particle/matrix interface, max > F, is satisfied from the beginning of fracture process at liquid nitrogen temperature in all steels studied in this work. Room temperature behavior of these steels is considerably different. The dominant fracture mechanism is still transgranular cleavage, but this is preceded by a lower (BS steels) or higher (AF steels) degree of ductile fracture. Calculation have shown that at the beginning of fracture , max < F. This means that the brittle crack initiated on brittle particles can not propagate; instead, the ductile crack will be initiated and propagated. During propagation, ductile crack is assumed to accelerate, what, in turn, increases the strain rate, and consequently, Y and max. At a critical ductile crack length, critical condition, max > F , is achieved, and brittle cracks, initiated in brittle particles ahead of the ductile crack tip are activated. These propagate across particle/matrix interface and cause fracture. Higher toughness of steels with AF structure requires a longer ductility crack to be formed, than in steels with BS structure, before requirement for brittle fracture, max = Y· n > F, is attained, because the strain hardening exponent (n) of the former steel is much lower and product Y· n is smaller in spite of Y is higher. The overall contribution of ductile fracture to the toughness is relatively small, because the shear decohesion mechanism, which dominates ductile fracture in both steels, is characterized by a low expenditure of energy. In spite of TiN inclusions are present, the primary nuclei are assumed to be carbides, smaller than 1µm. The TiN-cracks are blunted out before the conditions for cleavage are attained. This can be ascribed to influence of a large plastic zone which is produced ahead of the ductile crack. In addition to being more resistant to brittle crack propagation across particle/matrix interface, the steels with AF structure show the susceptibility to cracks being arrested at the grain boundaries, presumably AF plate boundaries.

1074

N. Radovic et al.

This feature is observed only in steels with AF and not with BS structure, providing thus additional barriers to crack propagation in former.

References 1.

Drobnjak, Dj. and Koprivica, A., Proceedings of theInt.ernational Conference Fundamentals and Applications of Microalloyed forging Steels, edited by C.V.Tyne, G.Krauss and D.K.Matlock, TMS, Warrendale PA, 1996, 93-106.

2.

Bhadeshia, H.K.D.W., Bainite in Steels, Institute of Materials, London, England 1992.

3.

Hraam, H., Mechanism of Brittle Fracture in Medium Carbon V-microalloyed Steels, MSc Thesis, Faculty of Technology and Metallurgy, University of Belgrade, 1998.

19. Structural Integrity Assessment in Theory and Practice

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COMPUTATION AND EXPERIMENTAL INVESTIGATIONS OF NOTCHED COMPONENTS FATIGUE LIFE ESTIMATION S. Maksimovic, Z. Burzic and K. Maksimovic VTI- Aeronautical Institute, Kataniceva 15, 11000 Belgrade, Serbia and Montenegro [email protected] This work considers the analytical methods and procedures for obtaining the stress intensity factors and for predicting the fatigue crack growth life for cracks in notched structural components. Many failures in aircraft structures are due to fatigue cracks initiating and developing from fastener holes at which there is large stress concentration. Stress intensity factor (SIF) solutions are required for fracture strength and residual fatigue life assessment for defects in structures, or for damage tolerance analysis [1] recommended to be performed at the stage of aerospace structure design. Many efforts have been made during the past two decade to evaluate the stress intensity factor for corner cracks and for through-the-thickness cracks emanating from fastener holes. A variety of methods have been used to estimate the SIF values, such as approximate analytical analysis, finite element (FE), finite element alternating, weight function, photoelasticity and fatigue tests. In this paper the analytic methods and procedures for obtaining the SIF and predicting the fatigue crack growth life for cracks at attachment lugs. Single through crack and single corner cracks in the attachment lug analysis are considered. For this purpose analytic expressions [2] are evaluated for SIF of cracked lug structures. For validation of the analytic stress intensity factors FEM with 3D cracked finite elements is used. Typical finite element model of cracked lug is presented in Fig. 1.

FIGURE 1. Finite Element Model of cracked lug with stress distribution The stress intensity factors of cracked lugs, analytic and finite elements, for through-thethickness cracks are shown in Table 1. Analytic results are obtained using relations derived in this paper. Good agreement between finite element and analytic results is obtained. It is very important because we can to use analytic derived expresions in crack growth analyses.

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TABLE 1. Comparisons analytic and FE results for SIF, KI Lug No.

a >mm@

K IMKE max

. K IANAL max

2 6 7

5.00 5.33 4.16

68.784 68.124 94.72

65.621 70.246 93.64

FIGURE 2. Analytic and test results for crack propagation in lug 2 – H = 44.4 mm; kt = 2.8 Figure 2 shows a comparison between the experimentally determined crack propagation curves and the load cycles calculates to Elber law [3] for several crack lengths. Relatively close agreement between test and presented computation results is obtained. The analytic computation methods presented in this work can to satisfy requirements for damage tolerance analyses of notched structural components such as lugs-type joints.

References 1.

MIL-A-83444, Airplane Damage Tolerance Requirements.

2.

Maksimovic, K., Nikolic-Stanojevic, V., and Maksimovic, S., Efficient Computation Method in Fatigue Life Estimation of Damaged Structural Components, FACTA UNIVERSITATIS, Vol. 4, No. 16, 2004.

3.

Walker, K., The effect of stress ratio during crack propagation and fatigue for 2024T3 Aluminum, ASTM STP 462, Effects of environment and complex loading history on fatigue life, 1970.

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FAILURE ANALYSIS OF LAYERED COMPOSITE STRUCTURES: COMPUTATION AND EXPERIMENTAL INVESTIGATION S. Maksimovic VTI- Aeronautical Institute, Kataniceva 15, 11000 Belgrade, Serbia and Montenegro [email protected] A geometric nonlinear finite element method based on the von Karman - High Order Shear Deformation Theory (HOST) is used to study the first-ply failure and the postbuckling behavior of laminated type composite structures. For this purpose and for the investigation of the failure responses improved 4-node layered shell finite elements are used. The finite element formulation is based on the third order shear deformation theory with four-node shell finite elements having eight degrees of freedom per node. The first-ply failure of laminates and the onset of delaminating process in first-ply failure computation are some of the features of geometric nonlinear formulation. The load-displacement curves for different types of graphite/epoxy laminates are obtained. Stresses are computed in order to determine the first-ply failure of the mentioned axially compressed laminated composite structure based on the maximal strain failure criterion. In this procedure postbuckling and failure behavior of axially compressed flat and curved composite panels are investigated numerically and experimentally. Computational results using linear and geometrically nonlinear analyzes are compared with experiments. The effects of stacking sequences on initial failure load are investigated. The HOST used here assumed the parabolic distribution of the transverse shear stresses across the laminate thickness. The displacement field for the parabolic transverse shear deformation through the shell thickness is 2 ª ww 4§ z · § ww ·º u1 x, y, z u  z« a  b> U while for U >> U* the JVU method agrees with the classic peak stress approach. In order to confirm this analytical failure criterion, two type of brittle material have been investigated. In figures 2 and 3 experimental failure nominal stress Vn against the stress concentration factor Kt (gross area) are reported. Additionally, in the same figures the failure prediction with the JVU parameter is reported. The two materials present different value of U*. The PMMA material shows a fully notch behaviour because the U* is greater then the smaller tested U value. On the contrary, the PVC material has the critical U* of the same order of the smaller tested U. Note that the nominal stress prediction with JVU gives a plateau for higher Kt value despite of the classic peak stress approach.

FIGURE 2: Experimental and analytical prediction for PMMA material for different U notch values

FIGURE 3: Experimental and analytical prediction for PVC material for different U notch values

References 1.

Livieri, P. A new path independent integral applied to notched components under mode I loadings. International Journal of Fracture, 123, 107-125, 2003

2.

Rice J.R., A path independent integral and the approximate analysis of strain concentration by notches and cracks. ASME-Journal of Applied Mechanics, Vol. 35, 379-386, 1968

3.

Anderson, T.L. Fracture Mechanics, fundamentals and applications. CRC Press, 1991

20. Critical Distance Theories of Fracture

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STANDARDIZATION OF STRENGTH EVALUATION METHODS USING CRITICAL DISTANCE STRESS Toshio Hattori, Naoya Nishimura and Minoru Yamashita Gifu Univ., Yanagido, Gifu City, Gifu, Japan [email protected] In previous paper[1][2], the authors present a new strength evaluation methods using stress singularity parameters H(intensity of stress singularity) and (order of stress singularity) for adhesive bonding edges and contact edges. Using these two parameters the stress distributions near these edges can be expressed as follows (see Fig. 1).

V

H rO

(1)

Fig. 1 Stress distributions near in stress singularity fields The difficulty with this method was in obtaining the critical value of intensity of stress singularity parameter Hc for each order of stress singularity .So, in this paper we present new method for formularizing Hc by based on critical distance stress (point stress) , which can be obtained typical material strength parameters such as the fatigue limit of smooth specimens w0 and the threshold stress intensity factor range Kth of the cracked specimens. The estimated example of these critical value of intensity of stress singularity parameter Hc for each order of stress singularity for Ni-Cr-Mo-V Steel are shown in Fig. 2, in this case the critical distance is 0.012mm and critical distance stress is 360Mpa. Using these easily obtained formularized critical value Hc(), we can estimate the fretting fatigue crack initiation criteria for each contact edge angle, and thus optimize the contact edge geometry. Finally, we discuss the development of these strength criteria in terms of stress singularity fields for general stress concentration fields.

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Fig. 2 Formularized critical value of intensity of stress singularity Hc for Ni-Cr-Mo-V Steel

References 1.

Hattori, T., et. al, J. Electronic Packaging, Trans ASME, vol. 1, 243-248, 1989.

2.

Hattori, T., et. al, Developments in Fracture Mechanics for the New Century, JSMS, Tokyo, Japan, 2001.

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APPLICATION OF POINT STRESS METHOD TO HYDRO-FRACTURING TECTONIC STRESS MEASUREMENT T. Ito Institute of Fluid Science, Tohoku University 2-1-1 Katahira, Aoba-ku, Sendai, Japan [email protected] Knowledge of tectonic stress magnitudes and orientation is essential for understanding the crustal dynamics. The stress at the depths in concern can be measured from the results of in-situ tests carried out at those depths in drilled boreholes. Especially for the measurement at depth more than 1 km, hydraulic fracturing has been used generally, since, compared with the other methods, its procedure and equipment of in-situ test are quite simple and appropriate for operating in such long and narrow space as boreholes. With this technique, an interval of a borehole which is free of natural fissures is sealed off with a straddle packer system and then pressurized by injection of fluid to generate a tensile circumferential stress around the borehole. When this tensile stress exceeds the strength of a rock and the concentration of tectonic stresses by the borehole, fracture initiation occurs on the borehole wall. Then, the so-called breakdown pressure Pf is observed as the borehole pressure at the fracture initiation. In addition to this pressure, several characteristic pressure related to the tectonic stresses are observed in the borehole pressure – time history during the test. Consequently, the tectonic stresses are computed from those observed pressures by using the formulae of theoretical relations between the tectonic stresses and the pressures which are derived theoretically in advance. The classical theory for interpreting the breakdown pressure Pf assumes that the fracture initiation occurs, when the maximum tensile stress reaches the tensile strength of the rock, Vf, on the borehole wall. This condition is expressed assuming vertical borehole as follows; ST

P Pf

V f , ST

S H  3S h  P

(1)

where P is the borehole pressure, ST is the circumferential stress on the borehole wall, and SH and Sh are the maximum and minimum tectonic stresses in a horizontal plane. On the other hand, there are infinite number of small pores inside almost rocks, while the pore’s shape and connectivity are dependent on the type of rock. The existence of such pores brings special feature in mechanical behavior of rocks, different to cases of other materials. First, the borehole pressure raised by fluid injection in hydraulic fracturing, penetrates through the pores into the rock from the borehole wall, and the fluid penetration causes an additional circumferential stress in compression at the borehole wall. Secondly, the pore fluid pressure has the effect to loose strength in failure, where this phenomenon is known as the Terzaghi’s effective stress law. Taking account both of the additionally-induced stress and the effect of the pore fluid pressure on tensile failure, Eq. (1) is modified as follows; ­S ® T ¯

P Pf





 A Pf  p0 ½¾  Pf ¿

Vf

(2)

where p0 is the initial value of the pore fluid pressure and A is a poro-elastic constant. Then we come up with the following theoretical relation between the tectonic stresses and the breakdown pressure Pf , which has been originally derived by Haimson and Fairhurst [1];

T. Ito

1118

Pf

3S h  S H  V f  Ap0 2 A

(3)

However, this breakdown equation is still not so sufficient that it cannot explain the dependency of Pf on increasing rate of the borehole pressure as shown in Fig. 1. To correct Eq. (3) taking account of the dependency on pressurization rate, we have proposed a theoretical model based on a criterion taking account of a length scale which characterizes the failure process [2]. Namely this model assumes that fracture initiation to occur when the maximum effective stress in tension reaches the tensile strength of rock at a point that is not on the borehole wall but is inside the rock by a radial distance of d. The d is a material constant of few millimeters. The solid line in Fig. 1 shows the breakdown pressure predicted by our model, and it is actually consistent well with the experimental results. Note that the gradient of pore fluid pressure developed around the borehole becomes steeper as the pressurization rate becomes larger, and as a result, both of the pore fluid pressure and the stress state at the distance d from the borehole wall change with the pressurization rate. This is the reason why the breakdown pressure predicted by our model varies with the pressurization rate. Furthermore, our model shows that if borehole diameter is sufficiently large compared with the characteristic length d, the breakdown pressure will be close to the breakdown pressure obtained by the conventional equation of Eq. (3), where the borehole diameter prepared for the laboratory experiments shown in Fig. 1 is 3 mm.

FIGURE 1. Comparison of observations obtained by laboratory experiments using boreholes of 3 mm in diameter [3], and theoretical predictions [1, 2].

References 1.

Haimson, B. and Fairhurst, C., Soc. Pet. Eng. J., vol. 7, 310-318, 1967.

2.

Ito, T. and Hayashi, K., Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., vol. 28, 285-293, 1991.

3.

Zoback, M.D., Rummel, R., Jung, R. and Raleigh, C.B., Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., vol. 14, 49-58, 1977.

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A UNIFIED FAILURE CRITERION FOR BRITTLE OR QUASI-BRITTLE MATERIALS UNDER ARBITRARY STRESS CONCENTRATION J. Li and X. B. Zhang University of Paris XIII, LPMTM, CNRS UPR 9001, France Blaise Pascal University of Clermont II, LaMI, France [email protected] The stress concentrations are of many types and of different levels. For brittle and quasi-brittle materials, failure criteria proposed by different authors are established to study different situations. For example, when a stress distribution is not uniform but does not present a singularity, the maximum stress criterion ( V V c ) is used. For the case of a crack, the criteria are based on the Linear Fracture Mechanics. When a stress concentration presents a singularity but weaker than a crack one, such as sharp notches, the failure criteria are kinds of combination of the criteria for the two above cases. In fact, each criterion only functions with a particular stress concentration case for which it was developed. Its extension to a more general case often induces important errors. Therefore, the purpose of the present work is to establish a unified crack onset criterion for brittle and quasi-brittle materials that enables to count for all types of stress concentrations. The study is based on two concepts: The first one is described by Leguillon [1] who combined consistently the material strengthVc and the material toughness for crack propagation Gc in the prediction of the crack onset from a sharp notch in brittle material. The second one is the stress concentration dependency of the energy dissipation in a new surface creation, issued from direct observation of the fracture surfaces in brittle materials. According to the observations on the fracture surfaces of specimens made of PMMA obtained from our experiments, we propose a three parameter criterion in order to predict the crack initiation from a smooth surface. A part from the two material parameters used in the Leguillon criterion, we suppose that there exists a third material parameter Gu which represents the material toughness under uniform tensile stress. This parameter can be regarded as the energy dissipation by unit nominal area when the material is subjected to uniform uni-axial tension. An empirical expression to determine this parameter is proposed in this work.

Proposed criterion The critical energy release rate for any local stress concentration level, the so-called specific fracture energy, can be estimated by interpolation rule as follows: Gs (D ) D mGc  (1  D ) n Gu

(1)

where m and n are two real constants to be adjusted by experimental data; D t 0 is a real parameter describing the local stress concentration level. D depends on the critical height of the crack band formed just before the main crack initiation. It is assumed that the micro-cracks develops within the zone where the maximal principal stress exceeds the material strength, i.e., V1 > Vc. The height of this zone h can be regarded as the height of the pseudo crack band. Therefore, D can be defined as follows:

D

hcrack h

(2)

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where hcrack is the height of the zone near a crack tip in which V1 > Vc when the crack grows. It can be calculated according to the near tip stress field. It is clear that D = 1 for the case of a crack and D = 0 when the material is under uniform tension. The proposed criterion with three material parameters is as follows: The crack initiation occurs at the direction where the tensile stress is maximal and if both the following conditions are satisfied: (a) In the non-cracked configuration, the maximum principal stress of the point at the characteristic distance V 1 (l ) reaches the material strength V c ; (b) In the virtual cracked configuration, the incremental energy release rate at the virtual crack tip situated at the same point G (l ) reaches the critical toughness Gs (D ) . Where the critical energy release rate Gs (D ) should be evaluated using Equations (1) and (2).

Results and conclusions In order to verify the proposed criterion, some experimental studies are carried out based on the experimental results performed by authors or found out in the literature. These experimental data are used to verify the accuracy of the proposed criterion. The predictions obtained by using the Leguillon criterion are also presented for comparison. The material selected in this study is the PMMA (polymethyl metacrylate), for its brittle characteristics. Three kinds of plane specimens are considered: plates with double V-notches under uni-axial tension, plates with a central hole under uni-axial tension and plates with double U-notches under uni-axial tension. Figures 1 and 2 show some results of the comparison. The experimental results have shown that the proposed criterion is physically reasonable, highly accurate and easy to apply. It can be used in crack initiation prediction of engineering structures made of brittle or quasi-brittle materials.

FIGURE 1. Critical loads for holed plates versus hole diameter

FIGURE 2. Critical loads for U-notched plates versus notch radius

Reference 1.

Leguillon D., Strength or toughness? A criterion for crack onset at a notch, European J. Mech. A/Solids, 21, 61-72, 2002

22. New Investigations on Very High Cycle Fatigue of Materials

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MORPHOLOGY OF STEP-WISE S-N CURVES DEPENDING ON NOTCH AND SURFACE ROUGHNESS IN HIGH STRENGTH STEEL H. Itoga, K. Tokaji1, M. Nakajima2 and H. N. Ko Nakanihon Automotive College, Sakahogi-cho, Kamo-gun, Gifu Prefecture 505-0077, Japan 1Dept. of Mech. and Systems Eng., Gifu Univ., 1-1 Yanagido, Gifu 501-1193, Japan 2Dept. of Mech. Eng., Toyota National College of Technology, 2-1 Eisei-cho, Toyota 471-8525, Japan [email protected] It has been indicated that subsurface fracture occurred at stress levels below the conventional fatigue limit in long life region more than 107 cycles, particularly in high strength steels (Dahlberg [1], Naito et al. [2], Nakajima et al. [3]). A notable feature of subsurface fracture is the presence of a fish-eye with an inclusion near its centre, and the formation mechanism of fish-eye has not been fully understood. High strength steels usually possess very high sensitivity to notch and surface defect. Therefore, it is very important to understand the effects of notch and surface roughness on crack initiation and associated S–N characteristics. In the present study, rotary bending fatigue tests have been conducted in laboratory air at ambient temperature using notched specimens with different stress concentration factors and specimens with roughened surfaces in high strength steel. The effects of notch and surface roughness on step-wise S–N characteristics, particularly on the transition stress, were discussed. The material used is a Ni–Cr–Mo steel, which was quenched at 880qC followed by tempered at 200qC. Specimens with hourglass-shape (smooth specimen), three types of notched specimens (stress concentration factor Kt=1.16, 1.51 and 2.0), and three surface-roughened specimens (maximum height Rz=10 m, 16 m and 19 m) were prepared. Fatigue tests were performed using cantilever-type rotary bending fatigue testing machine operating at a frequency of 52.5 Hz in laboratory air at ambient temperature. After experiment, fracture surfaces were examined in detail using a scanning electron microscope (SEM).

The S–N diagram of the notched specimens is shown in Fig.1, where the open and solid symbols represent surface-related crack initiation and subsurface crack initiation, respectively. The smooth specimen and the notched specimen with Kt=1.16 show subsurface fracture in long life region, while subsurface fracture is not seen in the notched specimens with Kt=1.51 and 2.0. In the

H. Itoga et al.

1122

surface fracture region, fatigue strength decreases with increasing stress concentration factor, but in the subsurface fracture region, there was no discernible difference in fatigue strength. It was found that the high strength steel studied had very high notch sensitivity. Figure 2 represents the SN diagram for the surface-roughened specimens. All surface-roughened specimens exhibit subsurface fracture, where the transition stress at which fracture mode changed decreases in the specimens with rougher surface. In the surface fracture region, fatigue strength decreases with increasing surface roughness, while in the subsurface fracture region, it does not depend on surface roughness. A fish-eye was always seen on fracture surfaces in subsurface fracture region, with a nonmetallic inclusion near its centre from which the crack initiated. It was found that fish-eyes were nearly circular and their periphery always touched the surface. Such morphologies of fisheyes were not affected by the presence of notch and surface roughness. The transition stresses, i.e. the conventional fatigue limits, for the surface-roughened specimens were predicted by using the —area parameter model (Murakami [4]).

(1) where Vwp: predicted fatigue limit (MPa), HV: Vickers hardness (kgf/mm2), R: stress ratio, D: 0.226+HVu10-4. The equivalent defect sizes for surface roughness were employed as the —area values (Murakami et al. [5]). The obtained results were listed in Table 1. It can be seen that the predicted fatigue limits are in good agreement with the experimental ones when the arithmetical mean deviation, Ra, was used as the height of surface roughness. TABLE 1. Fatigue limit predicted by the —area parameter model

References 1.

Dahlberg, E.P., Trans ASM, 58, 46–53, 1965.

2.

Naito, T., Ueda, H. and Kikuchi, M., Metal Trans, 15A, 1431–1436, 1984.

3.

Nakajima, M., Tokaji, K., Itoga, H. and H.-N. Ko, Fatigue Fract. Engng Mater. Struct., 26, 1113–1118, 2003.

4.

Murakami, Y., Effects of Small Defects and Non-metallic Inclusions, Yokendo Ltd., Tokyo, Japan, 1993.

5.

Murakami, Y., Takahashi, K. and Yamashita, A., Trans. Jpn Soc. Mech. Eng., A63, 16121619, 1997.

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VERY HIGH CYCLE FATIGUE BEHAVIOUR UNDER CYCLIC TORSION LOADING H. Mayer and S. Stanzl-Tschegg BOKU, Institute of Physics and Materials Science, Peter-Jordan Str. 82, 1190 Vienna, Austria [email protected], [email protected] Several technical components are stressed in cyclic torsion. Valve springs, for example or torque transmission shafts must withstand high numbers of torsion load cycles in service, and fatigue properties of materials under these loading conditions are of great interest therefore. The present investigation serves to determine cyclic torsion fatigue strength at high and very high numbers of cycles and to compare the measured data with results of axial loading experiments. Fatigue tests are performed using ultrasonic fatigue testing equipment. Specimens are stimulated to resonance vibrations, and the cycling frequency of about 20 kHz allows measuring high cycle fatigue data within relatively short testing times. Ultrasonic fatigue testing of materials is mainly performed in cyclic tension-compression with or without superimposed static loading. Similar electronic control equipment and power generators are used to perform cyclic torsion tests. Measurement and control of the vibration amplitude serves to control the magnitude of loading, and control of resonance frequency serves to automatically detect crack initiation and specimen failure. The mechanical equipment, however, had to be re-designed to account for the shorter wavelength of shear waves compared with tension-compression waves. Experiments are performed with the aluminium alloy 2024-T351 (ultimate tensile strength Rm=460 MPa, yield strength Rp0.2=352 MPa, fracture strain A5=18%) and with Ck15 (carbon steel with 0.15% C in normalized condition, Rm=834 MPa, Rp0.2=368 MPa, A5=9%). Axial and torsion fatigue properties are investigated under fully reversed loading conditions in the regime from 105106 to 109-1010 cycles. Results of cyclic torsion and cyclic tension compression S-N tests are shown in Fig. 1. Mises equivalent stresses are used to compare axial and torsion fatigue data, i.e. cyclic torsion stress amplitudes are multiplied with factor 3. Specimen failure is defined in cyclic torsion tests, when a fatigue crack of minimum 300 Pm length has formed. The aluminium alloy does not show a fatigue limit below 109 cycles in both loading conditions. S-N data may well be approximated using power law functions of stress amplitudes and cycles to failure. At the same equivalent stresses, cycles to failure in torsion tests are about factor 2-10 higher than lifetimes measured in axial loading tests. Cyclic tension compression tests of carbon steel deliver an S-N curve, which is approximately parallel to the abscissa at numbers of cycles greater 107. Fatigue data produced by cyclic torsion are comparable to the tension compression data using Mises equivalent stress. However, the limited data available until now prohibits further analysis.

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FIGURE 1. S-N data of Ck15 (circles) and 2024-T351 (squares) in cyclic torsion (closed symbols) and cyclic tension compression (open symbols) at fully reversed loading condition. Fatigue crack initiation is at the surfaces of the specimens in both materials in both loading conditions whereas the crack paths are different. High cycle torsion fatigue of 2024-T351 produced fatigue cracks oriented in the directions of maximum shear stresses, i.e. in specimen's length and circumferential direction, and cracks in length direction appeared first. Thus crack propagation is in the direction of maximum shear stresses and the crack tip is loaded in cyclic mode II. In contrast, cyclic axial loading of the aluminium alloy produced flat fracture surfaces at the crack initiation places, which are perpendicular to the applied principal stress. High cycle torsion fatigue of Ck15 produced crack paths, which are inclined by about 45° to the specimen's axis, i.e. the fracture surface is perpendicular to the principal stresses. Within single grains, however, the crack path follows one of the maximum shear stress directions. The macroscopically inclined crack path is caused by the alternative growth of the crack in specimen's length and circumferential direction. Fracture surface produced in high cycle tension compression fatigue testing of Ck15 is macroscopically oriented perpendicular to the principal stress.

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MODELLING OF FATIGUE CRACK GROWTH FROM EXFOLIATION AND PITTING CORROSION G. Clark, P. K. Sharp and R. Jones1,2 Air Vehicles Division, Defence Science and Technology Organisation, 506 Lorimer Street, Fishermans Bend 3207, [email protected] 1DSTO Centre for Structural Mechanics, Department of Mechanical Engineering, Monash University, P.O. Box 31, Monash University, Victoria, 3800, Australia 2Cooperative Research Centre for Integrated Assett Management (CIEAM), Department of Mechanical Engineering, Monash University, P.O. Box 31, Monash University, Victoria, 3800, Australia [email protected] When structures are operated in corrosive environments, fatigue failures can occur from the formation and propagation of cracks from exfoliation and pitting corrosion. Corrosion-nucleated fatigue can be particularly problematic in structures that are not thought to be fatigue critical, and are therefore not inspected, but can become critical in the presence of corrosion. Although the risk factor of corrosion-nucleated fatigue should never be ignored, the most demanding corrosionrelated issue is the escalating maintenance burden caused by use of a “Find and Fix” corrosion management policy. This “Find and Fix” policy exists largely because tools do not exist to accurately assess the structural significance of corrosion when it is detected. Hence corrosion must be treated as an immediate threat. The development of analytical tools capable of accurately assessing the effect of corrosion on the durability of a structure would be a major benefit in that the management philosophy could begin to transition to an “Assess and Monitor” framework. The success of such a philosophy would greatly reduce unnecessary maintenance and defer other actions to a more convenient time, such as when an aircraft is due for a heavy maintenance check. Pitting and exfoliation are the most significant types of corrosion being considered by DSTO for analytical tool development. In this paper, as in [1], pitting and exfoliation will be addressed together because from a fatigue perspective, the mechanisms driving structural life for these two damage types are very similar, see [1]. DSTO has developed a modelling approach for fatigue from exfoliation based corrosion [1] based on the concept that the exfoliation process requires development of pit-like intrusions into the substrate material, and that these can then be represented in the fatigue model as if they are pits. This common feature then allows the use of a single modelling approach to modelling cracking from both pitting and exfoliation (in aluminium alloys). In this context it should be noted that the work of C. G. Schmidt et al [2], and R. S. Piascik and S. A. Willard [3] found that the growth of small corrosion fatigue cracks could be described by the Frost Dugdale law [4], viz L n a

EN  Ln(ao )

or

a

a o e EN

(1)

where N is the “fatigue life”, E is a parameter that is geometry, material and load dependent, a is the crack depth and time N, a0 is the initial size of the defect. However, recent research [5] has shown that the Frost Dugdale law [4], which can also be viewed as a fractal based growth law, can be applied to a wide class of engineering problems resulting in an approximately exponential relationship between crack size and number of cycles. Examining the open literature, we show that the approximation presented in [3, 4] appears to be a reasonable fit to data on corrosion-

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initiated fatigue crack growth. Fig. 1 presents data from [5], showing that there is near linear relationship between the number of cycles and the log of the crack size. As a result a methodology is presented that links NASTRAN with FASTRAN to automatically assess the effect of corrosion on the structural performance of a component.

FIGURE 1 Experimental data presented in [5] for corrosion cracking

References 1.

P. K. Sharp, T. B. Mills, and G. Clark, “Modeling of Fatigue Crack Growth from Pitting and Exfoliation Corrosion”, International Committee on Aeronautical Fatigue, Toulouse, France, (2001).

2.

C. G. Schmidt, J. E. Crocker, J. H. Giovanola, C. H. Kanazawa, D. A. Shockey, “Characterization of Early Stages of Corrosion Fatigue in Aircraft Skin”, DOT/FAA/AR951108, February 1996.

3.

R. S. Piascik and S. A. Willard, "The Growth of Small Corrosion Fatigue Cracks in Alloy 2024," NASA Technical Memorandum 107755, NASA Langley Research Center, Hampton, VA (April 1993).

4.

N. E. Frost and D. S. Dugdale, “The propagation of fatigue cracks in test specimens”, Journal Mechanics and Physics of Solids, 6, pp 92-110, 1958.

5.

Barter S., Molent L., Goldsmith N. and Jones R., 2004, "An Experimental Evaluation Of Fatigue Crack Growth", Journal Engineering Fracture Mechanics, 2004.

6.

A.T. Kermanidis, P.V. Petroyiannis, S.G. Pantelakis, “Fatigue and damage tolerance behaviour of corroded 2024 T351 aircraft aluminum alloy”, Theoretical and Applied Fracture Mechanics, (2005).

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DOES COPPER UNDERGO SURFACE ROUGHENING DURING FATIGUE IN THE VH REGIME? Stefanie Stanzl-Tschegg, Hael Mughrabi1 and Reinhard Schuller Institute of Physics and Materials Science BOKU, University of Natural Resources and Applied Life Sciences, Peter-Jordan-Strasse 82, A-1190 Vienna, Austria 1Institute of Materials Sciences, University of Erlangen-Nuernberg Martensstrasse 5, D-91058 Erlangen, Germany [email protected], [email protected], [email protected] Extensive studies have been performed on nature and formation of persistent slip bands (PSBs) in the past. They have been identified as sites of localized cyclic plastic deformation, which are typically found in fcc metals, like copper, nickel or solid solutions of these metals. These sites of plastic deformation become visible as extrusions and microcracks (intrusions) on the specimen surface and as „ladder“, “vein“ or cell structures of the dislocations in the interior of the specimen. The stresses and plastic strains for their formation are determined by a plateau stress in the cyclic stress strain curve (CSS curves) >1@ with a typical plateau stress at approximately 28 MPa and a resolved shear strain between approximately 10-4 and 8x10-3 for copper single crystals. Additional investigations have been performed at stresses below the plateau regime at stresses between 3 and 26 MPa and number of cycles up to several 107 in order to study the evolution of sliding and dislocation characteristics >2@ In more recent time, the question on the fatigue behaviour and damage in the very high cycle regime (VHCR) obtained increased attention, after it was detected that failure is possible at cyclic stresses below the fatigue limit in steels after 109 or more cycles >3@. Mughrabi >4@, in a systematic survey, discussed possible mechanisms for the existence or non-existence of a fatigue limit not only in steels but other materials, like fcc metals. While inclusions were identified as sites of internal crack initiation below the conventional fatigue limit of high strength steels (named type II materials), shear band cracking in PSBs or grain boundary cracking by PSBs are the dominant failure mechanisms at intermediate and lower amplitudes in the HCF regime for copper or nickel or their solid solutions. A plastic strain fatigue limit has been defined as PSB threshold in a CoffinManson diagram and has been transformed into a stress fatigue limit of an S-N diagram. Below the PSB threshold, PSBs do not form and cyclic slip is reported to be more or less homogeneously distributed. Mughrabi proposed that finite slip irreversibility remains, although this irreversibility is much smaller at lower amplitudes. He assumed in a new model that failure occurs, if the irreversible slip steps at the surface lead to a critical surface roughness, whereby much smaller rates of its formation can be expected than for PSBs >5@ . The local plastic strain amplitudes at stresses slightly below the PSB threshold value may be expected to be an order of magnitude lower than in the PSBs and two or three orders of magnitudes lower than in the socalled matrix structure in single-phase materials. Therefore, it may be expected that the number of cycles required to develop the critical surface roughness in the absence of PSBs just below the PSB-threshold will be one to three decades larger than those required for failure in the presence of PSBs. Further reduction of the amplitude will finally lead to the so-called irreversibility limit, below which cyclic slip will be reversible and therefore non-damaging. Thus, a multi-stage S-N diagram has been predicted by Mughrabi for type I materials with the true fatigue limit at the irreversibility limit, after extremely high numbers of cycles, like 109 or higher.

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It is the aim of this study to characterize the response of copper on fatigue loading at cyclic strain amplitudes below the threshold PSB limit at very high numbers of cycles. Polycrystalline copper specimens with a diameter of 8 mm and a grain size of approximately 80 Pm were used after mechanical plus electrolytic polishing. They were ramp loaded up to a total strain and stress amplitude being slightly below the PSB threshold stress. At this stress, the specimen was then fatigued with the ultrasonic technique at a testing frequency of 20 kHz up to 1010 cycles The experiment was interrupted several times in order to investigate the resulting surface appearance in an SEM and AFM. Owing to the sine strain distribution along the specimen axis in the ultrasonic loading experiment, lower strains and stresses are present along the specimen length in one specimen, so that systematic studies of all desired stress amplitudes are possible with one specimen. Thus the induced surface appearance and roughness was determined in the centre of the specimens, where maximum strains and stresses were selected such that they were slightly below the PSB threshold, and in some specified distances apart from this, where defined smaller amplitudes are present. As first result, the distribution and extent of slip activity was determined for several defined strain and stress values below the PSB threshold. Secondly, the strain and stress limit has been determined, below which no cyclic slip traces are visible at the surface, i.e. where cyclic slip was reversible and therefore non-damaging. Thirdly, it could be shown that the portion of areas showing slip features depends on the applied number of cycles. Finally, surface roughness and profiles have been determined for several specified strains and stresses.

References 1.

H. Mughrabi, Mat. Sci. Eng., 33, 1978, 207-223)

2.

L. Buchinger, S. Stanzl and C. Laird, Phil. Mag. A, 1984, No. 2, 275-298

3.

T. Naita, H. Nueda and M. Kikuchi, Metall. Trans. 15A, 1431-1436

4.

H. Mughrabi, Fatigue Fract. Engng. Mater. Struct. Vol. 22, No. 7, 1999, 633-641

5.

H. Mughrabi, VHCF-3, Proc. Ehird Int. Conf. on VHCF, eds. T. Sakai and Y. Ochi, The Soc. of Mat. Sci., Japan, 2004, 14-18

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CRACK INITIATION MECHANISM OF BEARING STEEL IN HIGH CYCLE FATIGUE T. Sakai College of Science and Engineering, Ritsumeikan University 1-1-1 Nojihigashi, Kusatsu, Shiga, 525-8577 Japan Hisashi Harada and Noriyasu Oguma R&D Center, Koyo Seiko Co., Ltd. 24-1 Kokubu Higanjyo-cho, Kashiwara, 582-8588 Japan [email protected] In the last decade, fatigue behavior of metallic materials in very high cycle regime has been coming out as an important subject to guarantee the safety of mechanical structures during the long term service. The authors had developed special fatigue testing machines to perform the fatigue tests effectively in both rotating bending and axial loading in gigacycle region. By using these testing machines, long life fatigue tests were carried out for several kinds of metallic materials including the high carbon chromium bearing steel(JIS: SUJ2). Since a round-robin tests for this steel were performed as a common research project in the Research Group for Statistical Aspects of Materials Strength[RGSAMS], a number of fatigue test results were accumulated and analyzed. Among these results, typical examples of S-N property are presented in this paper together with the X-ray diffraction pattern for the microstructures at the crack initiation sites in the interior inclusion-induced fracture having the fish-eye. Specimens and Experimental Procedure

Materials used in this study is the high carbon chromium bearing steel (JIS: SUJ2). Chemical composition of this steel is provided in TABLE 1, and shape of the specimen is hourglass type with the stress concentration factor of D 1.06 . These specimens were quenched (1108 u K 40min + Oil quenching) and tempered (45 u 3K 120min + Air cooling). Hardness distribution over the cross section of this material was almost flat and the average value is given as HV=730. A multitype fatigue testing machine in rotating bending was used in the present project. By using this machine, four specimens can be simultaneously tested at the frequency of 3150rpm in the ordinary room atmosphere without control of the temperature and humidity. S-N property of this steel in gigacycle regime was first examined and fracture surface of every failed specimen was then observed by means of SEM and the microstructures at the crack origins were observed by TEM. In addition, the X-ray diffraction pattern was also examined for the microstructure at the crack initiation site in the interior inclusion-induced fracture. Experimental Results and Discussions S-N diagram obtained in this program is shown in Fig.1, in which fatigue data for surfaceinduced fracture are plotted by hollow marks and the data for interior inclusion-induced fracture are plotted by solid marks, respectively. S-N characteristics of this steel can be well explained as a duplex S-N curves consisting of S-N curves for the respective fracture modes of surface-induced fracture and interior inclusion-induced

T. Sakai

1130

fracture. In this figure, the S-N curve for surface-induced fracture has the fatigue limit at V w 1270MPa, but another S-N curve for interior inclusion-induced fracture has no fatigue limit until gigacycle regime.

FIGURE 1 S-N diagram for SUJ2 steel

FIGURE 2 SEM image of FGA at center of the fisheye

Fine granular area(FGA) was necessarily found around the inclusion at the center of the fisheye as indicated in Fig.2. Microstructure of the longitudinal section at position in Fig.2 was observed by TEM. The microstructure in thin layer of the FGA region was significantly polygonized into the fine granular structure, although the microstructure at deep portion kept the original microstructure. Image of SADP in such a thin layer with the fine granular structure was examined in order to reconfirm such a polygonization. Thus, we obtained the typical diffraction pattern forming some circular rings in the SADP image. But the pattern in the deep portion at FGA is isolated spots governed by the Bragg’s condition. These results indicate that the microstructure of thin layer inside the FGA becomes fine granular through the extensive polygonization of the original microstructure. In other words, fatigue crack in the very high cycle regime takes place through this polygonization and debonding of fine grain boundaries. Based on this mechanism, morphology of the characteristic area of FGA becomes fine granular. In addition, it was found that stress intensity factor range at the FGA front keeps almost constant of 4-6MPa corresponding well to the threshold value for the fatigue crack propagation.

m and this is

Conclusions 1

S-N characteristics of SUJ2 steel were well explained as duplex S-N property consisting of S-N curves for the respective curves for surface induced fracture and interior inclusioninduced fracture.

2

Fatigue cracks took place along the fine granular microstructure inside the FGA around the inclusion at center of the fish-eye.

22. New Investigations on Very High Cycle Fatigue of Materials

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VERY HIGH CYCLE FATIGUE BEHAVIOR OF HIGH STRENGTH STEELS Yoshiaki Akiniwa, Nobuyuki Miyamoto1, Hirotaka Tsuru and Keisuke Tanaka Mechanical Engineering, Nagoya University Furo-cho, Chikusa-ku, Nagoya 464-8603 Japan [email protected] [email protected] [email protected] 1Materials R&D Department, DENSO CORPORATION 1-1 Showa-cho, Kariya, 448-8661 Japan [email protected] Life extension of engineering plants and high-speed operation of engineering machines are required in various fields. In these situations, conventional fatigue strength determined as the strength for 107 cycles is not sufficient. It is necessary to adopt the data up to giga cycle regime for design and maintenance. In the present study, ultrasonic fatigue tests were conducted with smooth specimens of bearing steels (JIS SUJ2, 746HV and 777HV), alloy tool steels (JIS SKD11, 707 HV and 710HV) and martensitic stainless steels (661HV and 678HV). The fracture surface was examined with scanning electron microscopy to identify the crack nucleation site.

FIGURE 1. S-N curves Figure 1(a) shows the S-N curves for two batches of SUJ2. The open and solid marks indicate the data of surface fracture and internal fracture, respectively. The fine solid and dotted lines indicate the published data of the electro-polished smooth specimens obtained by rotating bending fatigue operated at a frequency of 50 Hz [1,2,3]. The data of ultrasonic fatigue are close to those of rotating bending fatigue, although they do not show a distinct two-step. For SUJ2-A, it is interesting to note that the surface fracture takes place not only at short fatigue lives, but also at very long lives. Figure 1(b) shows the data for SKD11. The S-N curve can be approximated by linear line. In our previous paper, the propagation process of fatigue cracks initiated from internal inclusions has been divided into three regions [4]. The first region surrounding inclusions is a fine granular facet area. The crack propagation in the facet region is called Stage A and the crack

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propagation outside the facet region is Stage B. In these regions, the cracks propagate without environmental effects of atmospheric air. When the fatigue cracks reaches the specimen surface, the fatigue cracks propagates as surface cracks (Stage C). Since most of the fatigue life for the VHCF regime is consumed in Stage A, the threshold condition of facet crack is very important. Figure 2 shows the relation between facet size and inclusion size for various steels [5,6]. The facet size increases with the inclusion size. When the fatigue limit is related to the facet size, the size can be evaluated from the distribution of the inclusion size.

FIGURE 2. Relation between facet size and inclusion size

References 1.

Shiozawa K, Lu L., Fatigue Fract Engng Mater Struct, Vol. 25, 813-822, 2002.

2.

Goto M, Yamamoto T, Nisitani H, Sakai T, Gawagoishi N., J Soci Mat Sci Japan, vol. 49, 786-792, 2000.

3.

Ochi Y, Matsumura T, Masaki K, Yoshida S., Fatigue Fract Engng Mater Struct, vol. 25, 823-822, 2002.

4.

Tanaka K, Akiniwa Y., Fatigue Fract Engng Mater Struct; vol. 25, 775-784, 2002.

5.

Miyamoto N., Asai H., Miyakawa S., Akiniwa Y. and Tanaka K., Trans Japan Soci Mech Eng A , vol. 70,1080-1085, 2004.

6.

Tanaka K, Akiniwa Y, Miyamoto N, Proc. 3rd VHCF,2004, 56-67.

23. Deformation and Fracture of Engineering Materials

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FRACTURE TOUGHNESS OF HYDRIDED ZIRCALOY-4 EXPERIMENTAL AND NUMERICAL STUDY C. Langlade, P. Bouffioux1 and M. Clavel MSSMat laboratory, Ecole Centrale Paris, Grande Voie des Vignes, 92295 Chatenay Malabry, France. 1EDF R&D/MMC, Site des Renardières, 77818 Moret s/ Loing Cedex, France. [email protected], [email protected], [email protected] Zircaloy-4 is used as cladding tubes in pressurized water reactors (PWR). Their oxidization by primary circuit water produces hydrogen. The tube picks up a fraction of hydrogen during irradiation. When the solubility limit of hydrogen into zirconium is reached, zirconium hydride platelets precipitation takes place. Hydrided stress-free platelets are oriented in the circumferential direction of cladding (Fig. 2) thanks to its texture. If a sufficiently high tensile stress is applied in the circumferential direction of cladding during hydriding process, ZrHx platelets are oriented in the radial direction (Fig. 2). This process is called reorientation. In order to study hydride platelets orientation effect on cladding fracture toughness, the pin loading test previously (PLT, Fig. 1) proposed by Gregoriev et al. ([1]) has been involved. Furthermore a better understanding of this test was allowed by a 3D finite element simulation. Tests made on Zircaloy-4 samples show that pin loading tests are reproducible. Zircaloy-4 samples exhibit a steady crack growth. Fracture surface consists in a ductile tearing 45° tilted in the sample thickness in agreement with the plane stress conditions. Zircaloy-4 with circumferential hydrides and an amount of hydrogen around 300 ppm exhibits very little change compared to Zircaloy-4 samples hydrogen free. Fracture surface consists in a ductile tearing, roughly plane in the sample thickness, with smooth areas corresponding to broken hydride platelets. Zircaloy-4 with circumferential and radial hydrides and an amount of hydrogen around 150 ppm exhibits a brittle fracture. Fracture surface consists in smooth and plane areas which have the size than radial hydride platelets clusters through which damage probably takes place ahead of the crack tip. Pin loading tests show that radial hydrides are much more deleterious than circumferential ones. In order to understand this effect, a mesoscopic plasticity model implemented in Abaqus finite element software by Hoc et al. ([2]) has been used for modelling hydrided microstructure. This one is based on continuous dislocation density evolution. In parallel, direct identification of parameters of the modelling have been done using TEM observations.

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FIGURE 1. Pin Loading Test principle

FIGURE 2. Pin Loading Test principle

References 1.

Grigoriev V., Josefsson B., Lind A. and Rosborg B., Scripta Met. et Mat., vol. 33, 109-114, 1995

2.

Hoc T., Rey C. and Raphanel J. L., Acta materialia, vol. 49, 1835-1846, 2001

23. Deformation and Fracture of Engineering Materials

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CRACK GROWTH BEHAVIOR IN A HIGHLY FILLED ELASTOMER C. T. Liu, R. Neviere1 and G. Ravichandran2 AFRL/PRSM, 10 E. Saturn Blvd. Edwards AFB CA 93524-7680 1SNPE, 91710 Vert-Le-Petit, France 2Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, CA 91125 [email protected] An important engineering problem in structural design is evaluating its integrity and reliability. It is well known that structural strength may be degraded during its design life due to mechanical or chemical aging, or a combination of these two aging mechanisms. Depending on the structural design, material type, service loading, and environmental condition, the cause and degree of strength degradation due to the different aging mechanisms differs. One of the common causes of strength degradation is the result of damage and crack development in the structure. Therefore, to effectively use the material in structural applications one needs to understand the damage initiation and evolution processes, the effects of damage and crack development on the material’s response, and the remaining strength and life of the structures. In recent years, a considerable amount of work has been done studying crack growth behavior in particulate composite materials under different loading conditions at ambient pressure [1-4]. Experimental findings indicate that power law relationships exist between the crack growth rate, da/dt, and the Mode I stress intensity factor, KI. These experimental findings support the theory developed by Knauss [5] and Schapery [6] in their studies of crack growth behavior in linear viscoelastic materials. It is known that classical fracture mechanics principles, especially linear elastic fracture mechanics, are well established for single-phase materials. Experimental data indicate that linear fracture mechanics theories can be applied to the particulate composite materials with varying degree of success. In this study, a series of experiments were conducted on uniaxial specimens with and without pre-crack to investigate the constitutive and crack growth behavior in a highly filled elastomer, hard particles embedded in a rubbery matrix. The specimens without pre-crack were tested at three different displacement rates (5, 50, and 500 mm/min.) in a dilatometer. For the pre-cracked specimens, a 6 mm crack was cut in the middle at one of the long edges of the specimen with a razor blade, and they were tested at a displacement rate of 25 mm/min. During the crack propagation test, a high-speed camera was used to monitor the test. In addition, the load and time were also recorded. The raw data was used to determine stress, strain, dilatation, and Mode I stress intensity factor for the onset of crack growth. In addition to the experimental study, stress-strain response and crack initiation at room temperature in the highly filled elastomer were analyzed using a modified version of a phenomenological damage model developed earlier [7] and accounting for time dependence of the homogenized material. Crack initiation is simulated in specimens with edge cracks subjected to prescribed displacement rates at the boundaries. The relaxation and damage parameters determined from the uniaxial stress-strain curves are used in the finite element calculations to update the local moduli and the damage parameter. Crack initiation is determined by the attainment of critical dilatation at a critical distance from the crack tip and is used as the failure criteria [8]. The predicted and the measured critical value for the stress intensity factor (KIc) for the onset of crack growth are 0.046 MPa m1/2 and 0.045 MPa m1/2, respectively. The good correlation between the

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measured and the predicted KIc validates the critical damage based simulations on the onset of crack growth. In conclusion, experimental and numerical modeling results reveal that a good correlation exists between the predicted and the measured KIC for the onset of crack growth.

References 1.

Beckwith, S. W., and Wang, D. T., 1978, “Crack Propagation in Double-Base Propellants,” AIAA, 78-170.

2.

Liu, C. T., 1990, sCrack Growth Behavior in a Composite Propellant with Strain Gradients – Part II,” Journal of Spacecraft and Rockets, 27, pp. 647-659.

3.

Liu, C. T., 1990, “Crack Propagation in a Composite Solid Propellant,” Proceedings of the Society of Experimental Mechanics, Spring Conference, pp. 614-620.

4.

Liu, C. T., and Smith, C.W., 1996, “Temperature and Rate Effects on Stable Crack Growth in a Particulate Composite Material,” Experimental Mechanics, 36(3), pp. 290-295.

5.

Knauss, W. G., 1970, “Delayed Failure – The Griffith Problem for Linearly Viscoelastic Materials,” International Journal of Fracture Mechanics, 6, pp. 7-20.

6.

Schapery, R. A., 1973, On a Theory of Crack Growth in Viscoelastic Media, Report MM 2765-73-1, Texas A&M University.

7.

Ravichandran, G., and Liu, C. T., 1995, “Modeling Constitutive Behavior of Particulate Composites Undergoing Damage,” Int. J. Solids and Structures, 32, pp. 979-990.

8.

Ravichandran, G., and Liu, C. T., 1998, “Crack-Tip Shielding in Particulate Composites Undergoing Damage,” Engineering Fracture Mechanics, 59, 713-723.

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CRACK TIP BEHAVIOR IN TIAL WHEN APPROACHING GRAIN BOUNDARY Fu-Pen Chiang, Sheng Chang and Kai Wang Mechanical Engineering Department Stony Brook University Stony Brook, NY 11794-2300, USA [email protected] [email protected] Lamellar titanium-aluminum alloys (TiAl) show high stiffness, high density-normalized strength and high fatigue resistance at elevated temperature. This is a promising substitute material for high performance jet engines. TiAl has two phases: the J(TiAl) phase and the D2 (Ti3Al) phase. Grains (or colonies) of TiAl are in lamellar form with alternating Jand D2 lamellae, but not necessarily in equal numbers. The mechanical properties of this material depend on the grain size, lamella orientation, etc. Intensive investigations have been carried out on the measurement of mechanical properties of TiAl (Maruyama et al. [1], Appel et al. [2], and Cao et al. [3]). However, most of them focus on the global mechanical properties of the material with either many grains together or just one large single grain because there is a lack of measurement techniques capable of mapping the local deformation at micro/nano scales. In this paper we introduce the SIEM (Speckle Interferometry with Electron Microscopy) technique (Chiang et al. [4]) to map the full field deformation around a crack tip in TiAl specimens under uniaxial tension. SIEM is a micro/nano experimental mechanics technique that is able to perform full field displacement mapping over a region of only several microns in size. The basic principle of SIEM is as followings. A speckle pattern consisting of micro or nano sized random particles is first deposited onto the specimen surface which is to be loaded inside the chamber of a SEM (Scanning Electron Microscope). Load is applied to the specimen with the speckles following the deformation. The speckle patterns are digitally recorded sequentially under incrementally applied loads and compared using a specially designed algorithm called CASI (Computer Aided Speckle Interferometry) (Chen and Chiang [5], Chiang et al. [6]). The result is a distribution of displacement vectors (or displacement contours) representing the deformation. Appropriate displacement-strain relations are used for the calculation of the strain tensor distribution. Length scale and the technique’s sensitivity are determined by the speckle size. Fig. 1 shows the shape and dimension of the specimen. We cut a notch on the side of the specimen. Then a fatigue machine was used to initiate the crack tip. The specimen was under uniaxial tension inside the SEM. The crack propagated either in a translamellar mode, cutting across several Jand D2 lamellae, or along the D2/Jinterface depending on the lamellar orientation. Fig. 2 shows that at the beginning of the load, the crack is almost perpendicular to the lamellar orientation and it adapts the translamellar mode. Later, after the crack advances into another grain whose orientation is about the same of the crack, the crack switches to mode II propagation as shown in Fig. 3.

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FIGURE 1. Uniaxial tension specimen with an initial crack.

FIGURE 2. Crack in translamellar mode.

FIGURE 3. Crack along D2/Jinterface.

In a separate study we have shown that the stiffness of the interface can be as much as 7 times stronger than that of the grains themselves. There is a noticeable resistance to crack growth across grain boundaries. There are new cracks initiated in the next grain across the boundary before the boundary is broken. The deformation fields around the crack tip are obtained by SIEM.

Acknowledgement The authors acknowledge gratefully the financial support provided through the AFOSR grant #FA95500410303 managed by Dr. Craig Hartley. The authors would like also to thank Dr. Hartley and Dr. James M. Larsen of AFRL/MLLMN for their intellectual support for this project.

References 1.

Maruyama, K., Suzuki, G., Kim, H.Y., Suzuki, M., and Sato, H., Materials Science and Engineering A329-331,190-195, 2002.

2.

Appel, F. and Wagner, R., Materials Science and Engineering R22, 187-268, 1998.

3.

Cao, G. Fu, L., Lin, J., Zhang, Y., and Chen, C., Intermetallics, Vol. 8, 647-653, 2000.

4.

Chiang, F.P., Wang, Q., and Lehman, F., In Nontraditional Methods of Sensing Stress, Strain and Damage in Materials and Structures, ASTM STP 1318, edited by Lucas, G.F. and Stubbs, D.A., American Society for Testing and Materials, 156-169, 1997.

5.

Chen, D.J. and Chiang, F.P., Applied Optics 3(2), 225-236, 1993.

6.

Chen, D.J., Chiang, F.P., Tan, Y.S. and Don, H.S., Applied Optics, 32(11), 1839-1849, 1993.

23. Deformation and Fracture of Engineering Materials

1139

EFFECT OF LOADING RATE ON THE ENERGY RELEASE RATE IN A CONSTRAINED ELASTOMERIC DISK H. K. Ching, C. T. Liu1 and S. C. Yen Materials Technology Center Southern Illinois University, Carbondale, IL 62901, USA 1AFRL/PRSM, 10 E. Saturn Blvd., Edwards AFB, CA 93524-7680 [email protected] Defects such as flaws and cracks may form in elastomeric materials due to the manufacturing, handling or ageing. To ensure the integrity and reliability for such structural components, fracture toughness should be ascertained so that the onset of the crack growth can be determined based on the fracture resistance of the material. The energy release rate is a measure of the fracture toughness, and commonly used as a criterion to determine the maximum operating loads for a given pre-existing defect. We have performed finite element analyses to find out the variation of energy release rate with the crack length for an elastomeric disc, which has a star-shaped hole located at the center, subjected to the pressure and isothermal loads (Fig.1). The deformations of the disc are constrained by a circular steel ring enclosing the disk. Numerical studies [1] have shown that that the value of energy release rate increases with the increase of the crack length, reaches a maximum value at 1 in. of crack length, and then decreases gradually. It was also found that the value of energy release rate strongly depends upon the material compressibility, and decreases sharply with the increase in Poisson’s ratio for the pressure loading case. In this study, we delineate the effect of the loading rate on the energy release rate. Due to the viscoelastic response of the elastomeric material, the stress-strain relation highly depends on the applied loading rate. Here, three different uniaxial stress-strain relations obtained from loading rates of 200ipm, 50ipm and 2ipm, respectively are used in the present analysis (Fig. 2). The disk is simulated either as a linear elastic material under the Hook’s law or hyperelastic material described by the Ogden strain energy potential. The present investigation shows that the energy release rate increases with an increase in the loading rates for the thermal loading case regardless of the material compressibility. For the pressure loading case, the energy release rate increases with the decrease in the loading rate when the material becomes more compressible while it decreases when the material approaches the incompressible limit. In addition, with the presence of the crack surface pressure, the energy release rate needs to be modified by including an additional line integral as shown in Eq. (1). The contribution to the value of the energy release rate from the work done by the crack surface pressure can thus be examined by plotting the crack opening deformation. Crack opening profiles for different loading rates will be drawn.

J

§

wu

·

wu

i 2 ³ * ¨ Wn1  Tij n j wx ds ¸  ³ * p wx dx1 1 1 © ¹ c

(1)

H. K. Ching et al.

1140

FIGURE 1. Specimen geometry

FIGURE 2. The stress-strain curves of the disk mateiral in tension under different loading rates

References 1.

H. K. Ching, C. T. Liu and S. C. Max Yen, “FE calculations of J-integrals on Crack Length in a Constrained Elastomeric Disc with Crack Surface Pressures and Isothermal Loads”, the ASME International Mechanical Engineering Congress, Anaheim, California, November,

2004

23. Deformation and Fracture of Engineering Materials

1141

ANALYSES OF PROGRESSIVE DAMAGE AND FRACTURE OF PARTICULATE COMPOSITE MATERIALS USING S-FEM TECHNIQUE Hiroshi Okada, Satoyuki Tanaka, Yasuyoshi Fukui and Noriyoshi Kumazawa Kagoshima University 1-21-40 Korimoto, Kagoshima 890-0065, Japan [email protected] In this paper, the s-fem (s-version FEM; an element overlay technique [1,2,3,4]) is applied to the damage analyses of particulate composite materials (Fig. 1 (a)). We conduct a series of unit cell analyses in which we assume many (~40) distributed reinforcing particles. We assume two kinds of damage modes in our analyses. One is due to microvoid formation in matrix material that is accounted for by a continuum damage model [5]. The damage constitutive model is extended so that the modes of damage can be split to dilatational and deviatoric parts. Another damage mode is “dewetting” between the reinforcing particles and matrix material. The cohesive zone model [6,7] is adopted to appropriately model the separation between particles and matrix material. Present authors have been developing the s-FEM technique that can be applied to the analyses of particulate composite materials [3]. In the s-FEM modelling for particulate composite material [3], finite element models for structure or the region of unit cell as whole and a particle and its immediate vicinity are built separately. Then, as shown in Fig. 1 (b) for a 2-D schematics, the finite element model for a particle and its immediate surrounding is placed in the analysis region repeatedly. Thus, a number of particles can be distributed without any difficulties even for 3-D cases. The s-FEM program [3] has been extended so that it can cope with elastic-viscoplasticity, elastic damage [5], dilatational/deviatoric elastic damage and dewetting between particles and matrix material using the cohesive zone model [6,7]. In the presentation, we discuss about some of our recent results.

FIGURE 1. The schematics of particulate (a) composite material and (b) s-FEM model. The formulation of s-FEM for elastic problems can be summarized as follows. The finite element model representing the structure or the unit cell as whole is called “global mesh” or “global model”. Ones that are for particles and their immediate vicinities are called “local mesh” or “local model”. The displacements ui are expressed by the sum of those based on the global model LI LJ G and the local models where they overlap. For example, let ui , ui and ui be the displacements that are expressed by the global and the I-th and J-th local models, respectively, and the displacements at a point which is inside the I-th and J-th local models are written to be:

H. Okada et al.

1142

ui

uiG  uiLI  uiLJ

(1)

Then, the displacements that are expressed like equation (1) are used in the statement of virtual work principle.



³: Gui , j Eijk"uk ,"d: ³: Guibi d:  ³w: t Guiti d w:

t

(2)

Thus, we get discretized equation. If we replace the virtual work principle (2) by its rate formulation, we can perform nonlinear analyses. The cohesive zone elements are implemented in the local models only. We do not need to give any special treatments to the cohesive zone elements, even they overlap with the global and the other local models. In Fig. 2, the distributions of stress in a unit cell model when an isotropic damage and dilatational damage cases are employed and are compared to each other. They are the typical results that have been obtained in present investigation. When the dilatational damage mode dominates, the damage progresses much faster than the case of isotropic damage.

FIFURE 2. The distributions of damage parameters (a) Isotropic damage and (b) Dilatational damage dominates.

References 1.

Fish, J., Computers & Structures, vol. 43, 539-547, 1992.

2.

Fish, J., Markolefas, S., Guttal, R., Nayak, P, Applied Numerical Mathematics, vol. 14, 135164, 1994.

3.

Okada, H., Liu, C.T., Ninomiya, T., Fukui, Y. and Kumazawa, N., CMES: Computer Modeling in Engineering & Sciences, vol. 6, 333-347, 2004

4.

Okada, H., Endoh, S. and Kikuchi, M., Engrg. Fracture Mech., vol. 72, 773-789, 2005.

5.

Simo, J.C., Ju, J.W., Int. J. Solids Structures, vol. 23, 821-840, 1987.

6.

Needleman, A., J. Appl. Mech., vol. 54, 525-531.

7.

Chandra, N., Li, H., Shet, C. and Ghonem, H. Int. J. Solids Structures, vol. 39, 2827-2855, 2002.

23. Deformation and Fracture of Engineering Materials

1143

FRACTURE MECHANICS ON PVDF POLYMERIC MATERIAL : SPECIMEN GEOMETRY EFFECTS L. Laiarinandrasana and G. Hochstetter Centre des Matériaux – Ecole Nationale Supérieure des Mines de Paris- UMR CNRS 7633 BP87 – F 91003 Evry Cedex – France ARKEMA - Centre d'Etude de Recherche et de Développement (CERDATO) F-17470 Serquigny - FRANCE [email protected], [email protected] Polyvinylidene fluoride (PVDF) is a semi-crystalline polymer that has been widely studied for structural applications, because it exhibits good mechanical properties and chemical resistance. Mechanical properties investigations of the PVDF under study have been already published elsewhere [1] where the macroscopic tensile and creep behaviour over several strain rate decades, and over a large range of temperatures have been investigated. During viscoplastic deformation, the material whitens after the onset of necking due to nucleation and growth of voids. In reference [1] notched specimens and cracked specimens were used in order to investigate damage development over a wide range of loading conditions. A numerical simulation of these tests is performed using a modified Gurson-Tveergard-Needlman model [2-4], which was adapted to the present material. The yield surface is expressed as:



) V ,V * , f



2 V eq

V

*2

§q V · 2  2 q1. f . cosh ¨¨ 2 kk ¸¸  1  q1 f © 2V * ¹

2

def .V *

0

(1)

V eq is the Von Mises stress, and V kk the trace of the stress tensor. f is the porosity, q1 and q2 are model parameters that were introduced to improve the model predictions for periodic

arrays of cylindrical and spherical voids. q2 was expressed as a function of the maximum principal plastic strain p1 . The constitutive model was validated on Double Edge Notch Tensile (DENT) and Single Edge Notch Bending (SENB) specimens. The numerical simulation well reproduces the observed instability on DENT specimens and the stable crack growth on SENB specimens. In the global approach of non linear fracture mechanics framework, the two-parameters approach indicates that according to the opening stress state in the remaining ligament, the crack growth can be more or less stable. Namely, tensile crack specimen such as DENT favours instabilities whereas bending specimens (like SENB) are proved to present stable cracking. Even the effect of specimen length of Single Edge Notch Tensile (SENT) specimens has been investigated for metallic materials [5-6]. The aforementioned two-parameters approach is not often used on polymers. Nevertheless, it seems that the same effects have been encountered on the present PVDF material. This work deals with comparing the already used local approach of fracture on this PVDF material with the global approach of fracture mechanics with single parameter J-integral, which is generally unable to predict the in fracture plane stress effects. Note that K and G load parameters will be ignored since the PVDF material under study does not exhibit any linear elastic mechanical response. Q-stresses on DENT and SENB specimens are computed with the help of FE modelling and a calculated Hutchinson Rice and Rosengren (HRR) field as reference stress. The material toughness

L. Laiarinandrasana and G. Hochstetter

1144

JIC is then determined by means of experimental data gathered with both specimens. If JIC depends on the geometry, then, we have to find out whether a unique JIC-Q curve exists for the PVDF material. In addition, the effects of specimen geometry on the resistance curve (crack propagation) will be analysed.

References 1.

Challier, M., Besson, J., Laiarinandrasana, L. and Piques, R. to be published in Engng. Fract. Mech., 2005

2.

Gurson, A. L., J Eng Mat Tech. 99:2-15. 1977

3.

Tvergaard, V. J Mech Phys Solids. 30:399-425, 1982;.

4.

Tvergaard, V. and Needleman, A., Acta Metall. 1984; 32:157-169.

5.

Paris, P.C., Tada, H., Zahoor, A. and Ernst, H. Elastic-plastic fracture, ed J.D. Landes, J.A. Begley and G.A. Clarke, ASTM STP 668, 1979, 5-36.

6.

Paris, P.C. and Hutchinson, J. W. Elastic-plastic fracture, ed J.D. Landes, J.A. Begley and G.A. Clarke, ASTM STP 668, 1979, 37-64.

23. Deformation and Fracture of Engineering Materials

1145

FRACTURE TOUGHNESS OF ALLOYED AUSTEMPERED DUCTILE IRON (ADI) Olivera Eric, Dragan Rajnovic1, Zijah Burzic2, Leposava Sidjanin1 and Milan T. Jovanovic Institute of Nuclear Sciences “Vinca”, Belgrade, Serbia and Montenegro 1University of Novi Sad, Faculty of Technical Sciences, Novi Sad, Serbia and Montenegro 2Military Technical Institute, Belgrade, Serbia and Montenegro [email protected] Austempered Ductile Iron (ADI) has been established as an advanced material because of its excellent mechanical properties based on a good combination of wear resistance, toughness and very high strength combined with a relatively high ductility. It has a unique acicular matrix structure that consists of high–carbon austenite and ferrite with graphite nodules dispersed in it >1@. Some previous studies >1-4@ have been carried out on the mechanical properties of alloyed ADI. However, very little information is available regarding the influence of microstructure on the tensile properties and fracture toughness of alloyed ADI. The present investigation was undertaken to examine the influence of microstructure on the tensile properties and the plane strain fracture toughness (KIC) of copper and copper nickel alloyed austempered ductile iron (ADI). Two ductile irons with chemical compositions (in wt.%): (a) 3.6C; 2.5Si; 0.28Mn; 0.04Cr; 0.45Cu; 0.01P; 0.014S; 0.066Mg, and (b) 3.07C; 2.15.Si; 0.26Mn; 0.04Cr; 1.6Cu; 1.5Ni; in both alloys balance was Fe, were produced in a commercial electro-induction foundry furnace. Specimens for mechanical testing were machined from the test section of the Y-block. Machined specimens austenitized in a protective argon atmosphere at 900oC for 2h were rapidly transferred to a salt bath at austempering temperature 350oC, held between 1 and 6h and then air-cooled to room temperature. The reported results represent the average values of three measurements. Fracture surfaces of specimens after tensile and fracture toughness tests were examined by a JOEL JSM6460LV scanning electron microscope (SEM) operated at 25kV. Metallographic investigations were carried out by light microscope. Change in the volume fraction of retained austenite during austempering was determined by the X-ray diffraction technique on diffractometer “Siemens D500” with Ni filtered CuK radiation. The microstructure of as-cast Cu alloyed ductile iron consisted of graphite nodules surrounded by ferrite in a pearlitic matrix. The as-cast microstructure of copper nickel alloyed ductile iron was predominantly (over 95%) pearlitic. The nodules count in the lower section of the keel block of both ductile irons was 100mm2. The microstructure of ADI alloyed with copper and copper nickel austempered at 350oC for 2h revealed the characteristic microstructure of ausferrite. The austempered microstructure was composed of ferrite (dark) and retained austenite (white) with graphite nodules dispersed in the matrix. Figure 1a,b shows typical fractographs of copper ADI and copper nickel ADI. The fracture surfaces of these specimens were mostly ductile showing extensive micro ductility.

O. Eric et al.

1146

FIGURE 1 Fracture morphology after austempering at 350oC for 2h (SEM) (a) copper ADI and (b) copper nickel ADI Table 1 reports the fracture toughness, hardness and volume fraction of ferrite and retained austenite of copper and copper nickel alloyed ADI. Values of fracture toughness satisfied all the necessary conditions for ASTM E 399 and therefore are valid KIC values. The test results show that the fracture toughness of copper and copper nickel alloyed ADI is lower than that of the unalloyed ADI >1@ at the same hardness level. This indicates that the addition of alloying elements like copper and nickel does not improve in ADI the fracture toughness. Bartosiewicz et al. >2@ studied the fracture toughness of two alloyed ductile irons austempered at four different temperatures and found that fracture toughness was only a function of the volume fraction of ferrite and retained austenite. Fracture toughness reached the maximum at a retained austenite content 30vol.% in the matrix. Results of this paper support the literature data, i.e. copper ADI with high amount of ferrite and retained austenite exhibits higher fracture toughness. TABLE 1. Mechanical properties and volume fraction of ferrite and retained austenite after austempering at 350oC

References 1.

O.Eric, L.Sidjanin, Z. Miskovic, Zec, M.T. Jovanovic,Mat. Let, Vol.58, 2707-2711, 2004

2.

Bartosiewicz, L., Krause, A. R., Kovacs, B. V., and Putatunda, S. K., AFS Transactions, American Foundry Society, vol.92, 135-142, 1992

3.

Bartosiewicz, L., Krause, A. R., Singh, I, and Putatunda, S. K., Materials Characterization, vol.30, 221-234, 1993

4.

Greech, M., Bowen, P., and Young, J.M., In Proceedings of The Second World Conference on ADI, edited by Ann Arbor, MI, B. Kovacs, 1992, 135-148

23. Deformation and Fracture of Engineering Materials

1147

PREDICTION OF CRACK GROWTH UNDER RANDOM LOAD IN RAILWAY WHEEL Rami Hamam, Sylvie Pommier and Frederic Bumbieler1 Lab. of Mechanics and Technology (LMT), 61 av. du Président Wilson, 94235 Cachan, France 1Agence d’Essai ferroviaire (AEF), 21 av. du Président Allende, 94407 Vitry sur Seine, France [email protected] Three aspects are indispensable to master railway systems: design, manufacture and maintenance. Maintenance should define surveillance intervals which are defined at present by experience. The aim of the French Railway Agency (SNCF) is to use fracture mechanic in order to satisfy to European interoperability imperative of railway stock. One study here crack growth in wheel disk under biaxial random load. An example of radial disk stress is shown in Figure 1; one can see the random aspect of the load even during straight line. Classic crack growth models are not able to predict propagation under this complex load.

FIGURE 1. Example of radial wheel stress the speed of the train is 100 km/h An incremental crack growth model is employed for this problem [2]; this model is developed to predict crack growth under any random load. We implement this model and we extend it to biaxiality load [3]. Incremental model is divided in two laws: •

A cracking law, which is an instantaneous relationship between crack growth and crack tip blunting: da D d U . This law contains only one adjustable material parameter dt dt adjusted using one fatigue crack growth experiment.

•

D

to be

The second one is the blunting law, it gives the evolution of the crack tip blunting according the Stress Intensity Factor (SIF), the material behavior and the geometry of the cracked structure :

dU dt

f  applied SIF, m aterial, geom etry .

This second law (blunting law) was established using finite element analysis. Figure 2 shows for instance the evolution of the crack tip blunting for a Griffith crack. The blunting law describes the evolution of these curves by system of time derivative equations; it is an elastic-plastic constitutive behavior for the cracked structure which contains a set of material parameters that are determined using the finite element method trough an automated identification protocol. One pushpull experiment is necessary to identify the constitutive behavior of the material.

R. Hamam et al.

1148

FIGURE 2. Evolution of the crack tip blunting versus applied load The model was integrated and applied on a few cases; it reproduces the main features of fatigue crack growth, namely the fact that the crack growth rate obeys the Paris law in constant amplitude fatigue (figure 3), the overload retardation phenomena and the sensitivity of the retardation behavior to the overload ratio.

FIGURE 3. Crack growth rate for 3 different R ratio

References 1.

Laird C, “The influence of metallurgical structure on the mechanisms of fatigue crack propagation”, In Fatigue crack propagation, STP 415, (1967), pp. 131-68.

2.

Pommier S and Risbet M, “Partial-derivative equations for fatigue crack growth in metal”, Int Jal of Fracture. Vol 131. Num 1. Pages 79-106. 2005.

3.

Hamam R., Pommier S., Bumbieler F., “Mode I fatigue crack growth under biaxial loading” accepted in International Journal of Fatigue.

24. Materials Damage Prognosis and Life Cycle Engineering

1149

PREDICTING THE EVOLUTION OF STRESS CORROSION CRACKS FROM PITS A. Turnbull, L. N. McCartney and S. Zhou National Physical Laboratory Queens Road, Teddington, Middlesex, TW11 0LW, UK [email protected] Predicting the evolution of stress corrosion cracks from pits and their subsequent growth has been a major challenge because of the need to address the statistics of pit growth, the transition to a stress corrosion crack, and the subsequent growth in the short and long crack domain. A purely statistical approach has constraints in its predictive capability but several deterministic models for pit and crack growth have been developed [1-4]. These all adopt the phenomenological requirements proposed by Kondo [5], that the pit depth must be greater than a threshold depth and that the crack growth rate should exceed the pit growth rate. Turnbull et al [5] developed a deterministic model for the evolution of pits and the pit-to-crack transition and applied the approach sucessfully to steam turbine disc cracking in simulated condensates with excellent prediction of the time evolution of the pit distribution and of the percentage of pits that transform to cracks at different pit sizes. The extension of this model to include the growth of cracks following the pit-to-crack transition is now described. It can be shown that the evolution of the pit size distribution function P(x,t) from an initial stable population is governed by the partial differential equation wP ( x, t ) wt



w [ g ( x) P ( x, t )] wx ,

(1)

where g(x) is the growth rate of the pit described by dx dt

g ( x)

ED 1 / E x (11 / E ) (2)

The crack growth rate is expressed by

dx dt

C Vp xq (3)

for short cracks and is considered independent of crack size for deep cracks. The transition to the experimentally measured growth rate for deep cracks is treated approximately by adopting a critical crack size, the value of which is determined by fitting. An example of the predictions from this model is given by Fig. 1.

A. Turnbull et al.

1150

FIGURE 1. Comparison of model prediction and experimental measurement of crack-size distribution for turbine disc steel in 1.5 ppm Cl- at 90 qC after 9187 h exposure. The total depth refers to the distance from the surface and includes the crack depth and the extension of the crack beyond the pit base. The ability to predict the crack size distribution so well is quite remarkable and very encouraging. Nevertheless, in view of the sparseness of experimental data, extension to other exposure periods is important to enhance confidence. There are limitations. The adoption of a sharp transition in growth rates at some critical crack size is artificial; a more gradual transition is to be expected. Furthermore, there is no independent measurement of crack growth rates in the short crack regime. The latter presents a challenge in measurement.

References 1.

Wei, R.P., In Proceedings of conference on Environmentally Assisted Cracking: Predictive methods for risk assessment and evaluation of material, equipment and structures, edited by. R.D. Kane, ASTM STP1401, ASTM, Pa, 2000, 3-19.

2.

Engelhardt, G., Macdonald, D.D., Zhang, Y. and Dooley, B., Power Plant Chemistry, vol 6, 647-661, 2004

3.

Engelhardt, G. and Macdonald, D.D., Corrosion Science, vol. 46, 2755-2780, 2004

4.

Turnbull, A., McCartney L.N. and Zhou, S. ‘A deterministic model of pitting corrosion and the pit-to-crack transition, submitted to Corrosion Science’, 2004.

5.

Kondo, Y. Prediction of fatigue crack initiation life based on pit growth, Corrosion, vol. 45, 711, 1989.

24. Materials Damage Prognosis and Life Cycle Engineering

1151

CORROSION PROBLEMS IN NUCLEAR INDUSTRY : LESSONS LEARNED AND PERSPECTIVES J. M. Boursier, F. Foct, F. Vaillant and E. Walle Electricité de France - R&D Materials and Mechanics of Components Department Site des Renardières 77818 Moret sur Loing Cedex. [email protected] In France, most of the electricity produced is of nuclear origin. To produce this energy, Electricité de France has been operating for many years 56 pressurized water reactors with a permanent concern for safety efficiency and availability. These reactors consist of a main primary system which includes the reactor vessel, the steam generators, the pressurizer, and the reactor coolant pumps for flowing the coolant : the water. The heat produced by the fission reactions is collected through the steam generator by the secondary system where the steam produced is transformed into mechanical energy by a turbine which drives a generator producing the electrical energy. The components of nuclear power plants operate in harsh conditions. High operating temperature and neutron radiation lead to a decrease of mechanical characteristics. The chemical media encountered inside the installations can lead to corrosion phenomena. These phenomena occur through time, this is also called ageing. Operating reactors safely is of major concern for Electricité de France. Therefore it is essential to have a good knowledge of the scale, the seriousness and the development of identified damages. Some phenomena are taken into account in the design: for example the embrittlement of the reactor vessel steel due to neutron radiation is controlled through regular check to ensure that the evolution of damage remains within the initially anticipated limits. On the other hand, others are unexpected and appears after several thousands hours of operation: this is the case for many corrosion processes. In some cases, it is necessary to replace the damaged component and to improve materials with a better resistance than those used previously. This is possible only with a good understanding of the mechanisms which cause the damage. This understanding is gained thanks to laboratory studies associated with the analysis of nuclear reactor feedback collected every year during controls on site or assessment of faulty component. For example, in the case of vessel head penetration stress corrosion cracking, the laboratory studies of alloy 600 cracking revealed that this phenomenon has 3 successive phases : an initiation period which lasts a few hundred hours and depends on the stress level, a slow propagation phase which corresponds to the longest part of the test, and finally a 10 time faster propagation phase before the final failure. This last phase is not always observed. When it is observed, only a few cracks, which have a critical size, reach this stage of propagation. The “slow to fast” transition is still under investigation. It may be due to a stress intensity factor threshold KISCC . From an industrial point of view, in the case of the adapters, as well as for other thick products made of alloy 600, the first two phases : initiation and slow propagation are considered as one “visible” initiation phase. The propagation is of interest when the cracks are deeper than a critical depth, which corresponds to the shift to the fast propagation phase (typically a few hundred microns) Stress corrosion susceptibility was studied in laboratory with various types of corrosion test in autoclave. The main tests are constant load tests on tensile test specimens and constant deformation tests carried out on Ubend type, or reverse U-bend type specimens. A classification relies on the definition of a stress corrosion sensitivity index (inversely proportional to the cracking time) containing the following elementary indexes : •

A stress index is = k1s4 : in this equation deduced from laboratory tests, an evaluation of the stress level of the component is introduced. The detrimental effect of surface strain hardening is taken into account by using an effective stress which is a function of the depth of the strain hardened layer, of the yield stress at the surface and inside and of the stress applied using the following formula.

J. M. Boursier et al.

1152

V eff

ª S V « 2 ¬« K IS C C

1 ,1 6 ap pliqu ée

³

ac

0

LI (a)

 1, 9

º da » ¼»



1 3 ,16

with LI the integral width of the X-ray diffraction peak measuring the surface strain hardening, ac is the crack critical depth depending on KISCC. •

A temperature index iT = k2.exp(-180 000 /RT), the activation energy is also determined from laboratory tests.

•

A material index iM defined during laboratory corrosion tests, either starting from the time to cracking of 10% of the test specimens taken from the same material as the component, or, in a more conservative way, starting from the initiation time of the first crack observed.

The cracking time (tf) of the component in operation conditions is determined using the equation:

t f (h)

10000 iV i T i M

The propagation kinetics of stress corrosion cracks in thick alloy 600 has been studied in laboratory in order to determine the effect of the main parameters (temperature, stress intensity factor, material parameters). Knowing their influence can help to improve the maintenance policy of the various components made of alloy 600 by optimizing their inspection time interval. These studies have been the subject of coordinate research programmes between European laboratories. Propagation rates of stress corrosion cracks were determined in primary system conditions using fracture mechanics test specimen, precracked by fatigue and in some cases equipped with a DCP monitoring of the crack. It depends on the temperature with an activation energy of 130 ± 20 kJ/mol. The fast propagation rate can be expressed as a function of the stress intensity factor K using a law da/dt = b (KTinitial – KISCC)g For thick products like adapters, g is equal to 0,3 and the threshold KISCC is close to 9 MPa÷m. The rates obtained are consistent with the CGRs measured in service using NDE techniques (4 mm/cycle). Another subject, which illustrates the contribution of R&D to the understanding and the fight against corrosion, is in nuclear waste storage. Today in France, no long-lived high-level radioactive waste storage site is defined. There is a big difference between the maintenance of industrial facilities over a few decades (30 to 60 years) and storage where the time scale is a few thousand years. The container properties and the surrounding medium are essential parameters which lead to an original approach to the fight against corrosion. It is important to emphasize that between laboratory tests (which are most of the time limited in scale and time) and the reality of millennial storage, corrosion test can be and have been carried out over intermediate time periods and scales. They have been carried out in underground laboratories under conditions representative of those expected during storage. The representative is not only at the level of the geological environment, but also of the temperature and the irradiation by including in the system heating facilities and irradiation sources. This is done in Mol (SCK-CEN, Belgium) where in situ exposure tests are being carried out for several years. The time duration of the test can be as long as 5 years. These tests enable the validation of laboratory tests as well as the models developed, despite the fact that these durations are still short in comparison with the thousand years required. Finally futures challenges for the Nuclear industry will be highlighted. Particularly, Very High Temperature Reactors (VHTR) have been selected in the framework of the Generation IV roadmap for the capability to reach high yields for energy production and for the possibility to produce hydrogen by mean of a water decomposition process. The high levels of temperatures reached in the reactor - i.e. more than 950 °C - arises the question of structural materials of this kind of concepts. Nickel based alloys are the most promising materials for the conception of the reactor. Apart from very important issues like thermal ageing or mechanical resistance of these kind of materials, their compatibility with the impure helium environment of the primary circuit – i.e. helium with traces of CH4, CO, H2O - remains to be demonstrated. That’s the reason why we defined an R&D program, with the aim to define : • Chemical specifications of the helium atmosphere to minimise the interaction with materials. • The maximum temperature of the materials • The nature and the kinetics of the degradation process.

24. Materials Damage Prognosis and Life Cycle Engineering

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ALUMINIUM ALLOYS FATIGUE EVALUATION METHOD S. Rymkiewicz Gdansk University of Technology Ul. G. Narutowicza 11/12, 80-952 Gdansk, Poland [email protected] Fatigue and corrosion-fatigue investigations are usually very expensive and time-consuming. Energetic criterion implemented in calculations makes it much cheaper and quicker to obtain the results. They are based on the statement of possible implications between fatigue and nonreversible dissipated energy during test of static loading. Assumption of accumulated fatigue deformation energy equal to static tensile test cracking energy, even approximately is in many cases sufficient [1]. Dependence between the total dissipated energy and the number of cycles to failure can be expressed by the equation: Nf

¦ Di

const

(1)

1

where Di demonstrates dissipation at the i cycle, and Nf is the number of cycles to failure. Identical to equation (1) is the expression: Nf

W

¦ Di

(2)

1

where W is the critical failure energy. C.Feltner and J.Morrow [4] accepted, that energy W is equal to the critical strain energy U in the static tension:

W

U

2kN f

m 1

Va

m 1 m

(3)

where k and m are the material constants calculated from the static tensile test, and Va is the calculated amplitude of cyclic loading. Calculated fatigue strength in comparison with experimental data is usually compatible with the 103 – 106 number of cycles range [1]. W.T.Troszczenko and L.A.Hamaza [1] assumed, that total dissipated energy is equal to:

W

U(

V rzz 4 ) Va

(4)

and after transformation they achieved: log V a

log V rzz 

1 log 2 N f 4m

(5)

Coefficient m for aluminium alloys shows equation [1]: m 15  4  0.675 log 2 N f

The final mathematical expression is:

(6)

S. Rymkiewicz

1154

log V a

log V rzz 

1 log 2 N f 15  0,675 log 2 N f

(7)

where: Vrzz - intensity of stress at the time of breaking the sample, Nf - number of cycles to failure and Va - amplitude of cyclic loading. The W.T.Troszczenko and L.A.Hamaza calculation procedure has been implemented in the experimentally obtained data calculations. The AlZn5Mg alloy has been selected for the research [2]. Standardized samples have been prepared for the tension tests. The parameters like fracture energy, time to failure, reduction in area in fracture zone and maximal strength to rupture have been determined in slow strain rate tests. The results are shown in the Table 1. TABLE 1. Slow strain rate test results (mean values).

Fatigue limit and corrosion fatigue limit have been calculated according to the formula (7). The obtained results can be considered as mere estimates due to the method of calculation applied for fatigue and corrosion fatigue limit based on energy criterion expressed in the formula by W.T. Troszczenko and L.A. Hamaza.

References 1.

Kocanda, S., Szala, J., Podstawy obliczen zmeczeniowych, PWN, Warszawa, Poland, 1997.

2.

Zielinski, A., Evaluation of operating properties of aluminium alloys for marine applications, Polish Academy of Sciences, Branch in Gdansk Marine Technology Transactions, Vol. 8, 233, 1997.

25. Mixed-Mode Fracture

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SINGULAR STRESS FIELDS SITUATIONS IN MODE-II AND MIXED-MODE LOADED CRACKS Daniel Fernández-Zúñiga, Jörg F. Kalthoff1, Antonio Blázquez2 and Alfonso Fernández-Canteli EPSIG, University Oviedo, Campus de Viesques, 33203 Gijón, Spain. [email protected] 1Dept. of Experimental Mechanics, Ruhr-University Bochum. Universitätsstr. 150, 44780 Bochum, Germany. [email protected] 2Dept. of Civil Engineering, Materials and Construction, University of Málaga, Plaza El Ejido s/n, 29013 Málaga, Spain. [email protected] The stress fields at initiation of a kinked (daughter) crack starting from a (mother) crack subjected to mode-II loading conditions and the influence of these stress fields on the instability condition is investigated. In the literature, often the stress distribution along the prospective propagation direction of the daughter crack (before the daughter crack is actually formed), is considered and postulated to be the actual driving force for the crack formation [1,2]. Special emphasis is given in this paper to the changes the stress fields experience in the transition phase from before to after the kinked daughter crack is initiated; in addition, the situation is studied for growing lengths of the daughter crack, from very small crack lengths approaching zero till medium sized crack lengths. It is found that, the conventional consideration of the stress distribution along the prospective path of the daughter crack represents a pseudo-mode-I stress distribution. This pseudo-mode-I situation shows a typical circumferential stress singularity but not a radial stress singularity. Numerical calculations are performed to investigate this discrepancy. The calculations show that as soon as the daughter crack is formed, a singular crack tip stress field according to the regular mode-I loading situation results, showing a radial stress singularity in addition to the circumferential stress singularity (see Fig. 1 and Table 1). This is the case even for vanishingly short lengths of the daughter crack. These different stress characteristics and the consequences are discussed with the aim of finding an appropriate model for describing realistically the instability process of mode-II loaded cracks for the stage from before to after the kinked crack is formed. The stress field that builds up at the corner notch after the kinked daughter crack initiated is also analyzed for comparison. The BEM, due to its inherent high spatial resolution [3,4], is used as an adequate technique for this kind of numerical investigation. The validity of the numerical data is confirmed by experimental results using shadow optical caustic and photoelastic techniques [5].

FIGURE 1. Stress intensity factors a) for the daughter crack, b) for the crack noctch and c) energy release rate as a function of the length of the daughter crack, aD

D. Fernandez-Zuniga et al.

1156

Da TABLE 1. Stress intensity factors, K IDa - and K Ir of the daughter crack, after its formation, normalized to the corresponding data of the mother crack.

* analytical results from Amestoy and Leblond [6].

References 1.

Erdogan, F., Sih, G.C., J. of Basic Engineering.Transactions of the American Society of Mechanical Engineering, ASME, 519-527, 1963.

2.

Richard, H.A., Materialprüfung, Vol. 45, 513-517, 2003.

3.

Blázquez, A., Kalthoff, J.F., Palomino, I., Fernández-Canteli, A., In Proceedings of the ICCES 04, Edited by S.N. Atluri and A.J.B. Tadeu, Madeira, 1783-1790, 2004.

4.

Blázquez, A., Manti, V., París, F., Cañas, J., Int. J. of Solids and Structures, Vol. 35, 24, 3259-3278, 1998.

5.

Podleschny, R., Kalthoff, J.F., In Proceedings of the Tenth European Conference on Fracture, Structural Integrity: Experiments, Models and Applications, 211-221, 1994.

6.

Amestoy,M., Leblond, J.B., Int. J. of Solids Structures, Vol. 29, No. 4, 465-501, 1992.

25. Mixed-Mode Fracture

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EVALUATION OF M-INTEGRAL FOR RUBBERY MATERIAL PROBLEMS CONTAINING MULTIPLE CRACKS J.-H. Chang and D.-J. Peng Department of Civil Engineering, National Central University, Chungli, Taiwan [email protected] An energy parameter Mc based on the concept of the M-integral ([1]) is proposed for describing the fracture behavior corresponding to a 2-D multi-cracked rubbery mechanical system under the action of large deformation. The parameter is defined by originating the coordinate system at the geometric center of the all the cracks, and then conducting the integration along a contour enclosing all the cracks. With such a definition, Mc appears to be a problem-invariant parameter. For problems containing rubbery materials, the aforementioned contour integral is applied with state variables reinterpreted with respect to this reference configuration when the body is subjected to large deformation. By definition, the integration is performed by taking the limiting case in which the portions of contours are shrunk onto the crack tips and lying along the crack surfaces. Note that, while the value of M varies with respect to different selections of origin O, the result of Mc appears to be invariant for a given problem. Attention is addressed to discussion of the physical meaning of Mc. It is shown that Mc can alternatively be related to (twice) the surface energy corresponding to formation of the cracks ([2]). In the special situation where the crack in an infinite body is subjected to a far-field uniform loading system such that the nominal stress field is homogeneous, it is observed that the M-integral then becomes equivalent to Mc. In such a case, the value of M appears to be dependent upon the stress state and the crack length, but remains unchanged for different selections of the origin O of the coordinate system. Due to path-independence (i.e., the integration contour can be arbitrarily chosen, as long as they contain the same set of cracks and no other singularity), the complicated singular stress field in the near-tip areas is not involved in the calculation of the Mc-integral. Based on this characteristic, it is therefore suggested that Mc be practically used as a fracture parameter for describing the degradation of material and/or structural integrity caused by irreversible evolution of cracks and/or other defects in rubbery media. The hyperelastic material behavior in this proposed research is modeled with an Ogden-type isotropic incompressible strain energy density function. In the numerical calculations, quadratic finite elements are to be used for interpolation of the displacement field. Also, non-conforming linear elements with reduced integration are to be used for the pressure interpolation in order to satisfy the discretized LBB condition. The applicability of Mc is illustrated in the following example, where a plane strain test specimen modeled in terms of Ogden strain energy density function ([3]) and containing N parallel cracks is considered. The deformed finite element mesh is shown in Figure 1, where the undeformed configuration is depicted in dashed lines. By arbitrarily choosing a remote contour (e.g. Figure 2), the results of the M-integral with respect to various coordinate origins are shown in Tables I .

J.-H. Chang and D.-J. Peng

1158

Figure 1 The deformed mesh of the specimen.

Figure 2

The integration contour.

Table I The results of M wrt different D's(Pa-m2).

References 1.

Budiansky, B. and Rice, J. R.. ASME, J. Appl. Mech., vol. 40, 201-203, 1973.

2.

Chang, J.H. and Chien, A.J. Int. J. Fract. vol. 114, 3, 267-289, 2002.

3.

Chang, J.H. and Chen, C.B. Fin. Elem. Anal. Des., vol. 28, 151-163, 1997.

25. Mixed-Mode Fracture

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USE OF A CRACK BOX TECHNIQUE FOR CRACK BIFURCATION IN DUCTILE MATERIAL D. Lebaillif, X. B. Zhang1 and N. Recho1 GIAT, Bourges, France 1Blaise Pascal University of Clermont II, LaMI, France [email protected] In this paper, an automatic Crack Box Technique (CBT) [1] is used to perform fine fracture mechanic calculations with iterative remeshings in elastic-plastic materials found in literature. Two types of experiments are analysed i.e. experiments carried out by Tohgo and Ishii [2] and those done by Li, Zhang and Recho [3]. In reference [2], experiments are based on single-edge-cracked specimens subjected to bending moment and shearing force, on aluminium alloy 6061-T651 (hardening exponent n|7). 2 threepoint-bending and 3 four-point-bending specimens have been tested, from pure mode I (beam A) to pure mode II (beam E) (see table 1). Experimental results give two critical fracture toughnesses : JIC=14N/mm and JIIC=46N/mm. Furthermore they show that cracks in beam A to C seem to initiate for mode I predominant loading (T: tensile type fracture) whereas cracks in beam D and E initiate for mode II predominant loading (S: Shear type fracture). TABLE 1 : mixed mode in elastic calculation

Plasticity calculations using CBT are based on small strain assumption and were carried out using ABAQUS [4]. The refined crack tip mesh is shown in fig. 1.

FIGURE 1 : crack box mesh inserted in automatic Delaunay triangulation The two associated J-integrals J*I and J*II are then computed accurately to determine the plastic mixity Mp parameter. It’s transition value between T and S type fracture is obtained from the experimental results which give the critical mixity parameter MPc = 0.75. Using ABAQUS [4], the calculated Mp is compared to MPc in order to obtain the bifurcation angle T for each beam. The tensile or shear type fracture prediction for all 5 beams are presented in table 2. Mp are given for two first steps of propagation to check that the crack keeps following either maximum circumferential stress criterion or slip band criterion. These predictions appear to be in good agreement with experimental observations.

D. Lebaillif et al.

1160

TABLE 1 : MP results and tensile/shear prediction

Finally, in reference [3], the static tests were conducted on 4mm thickness and 90 mm width CTS (Compact Tension Shear) specimens. A fatigue pre-crack was introduced up to a/w|0.6. The specimens were tested under 0 to 90° loading with respect to the crack axis. The specimen is made of the fine grained structural steel StE550 with a critical mixity parameter Mpc about 0.77. The numerical results of T-type crack growth are close to the experimental data. On the other hand, the S-type crack growth angles calculated numerically follow a different trend, with respect to the experimental values, as opposed to Togho’s specimen.

References 1.

Lebaillif D., Recho N. Crack Box Technique Associated to Brittle and Ductile Crack Propagation and Bifurcation Criteria. ICF11-the 11th International Conference of Fracture. March 20-25, 2005; Turin, Italy

2.

Tohgo K. and Ishii H. Elastic-plastic fracture toughness test under mixed mode I-II loading. Eng. Fracture Mech. 41, 529-540, 1992

3.

Li J., Zhang X.B. and Recho N. J-Mp based criteria for bifurcation assessment of a crack in elastic-plastic materials under mixed mode I-II loading. Engineering Fracture Mechanics. 2004; 71: 329-343

4.

ABAQUS Software Version 6.4.1. www.hks.com.

25. Mixed-Mode Fracture

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MIXED MODE FRACTURE OF LINEAR ELASTIC MATERIALS WITH CUBIC SYMMETRY D. E. Lempidaki, N. P. O’Dowd and E. P. Busso Department of Mechanical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK {d.lempidaki; n.odowd; e.busso}@imperial.ac.uk In order to analyse flawed structures, it is necessary to understand the behaviour of cracks under mixed-mode loading. A crack experiences mixed mode conditions (combined Mode I and Mode II) when it is subjected to remote combined tension and shear or when the crack is tilted with respect to one of the material axes or with respect to the loading axis. Under mixed mode loading, it has generally been observed that a crack in a homogeneous material will branch out of its initial plane. A number of criteria have been proposed to explain this behaviour, the most common of these being the maximum hoop stress criterion. Suresh et al. [1] provided the mixed mode fracture locus for isotropic materials. However, in order to obtain the corresponding result for anisotropic materials, the anisotropic crack tip fields are needed. The general anisotropic problem has been studied by Sih and Liebowitz [2]. More recently analytical solutions for orthotropic materials have become available, Liu et al. [3]. These solutions were phrased in terms of two dimensionless factors, originally introduced by Suo [4]. For the special case of materials with cubic symmetry (three perpendicular axes of symmetry) the crack tip fields depend only on one parameter, namely ,

U

2 s12  s66 2 s11s22

,

(1)

where sij are the usual terms in the linear elastic material stiffness matrix. A common definition of mode mixity is, M

2

S

§K tan 1¨¨ II © KI

· ¸ ¸ ¹

(2)

with M = 0 corresponding to pure Mode I loading and M = 1, pure Mode II loading. To obtain the mixed mode fracture toughness behaviour using the hoop stress criterion, the angle,, ,at which the maximum hoop stress is attained must be determined, i.e., wV TT wT

0 Ÿ KI

df (T , U ) df I (T , U )  K II II dT dT

0

(3)

where fI and fII are the angular crack tip distributions which depend on U. The mixed mode locus can then be phrased in terms of Uand the Mode I fracture toughness, KIC, as K KI f I (T , U )  II f II (T , U ) 1 K IC K IC

(4)

The dependence of the mixed mode crack tip fields for a cubic material on the parameter has been studied in Lempidaki et al. [5]. The analytical crack tip field solutions from [3] have been compared with finite element solutions for a range of -values and excellent agreement was

D. E. Lempidaki et al.

1162

obtained. Based on these solutions and using the maximum hoop stress criterion, the predicted crack initiation angle, as a function of mode mixity, and the corresponding mixed mode fracture toughness locus have been obtained. The results are shown in Fig. 1, which illustrates the dependence of the crack angle and mixed mode fracture locus on . It can be seen in Fig. 1(a) that for M = 0 (Mode I) T 0$ regardless of the value of , whereas for M =1 (Mode II) the value of increases with increasing . From Fig. 1(b) it can be seen that as the value of decreases, starting from the isotropic case ( = 1), the predicted fracture toughness locus expands from the value of KII/ KIC =0.87 to a value of KII/KIC approximately equal to 1.02 for = –0.5.

FIGURE 1. (a) Predicted crack initiation angle as a function of crack tip mixity parameter, M, and (b) predicted mixed mode fracture toughness locus using the maximum hoop stress theory.

References 1.

Suresh S., Shih, C.F., Morrone, A. and O’Dowd, N.P., J. Am. Ceram. Soc., vol. 73, 12571267, 1990

2.

Sih G.C. and Liebowitz, H., In Fracture: an Advanced Treatise, edited by H. Liebowitz, Vol. 2, Academic Press, New York, 1968, 67-190.

3.

Liu, C., Rosakis, A.J., Ellis, R.W. and Stout, M.G., Int. J. Fracture, vol. 90, 355-382, 1998

4.

Suo Z., J. Appl. Mech., vol. 57, 627-634, 1990

5.

Lempidaki, D.E., O’Dowd, N.P. and Busso, E.P. in Proceedings of the Fifteenth European Conference of Fracture, edited by F. Nilsson, ESIS, Stockholm, 2004

25. Mixed-Mode Fracture

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THREE-DIMENSIONAL EXPERIMENTAL AND NUMERICAL SIFS AND CRACK GROWTH Dan Mihai Constantinescu, Bogdan Bocaneala and Liviu Marsavina1 Department of Strength of Materials, University “Politehnica” of Bucharest, Splaiul Independentei nr. 313, Bucharest, Romania 1Department of Strength of Materials, University “Politehnica” of Timisoara, B-dul Mihai Viteazul nr.1, Timisoara, Romania [email protected], [email protected], [email protected] The desire to establish a three-dimensional framework for use in analyzing problems of stable mixed-mode crack propagation has received lately a considerable attention. The study of predicting crack paths under the most general possible hypotheses (three dimensions, arbitrary geometry of the body and of the crack, arbitrary loading) is an ambitious objective. Recently, Leblond [1] and Leblond et al. [2] established formulae which specify the general functional form of the successive terms of the expansions of the SIFs along the front of the extended crack and, as they underline, the formulation of the propagation criterion is an open problem only in the presence of mode III. Therefore, in a mode I+II situation, the widely accepted “principle of local symmetry” of Goldstein and Salganik [3] receives a general recognition. In numerical experiments the FRANC3D code uses new concepts with a model that allows for the implementation of 3D crack growth mechanics [4] with the support of both finite and boundary elements. Keeping in mind such beneficial developments, one should emphasize that for a specific geometry and loading we may obtain various experimental crack paths which are dependent on the local position of the initial crack, as any deviation from “symmetry” influences the future crack trajectory.

FIGURE 1. Tested model geometry. Results obtained by Smith et al. [5,6] from experimental tests using frozen stress photoelasticity gave very interesting insights on the complicated processes of crack growth trajectories. The geometry of the model studied here is shown in Fig. 1 and represents a motor grain configuration. A model contained two starter cracks, a symmetric and an off-axis crack separated by an uncracked fin to avoid any interference. The off-axis crack (located at the coalescence of the two radii of 1,3 mm and 11 mm ) can be inclined (as shown in Fig. 1) or straight-in – parallel with the fin axis. After inserting the starter cracks by striking a shaft with a blade at the end held normal to the inner fin surface, the models were capped with RTV rubber caps which were glued with PMC-1 adhesive and were subjected to the stress freezing cycle under internal pressure. Thus optical data (isochromatic fringes) can be converted into Mode I and Mode

D. M. Constantinescu et al.

1164

II SIFs, if the last one exists. All symmetric cracks remained in the plane of the axis of symmetry and grew as semi-elliptic cracks. Studies of 11 tests on the motor grain geometry [5,6] covered cracks in different locations with projected a/c values (crack depth/half length of crack in fin tip surface) of 0,5 to 0,9 and a/t values from 0,2 to 0,6 (t = 37,08 mm is the cylinder wall thickness at fin tip). It appears that both SIF values and crack geometry during growth are quite variable due to shear modes for the off-axis inclined cracks. On the other hand, the off-axis straight-in cracks situated parallel to the fin axis are quite predictable in their growth, as they tended to grow much more readily than the off-axis inlined cracks. Numerical 3D analyses were done by using the FRANC3D code [4], modelling half of the geometry (Fig. 2) and applying the internal pressure at which stresses were frozen in the experiment. FRANC2D/L results obtained under a plane strain assumption, and 2D and 3D track trajectories are compared and discussed. Only as an example, results for a symmetric crack which propagated in depth up to a/t = 0,28 are shown in Fig. 3 by comparing experimental and numerical normalized SIFs in the middle slice and at 20º from the surface of the fin.

FIGURE 2. Numerical 3D model

FIGURE 3. Normalized SIFs for a/t = 0,28

Off-axis cracks are retarded in growth by shear modes (II or II and III) and eventually gain their local and global symmetry.

References 1.

Leblond J.B., Int. J. Solids and Structures, vol. 36, 79-103, 1999.

2.

Leblond J.B., Lazarus V. and S. Mouchrif S., Int. J. Solids and Structures, vol. 36, 105-142, 1999.

3.

Goldstein R.V. and Salganik R.L., Int. J. Fracture, vol. 10, 507-523, 1974.

4.

Carter B.J., P.A. Wawrzynek P.A. and Ingraffea A.R., Int. J. Numer. Meth. Eng., vol. 47, 229253, 2000.

5.

Smith C.W., Constantinescu D.M. and Liu C.T., In Proceedings of the 2002 SEM Annual Conference& Exposition on Experimental and Applied Mechanics, Session 36, Experiments in Fatigue & Fracture, SEM, June 10-13, Milwaukee, Wisconsin, 2002, Paper 3.

6.

Smith C.W., Constantinescu D.M. and Liu C.T., In Proceedings of the 2002 International Conference on Computational Engineering & Sciences, Chapter 7, Technical Science Press, Irvine, Ca., 2002, Paper 5.

25. Mixed-Mode Fracture

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AN ARBITRARILY ORIENTED CRACK NEAR A COATED FIBER H. M. Shodja and F. Ojaghnezhad Sharif University of Technology Department of Civil Engineering, P.O. Box 11365-9313, Tehran, Iran [email protected] The stress intensity factors (SIFs) for an arbitrarily oriented plane crack in the vicinity of a coated circular fiber is being sought. The method of solution is based on Shodja and Sarvestani's [1] equivalent inclusion method (EIM) for multi-inhomogeneity systems, which is an extension of Eshelby's [2] theory for a single ellipsoidal inhomogeneity. The proposed approach is very robust in the sense that it can effectively and systematically be applied to wide variety of fundamental problems, which are essential for micromechanical studies of composite materials, for example, see, Shodja et al. [3], Shodja and Roumi [4,5]. To the best of the authors' knowledge, the present problem has not been solved in the literature. Atkinson [6] considers the symmetric problem of the interaction between a crack and a circular inhomogeneity, in which the crack plane is normal to the uniform far-field applied stress and coincides with the plane of symmetry of the circular inhomogeneity, Fig.1. Erdogan et al. [7] consider the same problem, except that the crack plane is parallel to a plane of symmetry of the inhomogeneity and is situated at a distance c away from it. In the current work, it is proposed that the fiber be coated and the crack be arbitrarily oriented as shown in Fig. 2.

FIGURE 1. A crack near a circular fiber For the sake of comparison and verification of the accuracy of the proposed approach, the special case considered by [6] and [7] are readily re-examined by the present methodology. For example, the SIFs for the problem considered by [6] are verified to be in good agreement with the results obtained using the present theory, Table 1. TABLE 1. Mode I SIFs corresponding to Fig.1

H. M. Shodja and F. Ojaghnezhad

1166

In Table 1, µ m and µ f are the shear modulus for the matrix and fiber, respectively. The Poisson's ratio is assumed to be 1/4, a c 1/2, ı$ 1, and a f 1 . The values of the SIFs are normalized in accordance to [6]. Note that the results of [6], which are presented in Table 1 are read visually from their plots.

FIGURE 2. An arbitrarily oriented crack near a circular coated fiber

References 1.

Shodja, H.M., Sarvestani A.S., Journal of Applied Mechanics, Vol. 68, 3-10, 2001

2.

Eshelby, J. D., Progress in Solid Mechanics, Vol. 2, Edited by I. N. Sneddon and R. Hill, North-Holland, Amesterdam, 1961, 89-140.

3.

Shodja, H.M., Rad, I.Z., Soheilifard, R., J. Mech. Phys. Solids, vol. 51, 945-960, 2003

4.

Shodja, H.M., Roumi, F., Mechanics of Materials, Vol. 37, 343-353, 2005.

5.

Shodja, H.M., Roumi, F., In XXI Int. Congress of Theoretical and Applied Mechanics, Warsaw, Poland, August 15-21, 2004.

6.

Atkinson, C., Int. J. Engng. Sci., vol. 10, 127-136, 1972

7.

Erdogan, F., Gupta, G.D., Ratwani, M., Journal of Applied Mechanics, vol. 41, 1007-1013, 1974

25. Mixed-Mode Fracture

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SIMULATION OF THE MIXED MODE FRACTURE OF CONCRETE WITH COHESIVE MODELS J. C. Gálvez, D. A. Cendón, E. Reyes1, J. M. Sancho2 and J.Planas E.T.S. Ingenieros Caminos, Universidad Politécnica Madrid c/ Profesor Aranguren s/n, 28040 Madrid, Spain 1E.T.S. Ingenieros Caminos, Universidad Castilla La Mancha Av. Camilo José Cela s/n, 13071 Ciudad Real, Spain 2E.T.S. Arquitectura, Universidad Politécnica Madrid c/ Juan de Herrera 4, 28040 Madrid, Spain [email protected] Considerable effort has been devoted to developing numerical models to simulate the mixed mode fracture of quasi-brittle materials. Traditionally, the numerical methods based on the Finite Element Method were classified into two groups [1]: smeared crack approach and discrete crack approach. In the smeared crack approach the fracture is represented in a smeared manner: an infinite number of parallel cracks of infinitely small opening are (theoretically) distributed (smeared) over the finite element [2]. The cracks are usually modelled on a fixed finite element mesh. Their propagation is simulated by the reduction of the stiffness and strength of the material. The constitutive laws, defined by stress-strain relations, are non-linear and show a strain softening. This approach was pioneered with fixed-crack orthotropic secant models and rotating crack models. However, strain softening introduces some difficulties in the analysis. The system of equations may become ill-posed, localization instabilities and spurious mesh sensitivity of finite element calculations may appear. These difficulties can be tackled by supplementing the material model with some mathematical condition. Other strategies are the non-local continuum models, the gradient models, and the micropolar continuum. These procedures are suited to specific problems, but none gives a general solution of the problem. The discrete approach is preferred when there is one crack, or a finite number of cracks, in the structure. The cohesive crack model, developed by Hillerborg and co-workers [3] for mode I fracture of concrete, was shown to be efficient to model the fracture process of quasi-brittle materials. It has been extended to mixed mode fracture (modes I and II) and incorporated into finite element codes [4-8] and into boundary element codes [9]. One of the difficulties associated with these codes is that they require the remeshing and/or refinement of the finite element mesh when the crack grows, and some of them also require an input of material properties that are difficult to evaluate. In recent years, a new methodology based on the so-called strong discontinuity approach (SDA) has been proposed [10]. The SDA complements the classical approaches, the smeared crack and the discrete crack, and has been successful in the analysis of the fracture of brittle materials. In contrast to the smeared crack model, in the SDA the fracture zone is represented as a discontinuous displacement surface. In contrast to the discrete crack approach, in the SDA the crack geometry is not restricted to interelement lines, as the displacement jumps are embedded in the corresponding finite element displacement field. A comparative review of the various approaches to the embedded crack concept is presented by Jirárek [11].

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Based on the above exposed we may conclude that there are two main procedures to incorporate the cohesive model in the discrete crack approach. One of them is based on the previous knowledge of the crack path, which is incorporated on the finite element mesh, and the cohesive model is implemented over the crack trajectory. The other one proposes a finite element model with a cohesive crack embedded. The paper compares both approaches, establishes the advantages and disadvantages of every one and compares the numerical results for different testing geometries. The experimental results from several researchers are modelled, and the differences between the numerical results are commented. Especial attention is devoted to the experimental results supplied by the authors, based on the TPB geometry, under proportional and non-proportional loading, obtained for three sizes of the specimens. These tests include a complete series of results, like the stresses in the crack during the test, very useful for the comparison of the numerical procedures.

References 1.

Elices M., Planas J. in: Fracture Mechanics of Concrete Structures,. Chapman & Hall, London, 16-66, 1989.

2.

Bazant Z.P., Planas J. Fracture and Size Effect in Concrete and Other Quasibrittle Materials, CRC Press, New York, 1998.

3.

Hillerborg A., Modéer M., Petersson P., Cement and Concrete Research, vol. 6, 773-782, 1976.

4.

Cervenka J. Discrete Crack Modelling in Concrete Structures, Ph.D. Thesis, University of Colorado, 1994.

5.

Xie M., Gerstle W., Journal of Engineering Mechanics, vol. 121, 1349-1358, 1995.

6.

Valente S., in: Fracture of Brittle Disordered Materials, Concrete, Rock and Ceramics, E&FN Spon, 66-80, 1995.

7.

Cendón D.A., Gálvez J.C., Elices M., Planas J., International Journal of Fracture, vol. 103, 293-310, 2000.

8.

Gálvez J.C., Cervenka J., Cendón D.A., Saouma V., Cement and Concrete Research, vol. 32, 1567-1585, 2002.

9.

Saleh A., Aliabadi M., Engineering Fracture Mechanics, vol. 51, 533-545, 1995.

10. Simo J., Oliver J., Armero F., Computational Mechanics, vol. 12, 277-296, 1993. 11. Jirásek M., Computer Methods in Applied Mechanics and Engineering, vol. 188, 307–330, 2000. 12. Gálvez J.C., Elices M., Guinea G.V., Planas J., International Journal of Fracture, vol. 94, 267284, 1998. 13. Galvez, J.C. Cendón, D.A., Planas J , International Journal of Fracture, vol 118, 163-189, 2002.

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MICROMECHANICAL ANALYSIS OF RUPTURE MECHANISMS IN MIXED MODE DUCTILE FRACTURE I. Barsoum and J. Faleskog Department of Solid Mechanics, Royal Institute of Technology Osquars backe 1, 100 44 Stockholm, Sweden [email protected] , [email protected] The fracture toughness of ductile materials may differ considerably under mode I and mode II/III loading. The main reason for this is that the fracture mechanisms differ in important aspects between the opening loading mode (mode I) and the shear loading mode (mode II/III). Experimental studies show that the mode I failure mechanism involves void nucleation, growth and coalescence. In mode II/III however, intense plastic straining ahead of the crack tip promotes nucleation of micro voids which typically experience limited growth before linking up under intense shear deformation. Hence, under general mixed mode loading, there will be at least two failure mechanisms that may co-operate or even compete. At lower stress triaxialities (mode II/III), the shear dimple rupture mode will be favoured, whereas at higher stress trixailities (mode I) the flat dimple rupture mode will be favoured. In the flat dimple rupture mode the final link up between voids occurs through necking of void ligaments until impingement. By contrast, in the shear dimple rupture mode, final link up between voids occurs through shear localization of plastic strain in the ligaments between voids. In the latter case, voids rarely grow until impingement. In this study we are focusing on the conditions that govern the transition between the two mechanisms. This is carried out by micromechanical modelling using finite element analysis. The localized type of deformation characterizing both failure modes fits well into the general theoretical framework of plastic localization introduced by Rice (1976). In that study the conditions for having a localized band in which the deformation varies with the position across the band were investigated. Figure 1 illustrates the band. Here we make use of the kinematical conditions for the deformation across the band to analyse the transition between the two failure mechanisms for ductile mixed mode fracture. The deformation gradient is homogeneous out side the band in the Rice model, whereas it varies in a continuous manner with position across the band. This facilitates localization into a symmetric mode, a shear mode or a combination of both modes. The micromechanical model employed consists of an array of equally sized cells located within the planar band shown in Figure 1. Each cell has the same thickness as the band and contains one spherical void located at its centre. Thus, nucleation of the void is not considered here. The periodic arrangement of the cells allows the study of a single cell as the representative volume element (RVE). To simplify matters within the framework discussed above, a state of generalized tension is used to represent pure mode I type of loading (symmetric) and a state of generalized shear is used to represent mode II/III type of loading (shear). Mixed mode loading can then be accomplished by a combination of the two generalized cases where the macro stresses (average stresses) acting on a cell are: 613

6 23

T

60  V ,

V t0,

62

63

60 ,

612

W t 0 and

0 , see Figure 1. Generalized tension corresponds to W

corresponds to V

Vm

61

60  V 3

and

0 and generalized shear 0 . The mean stress and the effective stress can be expressed as

Ve

V 2  3W 2 , respectively, with stress triaxiality defined as

V m V e . The mode mixture is here quantified by the parameter K

2

(2 S ) arctan(3W 2 V ) .

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The RVE is loaded in such a way that the macro stresses is kept constant, i.e. proportional stressing prevails throughout the loading. Geometrically, the RVE (see Figure 1) is characterized by the height aspect ratio defined as O

S x / S y , and the void spacing aspect ratio defined as F

The width and the depth of the RVE are set to be equal, S z

R / Sy .

Sy .

With the model described above the transition between the flat dimple rupture mode and the the shear dimple rupture mode will depend on stress triaxiality, T, mode mixture, K , and geometry, O and F . Results will be given for an elastic ideal plastic material and an elastic moderately hardening plastic material.

FIGURE 1. The representative volume element containing a spherical void, loaded in generalized tension and/or simple shear with a superposed hydrostatic stress.

References 1.

Rice, J.R., In Theoretical and Applied Mechanics 14th IUTAM Congress, edited by W.T. Koiter, North-Holland, Amsterdam, 1976, pp. 207-220.

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MODE I PRELOADING-MODE II FRACTURE IN WARM PRE-STRESSING M. R. Ayatollahi and M. Mostafavi Fatigue and Fracture Laboratory, Mechanical Engineering Department, Iran University of Science and Technology IUST, Narmak, Tehran, 16844, IRAN [email protected] The loading history of cracked specimens plays an important role in their in-use behavior. Warm Pre-stressing (WPS) can be mentioned as a pre-loading procedure that significantly changes the apparent fracture toughness in some steels. In this procedure the specimen is subjected to a preload in high temperature and is used in a lower service temperature. When the cracked specimen is preloaded and fractured both in mode I, it is well known that WPS improves the load bearing capacity of specimens [1]. Meanwhile, very little work has been conducted for cases where preloading and fracture take place in different modes of loading [2]. In this paper the finite element method is used to study the effects of mode I preloading on mode I and mode II fracture. The finite element analysis is conducted on a biaxially loaded center crack plate in which the crack makes an angle 45o relative to the loading direction (see Fig. 1). For O=1, the specimen is under pure mode I loading and for O= -1 it is loaded in pure mode II. The finite element code ABAQUS is employed for simulation of warm pre-stressing and fracture. It is assumed that the final fracture in reloading (whether in mode I or mode II) is always due to cleavage fracture. The RKR model [3] is used as fracture criterion. According to this criterion cleavage fracture initiates whenever the hoop stress reaches a critical value in a critical distance from the crack tip. Cleavage fracture is assumed to be initiated along the crack line in mode I fracture and along the direction of maximum hoop stress in mode II fracture.

FIGURE 1. Cracked specimen used for WPS simulation Four different crack lengths (a/W= 0.1, 0.2, 0.3 and 0.4) are considered in the specimen. For each crack length, the specimen is preloaded in pure mode I (i.e. O=1) with five different preloading levels corresponding to 20%, 40%, 60%, 80% and 95% of fracture J. After the unloading and cooling stages, the specimen is reloaded either in mode I (O=1) or in mode II (O= -1) till the hoop stress attains its critical value. The fracture loads with and without warm prestressing are then compared. Figs 2 and 3 show the improvement in fracture load when the specimen is reloaded in pure mode I and pure mode II, respectively. While a significant improvement in fracture load is seen for mode I preloading-mode I fracture, there is almost no improvement for mode I preloading-mode II fracture. The negligible effect of mode I preloading on mode II fracture can be attributed to the distribution of residual stresses around the crack tip after unloading.

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FIGURE 2.- Improvement in Mode I fracture load due to Mode I preloading.

FIGURE 3. Improvement in Mode II fracture load due to Mode I preloading.

References 1.

Smith, D.J., Hadidimoud, S., and Fowler, H., Engineering Fracture Mechanics, 2004. 71:2015-2032.

2.

Swankie, T.D. and Smith, D. J., Engineering Fracture Mechanics, 1998. 61: 387-405.

3.

Ritchie, R.O., Knott, J.F., and Rice, J.R., Journal of the Mechanics and Physics of Solids, 1973. 21: 395-410.

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PREDICTIONS OF MIXED MODE I/II FRACTURE TOUGHNESS FOR SOFT ROCKS M. R. Ayatollahi and M. R. M. Aliha Fatigue and Fracture Lab., Department of Mechanical Engineering Iran University of Science and Technology Narmak, Tehran, 16844, Iran [email protected] [email protected] Cracked rock masses are usually subjected to complex loading conditions. Therefore, it is among favorite concepts for rock fracture researchers to investigate the fracture of rocks under mixed mode I/II loading. There are numerous experimental studies on mixed mode I/II fracture of rocks using different test specimens. Semi-circular bend (SCB) specimen is one of the favorite test configurations for conducting mixed mode fracture toughness experiments in rock materials. This specimen is simple and its manufacturing is inexpensive. By changing the parameters a/R, S/R and E (see Fig. 1), the SCB specimen can provide pure mode I, pure mode II and any combination of modes I and II. In addition to the experimental studies, there are several fracture criteria for mixed mode fracture behavior of brittle materials. However, the results obtained from fracture tests on a synthetic soft rock called Johnstone [1] by using the SCB specimens can not be appropriately interpreted when the available fracture criteria are used. For example, the maximum tangential stress (MTS) criterion [2] fails to predict the test results; especially for mode II dominated loading conditions. As shown in Fig. 2, a great discrepancy exists between the experimental results [1] and predictions by the MTS criterion for the SCB specimen.

FIGURE 1. Cracked semi-circular bend (SCB) specimen. In this paper, improved predictions are achieved for fracture toughness of Johnstone by using a more accurate description of tangential stress in the MTS criterion. The tangential stress around the crack tip is outlined by the Williams [3] series expansion as:

V TT

1 2Sr

cos

Tª



T 3 º K , cos 2  K ,, sin T »  T sin 2 T  O r1 2 « 2¬ 2 2 ¼

(1)

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where r and T are the conventional crack tip co-ordinates. KI and KII are the mode I and mode II stress intensity factors, respectively and T is the non-singular stress term. While the stress intensity factors (KI, KII) describe the severity of stress singularity around the crack tip the magnitude and the sign of T-stress can also influence significantly the onset of fracture in cracked specimens subjected to mixed mode I/II loading [4]. It is shown in this paper that a modified MTS criterion which takes into account the effects of both singular term and the T-term of stress around the crack tip can predict very well the results obtained from mixed mode I/II fracture tests on Johnstone [1]. In the modified MTS criterion crack tip parameters (KI, KII, T ) are used for evaluating the fracture load of cracked specimens.

FIGURE 2. Mixed mode I/II fracture toughness envelop for SCB specimens with (a/R= 0.35 and S/ R = 0.5) made of a soft rock.

References 1.

Lim, I.L., Johnston, I.W.,. Choi, S.K, Boland, J.N., Int. J. Rock Mech. Min. Sci. Geomech. Abstr., vol 31(3), 199-212, 1994

2.

Erdogan, F., Sih, G.C., J. Basic Eng., Trans. ASME 85, 519-525, 1963

3.

Williams, M.L., J. Appl. Mech., vol, 24,109-114, 1957

4.

Smith, D.J., Ayatollahi, M.R., Pavier, M.J., Fatig. Fract. Eng. Mater. Struct., vol. 24, 137-150, 2001

25. Mixed-Mode Fracture

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AN INTERFACE MODEL FOR MIXED-MODE, BUCKLING-DRIVEN DECOHESION OF SUPERFICIAL LAYERS S. Bennati and P. S. Valvo Department of Structural Engineering, University of Pisa Via Diotisalvi 2, 56126 Pisa, Italy [email protected], [email protected] There are several situations in which the local phenomena acting in structural elements can lead to the partial detachment of a superficial layer from its underlying substrate. In the case of fibrereinforced composite laminates, for example, delamination is one of the most insidious events that can compromise their mechanical performance. Analogous decohesion phenomena can be observed, for instance, in film coatings, sandwich plates, etc. (Hutchinson and Suo [1]). When a structural element containing a partially detached layer is subjected to compression, local instability phenomena can easily arise (Kachanov [2]). These may in turn provoke the growth of the decohered area itself, as they result in high values of the interfacial stresses. In the framework of Fracture Mechanics, an adequate description of the process by which the detached region extends requires accounting for the so-called “mode mixity”, i.e., the ratio between the contributions (generally varying during the process) of the conventional fracture modes I, II and III (respectively, opening, sliding and tearing modes). For plane problems, where only modes I and II are present, according to Hutchinson [3], the mode mixity can be measured by the angle

\

tan 1

kII kI

(1)

where kI and kII are the stress intensity factors at the delamination front, corresponding to modes I and II, respectively.

FIGURE 1. Interlaminar stresses at the interface. Despite the complexity of the problem, a simple mechanical model, where separation is assumed to occur along an elastic-brittle interface joining the decohered layer and the substrate, has proven to be effective in describing the decohesion phenomenon (Bennati and Valvo [4]). Actually, an explicit solution to the problem has been deduced, allowing us to evaluate the evolution of the peak stresses at the delamination front (Fig. 1). Since these stresses attain finite values, the expression of the mode mixity angle (1) is conveniently modified as follows,

S. Bennati and P. S. Valvo

1176

\

tan 1

W XZ VZ

(2)

where WXZ and VZ are the interfacial stresses evaluated at the delamination front. Thus, the energy variations involved in its further crack extension can be deduced through direct calculations. In particular, both the mode mixity angle and the critical strain energy release rate can be obtained (Fig. 2). Finally, through the choice of appropriate growth criteria, it is possible to achieve an analytic description of the entire process of buckling-driven decohesion growth under both monotonic and cyclic loading conditions. In the authors’ opinion, the proposed model can help explaining many apparently strange and unsolved experimental results reported in the literature.

FIGURE 2. Mode mixity angle and critical strain energy release rate.

References 1.

Hutchinson, J.W., Suo, Z., Adv. Appl. Mech., vol. 29, 63-191, 1992.

2.

Kachanov, L.M., Delamination buckling of composite materials, Kluwer Academic Publishers, Dordrecht-Boston-London, 1988.

3.

Hutchinson, J.W., In Metal-ceramic interfaces, edited by M. Rühle, A.G. Evans, M.F. Ashby and J.P. Hirth, Pergamon Press, New York, 1990, 295-306.

4.

Bennati, S., Valvo, P.S., Key Eng. Mater., vol. 221-222, 293-306, 2002.

25. Mixed-Mode Fracture

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MXED-MODE FRACTURE ANALYSS OF ORTHOTROPC FUNCTONALLY GRADED MATERALS Serkan Dag, Bora Yildirim1, Duygu Sarikaya Department of Mechanical Engineering, Middle East Technical University, Ankara, Turkey 1Department of Mechanical Engineering, Hacettepe University, Ankara, Turkey [email protected], [email protected], [email protected] Functionally graded materials (FGMs) are multiphase composites that have spatial variations in the composition and microstructure. These variations are intentionally introduced in order to take advantage of different thermomechanical properties of the constituent materials. The fracture mechanics theory and analysis of functionally graded materials is based on the assumption of continuous variations in the related thermomechanical properties (see for example Yildirim et al. [1] and Kim and Paulino [2]). Fracture mechanics problems that occur in FGMs are generally observed to be either due to mode I edge cracks that are perpendicular to the free boundaries or due to the embedded cracks that are parallel to the material surface. These observations could be attributed to the fact that some of the processing methods used to create graded layers induce an oriented microstructure. For example, as shown by Sampath et al. [3], FGMs that are processed by the plasma spray technique have a lamellar structure which has weak fracture planes parallel to the boundary. Embedded cracks that can initiate at the weak cleavage planes are inherently under mixed-mode mechanical or thermal loading. One of the approaches to examine fracture mechanics problems in this type of structures is to model the functionally graded medium as orthotropic with principal directions of orthotropy parallel and perpendicular to the free surface (Ozturk and Erdogan [4]). The objective in the present study is to develop analytical and computational methods to examine embedded crack problems in orthotropic FGMs under mixed-mode loading. The geometry of the crack problem considered is depicted in Fig. 1. x1 and x2 in this figure are the principal directions of orthotropy. The layer is graded in x2-direction and contains an embedded crack of length 2a at x2

0 . The crack is loaded by normal and/or shear tractions which are applied at x2

0 and

x2 0 for x1  a . The problem is formulated using the averaged constants of plane orthotropic elasticity which are first introduced by Krenk [5]. The governing partial differential equations are obtained in terms of the displacement components and then they are reduced to a pair of singular integral equations using Fourier transforms. The integral equations are solved numerically using an expansion-collocation technique to compute the modes I and II stress intensity factors and the energy release rate at the crack tips.

Enriched finite element formulation for mixed-mode fracture analysis of orthotropic FGMs is developed by Dag et al. [6]. This method is used in the second part of the present study to solve the problem shown in Fig. 1. Enriched and graded finite elements are used to model the orthotropic functionally graded medium. Fig. 2 shows the deformed shape of the finite element model of an embedded crack subjected to uniform normal loading. Enriched crack tip elements contain the theoretical asymptotic displacement field and it is possible to compute the mixed-mode stress intensity factors directly from the solution of a linear equation system. The numerical results calculated using the analytical formulation and enriched finite elements technique are shown to be in good agreement. In the final part of the study, the effects of boundary conditions, material nonhomogeneity, orthotropy parameters and loading conditions on the mixed-mode stress intensity

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1178

factors and the energy release are explored by carrying out parametric analyses and the results are briefly discussed.

FIGURE 1. An embedded crack in an orthotropic functionally graded layer.

FIGURE 2. Deformed shape of the finite element model of the crack shown in Fig. 1.

References 1.

Yildirim, B., Dag, S. and Erdogan, F., Int. J. Fracture, vol. 132, 369-395, 2005.

2.

Kim, J.-H. and Paulino, G.H., Int. J. Numer. Meth. Eng., vol. 53, 1903-1935, 2002.

3.

Sampath, S., Herman, H., Shimoda, N. and Saito, T., MRS Bulletin, vol. 20, 27-31, 1995.

4.

Ozturk, M. and Erdogan, F., Int. J. Fracture, vol. 98, 243-261, 1999.

5.

Krenk, S., J. Compos. Mater., vol. 13, 108-116, 1979.

6.

Dag, S., Yildirim, B. and Erdogan, F., Int. J. Fracture, vol. 130, 471-496, 2004.

25. Mixed-Mode Fracture

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NEW SCHEME FOR FEA OF MIXED MODE STABLE CRACK GROWTH S. K. Maiti, S. Namdeo and A. H. I. Mourad1 Mechanical Engineering Department, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India 1Mechanical Engineering Department, Faculty of Engineering, United Arab Emirates University, Al-Ain, POB 17555, UAE [email protected], [email protected], [email protected] A scheme for elastic-plastic finite element analysis (FEA) has been proposed for the study of stable crack growth (SCG) from initiation to instability in both mode I and mixed mode (I and II). In the analysis the condition for crack extension at every stage of the SCG is considered to be CTOA/CTOD reaching a critical value (Newman [1], Maiti and Mahanty [2], Maiti and Mourad [3]). The scheme permits predictions of load variation with load line displacement (LLD), crack tip current plastic zone and crack edge profile. For the study of the whole span of SCG in mode I a single discretization is employed. For a similar study of a mixed mode problem a single discretization is carefully made basing on the assumption that the whole span of the SCG takes place along a straight line inclined with the main crack at an angle corresponding to the direction of initial crack extension (Fig.1). The direction of initial crack growth is predicted using a full field elastic analysis and the maximum tangential principal stress (MTPS) criterion. Most of the elements in a discretization are 8-noded quadrilaterals. Ahead of the crack tip, elements are squares of size 0.4 mm. External loads applied at node H and two nodes on its either side; simultaneously node G and two nodes on its either side are constrained (Fig.1). The predictions for the initial direction of crack growth for a few cases are compared with the experimental data reported by Mourad et al. [4] on AISI 4340 steel.

0

FIGURE 1. Typical discretization for study of crack growth for 75 loading angle. The proposed scheme of analysis of the whole SCG is done in a few stages using the ANSYS (version 8.0) software. The scheme is different from the schemes proposed by Newman [1], Maiti and Mahanty [2], and Miller and Kfouri [5]. Each stage is analyzed separately using a discretization, which is related very closely to that of the previous stage, and considering the domain to be free of any residual stresses and strains. In each stage crack is allowed to extend by 0.4 mm. The detail of the scheme is presented in the paper. Both mode I (a0/w = 0.42 and 0.43) and mixed mode problems (loading angle =75o, 65o and 60o) have been studied. This new scheme helps to determine the variation of fracture load with crack extension without requiring much computer storage and time. A typical variation of load with LLD is shown in Fig.2. Predictions for

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1180

the direction of initial crack extension in a mixed mode, initiation and maximum loads in both mode I and mixed mode compare very closely with the experimental results [4] in the case AISI 4340 steel.

FIGURE 2. Comparison of theoretical and experimental variation of load with load line displacement for mixed mode for 75o loading angle.

References 1.

Newman, J. C., Jr., Fracture Mechanics: Fifteenth Symposium, ASTM STP 833, edited by R. J. Sanford, American Society for Testing and Materials, 1984, 93-117.

2.

Maiti, S. K., and Mahanty, D. K., Engineering Fracture Mechanics, vol. 37, 1275, 1990.

1251-

3.

Maiti, S. K., and Mourad, A.H.-I., Engineering Fracture Mechanics, vol. 52, 378, 1995.

349-

4.

Mourad, A.H.-I., Alghafri, M.J., Abu Zeid, O.A., and Maiti, S.K., Nuclear Engineering and Design, vol. 235, 637-647, 2005.

5.

Miller, K.J., and Kfouri, A.P., Elastic-Plastic Fracture, ASTM STP 668, edited by J. D. Landes, J. A. Begley, and G. A. Clarke, American Society for Testing and Materials, 1979, 214-228.

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NUMERICAL SIMULATION OF NONLINEAR CRACK PROPAGATION UNDER MIXED-MODE IMPACT LOADING T. Fujimoto and T. Nishioka Kobe University 5-1-1 Fukaeminamimachi, Higashinada-ku, Kobe 658-0022 Japan [email protected], [email protected] In some of the accidents of industrial structure, which have been happened by collision, earthquake and etc., fast crack propagations caused in the parts of the structure. In some cases of these fractures, large deformation with plastic strain accompany the crack propagation. Prediction and control of crack propagation direction have been required to prevent critical destruction of the structure. In order to simulate and measure the crack propagation phenomena, some numerical methods have been proposed. The nodal release method [1] in FEM is one of very popular technique for non-linear crack propagation. However, because the crack propagation path has to be expressed by the boundaries of finite elements in the nodal release method, the nodal release method is not suit to predict non-straight crack propagation path. The element release method is adopted in some commercial code of FEM. In this method, an element in singular strain area near the propagating crack tip is removed and energy balance is not satisfied during crack propagation. In this study, accurate measurement of nonlinear propagating crack tip condition is considered by using the moving finite element method, which has been proposed by Nishioka and co-workers [2]. In the cases of some nonlinear fractures, distinct wake zone is observed near the crack propagation path. These plastic strain singularities are estimated by the moving finite element technique as shown in Fig. 1. Non-straight crack propagation path and/or crack bifurcation paths can be reproduced by the moving element technique [3]. In the moving FEM, the mappings of deformation parameters have to be operated at each time step. In order to estimate the solution at next time step t+'t, Nishioka [4] derived the variational principle to satisfy the equilibrium of total force based on the mapping parameters ()(t0). t ³V S ij ' t G u i , j dV  ³V U ui 0 ' t G u i dV





t  t t ³ S t t i 0  t i ' t G u i dS  ³V V ij 0 G u i , j dV  ³V U ui 0 G u i dV

(1)

FIGURE 1. Fine mesh subdivision near propagating path

where () means the time derivative of ( ) . S ij and V ij mean the Lagrange stress and the Cauchy stress, respectively. ui and ti are displacement and traction force, respectively. U denotes the mass density. In this study, the crack propagation path is predicted numerically. Some fracture path prediction theories have been proposed, and popular theories are summarized in Ref. [5]. Some of

T. Fujimoto and T. Nishioka

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the prediction theories are introduced into the moving finite element method. In order to discuss the validity of the numerical simulation and the numerical fracture path prediction algorism, the numerical results are compared with the experimental result for the fracture of pure aluminium (A1050) under mix mode load.

FIGURE 2. Pure aluminium specimen under mix-mode load

FIGURE 3. Progress of nonlinear crack propagation in pure aluminium The one of experimental set-up is shown in Fig. 2. The ultra-high speed camera records the history of deformation and crack propagation. Figure 3 shows the progress of crack propagation. Framing rate is 8000 frame/sec. Average of crack kinking angle is about 6 degree, and crack propagation velocity is 4.44m/s.

References 1.

Kobayashi A.S., Mall S., Urabe Y. and Emery A.F., Numerical Methods in Fracture Mechanics, Univ. College, Swansea, 709-720, 1978.

2.

Nishioka, T., JSME International Journal, Series A, Vol.37, No.4, 313-333, 1994.

3.

Tchouikov, S., Nishioka, T. and Fujimoto, T., Computers, Materials and Continua, Tech Science Press, Vol.1, No.2, 191-204, 2004.

4.

Nishioka, T. and Wang, Z.M., Constitutive and Damage Modeling of Inelastic Deformation and Phase Transformation, Neat Press, Fulton, Maryland, 741-744, 1999.

5.

Nishioka, T., "Computational Aspects on Dynamic Fracture", Comprehensive Structural Integrity, Volume 3: Computational Methods (R, de Borst and H.A. Mang), Chapter 4, Elsevier Science.

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ELASTIC-PLASTIC BEHAVIOUR OF CRACK PROPAGATION UNDER BIAXIAL CYCLIC LOADING T. Hoshide Department of Energy Conversion Science, Kyoto University Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan [email protected] The fatigue crack growth behaviour under biaxial stress state is affected by non-singular stress under elastic-plastic deformation. The effects of non-singular stress with plasticity on biaxial crack growth should be clarified for the integrity design of machineries under practical service loading. In this work, the aforementioned subjects were discussed by reconsidering previous works by Hoshide et al. [1, 2]. In previous studies, fatigue crack propagation tests were conducted by using cruciform specimens of low carbon steel under uniaxial, equi-biaxial and shear loading modes, and also by using thin-walled tubular specimens of pure copper under combined in-phase axial-torsional loading modes. The yield strength of the steel and the copper is 228MPa and 24.8MPa respectively. In cruciform specimens of steel, it was confirmed that the crack propagation rate correlated with the stress intensity range 'K was significantly affected by the non-singular stress in the direction parallel to the crack. The opening displacement at the centre of crack was monitored, and it was revealed that the above result was mainly caused by the crack closure behaviour influenced by the non-singular stress. The crack propagation rate was almost uniquely correlated with the effective stress intensity factor 'Keff. However, in the case of shear loading, significant plasticity was detected and the crack growth rate for the same 'Keff -value shifted toward higher rate region compared with that in other loading cases. In tubular specimens of copper, it was clarified that the cracking morphology was a bent-type in the combined mode and a branch-type in the torsional case. Cracks were found to propagate in such direction that the Mode II component of the stress intensity factor was minimized. By using a devise to detect the opening and sliding displacements at the centre of crack, the deformation behaviour of bent- or branch-cracked specimens was also examined to evaluate the crack opening point. It was remarked that tails appeared near both tips of the observed hysteresis loop in the case of reversed torsion. In this situation, any good correlation was not seen even if the effective stress intensity factor 'KIeff of Mode I was employed to correlate the growth rate. It was found that this behaviour was mainly associated with gross plasticity. A simple method to estimate the J integral for a centre-cracked plate under biaxial stresses was proposed based on the finite element analysis, and a tentative procedure to estimate the J integral was also developed for the bent crack. In both situations, it was cleared that the centre opening displacement should be used in evaluating the J integral range 'J. The growth rate of crack in cruciform specimen and bent crack in tubular specimen were correlated with 'J evaluated by using the proposed methods. Independently of biaxiality and plasticity, the crack propagation rate da/dN was found to be correlated with 'J by a unique power function as da dN

C ('J ) m

(1)

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Consequently, it is suggested that the parameter governing the crack propagation under biaxial stress state is the range of J integral which is evaluated by using the hysteresis loop of applied force versus opening displacement at the centre of crack.

References 1.

Hoshide, T., Yamada A. and Tanaka, K., J. Soc. Mater. Sci., Japan, vol. 32, 528-534, 1983

2.

Hoshide, T., Kawabata K., Yamakawa, N. and Inoue, T., J. Soc. Mater. Sci., Japan, vol. 38, 280-286, 1989

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NUMERICAL ANALYSIS OF MIXED-MODE CRACKING IN CONCRETE DAMS Z. Shi Research and Development Center, Nippon Koei Co., Ltd. 2304 Inarihara, Tsukuba, Ibaraki, 300-1259, Japan [email protected] Since the establishment of the fictitious crack model (FCM) for crack analysis of the mode-I type in concrete by Hillerborg et al. [1], continuous research effort has been made to apply the concept to model mixed-mode fracture because most of the practical fracture problems in concrete are of the mixed-mode nature, involving mode-I and mode-II. This paper presents a numerical study of the mixed-mode fracture in concrete dams, using the extended FCM by Shi et al. [2-4]. For crack propagation, the frequently adopted maximum principal stress criterion is used, which is based on the notion that the mode-I condition is dominant at the tip of a mixed-mode crack. As the tip stress reaches the tensile strength of concrete a mixed-mode crack propagates. A main feature of this study is that normal and tangential tractions are applied directly to the crack surface, following specific tension-softening and shear-transfer laws. The scale-model test of a concrete gravity dam subjected to equivalent hydraulic loads by Carpinteri et al. [5] is selected as a mixed-mode fracture problem to be solved. Two 1:40 scale models of a gravity dam were prepared, and each contained a horizontal notch on the upstream face located at a quarter of the dam height. Let W represent the dam thickness at the height of the notch. For brevity of presentation, only one of the three tests is studied in the following under the mixed-mode fracture condition, i.e., the second specimen with the notch size of 0.2W (Test 3). In numerical studies, the bi-linear tension-softening relation of Fig. 1a is applied to the normal traction and the crack opening displacement (COD). As for the shear-transfer law two types of bilinear shear-COD relation are assumed to exist between the tangential traction and the COD; see Fig. 1b and Fig. 1c.

FIGURE 1. Assumed tension-softening and shear-transfer relations of concrete As the influence of the shear force on the maximum load is found to be small and negligible, the following discussion is focused on the crack path, which may be the foremost concern for the crack analysis of concrete dams. Fig. 2 shows the obtained crack paths under the mode-I and the mixed-mode conditions, as well as the experimental observations. As seen, during the steady crack growth the mode-I path follows a trajectory with a larger downturn angle (measured from the horizontal plane of the notch) than that of the observed crack path. Under the mixed-mode condition of case 1 in which only a small shear strength fs = 0.1ft is assumed, the crack propagates

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along the mode-I path initially; as the shear transfer takes place after the COD reaches Ws1, it diverges to a new path that lies in between the mode-I and the actual crack trajectories with a much smaller downturn angle. Increasing the shear strength in case 2 to fs = 0.2ft, the crack propagates briefly along the mode-I path and then diverges to another path that merges with the observed crack trajectories. These cracking behaviors obtained are easy to comprehend. Under the mode-I condition, the discrepancy is caused by ignoring the frictional force or shear from the sliding surfaces of the crack, which is tantamount to omitting a local moment that acts against the surface deformation allowed under the mode-I condition. Here, the local moment is presumably formed by a pair of opposite shear forces acting on the two crack surfaces at the distance of a COD. Under the actions of these local moment forces in cases 1 and 2, the crack paths eventually diverge from the mode-I path and move upwards. As shown in Fig. 2, in the later stage of the unsteady crack propagation totally different fracturing behaviors are predicted by the numerical analyses that do not agree with the experimental observations. This is believed to be caused by a transition of the loading conditions that may have occurred during the experiments and is not reflected in the numerical studies [3].

FIGURE 2. Experimental results and numerical predictions of crack trajectories under mode-I and mixed-mode conditions with two types of shear-COD relations

References 1.

Hillerborg, A., Modeer, M. and Peterson, P. E., Cement and concrete research, vol. 6, 773782, 1976.

2.

Shi, Z., Ohtsu, M., Suzuki, M. and Hibino, Y., J. Struct. Engrg., vol. 127, 1085-1091, 2001.

3.

Shi, Z., Suzuki, M. and Nakano, M., J. Struct. Engrg., vol. 129, 324-336, 2003.

4.

Shi, Z., J. Struct. Engrg., vol. 130, 1738-1747, 2004.

5.

Carpinteri, A., Valente, S., Ferrara, G. and Imperato, L., In Fracture mechanics of concrete structures, edited by Z. P. Bazant, Elsevier Applied Science, New York, 1992, 351-360.

26. Fracture Mechanics Characterization of Wood

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SPECIES AND OTHER PHYSICAL EFFECTS ON PARAMETERS DESCRIBING A WOOD TOUGHNESS TEST. B. Thibaut and J. Beauchene CNRS French Guiana, Cirad French Guiana L3MA, IESG campus Saint Denis, 97300 Cayenne, France Cirad, ZI Pariacabo 973 Kourou, France [email protected], [email protected] Fracture mechanics is strongly dependant on material microstructure and defect occurrence in the specimen. Wood microstructure is rather complex at different levels. In order to investigate the influence of wood structural features, the Nordtest [1] specimen with 40mm height and 20mm thickness (Schatz [2]) was performed on ten homogeneous tropical species, at green state, in order to avoid drying checks, at room temperature and after 1 hour boiling in hot water at different temperatures up to 80°C (Bardet [3]). The test was performed with the LT plane as rupture plane and the L direction as rupture propagation direction. Table1 Values of the structural parameters for the ten species

Species were selected in order to have a rather wide range of structural parameters: vessel diameter: VD, number of vessels per mm2: VN, number of rays per mm: RN, fibre length: FL, fibre width: FW, double cell wall thickness: WT, WT/FW ratio, parenchyma abundance: PA, together with a wide range of basic density: BD (Table 1). Table 2 Values of the mechanical parameters for the ten species

Indicators of fracture toughness test were: equivalent rupture stress Sr and its value Sr/D after dividing by BD raised to the best statistical power at each temperature, fracture energy Gf and span at rupture Fr, the ratio between the values at 25°C and 80°C, Gf 25/80, Fr 80/25 and Sr 25/80 are indexes of temperature sensitivity of these parameters (Table 2).

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Table 3 Correlation coefficients between structural and mechanical parameters

Not surprisingly Sr has significant correlations, positive with WT/FW or density and negative with FW (table 3), these parameters being highly inter correlated. Sr/D is positively influenced by vessel diameter and parenchyma abundance. The same tendency was observed for Gf but with lower significant values. PA has a positive significant correlation with Gf at high temperature when density influence is low. Span at rupture is positively influenced by fibre length except for high temperature where density becomes influent. Temperature sensitivity is influenced for Gf by vessel density (+) and by parenchyma abundance (-), for Sr by vessel density (+), basic density and WT/FW (+), for Fr by density (+) and fibre width (-). Other parameters as chemical composition should be looked at because there are also strong variations between these species for that. Moreover, much more species should be investigated in order to examine how vessel porosity, parenchyma occurrence, fibre length and fibre geometry have a significant influence in conjunction with or explaining density role.

References 1.

Nord Test (1993), NT Build, 422. Wood: fracture energy perpendicular to the grain Nordtest, Espoo, Finland, From Gustafsson P.J., (1988): a study of strength of noched beams. CIB W18A paper 21-10-1 meeting Vancouver

2.

Schatz, T. (1995). "Determination de l'energie de rupture dans le bois." Holz als Roh- und Werkstoff: 171-176.

3.

Bardet S., Beauchene J., Thibaut B. (2003) Influence of basic density and temperature on mechanical properties perpendicular to grain of ten wood tropical species, Annals of Forest Science, vol. 60, 49-59.

26. Fracture Mechanics Characterization of Wood

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YEW AND SPRUCE WOOD: MECHANICAL PROPERTIES AND FRACTURE SURFACE STUDIES Daniel Keunecke, Christoph Marki and Peter Niemz Institute for Building Materials (Wood Physics Group), Swiss Federal Institute of Technology Schafmattstrasse 6, CH-8093 Zurich, Switzerland [email protected] Generally, there is a close connection between the anatomy of wood on the microscopic/ macroscopic level and its mechanical characteristics. Yew (Taxus baccata L.) and spruce (Picea abies [L.] Karst.) are gymnosperms with wide differences in their microscopic structure (fig. 1) and therefore in their fracture behavior and mechanical properties. Having been object of countless studies, the individual mechanical properties of spruce wood are best-known. In contrast to spruce wood, for the high dense yew wood only few reference values are available, even though it is known for its extraordinary toughness and its strength.

FIGURE 1. SEM-images of yew (left) and spruce (right) wood. The aim of this work was to compare selected mechanical properties of yew and spruce wood. The determined properties are •

static and dynamic modulus of elasticity (MOE),

•

fracture toughness KIC (ASTM E 399-90),

•

work to ultimate load (as defined by Bodig and Jayne [1]) and

•

impact bending strength.

Standard static test methods like the fracture toughness test (fig. 2) as well as micro tensile tests and nondestructive test methods like sound velocity measurement and resonance frequency measurement were applied. The portion of the elastic and plastic part of failure was examined, wherever applicable. Furthermore the fracture surfaces have been analyzed and compared in order to link the wood structure to the failure process.

FIGURE 2. Compact tension specimen: Dimensions [mm].

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The MOE which was determined by sound velocity and resonance frequency was within the known range for both species. The work to ultimate load of yew wood which was determined by 3point-bending was more than twice as high compared to spruce wood. The same applies for fracture toughness KIC, determined in the RL and TL crack propagation system. The impact bending strength of yew wood was also significantly higher. Table 1 gives a brief overview of selected mechanical results. TABLE 1. Material properties.

Reference 1.

Bodig, J. and Jayne, B.A., Mechanics of Wood and Wood Composites, Van Nostrand Reinhold, New York, USA, 1982.

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CRITICAL CRACK LENGTHS IN FRP REINFORCED GLULAM BEAMS Justin Desjarlais, William G. Davids and Eric N. Landis University of Maine Center for Advanced Engineered Wood Composites Orono, Maine 04469 USA [email protected], [email protected], [email protected] Tension reinforcement of glued-laminated (glulam) timber beams has been shown to be an effective way to utilize lower grade wood in structural applications. Fibre reinforced polymer (FRP) composites are a particularly good reinforcement because they can be fabricated to be compatible with the compliance properties of the wood substrate. While the reinforcement has been shown to be effective at improving strength and to some degree stiffness, there is a concern that long-term exposure to moisture and freeze-thaw cycles could lead to some delamination between the wood and the reinforcement. This is a particularly important issue when reinforced beams are used as bridge girders, as environmental exposure can be severe. In order to make quantitative assessments of the effects of these potential delaminations, a laboratory study of mixed mode fracture toughness was combined with numerical simulations of in-service load conditions. The goal was to make reasonable estimates of allowable delamination sizes for inservice conditions.

Numerical Simulation of Strain Energy Release Rate 3D numerical simulations were conducted in order to gain an understanding of the stress states at the bond line of a reinforced glulam. Fig. 1 illustrates the geometry of the beam considered. This beam geometry was also used in an extensive laboratory study of fatigue properties. Strain energy release rate, G, was determined for different load conditions by releasing pairs of adjacent nodes to simulate the crack. G is determined by evaluating the work required to reconnect the series of nodal pairs. In this manner, the contribution from mode I, mode II, and mode III can all be isolated. An example plot of G versus crack length is shown in Fig. 2 for a delamination starting from the end of the FRP. It is important to note that both mode I and mode II show significant contributions to the total G.

FIGURE 1. Geometry of simulated and tested glulam beam.

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FIGURE 2. Plot of G versus crack length for reinforced glulam beam.

FIGURE 3. Experimental configuration for mixed mode fracture measurement.

Mixed-Mode Fracture Energy Because of the contribution of both mode I and mode II in the calculated G for the beams, it was clear that the fracture toughness of the wood-FRP bond required a mixed mode analysis. Using a loading configuration as illustrated in Fig. 3, the contribution of mode II relative to mode I fracture can varied by adjusting the position of the load, P. As the position, x, increases, the contribution of mode II increases. Small laboratory fracture specimens were prepared according to the same material and bond specifications as the glulam beams, and were tested for fracture energy using the configuration of Fig. 3. Fracture energy was determined by measuring the change in compliance that accompanied a change in crack length. Fig. 4 shows the results of the fracture energy measurements plotted as in terms of mode I – mode II interaction. The results indicate a moderate amount of interaction, although scatter is significant. Furthermore, the results indicate the glulam beams can accommodate a significant level of delamination before crack lengths become critical.

FIGURE 4. Interaction of mode I and mode II fracture in mixed mode configuration.

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FAILURE ANALYSIS OF ENGINEERING WOOD PRODUCTS Ian Smith, Monica Snow and Andi Asiz University of New Brunswick Faculty of Forestry and Environmental Management, PO Box 44555, Fredericton, New Brunswick, E3B 6C2, Canada [email protected] This paper synthesizes information in the literature and results of studies at the University of New Brunswick (UNB) to provide guidance on failure analysis of engineering wood products (EWP). EWP are either solid materials like lumber and glued-laminated-timber, or composites manufactured by hot-pressing veneers, wafers or strands of wood that were pre-coated with synthetic adhesives. Important issues include size of specimen effects on apparent strength and how to handle situations where stress concentrations arise. Consideration is given to both bodies that are nominally undamaged and those that are pre-damaged (cracked) at the time of loading. This elucidates the extent to which one might validly apply common continuum failure theories. Limitations of continuum theories, whether or not they assume existence of a crack(s), are that they can not always reliably predict the load level at which damage initiates, nor the location of failures. Also, most theories cannot predict how failures propagate once initiated. This reflects limitations in theoretical postulates when applied to EWP (Smith et al 2003). Even when they have a physically correct basis fracture mechanics models still depend on an analyst’s ability to correctly locate cracks. An advanced ‘bridging fiber’ model has been developed to include closing forces to crack surfaces in a zone behind the crack tip (Smith and Vasic 2003). The closing forces replicate the effect of partially peeled wood cells that toughen any naturally formed crack. This means that the bridging crack model is capable of capturing a transition from an artificial crack to a ‘natural’ crack condition, meaning that it can be used to model crack propagation processes. Other fracture models cannot represent the artificial to natural crack transition so are unsuitable for predicting crack growth. Ability to predict crack growth equals ability to predict collapse loads for initially stable systems. Whatever fracture model is employed, one still requires a reliable empirical knowledge or algorithm of how crack fronts will advance. Usually, but not always, cracks in solid wood develop in planes that lie parallel to the grain direction. For EWP composites prediction of how cracks, or other damage, will develop is a much less certain undertaking! A very promising generalized failure prediction tool is discrete element (lattice network) based models (Smith et al 2003). Potentially discrete element models are the most powerful tools for failure analysis of EWP materials, because they can mimic effects of various morphological structures. Lattices can account for global and local structured variations in properties, and localized random variations using simulation techniques. This said, much remains to be done on the subject, particularly in regard to modeling strategies and element property calibrations for composite EWP. Modern composite EWP exhibit morphological characteristics at multiple scales. Researchers at UNB and elsewhere are addressing these issues. The remainder of the document presents a typical example of work in progress to predict failure processes in EWP materials. The chosen example is assessment of how members of solid wood (Pine lumber) an Laminated Strand Lumber (a modern composite made from wood strands) fail under loading from steel bolts that passes through them, to create a connection in which the bolts load the EWP perpendicular to the strong material axis, Fig. 1. LSL like lumber is a distinctly anisotropic material, but because of cross laminating between bonded strands the former is relatively resistant to splitting. The test arrangement loads the bolts in double shear. Transparent high strength side-plates were used instead of steel, as would be normal, so that fracturing patterns

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could be observed. A continuum finite element model was created to analyze the arrangement and assist in interpretation of the failure development. Predicted element stresses were used in conjunction with the Tsai-Wu failure criterion (Tsai and Wu 1971) to predict likely locations of damage, i.e. the potential sites for initiation of global failure, Fig. 2. As can be seen different failure initiation sites are predicted for Pine and LSL members, and different stress components govern depending on the zone within the member. These predictions match experimental observations well. The most likely failure for a Pine member is fracturing between the bolts, while for a LSL member the most likely failure process is excessive tension on the bottom face. This reflects the effects of the different stiffness and strength properties of the two materials.

FIGURE 1. Test with failed pine center member

FIGURE 2. Predicted likely failure initiation sites: a) Pine member, b) LSL member

References 1.

Smith, I., Landis, E. and Gong, M. 2003. “Fracture and fatigue in wood”, Wiley & Sons, Chichester, UK.

2.

Smith, I. and Vasic, S. 2003. ”Fracture behaviour of softwood”, Mechanics of Materials, 35(2003): 803-815.

3.

Tsai, S. W. and. Wu, E. M. 1971. “A general theory of strength for anisotropic materials”, Journal of Composite Materials, (1): 58-80.

26. Fracture Mechanics Characterization of Wood

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MODELIZATION OF SLOW CRACK GROWTH IN WOOD CONSIDERED AS A DAMAGE VISCOELASTIC MATERIAL M. Chaplain and G. Valentin Laboratoire de Rheologie du Bois de Bordeaux - France 69 route d’Arcachon 33612 Cestas Cedex [email protected] Prediction of delayed failure of wooden beams is an important problem in timber engineering especially for beams containing stress concentrations (as notches or tapered end-notches or openings). Several models have been developed to provide duration of load (DOL) of timber structures. The damage theory is probably the most employed one to predict the time to failure of wood elements. However, the fracture mechanics approach developed to provide the crack growth can be performed to obtain the time to failure as well. A correct modelling of delayed fracture needs to model two durations: duration before the apparition of the crack (incubation time) and duration of the crack growth, that is the time to reach a critical length [1]. The incubation time may be predicted by a damage approach using a damage model. The second model of Barrett and Foschi [2], with non-linear damage evolution and non-linear cumulative damage, has been chosen (1): ­ ° dD ° dt ® ° dD ° ¯ dt

§ F (t)  F o · ¸¸ a ˜ ¨¨ Fs © ¹

b

0

 O .D(t)

if if

F (t) ! F o

F (t)  F o

(1)

Where F is the applied load, Fs the static strength and Fo a threshold load. a, b and O are parameters depending on the material properties.The Fo and the parameters used in the damage model is calculated from the results of short term tests on notched beams. In this approach, damage appears as a characteristic parameter D ranging from 0 at the beginning of loading to Di at the crack initiation. The critical damage parameter Di is evaluated from stiffness variation finite elements calculations for a crack length equal to 5 mm. The viscoelastic crack model (VCM) used in this study is based on the Schapery theory [3]. The crack grows in an orthotropic viscoelastic medium and a damage area is assumed to exist at the crack tip. This fracture mechanics model introduces a viscoelastic compliance. Mixed mode crack propagation can occur in notched beams. However the model has only been established for the growth of a crack along the grain direction in opening mode. The reduced creep compliance in mode I,

N 22v (t ) can be assumed to be represented by a power law (2): N 22v ( t )

A o  A 2 .t n

Ao, A2 and n are material parameters.

(2)

M. Chaplain and G. Valentin

1196

da The crack velocity isgiven by [4] : dt

with K Ic

ª « C2 S « 2 2 « § « 8* ¨1  K I 2 « ¨© K Ig ¬

º » » ·» ¸» ¸» ¹¼

1/ m

O1m/ m

K I2 (11 / m ) V m I 1 2

(3)

2 G I / A o is the critical stress intensity factor

For finite dimension beams, an expression of the stress intensity factor KI depending on the shape of the beam and of the type of loading and on the elastic stiffness properties of the material is introduced in VCM. It can be obtained by finite element calculations. The duration of load predicted by the model are compared to experimental results of bending tests up to three months on notched Laminated Veneer Lumber beams (LVL). The figure 1 illustrates the evolution of the crack length and of the propagation time obtained experimentally and by simulation under a step by step loading.

FIGURE 1. Step by step loading on LVL notched beams : propagation time (a) - crack evolution (b) : experiments and simulations The predictions of this damage model are compared to the relation proposed by Nielsen [5]. Compared to experiments on notched LVL beams, both models give fair predictions of the time to failure.

References 1.

Chaplain, M., Valentin, G., In Proceeding of the Third international Conference of the ESWM, Villa Real, Portugal, 2004,135-142.

2.

Barrett, J.D., Foschi, R.O., Can. J. Eng. Vol 5,. 505-514, 1978

3.

Schapery, R. A., International Journal of Fracture, vol 11: 141-159, 1975

4.

Valentin, G., Chaplain, M., In Proceeding of the first international Conference of the ESWM, Lausanne, Switzerland, 2001, 243-253

5.

Nielsen, L. F., In Proceeding of the International Workshop on Duration of Load in Lumber and Wood Products, Richmond, Canada, 1985, 67-78

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MODE I CRACK PROPAGATION IN SOFTWOOD, MICROANALYSES AND MODELING P. Navi and M. Sedighi-Gilani Institute of Material Science Ecole polytechnique Federale de Lausanne MX-G Station 12, 1015 Lausanne, Switzerland [email protected] [email protected] A method was developed for microscopic observation of cracks in wood which provides instructive information on crack initiation and crack propagation. This method has been used on softwoods to understand their fracture behavior at cellular level during cracking in mode I and mode II. It has been shown that different mechanisms would be activated depending on the orientation of the growth rings with the plane of fracture. In order to observe clearly crack extend and network of microcracks in the complex microstructure of wood, the cracked part was cut out of the test specimen and impregnated with epoxy resin[1]. A fluorescent dye was added to the resin to give a good contrast during microscopic observation. This resin has high fluidity and penetrates easily into the wood. To prepare the slices for microscopic observations, the impregnated sample containing the crack could be cut at any directions. In RL and TL crack propagations most information can be extracted from perpendicular to the grain direction cuts. A confocal microscope with a 488 nm laser was used for observation. To stop the fracture process of the specimen before complete cracking during test, fracture test has to be conducted with any specimen giving stable crack propagation. Our microscopic observations haven’t showed the classically defined “fracture process zone” as a wide network of micro-cracks was formed in front of the crack. Initial damage that could be observed optically is localized on a few cells and expands until a continuous crack is formed. In this sense a fracture process zone within certain distance along the specimen width could be defined. In typical RL crack propagation, the crack develops through earlywood ring as this is the weakest part of the structure. The first micro-cracking, that has been observed is located along a line and consist both on intercellular separation of cells and intercellular break of cell walls. All micro cracks seems to be located within one or two cells width and no other disperse micro-cracks are observed. When a crack crossing the late wood ring, the crack can be wide open with the block of latewood cells bounded to both sides of the crack making a bridge. Such bridge can transmit forces both in vertical and lateral direction of the crack. In the TL crack propagation the cracking process is quite different. As the late wood ring has a higher modulus of elasticity than the earlywood ring, it supports most of the stress and as the interface between the cells or between the layers S1 and S2 of the cells are the same, the cracks begin into the latewood ring and then traverse the early wood. This is what was usually observed during the microscopic observation. In the case where the crack propagation occurs at angle between TL and RL, either one or the other mechanism typical for TL or RL will dominate. If the angle of the annual ring with crack plane is more than 30 – 40, then the TL mechanism will dominate and the first damage will occur in the latewood. To better understand the role of the micromechanical characteristics of wood and fibers in the wood fracture mechanics a fracture model is being developed. Morphological based models, i.e. lattice model, was used, as comparing to continuum fracture mechanics, it has the capacity to represent the specific features of wood microstructure and predict the damage pattern and force-

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displacement curve of wooden samples[2, 3]. However if lattice is represented in cellular level (each elements as a wood fiber), the computational needs to model the large-scale specimens becomes quite large. As the crack path and fracture process zone prior to crack propagation in wood is approximately predictable, to reduce the computing time and storage requirements, only the neighborhood of fracture process zone was modeled with lattice network. As the first step, to model the fracture propagation, a 3D lattice of beam elements was defined. The beam elements, depends to representing the earlywood or latewood fibers, have different properties and cross sectional area. To consider the effect of bordered pits and non-uniformities of microfibril angle in earlywood fibers[4], each fiber was modeled by three different beam segments with different properties. As the microfibril angle along latewood fiber is approximately uniform, each latewood fiber was modeled by one beam element. Each fiber was connected to its neighbors by diagonal and vertical beam elements representing the bounding between fibers (intercellular layers). The effective properties of lattice are estimated through the behavior of two parts, solid and lattice, by homogenization method. The lattice is placed in fracture process zone of the 3D continuum body which has common nodes in its boundary interfaces with lattice part. Removing the beam elements with limit strain criteria during the loading process shows the crack propagation paths in cellular level of microstructure.

References 1.

Job, L. and P. Navi. Microscopic analysis of crack propagation in softwood, model I and II. in International COST 508 wood mechanics conference. 1996. Stuttgart, Germany.

2.

Landis, E.N., et al., Coupled Experiments and Simulations of Microstructural Damage In Wood. Experimental mechanics, 2002. 42(4): p. 1-6.

3.

VanMier, J.G.M. and M.R.A. VanVliet, Influence of micostructure of concrete on size/scale effects in tensile fracture. Engineering fracture mechanics, 2003. 70: p. 2281-2306.

4.

Sedighi-Gilani, M., H. Sunderland, and P. Navi, Within-fiber nonuniformities of microfibril angle. accepted to be published in Wood and fiber science.

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FRACTURE PROPERTIES OF PINE AND SPRUCE IN MODE I N. Dourado1, S. Morel2, M. F. S. F. de Moura3, G. Valentin2 and J. Morais1 1 CETAV/UTAD, Depart. de Engenharias, Quinta de Prados, 5001-911 Vila Real, Portugal 2 LRBB, UMR 5103 (CNRS/INRA/Univ. Bx1), 69 route d'Arcachon, 33612 Cestas, France 3 Fac. de Engenharia da Universidade do Porto, R. Dr. Roberto Frias, 4200-465, Porto, Portugal [email protected], [email protected], [email protected] The fracture behaviour of a quasibrittle material such as wood, characterized by the development of a large fracture process zone (FPZ), is nowadays well-known to be efficiently described by cohesive crack models. The most common applications of fictitious or cohesive crack models used to simulate nonlinear fracture mechanics of quasibrittle materials are considered as variations [1] of a model proposed by Hillerborg and co-workers [2]. These applications need to introduce a cohesive zone at the crack tip, i.e., a fictitious line crack transmitting normal stress V dependent on the corresponding opening displacement w. Cohesive crack models are typically applied through finite elements calculations. Interface elements or springs [3] with prearranged strain-softening properties are integrated into the structural model along the most probable crack path. Since the pioneering application of cohesive crack models to wood due to Boström [4], a so called bilinear strain-softening model was applied by Stanzl-Tschegg et al. [5] to obtain wood load-deflection curves according to a developed wedge-splitting test protocol. In this study, from Three Point-Bending (TPB) fracture tests inducing a mode I failure in two species of wood: Maritime pine (Pinus pinaster Ait., Lin.) and Norway spruce (picea abies L.), the Load-Deflection curves and the corresponding resistance curves (R-curve) (Lawn, 1993[6]) are estimated, then simulated through FE calculations using a cohesive crack model. In a first step of this study, from the Load-Deflection curves, the corresponding resistance curves are estimated in the framework of ‘equivalent linear elastic fracture mechanics (LEFM)’ in which the increase of the specimen compliance due to the FPZ development is attributed to the propagation of a linearly equivalent elastic crack (Morel, 2005 [7]). On this basis, typical rising R-curve, common among materials that exhibit toughening mechanism, are observed. After a characteristic equivalent crack length ac, the resistance to crack growth becomes independent of the equivalent crack length defining a plateau value of the resistance to crack growth also called critical resistance and noted here as GRC. Note that such a levelling off of the R-curve at longer crack lengths might indicate that the influence of the toughening mechanism is not infinite, especially for wood, where fibre bridging requires sufficient deformation to produce closing force (Smith et al., 2003 [1]). The second step consists on simulating the Load-Deflection curves on the basis of a cohesive crack model. First, the fracture energy GF characterizing the area under the softening function is fixed to the plateau value GRC of the experimental resistance curve, as suggested in (Coureau and Morel, 2004 [8]). We show that this assumption can be easily verified through preliminary simulations. On this basis, a developed Genetic Algorithm is used to estimate the characteristic values of the softening function, such as the break point coordinates (wb, fb), and the tensile strength ft or the critical opening wc (Figure 1), enabling to obtain a good agreement between simulated and experimental Load-Deflection curves (Figure 2). The classical bilinear softening function used in these simulations allows discussing the obtained results in terms of fracture energy associated to microcracking and to fibre bridging. Finally, it is shown that the characteristic values of the bilinear constitutive law estimated for both wood species induce different critical sizes of the softening zones. The implications of these FPZ sizes on the fracture properties of both wood species are discussed.

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FIGURE 1. Bilinear softening model. GRC=Gf1 + Gf2.

(a)

(b)

FIGURE 2. Load - displacement curves (a) Pinus pinaster (b) Picea abies. CCM: Cohesive Crack Model.

References 1.

Smith, I., Landis, E. and Gong, M., Fracture and Fatigue in Wood, John Wiley & Sons, 2003.

2.

Hillerborg, A., Modeer, M. and Petersson, P.E., Cement and Concrete Research vol. 6, 773782, 1976; Hillerborg, A., Int. J. Frac. vol. 51, 95-102, 1991.

3.

de Moura MFSF, Gonçalves JPM, Marques AT, Castro PMST. Modelling compression failure after low velocity impact on laminated composites using interface elements. Journal Composite Materials 1997; 31:1462-79.

4.

Bostrom, L., Method for determination of the softening behaviour of wood and the applicability of a nonlinear fracture mechanics model. Universitatis Gothorum, CODEN: LUTVDG/(TVBM-1012) 1: 132, 1992.

5.

Stanzl-Tschegg, S.E., Tan, D.M. and Tschegg, E.K., Wood Sc. Tech. vol. 29, 31-50, 1995.

6.

Lawn, B.R., Fracture of Brittle Solids, 2nd Ed., Cambridge University Press, 1993.

7.

Morel, S., Dourado, N., Valentin, G. and Morais, J., Int. J. Fract. vol. 131, 385-400, 2005.

8.

Coureau, J.-L., Morel, S., In Proceedings of the Third Conference of the European Society of Wood Mechanics, ESWM2004, Vila Real, Portugal, September 6-8, 2004.

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INFLUENCE OF THE SPECIMEN GEOMETRY ON R-CURVE: NUMERICAL INVESTIGATIONS. Christophe Lespine, Stephane Morel, Jean-Luc Coureau and Gerard Valentin Lab. de Rhéologie du Bois de Bordeaux, UMR 5103 (CNRS/INRA/Univ. Bordeaux. 1) Domaine de l’Hermitage, 69 route d’Arcachon, 33612 Cestas Cedex, France [email protected] During fracture test of quasibrittle materials such as concrete, rocks, or wood, a fracture process zone (FPZ) is observed ahead of the crack tip. Various toughening mechanism take place in this FPZ such as microcracking, crack branching or crack bridging. If Linear Elastic Fracture Mechanics (LEFM) cannot be directly applied to such quasibrittle fractures, an adaptation of LEFM, which consists in considering an equivalent linear elastic problem, provides useful approximations of fracture properties [1,2,3]. Within the framework of ‘equivalent LEFM’, the increase of the specimen compliance due to the FPZ development is attributed to the propagation of an elastically equivalent crack. On this basis, the fracture behaviour of quasibrittle materials is characterised by a more or less pronounced rising resistance curve, briefly called R-curve [4]. For instance, R-curve obtained from a Norway spruce (Picea Abies L.) Double Cantilever Beam (DCB) and two kinds of Tapered DCB (TDCB) specimens extracted from [3] are plotted in Fig. 1. Such rising R-curves are common among materials that exhibit toughening mechanism. In fracture perpendicular to grain of wood, it has been shown that the main toughening mechanism is crack bridging [5,6]. After a characteristic equivalent crack length ac, the resistance to crack growth becomes independent of the equivalent crack length defining a plateau value of the resistance to crack growth also called critical resistance and noted here as GRC.

Fig 1.Experimental R-curves obtained from Norway Spruce DCB, TDCB30 and TDCB60 specimen [3] Several experiments have evidenced that the R-curve behaviour is not an intrinsic material property but appears geometry dependent. As shown in Fig. 1, the dependence on the geometry is usually observed on the critical resistance GRC but also on the crack length ac for which this plateau value is reached. On the other hand, cohesive crack models are nowadays well-known to successfully describe quasibrittle fracture behaviour and especially for wood [7] where crack bridging induces strong toughening.

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In this study, numerical investigations using cohesive crack model implemented in jointelements are used to study the link between specimen geometry and R-curve behaviour. In a previous study [8], it has been suggested that the fracture energy GF characterizing the softening behaviour must equal the crack growth resistance GRC, hence, the fracture energy GF can not be considered as an intrinsic material property, GRC being geometry dependent as shown in Fig. 1. On this basis, we propose to consider the fracture energy GF as GF =GD * eFPZ where GD is a critical damage energy release rate per unit volume of damaged material (i.e. per unit volume of FPZ) and eFPZ corresponds to the width of FPZ which is proportional to the characteristic size of the damaged zone. The critical damage energy GD is assumed to be an intrinsic material property and hence the width of the FPZ eFPZ should be dependent on the specimen geometry. Moreover, from a classical bilinear softening behaviour, we show that the tensile strength of the interface can be considered as an intrinsic material property while the ultimate opening of the interface can be assumed dependent on the width of the FPZ eFPZ. We show that the assumptions concerning the parameters characterizing the softening behaviour allow us to obtain simulated Load-Deflection curves in agreement with those obtained from DCB and the two kinds of TDCB specimens extracted from [3]. Finally the implications of such a softening behaviour on the fracture properties of wood are discussed.

References 1.

Bazant, Z.P., Eng. Fract. Mech. vol. 69, 165-205, 2002.

2.

Morel, S., Dourado, N., Valentin, G. and Morais, J., Int. J Fract. vol.131, 385-400, 2005.

3.

Morel, S., Mourot, G. and Schmittbuhl, J., Int. J. Fract. vol. 121, 23-42, 2003.

4.

Lawn, B.R., Fracture of Brittle Solids, Cambridge University Press, 2nd ed, 1993.

5.

Vasic, S. and Smith, I., Eng. Fract. Mech. vol. 69, 745-760, 2002.

6.

Smith, I., Landis, E. and Gong, M., Fracture and Fatigue in Wood, John Wiley and Sons Ltd, 2003.

7.

Stanzl-Tschegg, S.E., Tan, D.M. and Tschegg, E.K., Wood Sc. Tech. vol. 29, 31-50, 1995.

8.

Coureau, J.L. and Morel, S., In Proceedings of the Third Conference of the European Society of Wood Mechanics, ESWM2004, Vila Real, Portugal, September 6-8, 2004.

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FRACTURE BEHAVIOUR AND CUTTING OF SMALL WOOD SPECIMENS IN RT-DIRECTION S. Koponen and P. Tukiainen Senior Research Scientist, Research Scientist Helsinki University of Technology [email protected], [email protected] Wood is strongly anisotropic and inhomogeneous material. The total number of different fracture propagation systems is 8. Most of the earlier tests in Mode I are performed in LR- or LT-system and only few in RT system. RT crack propagation system is important in rotary peeling of veneer logs, in defibration process, Persson [1], in the case of stresses perpendicular to grain in curved glulam beams, Dill-Langer et al. [2], and in the case of drying stresses, Boström [3], for example. The aim of this work is to study fracture in RT-system, and the main emphasis is in pure Mode I loading, but limited number of cutting tests with knife and razor blade has been performed to understand veneer-manufacturing process. The quality of the veneers depends on the mechanism of the crack propagation in cutting process, the material property variation of wood (density e.g.), moisture content of wood and the temperature of log. Fracture properties and crack propagation under pure Mode I loading of wood in RT crack propagation system are studied. The main test series and theoretical analysis were made for birch hardwood. Limited number of tests for spruce has also been performed. The moisture content (MC) of test pieces was either 14 % or the tests were done using green wood (birch MC=63 %). The oven density Ug based on green volume of tested birch was 525 kg/m3. In tests small specimens were used and the tests were performed with micro-testing device. The size of the specimen was 37.5x36x15mm3 and the use of micro-testing device makes it possible to observe the behaviour of process zone for example under light microscope or in situ tests in the chamber of Environmental Scanning Electron Microscope (ESEM). In these tests the digital camera and light microscope were used. The crack mouth opening (CMOD) displacement was measured using dial gauge, and deformation of the specimen and crack propagation were calculated from digital images using image correlation technique. The specimen size, the characteristic length of the specimen and the ligament length (15 mm) were small compared to the process zone size (1…5 mm). Thus, Linear Elastic Fracture Mechanics (LEFM) is not valid and clear size effect on fracture energy is expected. The analysis is done using Nonlinear Fracture Mechanics (NFM). Fictitious crack model (FCM) and Finite Element Method (FEM) were used in the numerical simulations. The micro cracking and bridging is taken into account using ‘cohesive zone’ with closing stress as a function of crack opening displacement. In this paper the crack mouth opening displacement (CMOD) is the increase of the dimension c at the line between loading bolts (Fig 1.). The initial crack was made with small band saw and razor blade. The initial length of crack, a, is 15 mm. Fig. 1 shows the CT-tests specimen and loaddisplacement curves obtained for wet birch in RT propagation system.

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FIGURE 1. Test specimen (w=30mm, b=14.5 mm, t=15mm, a=15mm, c=6.3mm) and loading curve of wet CT-specimen (RT004, RT006 and RT007). The digital images were used to measure the increase of the distance of lines located at the positions ±c/2 from the symmetry line of the specimen. The increase of this distance is called crack opening displacement (COD) in this paper and it was compared to calculated values. Theoretical stresses were also analyzed and stresses along the ligament are shown in fig. 2.

FIGURE 2. Calculated stress distributions along the ligament (FCM: ft=3N/mm2, Gf=480N/m) The measured fracture energy Gf for wet birch specimen was 697 N/m and it was 850…1100 N/m at 14 % MC. The calculated crack propagation and the opening deformation were in good agreement with test results. The process zone length was 3…4 mm.

References 1.

Dill-Langer, G. and Lütze, S. and Aicher, S., Wood Sci. Technol., vol. 36, 487-499, 2002

2.

Persson, K., Micromechanical modelling of wood and fibre properties, Doctoral thesis, Publ. TVSM-1013, Div. of Struc. Mech., Lund University, Sweden, 2000.

3.

Bostrom, L., Method for Determination of the Softening Behaviour of Wood and the Applicability of a Nonlinear Fracture Mechanics Model, Doctoral thesis, Report TVSM1012, Div. of Struc. Mech., Lund, Sweden, 1992.

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FRACTURING OF WOOD UNDER TORSIONAL LOADING: FRACTURE MECHANISMS AND MECHANICS E. K. Tschegg and S. E. Stanzl-Tschegg Vienna Technical University, Institute of Solid State Physics Karlsplatz 13, A-1040 Vienna, Austria BOKU, University of Natural Resources and Applied Life Sciences, Institute of Physics and Materials Science Peter-Jordan Strasse 82, A-1190 Vienna, Austria [email protected], [email protected] Damage of wood under mechanical loading is mostly induced by some kind of mixed mode loading, like for example, superposition of a crack opening mode (mode I) plus torsional load (mode III). In addition, the high anisotropy of wood itself, with directions and paths for easy crack propagation in the neighbourhood of areas with high crack resistance, leads to a mixed-mode loading condition. In order to characterize superimposed loading, systematic studies have been performed of loading under pure mode I, and it was tried, to also realise pure mode II or mode III testing conditions. It could be shown, however, that sliding modes cannot be realized in practice without any mode I component being present, as fracture surface roughness, causes crack tip opening. Therefore, Ehart et al. >1@ and Frühmann et al. >2@ have performed studies on this fracture surface interaction and resulting mixed mode fracture, as well as on damage and fracture mechanisms during nominal mode III loading of wood and wood composites. In addition, a testing technique has been developed >3@ to perform mixed mode (mode I plus II) fracture experiments, with different defined mode II and, respectively, mode I components. The characterization of fracture of wood as a highly anisotropic material was concentrated on concepts of linear elastic fracture mechanics (LEFM) mostly in the past, before Schniewind and Pozniak >4@, Aicher and Reinhardt >5@, Boatright and Garrett >6@, Holmberg et al. >7@ and Tschegg et al. >8@, among others, introduced and used non-linear elastic fracture mechanics parameters, like the fracture energy as a characterizing parameter. To obtain this, complete load-displacement diagrams have to be detected, which is made possible by testing procedures that allow stable crack propagation during the whole experiment, until final fracturing takes place. As a useful technique, the wedge splitting technique has been developed >9@. This technique has been further developed to perform superimposed mode I plus mode II load experiments >3@, and investigations by systematically varying the portions of mode II and I, respectively, demonstrated that the contributions are not additive, but coupled >10@. To the authors´ knowledge, no systematic experimental investigations exist on superposition of mode III and mode I loading on wood. As has been pointed out by Ehart et al. >1@ and Frühmann et al. >2@, remarkable portions of crack opening forces and thus mode I loads are present under nominal mode III loading owing to sliding and friction of the already formed fracture surfaces. As a consequence, in a new study, experiments were performed by varying the tension (mode I) and torsion (mode III) components and detecting the resulting load-displacement curves. The influence of mode III and mode I can be studied separately, as they can be changed independently with the used tension-torsion machine. With this, wood of spruce and beech was tested with a special testing set-up in different orientations. Load-displacement diagrams have been recorded, which allow to determine the specific fracture energy and other characteristic values, like maximum load and stress intensity or initial slope of the load-displacement diagram, which characterizes the material stiffness. The results allow discussing the different mechanisms of

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cracking and demonstrate the importance of quantifying the components of mode III and mode I in order to better understand their influence on damage of wood. Fracture mechanical values, as well as fractographic features strongly depend on wood species, its structure and orientation, as well as its humidity and other influencing parameters.

References 1.

R.J.A. Ehart, S.E. Stanzl-Tschegg and E.K. Tschegg, Eng. Fracture Mechanics 61 (1998) 253-278

2.

K. Fruhmann, A. Reiterer, E.K. Tschegg and S.E. Stanzl-Tschegg, Phil. Mag. A, Vol. 82 (2002) 3289-3298

3.

E.K. Tschegg and S.E. Stanzl-Tschegg, Patent No. AT 409.038, 7.2.2002

4.

A.P. Schniewind and R.A. Pozniak, Eng. Fracture Mechanics 2 (1971) 223

5.

S.W. Boatright and G.G. Garrett, J. Mat. Science 18 (1983) 2181

6.

S. Aicher and H.W. Reinhardt, Holz als Roh- und Werkstoff 51 (1993) 215

7.

S. Holmberg, K. Persson and H. Petersson, Comp. Struct. 72 (1999) 459

8.

S.E. Stanzl-Tschegg, D.M. Tan and E.K. Tschegg, Wood Sci. and Technology 29 (1995) 3150

9.

E.K. Tschegg, Patent No. AT 233/96, 390 328, 1986

10. E.K. Tschegg, A. Reiterer, T. Pleschberger and S.E. Stanzl-Tschegg, J. of Materials Science 36 (2001) 3531-3537

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ON THE INFLUENCE OF HUMIDITY CYCLING ON FRACTURE PROPERTIES OF WOOD S. Vasic and S. Tschegg Marie Curie EU Fellow, Professor Institute for physics and materials science, BOKU University, Peter Jordan Strasse 82, 1190 Vienna, Austria [email protected] [email protected] The importance of environmental effects on the wood structural performance has been known for ages, moisture being the most pronounced degradative effect that needs to be taken into account at different levels of wooden structures durability. Moisture content has an effect on many mechanical properties bellow the fibre saturation point, with the increase in the property with the decrease in moisture content. In-service, wood is exposed to both long-term (seasonal) and short-term (daily) changes in the relative humidity and temperature. These changes are usually gradual, and short-term fluctuations tend to influence only the wood surface in large cross-section wooden components. It is a common wood technology practice to have the drying targeted moisture content as close as possible to the one wood will experience in the in-service conditions. This minimizes the seasonal variation in moisture content and the dimensional changes after the installation, avoiding the problems such as permanent deformations and cracking. However, this strategy has its limits, and it was deemed necessary to perform the fracture mechanics study on the influence of humidity cycling on the fracture properties. The results of the experimental and numerical investigations are reported herein. Four different wood species were chosen for this study, namely spruce, pine, oak and beech, all cut in green state in the Lower Austria. The specimens prepared for opening mode I tests were conditioned from the green state to the relative humidity of 65 percent, at 20oC. The wood samples were then subjected to varying humidity 30-70 percent and for the harsher environment 40-90 percent relative humidity. The number of humidity cycles was a variable, ranging from 1 to 5 to 10 cycles. The length of a humidity cycle was chosen to be 1 week, which was considered sufficient for small fracture specimens to reach equilibrium through each cycle, resulting in steady-state moisture conditions. In order to investigate the physical mechanisms of woods fracture when different humidity cycles are imposed, in-situ real-time Environmental Scanning Electron Microscope (ESEM) experiments were performed. For this purpose, wedge-splitting loading stage has been built to enable specimen loading and fracture propagation observations at the same time (Fig. 1, Frühmann et al. [1]). The in-situ real-time ESEM experiments enable evaluation of complete stable loaddeformation curves, from which it is possible to derive common fracture mechanics properties.

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FIGURE 1. Schematics of wedge-splitting loading set-up in ESEM Fracture toughness is obtained using Finite Element Method with the orthotropic material model, while total fracture energy and specific fracture energy can be obtained directly form the load-deformation curves. Different physical mechanisms of fracture initiation and propagation were evidenced depending on the magnitude of humidity, the number of cycles and wood species. This implies the interplay of the effect of moisture content and its history with the wood ultrastructure. Also, fracture parameters such as fracture toughness, total fracture energy and the specific fracture energy were affected by the humidity conditions and the wood species. In softwoods, bridging of fibres behind the crack tip was evidenced as the main toughening mechanism, similar to previous findings (Vasic and Smith [2]). The number of humidity cycles tends to decrease the fracture parameters such as fracture toughness and fracture energy, implying the development of damage through the humidity cycling. Numerical modeling of the moisture transfer was performed using the commercial code Abaqus 6.2 [3]. The moisture transfer analysis was coupled to stress analysis of the wooden specimens, with the adjustment of elastic properties depending on the moisture content and wood species and their anisotropy. The numerical analysis resulted in the computation of stress intensity factors employing the quarter-point Barsoum finite elements. It was shown that the obtained numerical values correlate well with the experimental data. Further numerical efforts will concentrate on incorporating the moisture transfer analysis into lattice fracture finite element model, in order to simulate complete load-deformation curves and damage patterns throughout the crack propagation process.

References 1.

Fruhmann, K., Burgert I., Stanzl-Tschegg S.E., Tschegg E.K., Mode I Fracture Behaviour on the Growth Ring Scale and Cellular Level of Spruce (Picea abies [L] Karst.) and Beech (Fagus sylvatica L.) Loaded in the TR Crack Propagation System, Holzforschung, 57, 653660, 2003

2.

Vasic S., Smith I., Bridging Crack Model for Fracture of Spruce, Engineering Fracture Mechanics, Vol. 69, 745-760, 2002

3.

ABAQUS/CAE, User’s Manual, Version 6.2, Hibbit, Karlsson & Sorensen, Inc. 2001

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DETERMINATION OF COHESIVE FRACTURE PARAMETERS FOR WOOD T. Astrup1, J. F. Olesen1, L. Damkilde2 and P. Hoffmeyer1 1 Department of Civil Engineering, Technical University of Denmark, Denmark 2Esbjerg Institute of Technology, Aalborg University, Denmark [email protected], [email protected], [email protected], [email protected] The application of non-linear fracture mechanics to wood is a relatively new topic in the area of wood science, however, linear elastic fracture mechanics (LEFM) was first applied to wood in the nineteen sixties. The fracture propagation in wood is mainly governed by two aspects, namely the direction of the principal stresses, and the microstructure. There are six principal crack propagation systems in wood, which are illustrated in Fig 2, see eg. Smith et al. [1] or Reiterer and Tschegg [2]. The usual presumption is that wood is perfectly brittle–elastic (LEFM). When a crack propagates perpendicular to grain, the observed fracture behaviour is quasi-brittle, i.e. a tensile softening branch exists [2]. This indicates that a fracture process zone of some length exists. The LEFM approach is not an adequate approximation if the specimen size is of the same order of magnitude as the length of fracture process zone.

FIGURE 1. Wedge splitting test. Specimen and experimental setup. From [6] In recent years this quasi-brittle fracture behaviour has been studied by e.g. Reiterer and Tschegg [2] ,Stefansson [3] ,Gustafson [4] and several references given in [1]. In this paper the quasi-brittle fracture behaviour of Norway spruce (picea abies) is studied. The wedge splitting test (WST), shown in Fig. 1 and further described by Rossi et al. [5] is used to produce stable crack growth, i.e. to obtain a softening branch, as shown in Fig. 3. The inverse analysis, as described by Østergaard [6], is performed in order to determine the stress-crack opening relationship from the global load-crack mouth opening displacement curve (CMOD curve), i.e. the softening behaviour. Several different test specimens conditioned at varying climates are used, in order to investigate the influence of moisture content on the fracture behaviour. Similar tests have been performed by Reiterer and Tschegg [2]. However, only the fracture energy and the relationship between the load and CMOD were presented, whereas the softening behaviour in terms of the stress-crack opening relationship was not extracted.

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FIGURE 2. Principal crack propagation systems of wood. From [2].

FIGURE 3. Typical load–CMOD curves for crack propagation perpendicular to grain. From [2].

The stress-crack opening relationship can be used to model crack propagation e.g. in endnotched beams or around mechanical joints.

References 1.

Smith, I., Landis, E. and Gong, M., Fracture and Fatigue in Wood, WILEY, England, 2003.

2.

Reiterer, A. and Tschegg, S., Journal of Materials Science, vol. 37, 4487-4491, 2002

3.

Stefansson, F., Fracture Analysis of Orthotropic Beams, Lund University., Licentiate Dissertation, 2001.

4.

Gustafsson, P.J., Fracture Perpendicular to Grain – Structural Applications, in Thelanderson, S. and Larsen, H. J., Timber Engineering, WILEY, England, 2002

5.

Rossi, P., Brühwiler, E., Chhuy, S., Jenq, Y.-S. & Shah, S. P., Fracture properties of concrete as determined by means of wedge splitting tests and tapered double cantilever beam tests, in S. Shah & A. Carpinteri, eds, `Fracture Mechanics Test Methods for Concrete', Chapmann & Hall, 1991

6.

Østergaard, L., Early-Age Fracture Mechanics and Cracking of Concrete, Technical University of Denmark, Ph.D Thesis, 2003

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THE ROLE OF FRACTURE TOUGHNESS IN THE CUTTING OF WOOD T. Atkins Department of Engineering, University of Reading, Reading, RG6 6AY, England [email protected] When chips in wood cutting are formed by through thickness shear along a major shear plane emanating from the tip of the tool to the free surface of the timber, the Ernst-Merchant theory (e.g. Ernst and Merchant, 1944), originally propounded for continuous-chip cutting in ductile metals, is often employed for analysis of wood cutting forces. The original rigid-plastic theory considers that the forces in cutting are determined by two work components, viz: (i) work required permanently to deform the chip and (ii) work against friction. Despite all the improvements to the basic ErnstMerchant model (secondary shear giving chip curl, the effect of work hardening, temperature and rate effects, and so on) and improved modelling of friction, it remains a fact that such algebraic analyses are not able to predict some well-established features of the mechanics of cutting. For example, the theory predicts that the primary shear plane angle is independent of the metal being cut whereas experiments show that the angles vary not only with friction but also with the metal and mechanical properties. Again, when experimental cutting forces are plotted against the uncut chip thickness (depth of cut), there is invariably a positive force intercept at zero uncut chip thickness: the theory predicts that force vs uncut chip thickness plots should pass through the origin of coordinates. The same experimental facts, not agreeing with the theory, are also found when cutting other materials such as plastics and wood. An explanation, for the failure of all algebraic theories of cutting that employ plasticity and friction only in the modelling, was given by Atkins (2003). Shortcomings of the old theory have been largely removed. The improved model has been assessed against experimental data for various materials, and has also been employed to consider discontinuous chip formation and tear (split) chip formation, Atkins (2004a,b). The new model also explains why, in FEM simulations of cutting, the tool will not move appreciably unless an additional criterion (a so-called separation criterion) is invoked at the tip of the tool. (The same FEM codes are quite able to simulate other metal forming processes such as forging, extrusion etc, without the additional criterion). The key to the re-examination is the inclusion of significant work of surface separation in the algebraic model as well as the usual components of plasticity and friction. Inclusion of fracture toughnesses at the kJ/m2 level typical of ductile metals, contrasts with the analysis by Shaw and co-workers (Cook et al, 1954) which used ‘surface free energy’ values of a few J/m2, from which study it was concluded that the work of creating new surfaces in cutting would be insignificant, which has been the received wisdom ever since. But inspection of FEM simulations revealed that the specific energy associated with separation criteria were at the kJ/m2 levels typical of the fracture toughnesses of ductile metals. The new theory has been able to resolve the question why, if a separation criterion is essential to FEM simulations of metalcutting, is it not required in ErnstMerchant type algebraic models. The present paper applies the new analysis to experiments on 30 mm diameter beech, oak and Douglas fir cylinders. The samples were cut both along, and across, the axes of the cylinders in order to investigate anisotropy. The tool employed had a small rake angle so that chips were formed by shear so that the modified Ernst-merchant model was appropriate for analysis. (Note

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that the model is inappropriate for those types of tools having large positive rake angles as employed in the production of veneer. Veneer sheets are removed by a bending and splitting action rather than by shear through the thickness to the free surface, Wyeth & Atkins, 2005). For both beech and oak, fracture toughnesses of some 4 kJ/m2 were determined for cutting in the axial direction and some 2 kJ/m2 in the radial direction. For Douglas fir, the corresponding toughnesses were 7kJ/m2 and 0.2 kJ/m2. The relationship between these average values and the cyclicallychanging grain structure as the cylindrical testpieces are cut, and the appearance of the cut surfaces, is discussed.

References 1.

A G Atkins “Modelling Metal Cutting using Modern Ductile fracture mechanics: Quantitative Explanations for some Longstanding Problems” Int J Mech Sci 2003 45 373-396

2.

A G Atkins “Rosenhain and Sturney Revisited: the ‘Tear’ Chip in Cutting” Proc I MechE Part C (J Mech Engr Sci) 2004a 1181-94

3.

A G Atkins “Toughness and Cutting: a New Way of Simultaneously Determining Ductile Fracture Toughness and Strength” Engr Fract Mech 2004b

4.

N H Cook, I Finnie and M C Shaw Discontinuous Chip Formation Trans ASME 1954 76 15362

5.

M E Merchant Basic mechanics of the metal Cutting Process J Appl Mech 1944 11 A168-75

6.

V Piispannnen Eripaines Teknillisesla Aikakauslehdesla 1937 27 315-22 (see also J App Phys 1948 19 876-95)

7.

D J Wyeth and A G Atkins “Cutting Forces for Wood Determined on an Instrumented Sledge Microtome” Proc COST Action E35 University of Technology, Laapeentranta, Finland 2005

28. Short Fatigue Crack Growth under Multi-axial Loading Conditions

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SHORT FATIGUE CRACKS OF IN-SERVICE FATIGUED TURBINE BLADES A. A. Shanyavskiy, M. A. Artamonov, A. L. Tushentsov and Yu. A. Potapenko State Centre for Safety Flight of Civil Aviation, Moscow, Russia 124340, Moscow, Airport Sheremetievo, P.O. Box 54, SCSFCA [email protected] It will be discussed features of the in-service short crack growth (SCG) through the foil base of the turbine blades manufactured from the superalloy GS6K, Fig.1. There were several cases of inflight fatigue failures turbine blades at the airplane have flown (500-1500) hours. The blade frequency during flight under the biaxial cyclic loads of bending-torsion is approx. 4 kHz. So, the material in-flight fatigue failure took place in VHCF (very-high-cycle-fatigue) area – (4000x3600x[500-1500]) = (0.7-2.0) x1010 cycles. There was during flight temperature neat to the 5000C around the blade volume where the fatigue fracture process was performed. The paper reviewed cases studied of the blade fatigue failures and discussed the SCG rate in a number of flights. The short and long crack growth rates dependences on the crack length were joined, Fig.2. The stress equivalent for the crack resistance in VCHF area was also calculated on the basis of the well-known Murakami’s equation.

FIGURE 1. Overview of the origin area of in-service fatigued turbine blade at the number of 2x1010 cycles.

FIGURE 2. Spacing of the meso-line, h, and number of cycles, Np, of the short (less than 1mm) and long crack growth against the crack length, cr, in the right hand of the origin.

28. Short Fatigue Crack Growth under Multi-axial Loading Conditions

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SHORT CRACK GROWTH UNDER CYCLIC TORSION WITH STATIC TENSION Isao Ohkawa1, Shun Hirano2, Toyokazu Negishi2 and Masaaki Misumi3 1Department of Mechanical Engineering, Faculty of Engineering, Hosei University 3-7-2 Kajino-cho, Koganei, Tokyo, Japan 184-8584 2Division of Engineering, Graduate School, Hosei University 3Department of Electrical and Mechanical Engineering, Faculty of Science and Technology, Seikei University [email protected] The superposition of static loading on cyclic torsion has been recognized to affect the crack growth behavior and fatigue life of materials, due to the mean stress acting on the crack planes. However, the effect of static loading on torsional fatigue is different depending on the material type. This appears to be related to the difference in microstructure and cyclic hardening/softening characteristics of the materials. This paper presents the results of an extensive experimental study on the effect of static tension on short crack growth and fatigue life under torsional loading. Load- and stress-controlled tests were performed at room temperature in an intermediate cycle regime on smooth tubular specimens of four different materials, structural carbon steel S45C, carbon steel for pressure vessels SGV410, austenitic stainless steel SUS316NG and aluminum alloy A6N01. In the stress-controlled test, load and torque were corrected intermittently taking account of the influence of cyclic ratcheting. The distribution of microcracks and development of dominant crack were observed in details. Furthermore, stable cyclic shear stress-strain response and cyclic ratcheting strain were measured under various tensile loading conditions. Majority of microcracks initiated in the vicinity of the maximum shear stress amplitude planes rather than the planes of the maximum shear stress, irrespective of the materials and stress conditions.However, growth behavior of the dominant crack was different depending on the microstructure and existence of the static tension. In S45C steel having banded ferrite and pearlite microstructure along the specimen axes, the dominant crack in pure torsion grew accompanying the coalescence of many shear microcracks in axial direction and branched along the principal stress planes. Cycle ratio at the branching was 0.5 to 0.8. For application of static tension, the crack tends to grow in circumferential direction due to mean tensile stress acting on the crack plane. SGV410 steel also has banded ferrite and pearlite microstructure but distances between the bands on the surface vary continuously along the circumferential direction.The shear crack in pure torsion developed along the axial direction. However, with superposition of static tension, the cracks around the region with wide spacing between the bands joined together and grew preferentially in circumferential direction. The crack branching occurs in a later stage of the life and thus majority of the life is spent for shear crack growth. In SUS316NG stainless steel, dominant crack developed along axial or circumferential direction for pure torsion, while grew only in the latter direction with application of tension. Except for lower stress levels, the shear crack growth occupies more than 90% of the life. For A6N01 aluminum alloy, a few cracks grew only in circumferential direction, irrespective of tensile stress levels. The cracks initiated later than half life and branched close to final failure. For S45C, SGV410 and SUS316 steels, a marked influence of the microstructure on the crack growth rate, alternating deceleration and acceleration, was observed in the region up to about 300 m in length but no significant deceleration was revealed in A6N01 alloy.

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I. Ohkawa et al.

Although a little effect of static tension on fatigue life was revealed in S45C, the lifetime of SGV410 and A6N01 reduced evidently than in pure torsion. On the contrary, addition of static tension increased the torsional fatigue life of SUS316. The difference in effect of static tension appears to be related to deformation behavior of the materials. While cyclic stress-strain relation in SGV410 and A6N01 remained unchanged with superposition of tension, plastic shear strain in S45C and SUS316NG reduced due to an additional hardening. Although mean tensile stress acting on the crack planes promotes the crack growth, the additional hardening can reduce the mean stress effect. Based on an empirical small crack growth law proposed by Hobson and Brown, a model which can express the difference in effect of static tension on torsional fatigue of the materials was investigated. Crack growth rate was assumed to vary as a power function of equivalent stresses incorporating the effect of mean tensile stress on Mode and growth planes. Regarding decrease of the plastic shear strain as a measure of hardening with superposition of tension, effect of the additional hardening was taken into consideration. For load-controlled tests, effect of stress increase induced by cyclic ratcheting was incorporated in the model. It has shown that the model can explain the influence of static tension on the crack growth and the lifetime in torsional fatigue of the present materials.

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RESISTANCE-CURVE METHOD FOR PREDICTING FATIGUE THRESHOLDS UNDER COMBINED LOADING Keisuke Tanaka, Yoshiaki Akiniwa and Masami Wakita Department of Mechanical Engineering, Nagoya University, Nagoya 464-8603, Japan [email protected] The fatigue threshold of materials with small defects or sharp notches is not controlled by the nucleation of fatigue cracks, but by its propagation. After nucleation, the fatigue crack first decelerates and then stops when the applied stress amplitude is below the fatigue threshold. Tanaka et al have shown that the development of crack closure with crack extension is primarily responsible for crack deceleration and stoppage. They have proposed the R-curve method for predicting the fatigue thresholds of notched components and have shown a good agreement with the experimental results for uniaxial loading cases. In this paper, this method is applied to the fatigue thresholds under combined loading. The effective stress intensity factor range, Keffth, at the crack stoppage takes a constant value irrespective of the notch geometry or stress amplitudes. The threshold value of the maximum stress intensity factor, Kmaxth, is defined by K m a x th

' K e ffth  K op th

(1)

where Kopth is the stress intensity factor at the crack-tip opening at the threshold. The value of Keffth is a material constant independent of the defect geometry. Once the change of Kmaxth with crack extension is known, the fatigue limit and the nonpropagating crack length can be determined on the basis of the R-curve method. The R-curve method is illustrated in Fig. 1, where the Kmax value is taken as the ordinate. The R-curve is drawn with the solid line and the applied Kmax value at a constant stress amplitude with the dashed lines. The fatigue thrreshold for crack initiation, w1, is the stress amplitude corresponding to the applied Kmax value equal to the Keffth at the Stage I crack length c1. The fatigue threshold for fracture, w2, is the stress amplitude where the applied Kmax curve is the tangent of the R-curve. At stress amplitudes between w1 and w2, the length of nonpropagating cracks is determined as the intersection of two curves. The effect of the stress multi-axiality on the fatigue threshold may be evaluated simply by changing the applied Kmax curve, because nonpropagating cracks are mode I crack in Stage II even under combined loading. Thin-walled tubular specimens made of a medium-carbon steels (JIS S45C) with a hole of 0.2 mm diameter were fatigued under cyclic torsion (case A), cyclic torsion superposed on in-phase cyclic tension compression (case B), and cyclic tension compression (case D). The stress ratio was R = -1 for all cases. The stress intensity factor for a crack from hole in the biaxial stress filed was calculated by the boundary element method. The change of Kopth ( MPa m ) with crack length cnp (m) for S45C is expressed by K o p th

9 8 .8

K o p th

K opthf

c n p  c1

where c2 is the crack length at K op th

fo r

c1 d c n p d c 2

(2)

fo r

c 2 d c np

(3)

K o pth f , c1 is given by

K. Tanaka et al.

1218

c1

and K m ax th f

 ' K e ff th

2 .9 4 M P a

1 .1 2 2 V

w0

2 S

m , ' K effth

(4)

2 .9 4 M P a

m and V

w0

22 3M P a .

Figure 2 shows the prediction of the fatigue thresholds under combined loading of cyclic torsion and tension-compression, where the dotted and solid lines indicate the fatigue thresholds for crack initiation and for fracture, respectively. The experimental data obtained for cases A, C and D agree fairly well with the prediction. The length of the nonpropagating cracks predicted also agree with the value observed experimentally.

Fig. 1. Resistance-curve method.

Fig. 2. Fatigue threshold under combined loading.

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THE GROWTH OF SHORT CRACKS FROM DEFECTS UNDER MULTI-AXIAL LOADING M. Endo and A. J. McEvily Dept. of Mech. Engng., Fukuoka Univ., Fukuoka 814-0180, Japan, [email protected] Dept. Mats. Sci. and Engng. and Inst. Mats. Sci, Univ. of Connecticut, Storrs, CT, USA [email protected] Multi-axially loaded components may contain defects which under cyclic loading can facilitate the initiation of fatigue cracks. This paper describes a means for predicting the threshold levels and the fatigue lifetimes of such components. The basic equation used in the analysis is (McEvily et al. [1]): da dN

A ' K eff  ' K effth

2

(1)

where a is the fatigue crack length, N is the number of cycles, A is a material constant, 'Keff is the effective range of the stress intensity factor, and 'Keffth is the effective range at the threshold level. In order to make use of this relationship in the short crack range, three modifications are needed. These are: (1) a modification to take into account the elastic-plastic behavior of short cracks, (2) consideration of the Kitagawa effect, and (3) a modification for crack closure development from zero up to the macroscopic level as a newly developed crack extends. With these modifications the stress intensity factor for a Mode I crack is expressed as da dN

A

>

2 S re F  Y



S aF ' V  (1  e  O k )( K op max  K min )  ' K effth

@

2

(2)

where re is a material constant of the order of 1 Pm, F is an elastic-plastic correction term equal to

SV max 1 (1  sec ) , Vmax is the maximum stress in a loading cycle, VY is the yield stress, Y 2 2V Y is a shape factor, equal to 0.73 for a semi-circular surface crack, k is a material constant, O is the length of a newly formed crack, Kopmax is the crack opening level for a macroscopic crack, and Kmin is the minimum stress intensity factor in a loading cycle. Equation 2 is modified for the cases of torsion and equi-biaxial loading. It is assumed that under biaxial loading fatigue cracks grow from defects as Mode I cracks. On this basis it is possible to predict the fatigue strength of part containing surface defects for various multi-axial loading conditions. F

Fatigue tests were carried out under in-phase combined tension and torsion loading at R of -1. Materials tested were an annealed 0.37 % carbon steel with VY of 328 MPa and a heat-treated CrMo low alloy steel with VY of 851 MPa. To simulate a small defect, an artificial small defect was introduced into the surface of bar specimens. Geometries of specimen and defects are shown in Fig. 1. Both the major axes of in-line holes and the crack faces were perpendicular to the maximum principal stress. A servo-hydraulic combined tension and torsion testing machine was used at operating speed of 30-50 Hz. A relationship between the initial defect size, a0, and number of cycles to failure, Nf, as a function of stress amplitude was obtained by integrating Eq. 2 between the limits a0 and the final crack length, af, with the value of af taken to be 5 mm. Figure 2 shows the S-N curves, in which a comparison of calculated results (solid lines) and experimental data is made. The initial size of

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M. Endo and A. J. McEvily

holes was converted into the depth, a0, of an equivalent semi-circular crack by use of the relation: a0 = 2 / S area (Murakami [2]). The principal stress ratio, V3/V1, is 0 for tension, -1 for torsion and -0.382 for combined tension and torsion with the same stress amplitude. It is seen in Fig. 2 that the finite life and the fatigue limit stress are well predicted. It is noted that at the same value of a0, the influence of load types is greater for annealed steel with a low yield stress than for the heat-treated steel with a high yield stress. In this paper, crack growth curves and design charts of fatigue strength are given. Experimental data obtained using cruciform specimens, which include crack growth data for biaxial tension, are also investigated.

FIGURE 1. Shapes and dimensions of specimen and defects.

FIGURE 2. S-N curves.

References 1.

McEvily, A. J., Eifler, D. and Macherauch, E., Engng Fract Mech, vol. 40, 571-584, 1991.

2.

Murakami, Y., Metal Fatigue: Effects of Small Defects and Nonmetallic Inclusions, Elsevier, Oxford, 2002.

28. Short Fatigue Crack Growth under Multi-axial Loading Conditions

1221

SHORT FATIGUE CRACKS IN NOTCHED AND UNNOTCHED SPECIMENS UNDER NON-PROPORTIONAL LOADING Olaf Hertel1, Timm Seeger1, Michael Vormwald1, Ralph Doring2 and Jens Hoffmeyer3 1Technische Universität Darmstadt, Fachgebiet Werkstoffmechanik Petersenstraße 12, D-64287 Darmstadt, Germany 2IAMT mbH, Morgenbergstr. 19, D-08525 Plauen, Germany 3Volkswagen AG, D-38436 Wolfsburg, Germany [email protected], [email protected], [email protected], [email protected], [email protected] A dominant part of fatigue life is spent in short crack growth. Modelling this process using fracture mechanics based methods has led to both increased insight into fatigue and improved prediction accuracy. A short crack growth model for the prediction of constant amplitude fatigue life to technical crack initiation under multiaxial nonproportional loading has been proposed by Döring et. al. [1]. Here, results of further work are presented which are intended to improve and extend the mentioned short crack model. The model is based on the integration of a Paris type crack growth equation expressed in terms of the effective range of the cyclic J-integral 'J eff . The basis for using this approach is the information on the complete local stress and strain histories at the critical location. These histories are calculated applying a plasticity model also developed by Döring et. al. [2]. This plasticity model allows for a realistic description of cyclic hardening and softening, Ratchetting, mean stress relaxation and also nonproportional hardening. A very important aspect is crack closure, which is taken into account. Sound estimates on the crack opening behaviour are fundamental for predicting realistic crack growth rates and fatigue lives. According to [1] an extended Newman formula [3] is used, applicable for multiaxial nonproportional loading. Additionally to Mode I crack closure, Mode II crack closure is taken into account to obtain effective shear stress and shear strain ranges considering roughness of crack surfaces in combination with normal stress dependent shielding effects. Modelling of short crack growth follows the critical plane concept, where the angle of the critical plane is determined by the criterion of maximum crack growth rate and minimum fatigue life, respectively. In [1] the influence of microstructure and stage I crack growth is mirrored only in a starter crack length a0, which is determined by backward integration of the crack growth law (based on

'J eff ) from uniaxial experimental fatigue life data. The starter crack length a0 is substituted by an intrinsic crack length ã0 of the same dimension (26µm steel S460N, 36µm Al5083). Introducing an intrinsic crack length in spite of a starter crack length, the damage variable (e.g. crack length) now starts at zero. Therefore, measured crack growth curves are described more precisely, except for the rare cases of broken inclusions, where real starter cracks can be found. Crack coalescence as well as environmental influences on crack growth are not considered within the framework of the short crack model. The short crack model [1] is based on the assumption of a semi-circular surface crack growing with constant shape in a homogenous stress field. Within the current work the model is extended to

O. Hertel et al.

1222

semi-elliptical surface crack with variable shape in linearly varying stress fields. Therefore, the size effect of notches according to stress gradients can be taken into account. A satisfying accuracy of calculated fatigue lives is achieved. This is verified by experimental data (Hoffmeyer et. al. [4]) for notched shafts and unnotched hollow tube specimen of two different materials (S460N, Al5083) under a variety of multiaxial nonproportional loading sequences. The correlation between the perception as stated in the model and real damage evolution is shown comparing calculated and experimentally determined short crack growth curves and initiation angels, measured with a replica technique (Fig. 1).

n=17011

n=21507

n=26007

FIGURE 1. REM pictures of a short crack taken by replica technique (Al5083, 90° out-of-phase loading, Ja=0.4%, Ha=0.231%).

References 1.

Doring, R., Hoffmeyer, J., Seeger, T. and Vormwald, M., In Proceedings of the Seventh International Conference on Biaxial/Multiaxial Fatigue and Fracture, DVM, Berlin, 2004, 253-258.

2.

Doring, R., Hoffmeyer, J., Vormwald, M. and Seeger, T., Comp. Mat. Sci., vol. 28, 587-596, 2004.

3.

Newman, J.C., Int. J. Fract., vol. 24, R131-R135, 1984.

4.

Hoffmeyer, J., Döring, R., Seeger, T. and Vormwald, M., In Proceedings of the Seventh International Conference on Biaxial/Multiaxial Fatigue and Fracture, DVM, Berlin, 2004, 223-228.

28. Short Fatigue Crack Growth under Multi-axial Loading Conditions

1223

MICROCRACKS GROWTH IN PUSH-PULL AND REVERSED TORSION IN STAINLESS STEEL. V. Doquet and G. Bertolino Laboratory of Solids Mechanics. CNRS. Ecole Polytechnique. 91128 Palaiseau cedex. France [email protected] In many metals, like stainless steel, the arrest of Stage I cracks on grain boundaries (G.Bs.) determines the endurance limit. The mechanisms of crack growth beyond a grain boundary in a globally elastic polycrystal have thus to be understood and properly modelled. In most models, the resistance of a GB to crack growth is considered overcome as soon as plasticity has been activated in the next grain, which leads to a critical resolved shear stress criterion on a potential dislocation source ahead of the blocked slip band. Either this condition is fulfilled and the crack is considered to grow immediately into the next grain or it is not and the crack is considered arrested once and for all. However, microcracks are often observed to stay arrested for a large number of cycles at GBs and then resume propagation (see below). This suggests that crack growth beyond a GB requires an incubation period after the activation of a slip system, during which a microcrack could initiate in the next grain, due to local cyclic plasticity and link with the arrested one, thus allowing further propagation. Such an incubation period was modelled by Morris et al [1] and the present authors [2]. In both cases, it was evaluated from the resolved shear stress on a potential slip system in the next grain. However, the comparison of arrest periods at GBs in push-pull and reversed torsion reported below suggest that it should rather depend on a combination of shear and opening stress on this slip system. Stress-controlled push-pull and reversed torsion tests were performed on 316LN steel specimens in the high-cycle range (2.105 to 2.106 cycles). The tests were periodically interrupted for preparation of replicas, which allowed tracing back of microcracks development (Fig.1). Microcracks initiated early (in some cases, the main crack was already present at 15% of the fatigue life) and propagated along slip bands over 1 to 5 grains, depending on the stress range and loading mode: longer Stage I cracks were observed for smaller stress ranges and push-pull led to earlier transition to stage II than reversed torsion for equivalent stress ranges. Stage I transgranular crack growth rates were less than 10 Burgers vectors/cycle and showed no clear correlation with the stress range or loading mode. Microcracks were frequently arrested for tens to hundreds thousands cycles at grain boundaries and then resumed propagation. The smaller the applied stress range, the longer the arrest periods (Fig. 2). The scatter in arrest periods increased as the stress range decreased. In reversed torsion under r260MPa Tresca equivalent stress range, arrest periods up to 105 cycles were observed at some G.Bs, while for a smaller equivalent stress range (r215MPa), arrest periods do not exceed 4.104 cycles, in push-pull. Further tests in torsion are in progress to document this point.

1224

V. Doquet and G. Bertolino

FIGURE 1. Crack growth kinetics: a-c) reversed torsion, r130MPa d-e) push-pull, r215MPa

FIGURE 2 Fatigue life and arrest periods as a function of VeqTresca.

References 1.

Morris W.L, James M.R. and Buck O., Metall Trans., vol.12A:57-64, 1981.

2.

Bertolino G., Doquet V. and Sauzay M., Int Journ Fatigue, vol 27/5, 471-480, 2005.

28. Short Fatigue Crack Growth under Multi-axial Loading Conditions

1225

HYDROGEN AND NOTCH EFFECTS ON TORSIONAL FATIGUE OF STAINLESS STEEL Y. Kondo, M. Kubota and K. Ohguma Dept. of Intelligent Machinery and Systems, Kyushu University 744, Moto-oka, Nishi-ku, Fukuoka, 819-0395, Japan [email protected]

1. Introduction It has been pointed out that absorbed hydrogen in metal has detrimental effect in the case of fatigue as well as in hydrogen embrittlement. Austenitic stainless steel is regarded as one of the most promising materials for hydrogen utilization machines. The effects of hydrogen and small notch on the high cycle torsional fatigue of SUS304, SUS316 and SUS316L were studied.

2. Effect of hydrogen on austenitic stainless steels with different hardness The tensile strength was varied by cold work, hot drawing and solution treatment. Torsional fatigue test was done using buff-finished bar specimen at a stress ratio of R=-1. The absorption of hydrogen was done continuously during fatigue test by cathodic charge in dilute sulfuric acid (pH=2.0). S-N curves of SUS316 are shown in Fig.1 as an example. The fatigue strength of hardened materials substantially decreased in cathodic charge condition (Fig.1(a),(b)). In the case of solution heat treated material, however, no significant reduction was observed (Fig.1(c)). This tendency was observed irrespective of chemical composition (Fig.1(d)).

(a)SUS316-WPA cold worked material

(b) SUS316 drawn material

(c) SUS316 solution treated material

(d)Reduction of fatigue limit under cathodic charge

FIGURE 1. Effect of tensile strength on the fatigue strength under cathodic charge A small shear crack was observed at the crack origin (Fig.2). The crack nucleated in shear mode and formed a triangular facet on the fracture surface. It changed into a crack perpendicular to the principal stress and continued to propagate to the final fracture as a mode I crack.

Y. Kondo et al.

1226

FIGURE 2. Crack origin of buff-finished specimen under cathodic charge (SUS316-WPA cold worked, a = 178MPa, Nf =7.24×106)

3. Effect of small notch introduced by pre-corrosion In order to simulate small surface notches, a buff-finished specimen was pre-corroded by anodic polarization. Grain boundaries, slips and twins were etched and very small defects were introduced. The pre-corroded specimen was torsional fatigue tested under cathodic charge condition. The test result is shown by triangular symbols in Fig.3. The pre-corrosion gave a reduction of fatigue strength. The crack origin was quite different from those of buff-finished specimen. No distinct shear mode crack was found at the crack origin in the case of pre-corroded specimen. Corrosion traces of slip and grain boundaries were found near the crack origin. These corrosion trace and cathodic charge enabled the crack initiation without the formation of shear mode crack and resulted in lower fatigue strength.

FIGURE 3. Torsional fatigue of pre-corroded specimen in cathodic charge (SUS316

cold

worked) 4. Conclusion 1

The absorbed hydrogen gave a detrimental effect even on the torsional high cycle fatigue of work hardened austenitic stainless steels irrespective of chemical compositions. On the contrary to this, no significant effect was seen in the case of solution heat treated material.

2

High hardness caused by work hardening and small notch were detrimental factors for the torsional fatigue of austenitic stainless steel used in hydrogen environment. Care should be taken in the usage for the hydrogen utilization equipment.

30. Integrity of gears

1227

INFLUENCE OF MOVING TOOTH LOAD ON GEAR FATIGUE BEHAVIOUR D. T. Jelaska and S. Podrug University of Split, FESB, R. Boskovica b.b., HR 21000 Split, Croatia Tel: + 385 21 305874, Fax: + 385 21 463877 [email protected] A computational model for determination of service life of gears in regard to bending fatigue in a gear tooth root is presented. Two cases are being explored, first in which gear tooth was loaded with normal pulsating force acting at the highest point of single tooth contact, and second in which the fact that in actual gear operation the magnitude as well as the position of the force changes as the gear rotates through the mesh is taken into account. A quasi static numerical simulation method is presented in which the gear tooth engagement is broken down into multiple load steps and analyzed separately, Lewicki et al. [1], Spievak et al. [2]. The fatigue process leading to tooth breakage is divided into crack initiation and crack propagation period. The critical plane damage model, Socie and Bannantine [3], has been used to determine the number of stress cycles required for the fatigue crack initiation. Critical plane approaches are based upon the physical observation that fatigue cracks initiate and grow on certain material planes, called critical planes, the orientation of which is determined by both stresses and strains at the critical location. Depending upon strain amplitude, material type and state of stress, materials generally form one of two types of cracks – shear cracks or tensile cracks. Consequently, the critical plane methods predict not only fatigue crack initiation life, but also the initiated crack direction, which makes a good starting point for further fatigue crack propagation studies. Finite element method and linear elastic fracture mechanics theories are then used for the further simulation of the fatigue crack growth under a moving load. Moving load produces a nonproportional load history in a gear's tooth root (the ratio of KII and KI changes during the load cycle). Consequently, the maximum tangential stress theory will predict a unique kink angle for each load increment, but herein is refined procedure given in [2] which compute crack’s trajectory at the end of the load cycle. An approach that accounts for fatigue crack closure effects is developed to propagate crack under non-proportional load. Effective range of FIN is calculated using Budiansky and Hutchinson model, Budiansky and Hutchinson [4], Newman et al. [5], for plasticity induced crack closure, and influence of oxide induced crack closure, and roughness induced crack closure is taken into account by the concept of partial crack closure, Kujawski [6]. The total number of stress cycles for the final failure to occur is then a sum of stress cycles required for the fatigue crack initiation and number of loading cycles for a crack propagation from the initial to the critical length. The computational results are compared with other researchers’ numerical results and with service lives of real gears. The fatigue lives (Fig. 2) and crack paths (Fig. 1) determined in this paper exhibits a substantial agreement with experimental results and significant improvement compared with the existing numerical models.

D. T. Jelaska and S. Podrug

1228

FIGURE 1. Comparison of crack paths: A – for a load in HPSTC, B – for a moving force.

FIGURE 2. Loading cycles for a crack propagation from the initial to the critical length.

References 1.

Lewicki, D.G., Spievak, L.E., Handschuh, R.F., Consideration of Moving Tooth Load in Gear Crack Propagation Predictions, NASA/TM-2000-210227, 2000.

2.

Spievak, L.E., Wawrzynek, P.A., Ingraffea, A.R., Lewicki, D.G., Simulating Fatigue Crack Growth in Spiral Bevel Gears, Engineering Fracture Mechanics, 68, 53-76, 2001.

3.

Socie, D., Bannantine, J., Bulk Deformation Damage Models, Materials Science and Engineering, A103, 3-13, 1988.

4.

Budiansky, B., Hutchinson, J.W., Analysis of Closure in Fatigue Crack Growth, Journal of Applied Mechanics, 45, 267-276, 1978.

5.

Newman, J.A., Riddell, W.T., Piascik, R.S., A Threshold Fatigue Crack Closure Model: Part I – Model Development, Fatigue Fract Engng Mater Struct, 26, 603-614, 2003.

6.

Kujawski, D., Enhanced Model of Partial Crack Closure for Correlation of R – Ratio Effects in Aluminum Alloys, International Journal of Fatigue, 23, 95-102, 2001.

30. Integrity of gears

1229

COMPARISON OF SOLID SPUR GEAR FACE LOAD FACTORS G. Marunic University of Rijeka Faculty of Engineering Vukovarska 58, 51000 Rijeka, Croatia [email protected] The research into stress state of standard spur gear has enabled the comparison of analytically and numerically established effect of a load distribution over the facewidth, upon the stresses at the tooth-root. Numerous investigations of spur gear based upon 3D approach accomplished by Curti et al. [1], Flašker et al. [2], Glodež and Ren [3] and Baret et al. [4], have underlined the difference between the actual state of stress at tooth-root and the stress results obtained by analytical procedure proposed by the standard ISO [5]. The comparison of numerical results accomplished by use of FEM simulation, with the corresponding ones resulting from the procedures according to the standards, points to some advantages of numerical over standard methods. The stress field at the tooth-root was determined by means of 3D FEM and the developed single gear model. The different linear shape load distributions, from constant load to the triangular shape (Fig. 1), were applied at the outer point of single pair tooth contact, as critical engagement position. The calculations were performed for the gear of the chosen geometrical parameters, covering the range of facewidth values. These facewidths were subjected to equal specific load. The ratio U = 'w/w0 [4] was established, relating the difference between maximum and minimum value of the applied specific load 'w, and the mean value of the applied load w0. The procedure proposed by the standard ISO 6336, introduces the face load factor for toothroot stress calculation that takes into account uneven distribution of load over the facewidth due the mesh-misalignment caused by inaccuracies in manufacture, elastic deformations, etc. Analytically determined face load factors are directly compared to maximum tooth-root stress increment caused by non-uniform load distribution. The local load increase related to its average value in the case of uniform load distribution, i.e. the ratio V1max/Vm0, is taken into account.

FIGURE 1. Linear shape load distribution. Analytical and the corresponding numerical values of the face load factors are presented on Fig.2 for the facewidth value b/mn =8 (mn – module) and the chosen load distribution cases expressed by the ratio U.

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G. Marunic

FIGURE 2. Comparison of analytical and corresponding numerical results of face load factors. The obtained results proved the actual non-uniform stress distribution along the facewidth for the case of uniform load distribution. Maximum stress always appears approximately at the middle of the facewidth, and the stress decrement at the tooth edges strongly depends on the tooth actual facewidth, as well as the achieved agreement of analytically and numerically determined face load factors for different linear shape load distribution. In the case of the adopted uniform load distribution, non-uniform tooth-root stress distribution is taken into account for numerical data that are compared with analytical values of the face load factors provided by the standard ISO, and this fact has initially determined the magnitude of the differences. For the cases of non-uniform load distribution, numerical values of the face load factors are in good agreement with the analytical ones for the facewidth b/mn =6, and U >1.

References 1.

Curti, G., Raffa, F.A., Garavelli, D., Baret, C., In Proceedings of the JSME International Conference on Motion and Powertransmissions, JSME, Hiroshima, 1991, 787-794.

2.

Flasker, J., Glodez, S., Pehan, S., J. of Mech. Engineering, vol.39, 299-308, 1993

3.

Glodez, S., Ren, Z., In Proceedings of International Design Conference-Design ´98, edited by D. Marjanovi, FSB, WDK, CTT, Dubrovnik, 1998, 133-138.

4.

Baret, C., Coccolo, G., Raffa, F.A., In Proceedings of International Gearing Conference, edited by J.N. Fawcett, UK National Gear Metrology, Univ. of Newcastle Upon Tyne, British Gear Assn., Newcastle Upon Tyne, 1994, 149-154.

5.

ISO 6336-1, Calculation of load capacity of spur and helical gears, Part 1: Basic principles, introduction and general influence factors, 1996.

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PREDICTION OF CONTACT FATIGUE INTERNAL CRACK PROPAGATION IN HYPOID GEARS M. Vimercati1, M. Guagliano1, L. Vergani1 and A. Piazza2 1Politecnico di Milano, Mechanical Engineering Dept. - Via La Masa 34, 20158 Milan (ITALY) 2Centro Ricerche FIAT ScpA - Strada Torino 50, 10043 Orbassano (TO) (ITALY) [email protected] Rolling contact fatigue is becoming more and more important in the design of many mechanical systems like gears and bearing. This is due to the ever more severe load conditions that components in contact must undergo if lightness is a primary goal of the design process. This objective can be achieved only by the application of a “design by analysis” procedure. This means that the definition of a more refined design approach requires the ability to develop very accurate simulation procedures to reproduce accurately the actual working condition of the element in contact. One of the damage type occurring in RCF of gears is called “spalling” and consists in the removal of the surface layer of material as a consequence of the stable propagation of a crack initiated at some distance from the surface, most of time in correspondence of an internal defect sited near the position of maximum shear stress, according to the Hertzian stress distribution. Since this type of damage can be tolerated till the material is macroscopically removed, from the designer point of view it is of great importance to predict the number of cycles necessary for this to happen. In particular, since crack propagation begins after a very small fraction of the total life of the components, the prediction of the crack growth rate is a fundamental importance for an accurate sizing of contact elements. This result cannot be obtained without an accurate knowledge of the contact pressure distribution and without knowing the values of the stress intensity factors concerning Modes I, II and III of propagation. With this aim it is very useful to develop a numerical approach able to predict both the contact pattern and the stress intensity factor values during the whole meshing cycle. However this objective is not easy to achieve when the geometry of the gear tooth is complex and the deflection of the tooth shares the load over more than one tooth. In this paper an approach for calculating the SIF of internal cracks in hypoid gears, characterized by high spiral angle values and complex meshing conditions, is discussed: it derives from a previously developed approach aimed to study cracked railway wheels [1] and it is based on two different steps, the one concerning the uncraked tooth and the second one regarding the cracked part of the tooth. Firstly, starting from an accurate geometry description of the gear tooth [2], a contact-FEM analysis carried out by means of an advanced contact solver [3] allowed to obtain the contact pressure distribution and the stress state over the entire meshing cycle [4]. In Fig. 1 it is shown the studied hypoid gear transmission; Fig. 2 reports the pinion teeth with the contact pressure distribution calculated in an instant of meshing.

M. Vimercati et al.

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FIGURE 1. Finite Element model of the studied hypoid gear transmission.

FIGURE 2. Contact pressure distribution over studied pinion teeth.

Once the stress and displacements state in the uncracked tooth are known, they are applied as boundary conditions to a second finite element model of the cracked zone, being the aim the stress intensity factor calculation for the mode I, II, III along the crack front. It was verified that the displacement field induced by the presence of the crack does not affect the boundary of the model. The model includes the contact between the crack faces, with or without friction. By using the proposed approach it is possible to easily considerate different crack dimensions, positions and applied loads, without constructing different and expensive FE models. In the present paper the results obtained by considering circular and elliptical cracks are shown. By opportunely making dimensionless the results it was possible to give them a more general interpretation. The results, together with the knowledge of the threshold value of range of 'K of the material, allows to evaluate the conditions of propagation of internal defects.

References 1.

Guagliano M. and Vergani L., “Experimental and numerical analysis of sub-surface cracks in railway wheels”, Eng. Fr. Mech., vol. 72, 255-269, 2005.

2.

Vimercati M., “Mathematical Model for Tooth Surfaces Representation of Face-Hobbed Hypoid Gears”, submitted to Comp. Meth. App. Mech. Eng..

3.

Vijayakar S.M., “A Combined Surface Integral and Finite Element Solution for a ThreeDimensional Contact Problem”, Int. J. Numer. Methods Eng. vol 31, 525–545, 1991.

4.

Vimercati M. and Piazza A., “Computerized Design of Face Hobbed Hypoid Gears: Tooth Surfaces Generation, Contact Analysis and Stress Calculation”, submitted to AGMA Fall Technical Meeting, Detroit, Michigan, USA, 2005.

30. Integrity of gears

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FATIGUE CRACK INITIATION ALONG INCLUSION INTERFACES OF CONTACTING MECHANICAL ELEMENTS S. Glodez, M. Ulbin and J. Flasker University of Maribor, Faculty of Mechanical Engineering Smetanova 17, 2000 Maribor, Slovenia [email protected], [email protected], [email protected] This paper utilises the theory of fatigue crack initiation along inclusion interfaces of contacting mechanical elements. The assumption is warranted by the fact that hard inclusions in form of carbides are often present in high strength steels and have a significant impact on local strength reduction. If the inclusion and the interface are strong enough to withstand breaking during the initial loading, the plastic deformation is accumulated in the grain matrix after some cyclic loading. The motion of dislocations in the matrix is blocked by inclusion. Fig. 1 illustrates the theoretical model with inclusion of radius R residing within the slip band zone (Tanaka and Mura [1]). The slip band zone is elliptic with semi-major axis l1 and semi-minor axis l2. The inclusion is assumed to be much smaller than the slip band zone.

FIGURE 1. Inclusion in the zone of multiple slip bands If the plastic zone spreads over the whole circular grain, i.e., l1=l2, the number of stress cycles Ni required for the fatigue crack initiation can be determent with following equation [1]: Ni

Gv  G G ˜J ˜ Gv R ' W  2W



2

f

˜

2 f f

(1)

where G is the shear modulus of the material matrix, Gv is the shear modulus of the inclusion, J is the fracture energy per unit interfacial area, 'W is the grain stress range, Wf is the frictional stress and f is the irreversibility factor of dislocations. Experimentally determined values of irreversibility factor f are small and range from 10-4 for small to 10-1 for large plastic strain amplitudes (Zhou et al [2]). The grain stress loading range 'W can be represented either with the shearing stresses or with the equivalent Mises stress (Mura and Nakasone [3]). The presented model is used for the numerical determination of crack initiation period Ni in a contact area of a spur gear pair made of flame hardened steel AISI 4130. The maximum equivalent von Mises stress (Veq)max=800 N/mm2 and its position (depth H=0.126 mm under the contact surface) in the contact area of gear flanks have been determined numerically using FEM. For the case of fatigue crack initiation along inclusion interfaces the number of stress cycles Ni required for the crack initiation can then be determined with eq. (1), where the computed maximum

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equivalent stress (Veq)max=800 N/mm2 is used as the applied stress amplitude 'W to the grain. The frictional stress Wf is material resistance to the motion of dislocations and is for metals equal to Wf|25 N/mm2 [3]. The dislocation pileup length 2l can be equalled to the grain diameter (2l=D), where the average value of the grain diameter D|50 Pm has been determined previously (Glodež [4]). For the treated material with relatively small plastic strain amplitudes, the irreversibility factor is taken to be in the range f=10-4 to 10-3 and the crack surface energy to be in the range J=1 to 10 N/m [2, 3]. Using this data set the number of stress cycles Ni required for the fatigue crack initiation along inclusion interfaces is computed according to eq. (1) for various combinations of the shear modulus of the inclusion Gv and inclusion radius R. The results are presented in Fig. 2. From these computations it can be concluded, that the number of stress cycles Ni required for the fatigue crack initiation decreases with increase of the inclusion radius R and its shear modulus Gv. Taking into account that the usual values for 2R/D lie in the interval from 0.01 to 0.1, the computed number of stress cycles Ni required for the fatigue crack initiation along inclusion interfaces is between 1.372˜102 and 2.286˜105 load cycles.

FIGURE 2. Stress cycles Ni for the fatigue crack initiation

References 1.

Tanaka, K. and Mura, T., Metallurgical Transactions, vol. 13A, 117-123, 1982.

2.

Zhou, R.S., Cheng H.S. and Mura, T., ASME Journal of Tribology, vol. 111, 605-613,1989.

3.

Mura, T. and Nakasone, Y., ASME Journal of Applied Mechanics, vol. 57, 1-6, 1990.

4.

Glodez, S., PhD thesis, Faculty of Mechanical Engineering, University of Maribor,1995.

30. Integrity of gears

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ENERGY BASED GEAR FAULT DIAGNOSTICS S. J. Loutridis Technological Education Institute of Larissa Department of Electrical Engineering GR 41-110 Larissa, Greece [email protected] Gear mechanisms are widely used in rotating machinery. For this reason, gear health monitoring has been the subject of intensive investigation and research. Among several other methods, vibration measurement and analysis is considered as the most general basis for fault detection. Practical condition monitoring systems need quantities that can be used as features for the diagnostic procedure. In this work energy-based features are proposed. The instantaneous energy density calculated using advanced signal processing techniques, is shown to obtain high values when defected teeth are engaged and consequently can be directly related to damage magnitude. The experimental rig consists of two electrical machines, a pair of spur gears, a power supply unit with the necessary speed control electronics and the data acquisition system. A DC machine of 1.5 kW rotates the pinion and the load is provided by an AC asynchronous machine, which is configured as a brake. The transmission ratio is 35/19 = 1.842. The vibration signal generated by the gearbox was picked up by an accelerometer bolted to the pinion body. and the electrical signal was transferred to an external charge amplifier through slip rings and recorded by a PCMCIA acquisition card with a sampling frequency of 20 kHz. The Wigner-Ville distribution [1], is a very important quadratic form time-frequency distribution defined as

W xx t , f

f

³ x §¨ t  W ·¸ x §¨ t  W ·¸ e  j 2 S fW d W . 2¹ © 2¹ © f

(1)

FIGURE 1. Prediction based on Wigner distribution. The instantaneous energy per unit time (power) is calculated by considering the absolute value. E t

f2

³ W t , f df . xx

f1

(2)

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S. J. Loutridis

In practice, integration is approximated by a summation over all frequency bins and the result is divided by the number of bins for normalization. A prediction for a range of crack magnitude from 15% up to 75% of tooth root is shown in Fig.1. The empirical mode decomposition (EMD) pioneered by Huang et al [2], decomposes a timeseries into a finite set of oscillatory functions called the intrinsic mode functions (IMF). An IMF is a function that satisfies two conditions: (1) the number of extrema and the number of zero crossings must either equal or differ at most by one; (2) the running mean value of the envelope defined by the local maxima and the envelope defined by the local minima is zero. The intrinsic modes represent the embedded time scales in the signal. Instantaneous energy density can be calculated directly from the IMFs by application of the Hilbert transform. A prediction is shown in fig. 2.

FIGURE 2. Prediction based on EMD

References 1.

Claasen, T.A.M. and Mecklenbrauker, W.F.G., Philips Journal of Research, vol. 35, 217-250, 1980.

2.

Huang, N.E., Shen, Z., Long, S.R., Wu, M.C., Shih, H.H., Zheng, Q., Yen, N., Tung C.C. and Liu H.H.,1998 Proc. Royal Society of London Series, vol. A454, 903-995, 1998.

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CRACK PROPAGATION IN GEAR TOOTH ROOT S. Pehan, B. Zafosnik and J. Kramberger University of Maribor Slovenia, 2000 Maribor, Smetanova 17 [email protected] The paper describes the problem of crack propagation. The object of consideration are the common gearbox gears. From the measurements it is obvious that the crack can appear at the very different locations in tooth root and then propagate in their own direction, Pehan [1]. Theoretically it can happened in very narrow field on the tooth root surface where the principal stresses are the highest. Few reasons are discussed that can influence on the start position of crack initiation: the loading distribution over the tooth flank, the undercutting of the tooth and the tracks that remains from the cutting tool. It is confirmed that all counted phenomena can cause wide scatter of crack propagation in tooth root, Pehan [2]. The service life of the gearbox already exceed one and half millions kilometers what means that all components should be designed very carefully in order not to become a critical component. One of the most exposed elements in the gearbox are gears, because they are carried the high specific loading all the service time. For that reasons the material and heat treatment also of gear are chosen very carefully. Due to the good thermal treatment of the gear the tiny surface layers are very hard and have high resistant to the wear but consequently such gears are sensitive to cracks in the tooth root. And to understand the reasons for starting crack at the appointed location is the problem that is discussed in presented paper. Many things about the crack initiation and the crack propagation are known quite well. Theory, which is mostly based on the linear fracture mechanic, was developed in previous century already. For example, in theory the initial crack should appears on the surface where the tension or principal stresses are the highest. Theoretically it is quite easy to find this location in tooth root. But the problem still exist because the experimental results deviate from the theory quite a lot. The experts explain this phenomenon by not understanding all the influences about the crack propagation procedure. It is surely truth. So in order to improve the theoretical models and to make it more efficiency a lot of scientist try to modify the theoretical equations by adding additional members. In our case it will be shown that theoretical accessories maybe works correctly if the new edge conditions are considered. The loading spectra that is characteristic for delivery truck is calculated by on propeller shaft measured torques.. However, the final failure of gearbox gears is not the wear but the fracture. A few results of crack path measurement is presented, where the big scatter or dissemination of crack path is obvious. The wideness of the scatter is grater than one millimeter, for what is to be concerned. This wide scatter of fractures means namely that also the service life of such gear can be shorter as it is expected, because of uncontrolled influences. In the continuation the few possible reasons for resulting the wide scatter of fractures are listed. From the gearbox design it is known that the loaded shafts are never parallel. Due to the radial forces the shaft is deformed and the gear mounted on it is positioned in such way that the load over the tooth flank is not distributed equal. The position of the Mises pick stress in tooth root is not always at the exactly same position. It is discussable where is actually the point of the highest stress. It seems to be considered also the influence of the FEM mesh density. The gear model was meshed on different ways and it become clear that mesh indeed have quite big influence on appearance of initial crack. Especially important

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becomes the FEM mesh in case of accounting different effects that are results of preliminary treatments. The final treatment for vehicle gears are normally grinding, preliminary treatment are usually milling, which left on tooth root great tracks. According to the valid laws of linear elastic fracture mechanics the stress field at the tip of a crack is fully described by the stress intensity factor. Due to the complex load distribution and complex gear tooth geometry the stress intensity factor can be determined by numerical methods only. The gear thickness allows plain strain conditions to be assumed, but the validity of linear fracture mechanics should b permanently monitored by checking the size of the yield zone at the crack tip. In our case for each crack length the all three stress intensity factors: KI , KII and KIII and Tstresses are calculated. In order to get confidence in obtained results and to get the better filling the 2-dimensional and 3-dimensional analysis were done. The biggest importance on crack propagation have stress intensity factor KI. Other influences including T-stresses can be neglected. The observation of T-stresses was primary introduced in order to better explain the crack propagation in tooth root. In case of the exactly known position of the initial crack the crack path and the distribution of so called effective stress intensity factor along the crack can be determined easily. When the theoretic value of Keff touches the critical material value called KIc (core material) then crack gets the sound velocity and the tooth root is broken in the moment. Due to the preliminary treatment that easily cause the surface defects on the tooth root the initial crack can appear in many places. The path of crack propagation strongly depends on initial crack. Presumably the direction of crack propagation is determined by the position of highest virtual stress intensity factor in each crack tip. Consequently also the distribution of the stress intensity factor along the length depend from the crack propagation path. It was clearly shown the existence of few obvious influences that could have decisional effect on appearance of initial crack. Before the designers would calculate the service life of the gears they must carefully investigate the actually state of tooth root in order to be sure that the initial crack is positioned on the proper place. The more research is in progress in order to evaluate the effects of separate influences.

References 1.

Pehan S, Helen T H, Flasker J, Applaying Numerical Methods for Determining the Service Life of Gears, Fat. Frac, Engng., Mater. Struct., 18(9), pp.971-979, 1995

2.

Pehan S, Helen T H, Flasker J, Glodez S., Numerical Methods for Determining Stress Intensity Factors vs Crack Depth in Gear Tooth Roots, Int. J. Fatigue, 19(10), pp.677-685, 1997

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EXPERIMENTAL EVALUATION OF STRESS INTENSITY FACTORS IN SPUR GEAR TEETH V. Spitas1, G. Papadopoulos2, Th. Costopoulos3 and C. Spitas3 1Laboratory of Applied Mechanics, Technical University of Crete University Campus, 74100, Chania, GREECE [email protected] 2Laboratory of Strength of Materials, National Technical University of Athens Iroon Polytechniou 7, Zografou, GREECE [email protected] 3Laboratory of Machine Elements, National Technical University of Athens Iroon Polytechniou 7, Zografou, GREECE [email protected] In most engineering applications, gears are the most widely used machine elements for the transmission of power and motion from one shaft to another. Hence it is evident that there is a need for reliability and longer service-life, which requires precise knowledge of the stress field developed in the gear tooth. However this stress analysis becomes more complex when a small crack appears after overloading or fatigue conditions. It is therefore critical to calculate either the remaining life of the cracked gear under the same loading conditions, or the new maximum failsafe operating load to cover the initially calculated service time. Any attempt to approach the problem of the estimation of the service life of gears must pass through crack analysis. The majority of the catastrophic gear-tooth failures usually results from overloading of a single tooth in which one or multiple fatigue cracks have already appeared and propagated. As even a standard gear tooth undergoes highly variable loading in terms of both load magnitude, direction and position on the tooth flank, it becomes evident that the analysis of such a phenomenon is quite complicated and difficult. Up to now a number of works have been carried out investigating gear tooth cracks using numerical tools for the calculation of the Stress Intensity Factors (SIFs) (McAldener and Olsson [1], Spievak et al. [2], Guagliano and Vergani [3], Pehan et al. [4], Sfakiotakis and Anifantis [5]). Few of them used also experimental techniques (such as strain gauges or potential drop methods Glodez et al. [6]) to verify the numerical predictions but with controversial and difficult to interpret results. The classic experimental techniques for stress-analysis fail to focus at the extremely small dimensions of the plastic zone at the crack tip with the high stress gradients and also need excessive time to post-process the results particularly due to the tooth / crack geometry dependent stress field. Photoelasticity in particular is unable to assess the stress condition at singular points such as crack tips or contact points since the density of the isochromatic fringes at the vicinity of the stress singularity is so high that it is impractical to measure the fringe order in this region. In this work the crack path is determined through static fracture experiments of several gear teeth. Then the stress concentration and the stress intensity factors in modes I and II are determined numerically using FEM for various crack lengths along the geometry dependent fracture curve. The findings of the analysis are verified with photoelasticity regarding the stress field and with the stress-optical method of caustics on specially machined cracked tooth specimens regarding the SIFs.

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The results indicate that there is a good agreement between numerically predicted and measured values. Moreover they indicate that the mode of crack propagation is mixed and not uniform as gear tooth cracks tend to be almost pure mode I cracks near the surface (root fillet of the tooth) whereas mode II becomes considerable as the cracks propagate towards the interior of the tooth. Finally it should be noted that this is the first time that the stress optical method of caustics is applied for measuring the SIFs in cracked gear teeth.

Reference 1.

McAldener, M., Olsson, M., Eng. Fracture Mechanics, vol. 69, 2147-2162, 2002.

2.

Spievak, L.E., Wawrzynek, P.A., Ingraffea, A.R. and Lewicki, D.G., Eng. Fracture Mechanics, vol. 68, 53-76, 2001.

3.

Guagliano, M., Vergani, L., Int. J. of Fatigue, vol. 23, pp. 65-73, 2001.

4.

Pehan, S., Trevor, H.K., Flasker, J. and Glodez, S., Int. J. of Fatigue, vol. 19 (10), 677-685, 1997.

5.

Sfakiotakis, V.G. and Anifantis, N.K., Fin. El. in Analysis and Design, vol. 39, 79-92, 2002.

6.

Glodez, S., Pehan, S. and Flasker, J., Int. J. of Fatigue, vol. 20 (9), 669-675, 1998.

35. High Temperature and Thermomechanical Fatigue

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ISOTHERMAL AND THERMOMECHANICAL FATIGUE BEHAVIOR OF THE ODS SUPERALLOY PM1000 W. O. Ngala, G. Biallas and H. J. Maier Lehrstuhl für Werkstoffkunde, Universität Paderborn Pohlweg 47-49, D-33098 Paderborn, Germany [email protected] PM1000 is an oxide dispersion strengthened (ODS) nickel based superalloy with applications in the aerospace and glass processing industries. It contains about 0.6 weight percent of incoherent finely dispersed yttria particles. Earlier work has addressed the high- temperature isothermal lowcycle fatigue (LCF) [1-2], creep [3] and oxidation [4] behaviour of PM1000. However, no known work has been done to characterize the thermomechanical fatigue (TMF) performance of this superalloy. The present work therefore involved a study of the high-temperature cyclic stressstrain response of PM1000 under isothermal fatigue (IF) and TMF loading conditions. Both IF and TMF tests were conducted in the temperature range from 450 to 950 °C, with mechanical strain amplitudes varying from 0.35 to 0.5% in laboratory air conditions. The maximum mechanical strain and maximum temperature occurs simultaneously in in-phase (IP) TMF, while out-of-phase (OP) TMF has the maximum strain coinciding with minimum temperature. The experiments were done on a servohydraulic Material Testing System (MTS 810). All fatigue tests were conducted in fully reversed symmetrical push-pull using a triangular wave shape as the strain command signal. Axial strains were measured with a high-temperature MTS extensometer with 12 mm gauge length, attached to the specimens. The specimens were heated with a high frequency induction heater. Temperature gradients along the specimen gauge length were typically less than 4 °C, as monitored by a pyrometer. The effects of the applied strain amplitudes, test temperatures and strain rates on the cyclic deformation behaviour and fatigue life were examined. Figure 1 shows IP TMF hysteresis loops recorded in the first cycle and at half life during a 450 to 850 °C temperature range test. As expected, a compressive mean stress was observed in IP TMF, while OP TMF tests resulted in a tensile mean stress. Slight hardening characterized the first few cycles of the IP TMF test, which was followed by pronounced cyclic saturation. The stress-strain response observed compares quite well with the work of Linde [5], where the TMF behaviour of MA 754, a British analogue of PM1000, was investigated. The initial hardening observed in the IP TMF is attributed to the yttria particles blocking dislocation slip in the low temperature part of the cycle, thus resulting in an increase in dislocation density. By contrast, initial softening was observed during the first few cycles of the IF tests, followed by stable cyclic stress-strain response until macro crack growth set in.

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FIGURE 1: IP TMF hysteresis loop for the 450-850 °C temperature range. The saturated isothermal stress amplitudes compare quite well with the corresponding stresses at the maximum temperature of the TMF cycle, an indication of good microstructural stability. Despite the similarity in stress amplitudes, it was found that fatigue lives are strongly dependent on the actual loading conditions. IP TMF presents the most damaging test mode followed by IF, while OP TMF resulted in the longest fatigue life. The ramifications of the observations made with respect to modeling of cyclic stress-strain response and damage evolution will be discussed.

References 1.

Müller, F. E. H., Heilmaier, M. and Schultz, L., Mater. Sci. Eng., vol. A234-236, 509-512, 1997.

2.

Heilmaier, M., Maier, H.J., Jung, A., Nganbe M., Müller F.E.H. and Christ H.-J., Mater. Sci. Eng., vol. A281, 37-44, 2000.

3.

Estrin, Y., Heilmaier M. and Drew, G., Mater. Sci. Eng., vol. A272, 163-173, 1999.

4.

Weinbruch, S., Anastassiadis A., Ortner, H.M., Martinz, H.P. and Wilhartitz, P., Oxidation of Metals, vol. 51, 111-128, 1999.

5.

Linde, L. and Henderson, P.J., Scripta Metall. Mater., vol. 26, 1687-1692, 1992.

35. High Temperature and Thermomechanical Fatigue

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FATIGUE-CREEP-ENVIRONMENT INTERACTIONS IN A DIRECTIONALLYSOLIDIFIED NI-BASE SUPERALLOY A. P. Gordon1, M. M. Shenoy2, R. W. Neu3 and D. L. McDowell4 1George W. Woodruff School of Mechanical Engineering, Atlanta GA 30332-0405 2School of Materials Science and Engineering, Atlanta GA 30332-0245 [email protected], [email protected], [email protected], [email protected] Directionally solidified (DS) GTD-111 is a Ni-base superalloy designed to withstand creep damage occurring in the first and second stage blades of gas-powered turbines. The service conditions in these components, which generally exceed 600ºC, facilitate the onset of one or more damage mechanisms via fatigue, creep, and environmental corrosion. Under these conditions microstructural damage mechanisms operate interactively and independently to initiate cracks that lead to the eventual reduction of service life. Because of the distinctive microstructure of DS GTD-111, the manner in which these mechanisms interact to initiate cracks is related to grain structure and chemical composition. In addition to fatigue cycling, certain sections of these high temperature components are subjected to sustained dwell periods (i.e., creep) either in tension or compression. Experiments have been carried out to simulate a variety of thermal, mechanical, and environmental operating conditions endured by longitudinally (L) and transversely (T) oriented DS GTD-111. In some case, tests in extreme environments/temperatures were needed to isolate one or at most two of the damage mechanisms. Assuming a unique relationship between the damage fraction and cycle fraction with respect to cycles to crack initiation for each damage mode, the total crack initiation life has been represented in terms of the individual damage components (fatigue, creep-fatigue, creep, and oxidation-fatigue respectively), and is based on that developed by Neu and Sehitoglu [1] and modified by Gordon et al. [2]:

1 Nitot

1 1 1 1  c  f  cr  ox fat Ni Ni Ni Ni

(1)

Observations from micrographs (Fig. 1) of sections of oxidized, fatigued, and crept samples have been incorporated to develop damage mechanism maps (DMMs). The DMMs, which quantify the transitions between damage mechanism regimes, have been applied to develop physically-based relationships for each of components of a crack initiation model. A crystal plasticity based model has been formulated by Shenoy et al. [3] to capture the stress strain behavior in the material. Fatigue (Fig. 2) and creep data were used to calibrate the model which was implemented as an UMAT in ABAQUS. Using numerical simulations of experiments, damage and crack initiation life predictions have been made. It was determined that under high frequency and isothermal conditions with large plastic strain ranges and low temperatures, fatigue damage dominates. The contribution of the coupled creep-fatigue mechanism appears by increasing either the temperature or cycle time. Tests with small plastic strain range including those with superimposed thermal cycling, are subject to environmental-fatigue damage since the surface-related mechanisms are active at long exposure times.

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FIGURE 1: Oxide spiking observed in L-oriented DS GTD-111 with 982qC, 'H=0.5%, R=1, and 2min compressive holds.

FIGURE 2: Simulated and actual experimental responses of DS GTD-111 under isothermal LCF in (a) L-orientation and (b) T-orientation at two strain rates. For each case 982qC (1800qF), RH=-1, and 'H = 1.0%.

References 1.

Neu, R. W., and Sehitoglu, H., Metallurgical Transactions A, vol. 20, 1769-1783, 1989.

2.

Gordon, A. P., Shenoy, M. M., and Neu, R. W. (2005). In Proceedings of 11th International Congress of Fracture (ICF11), Turin, Italy, Elsevier Science.

3.

Shenoy, M. M., Gordon, A. P., Neu, R. W., and McDowell, D. L., In press for publication in the Journal of Engineering Materials and Technology, 2005.

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THE EFFECTS OF MICROSTRUCTURE, DEFORMATION MODE AND ENVIRONMENT ON FATIGUE S. D. Antolovich and B. F. Antolovich School of MSE, Georgia Tech, Atlanta Georgia, 30332, USA Centre de Recherche de Trappes, Trappes, France 78193 [email protected], [email protected] So-called laws for predicting the lives of components at high temperatures have been proposed (e.g. strain range partitioning, frequency modified fatigue life, time and cycle fraction etc.). These “laws” usually work quite well for certain situations but are less successful in predicting life for other conditions and materials that are quite similar. These laws are based on generic notions of damage with several adjustable parameters. Such laws are useful from an engineering perspective when considerable data base is available. However, they are far less successful in predicting behaviour of new materials or existing materials under different external conditions. In essence, most of these models have evolved into very sophisticated curve fits and generally fail to take into account the actual behaviour of the material. For example, interactions between deformation mechanisms in the material and environmental attack and the changing nature of the material are not explicitly considered. In this paper, the physical damage processes that take place in high temperature fatigue and fatigue crack propagation (FCP) of different commercial high temperature alloys is presented. This information is used to develop fatigue physically-based models. High Temperature Low Cycle Fatigue (LCF). In one set of studies, the LCF behaviour of a series of Ni-base alloys was studied by Antolovich and co-workers [1,2,3,4]. Fatigue testing was done over a range of temperatures, strain rates and strain ranges in air. Even after a very small number of cycles significant microstructural changes which can have profound effects upon the life were seen. Prominent changes that were observed included the following: rapid coarsening of the J cprecipitates, extensive oxidation along grain boundaries and slip bands and precipitation of carbides precipitates on slip bands and grain boundaries. These microstructural changes interacted with the basic cyclic deformation mechanisms to cause damage. One example is shown in the micrograph of Fig. 1. Slip bands are impinging on oxidized grain boundaries. Microcracks are seen quite clearly at the tips of these slip bands where the stresses are very high. Furthermore, detailed examination by selected area diffraction and dark field TEM conclusively demonstrated that carbides precipitated on the slip bands and were themselves at least partially oxidized. The behaviour depends sensitively on the nature of the cycle, the kinetics of stress-assisted precipitation and the deformation mode; it is not captured in conventional life prediction methodologies. Such information is used to develop a set of physics-based TMF models.

FIGURE 1. Slip-band-induced cracking of oxidized grain boundaries in Waspaloy tested in LCF at 1073K . Microcracks are indicated by the dark arrows.

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S. D. Antolovich and B. F. Antolovich

FCP in Single Crystalline Ni-base Alloys. Fatigue crack propagation studies were carried out on CMSX-2, a typical superalloy used in blade applications which have been partially reported elsewhere by Antolovich et al. [5]. Duplicate specimens were tested as a function of temperature (298K and 973K), environments (air and 10-8 torr) and crystallographic orientation ([010] or [110] with a common projected (100) crack plane). A detailed FEA analysis including the elastic anisotropy was carried out to understand the different cracking modes that were observed for the different conditions. It was found that the morphology of the crack surface was either “shearing” or “precipitate avoidance” depending upon the ratio of the normal stress to the shear stress at a given temperature and environment. Basically precipitate shearing and large crystallographic facets which were not normal to the plane of loading were favored by low temperature, low stress ratio, and vacuum. The two cracking modes are shown in Fig. 2.

FIGURE 2. Typical FCP fracture surface morphologies of CMSX-2. Precipitate shearing (a) and avoidance (b). Morphology depended on temperature, orientation and stress ratio. Detailed calculations for LCF and FCP that are based on fundamental physical processes are presented in the full paper.

References 1.

Lerch, B. A., Antolovich, S.D., and Jayaraman, N., J. Mat. Sci. and Engr., 151-165, 1984

2.

Domas, P. D. and Antolovich, S.D., J. Engrg. Fract. Mech., Mechanics, 21, 203-214, 1984

3.

Antolovich, S.D., Rosa, E and Pineau, A., J. Mat. Sci. and Engr., 47, 47-57, 1981.

4.

Antolovich, S.D., Liu, S., and Baur, R., Met. Trans., 12A, 473-481, 1981.

5.

Antolovich, B.F., Saxena,A., and Antolovich, S.D., In Superalloys 1992, Edited by S.D. Antolovich, R.W. Stusrud, R.A. MacKay, D.L. Anton, T. Khan, R.D. Kissinger, D.L. Klarstrom , AIME, Warrendale, PA, 1992, 727-736.

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COMPARING FATIGUE BEHAVIOUR OF TI6242 AND NOVEL TIAL INTERMETALLICS T. K. Heckel, A. Guerrero-Tovar and H. J. Christ Universität Siegen, Institut für Werkstofftechnik 57068 Siegen, Germany [email protected] In the present study the isothermal and thermomechanical fatigue behaviour of the commercial near-alpha titanium alloy Ti6242 and the novel gamma-TiAl alloys TNB-V2 and TNB-V5a was investigated and compared. The comparison was carried out in order to define the suitable temperature range of application for each of these alloys and to illustrate the similarities and differences in the cyclic deformation behaviour and damage evolution. Ti6242 is the most widely used near-alpha high-temperature titanium alloy often applied in the high-pressure compressor of civil jet engines. Although near-alpha titanium alloys feature a good mechanical capability up to temperatures of 650°C, which represents the current compressor outlet temperature, the maximum service temperature is restricted to 540°C because of the potential risk of titanium fire. Therefore, it is still necessary to revert to heavy Ni-base superalloys in the last stages of high-pressure compressors. TNB-V2 and TNB-V5a belong to the latest developed near-gamma TiAl alloys (third generation TiAl alloys), which possess superior mechanical properties compared to those of previous generations (Paul et al. [1], Appel et al. [2], Appel et al. [3]). The increase in strength, ductility and oxidation resistance is caused by a relatively high content of niobium (5-8 wt.%). This class of near-gamma TiAl alloys holds the potential to fill the gap to the design of an all titanium-based compressor, which would reduce weight and thus increase efficiency of jet engines. Therefore it is essential to determine the fatigue properties of these novel alloys and compare the observations to the rather well-known behaviour of commercial near alpha high-temperature Tibased alloys. Isothermal as well as thermomechanical tests were conducted in both, laboratory air and vacuum environment. The main purpose of the vacuum tests was to eliminate the effect of gasmetal interaction on cyclic life, in order to characterize and quantify the extent of environmentallycaused life reduction by means of a comparison with the cyclic life data obtained in air. All tests were conducted in total strain control using a triangular command signal at a strain range of 1.4% and a R-ratio of -1. The thermomechanical fatigue tests were carried out at a phase shift of 0° or 180° between strain and temperature signal (i.e., in-phase and out-of-phase loading, respectively). Temperature ranged from 350 to 650°C for Ti6242 and from 550°C to 850°C for TNB alloys. The microstructural changes were studied applying optical and transmission electron microscopy. Crack initiation and propagation were investigated by means of scanning electron microscopy often in combination with orientation imaging (OIM). Figure 1 shows the stress amplitude and the corresponding cyclic life of Ti6242 observed in isothermal fatigue tests. The materials was studied in the bi-modal condition, which is recommended for applications in jet engines, since the bi-modal microstructure exhibits a good balance between creep and fatigue properties (Eylon et al. [4], Lütjering and Williams [5]). It is clearly seen in Fig. 1 that the cyclic strength of the material decreases continuously with increasing temperature. More important, the cyclic life is tremendously reduced limiting strongly the temperature range of application.

T. K. Heckel et al.

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The deformation behaviour of the TNB alloys, which were produced and heat-treated by GKSS Research Centre, Geesthacht, Germany and which were tested in the lamellar condition, is characterized by a rather pronounced ductile to brittle transition (DBT). As a consequence of the high Nb content, the DBT temperature lies in the range of 750°C-800°C, i.e. well above the DBT temperature of previous TiAl alloy generations. The cyclic stress-strain response and the microstructure were found to be very stable both under isothermal and thermomechanical conditions. However the materials are very susceptible to thermomechanical out-of-phase loading, since this testing mode is connected with a tensile mean stress, oxidation in the high-temperature part of the cycle, and a brittle behaviour (i.e. low damage tolerance) in the tensile-going lowtemperature cycle part.

FIGURE 1. Stress response and fatigue lifetime vs. temperature of Ti6242.

References 1.

Paul, J.D.H., Appel, F. and Wagner, R., Acta Mater., vol. 46, 1075-1085, 1998.

2.

Appel, F., Oehring, M. and Wagner, R., Intermetallics, vol. 8, 1283-1312, 2000.

3.

Appel, F., Oehring, M., Paul, J.D.H. and Lorenz, U., In: Structural Intermetallics 2001, Proceedings of the Third International Symposium on Structural Intermetallics, edited by K.J. Hemker, D.M. Dimiduk, H. Clemens, R. Darolia, H. Inui, J.M. Larsen, V.K. Sikka, M. Thomas and J.D. Whittenberger, TMS, Warrendale, 2001, 63-72.

4.

Eylon, D., Fujishiro, S., Postans, P.J. and Froes, F.H., Journal of Metals, vol. 36, 55-62, 1984.

5.

Lütjering, G. and Williams, J.C., Titanium, Springer, Berlin, Germany, 2003.

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A TBC FAILURE MODEL BASED ON CRACK NUMBER DENSITY Xijia Wu1, Zhong Zhang2 and Rong Liu2 1Structures and Materials Performance Laboratory National Research Council of Canada 1200 Montreal Road, Ottawa, ON, Canada K1A 0R6 Tel: 1-613-990-5051; Fax: 1-613-990-7444 2Department of Aerospace and Mechanical Engineering Carleton University 1125 Colonel By Drive, Ottawa, Ontario, Canada K1S 5B6 [email protected] Thermal barrier coatings (TBC) are used as protective coatings for hot-section components in advanced gas turbine engines. When exposed to the hot gas, a layer of thermally grown oxides (TGO) forms at the interface between the ceramic topcoat and the metallic bond coat in TBC, which often causes cracking and eventually leads to TBC spallation. The damage accumulation in TBC appears as the collective results of nucleation and growth of numerous microcracks. A description of the evolution of such a process is the key to assess TBC durability. Based on the crack number theory, the evolution of the crack number is given as [1]: wn w  [ c n ] wt wc

nN

(1)

where n is the number of cracks at time t, c is the crack length and c is the crack growth rate, and nN is the crack nucleation rate. Generally, Eq. (1) determines the crack number distribution against the crack size as function of time, at given nucleation and growth rates. An air-plasma sprayed TBC was examined. A comparison of the above model with experimentally established crack number distribution is presented, as shown in Fig. 1. The mechanism of crack nucleation and growth will also be discussed.

FIGURE 1. Crack number function for 24 hour exposure at 1200oC.

References

1250 1.

X. Wu et al.

Fang, S B., Hong, Y.S., and Bai, Y.L. “Experimental and theoretical study on numerical density evolution of short fatigue cracks”, Acta Mechanica Sinica (English Edition) 11, 144152.

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IMPACT INDUCED COMPOSITE DELAMINATION: STATE AND PARAMETER IDENTIFICATION VIA UNSCENTED KALMAN FILTER Alberto Corigliano, Aldo Ghisi and Stefano Mariani Dipartimento di Ingegneria Strutturale, Politecnico di Milano Piazza Leonardo da Vinci 32, 20133 – Milano, ITALY [email protected], [email protected], [email protected] The problem of impact induced delamination in layered composites (Abrate [1]) is considered and numerically modelled on the basis of the following assumptions: the layers are elastic, interface softening laws are used to simulate the progressive interlaminar decohesion due to delamination (Allix and Corigliano [2], Corigliano [3]). An explicit dynamic finite element code is used for the step by step analysis. The main purpose of the present study is to evaluate the performance of the recently proposed sigma-point Kalman filter, also termed unscented Kalman filter (Wan and van der Merwe [4], Ljung [5]), for real-time identification of the unknown interface properties and of the debonding surface(s) under impact loading. Only free-surface measurements are used to drive the identification procedure. Among the most important features of the unscented Kalman filter, it is important to mention that: it does not require the computation of the gradient (Jacobian) of the equation of motion; the statistics of the system state variables (model parameters and nodal displacements-velocitiesaccelerations) are accurately propagated in time up to the third-order. Hence, the sigma-point transformation turns out to be superior to the first-order approximation featured by the extended Kalman filter (see Corigliano and Mariani [6], Mariani and Corigliano [7]).

FIGURE 1. Impact on a SiC specimen. (a): space-time diagram; (b): free-surface velocity record. The filtering procedure is here applied to the experimental results of Dandekar and Bartkowski [8], concerning Silicon Carbide specimens subject to shock loading. In these tests, spalling takes place across a material interface whose location is determined by means of an elastic-brittle analysis; the free-surface velocity is considered as the only available experimental datum (see Fig. 1). Key constitutive parameters, like the fracture energy, are identified and the performances of the extended and of the unscented Kalman filters are critically compared (see Fig. 2).

A. Corigliano et al.

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FIGURE 2. Impact on a SiC specimen: current estimated value of the fracture energy.

References 1.

S. Abrate. Impact on composite structures. Cambridge University Press, 1998.

2.

O. Allix and A. Corigliano. International Journal of Solids and Structures, vol. 36, 21892216, 1999.

3.

A. Corigliano. Comprehensive Structural Integrity, vol. 3, chapter 9. Elsevier Science, 2003.

4.

E.A. Wan and R. van der Merwe. In S. Haykin, editor, Kalman filtering and neural networks, 221-280. John Wiley & Sons, Inc., 2001.

5.

L. Ljung. System identification. Theory for the user. Prentice Hall, 1999.

6.

A. Corigliano and S. Mariani. Computer Methods in Applied Mechanics and Engineering, vol. 193, 3807-383, 2004.

7.

S. Mariani and A. Corigliano. Computer Methods in Applied Mechanics and Engineering, in press, 2005.

8.

D.P. Dandekar and P.T. Bartkowski. Technical Report ARL-TR-2430, Army Research Laboratory, Aberdeen Proving Ground, 2001.

36. Impact Failure of Laminated and Sandwich Composite Structures

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MODELLING IMPACT DAMAGE IN SANDWICH CONCEPT STRUCTURES A. Johnson and N. Pentecote German Aerospace Center (DLR), Institute of Structures and Design Pfaffenwaldring 38-40, 70569 Stuttgart, Germany [email protected], [email protected] To reduce development and certification costs for composite aircraft structures, efficient computational methods are required by the industry to predict structural integrity and failure under dynamic loads, such as crash and impact. By using meso-scale models based on continuum damage mechanics (CDM), proposed by Ladevèze and co-workers [1], [2], it is possible to define materials models for FE codes at the structural macro level which embody the salient micromechanics failure behaviour. CDM provides a framework within which in-ply and delamination failures may be modelled. In previous work [1], [3] ply failure models were developed for unidirectional (UD) fibre and fabric reinforced plies with three scalar damage parameters representing in ply microdamage and damage evolution equations introduced relating the damage parameters to strain energy release rates in the ply. Delamination models for interply failure were obtained by applying the CDM framework to the ply interface, as described in [2]. Failure at the interface is modelled by degrading stresses using two interface damage parameters corresponding to interfacial tension and shear failures, whilst fracture mechanics concepts are introduced by relating the total energy absorbed in the damaging process to the interfacial fracture energy. The ply CDM and delamination models have been implemented into a commercial explicit FE crash and impact code [3], which uses a numerical approach for delamination modelling based on stacked shell elements with contact interface conditions, which may separate when the interface failure condition is reached. The paper describes the application of these simulation methods to design concept studies on a novel form of double-walled composite panels with energy absorbing cores currently being assessed for use in aircraft structures. These are non-standard sandwich structures, in which a main load-bearing composite laminate is protected from impact damage by an energy absorbing core and a second cover laminate. Core materials being considered include folded composite plate structures, polymer foams and Nomex honeycomb. Impact load cases of interest include high velocity impacts from steel impactors and deformable, soft body impactors such as ice and rubber. Representative structures are modelled and FE simulation results are presented, which simulate numerically the observed impact failure modes and failure progression under medium to high impact velocities representative of civil aircraft applications. Of particular interest is to determine the impact damage threshold in the inner load-bearing laminate for impacts on the cover laminate, as impactor type and impact energy is varied. Effective delamination models are required in this inner laminate to determine damage levels for the cases when the projectile penetrates the cover laminate and core. FE simulation results are compared with gas gun impact test data on idealised double-wall panel structures at impact velocities in the range 60 – 250 m/s. The sandwich skin composite laminate is modelled by layered shell elements or stacked shells with a contact interface which may fail by delamination. The shells are composed of composite plies which are modelled as a homogeneous orthotropic elastic damaging material whose properties may be degraded on loading by microcracking prior to ultimate failure. The simulation results presented here are based on the ‘bi-phase’ ply model for UD and fabric plies in which it is supposed that damage evolution is dependent on strain invariants. In the layered shell element the stiffness properties of the plies are degraded as the shear strain invariant increases until eventually a damaged shell element is eliminated from the computation when the shear strain invariant

A. Johnson and N. Pentecote

1254

reaches a pre-defined critical value. A delamination model [3] is implemented in the PAMCRASHTM code, with the laminate modelled as a stack of shell elements. Each ply or sublaminate ply group is represented by a set of layered shell elements and the individual sublaminate shells are connected together using a contact interface with an interface traction-displacement law. Contact may be broken when the interface energy dissipated reaches the mixed mode delamination energy criteria. This ‘stacked shell’ approach is an efficient way of modelling delamination, with the advantage that the critical integration timestep is relatively large since it depends on the area size of the shell elements not on the interply thickness.

FIGURE 1. Impact model of foldcore sandwich plate (M = 22 gram, V0 = 105) There is current interest in sandwich panels with carbon composite skins and a folded aramid paper composite core (foldcore), with a complex periodic folded geometry. The core is modelled in detail by shell elements with the bi-phase materials model, together with layered shells or stacked shell elements and delamination interfaces for the sandwich skins. Fig. 1 shows simulation results for impact penetration from a 22 gram rigid projectile at 105 m/s normal impact. These conditions model stone impact and gas gun tests at the DLR led to penetration of the outer skin, which was also predicted in the FE model. Thus the methodology developed here may be used further to evaluate monolithic, double shell and sandwich design concepts for aircraft fuselage and wing structures subjected to high velocity impact loads.

References 1.

Ladevèze, P., Inelastic strains and damage, Chapt. 4 in Damage Mechanics of Composite Materials, R. Talreja (ed), Composite Materials Series, Vol 9, Elsevier, 1994.

2.

Allix, O., Ladevèze, P., Interlaminar interface modelling for the prediction of delamination, Composites Structures, 22, 235-242, 1992.

3.

Johnson, A.F., Pickett, A.K., Rozycki, P., Computational methods for predicting impact damage in composite structures, Composites Science and Technology, 61, 2183–2192, 2001.

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PUNCH SHEAR BEHAVIOR OF COMPOSITES AT LOW AND HIGH RATES B. A. Gama and J. W. Gillespie Jr. University of Delaware Center for Composite Materials (UD-CCM) 209 Composite Center, UD, Newark, DE 19716, USA [email protected], [email protected] A quasi-static penetration model of ballistic penetration of thick section composites is proposed. Quasi-static punch shear tests (QS-PST) and ballistic punch shear tests (B-PST) are conducted to identify five different phases of ballistic penetration, i.e., i) impact-contact, ii) hydrostatic compression, iii) compression-shear, iv) tension-shear, and v) structural vibration. It is well known that the energy absorption in QS-PST is much lower than the B-PST e.g., Mines et al [1]; and the physics of ballistic penetration is difficult to model with quasi-static models. In order to bridge the gap between QS-PST and B-PST energy absorption, conservation of momentum and energy principles is used to predict the rest kinetic energy of the projectile-laminate system in case of a partial penetrating projectile. Combining the QS-Penetration model and the analytical rest kinetic energy model, a good prediction of ballistic energy absorption is obtained.

FIGURE 1. Quasi-Static Punch Shear Test: Load-Deflection and Damage. The authors [2, 3] have shown that QS-PST at different span to punch ratio (SPR) can be used to simulate different phases of ballistic damage mechanisms e.g., hydrostatic compression (SPR = 0.0), compression-shear (SPR = 1.1 & 2.0), and tension-shear (SPR = 4.0 & 8.0). Fig. 1 shows the QS-PST behavior of plain-weave (814 g/m2) S-2 glass/SC15 composites as a function of SPR. The energy absorption in QS- and B-PST is summarized in Table 1. Clearly, the energy absorption increases with SPR pointing to the fact that an increase in SPR involves more volume of material and the plate goes under large deformation. At SPR = 8, the ratio of ballistic to QS-PST is about 1.82, a well documented phenomenon in Ref. [1]. Comparing the ballistic penetration phases and QS-PST load-deflections as a function of SPR, a QS-Penetration model of ballistic penetration is proposed by the authors [3]. P

C Pmax

§G GF · P0  P1 ¨ ¸ © G ¹

C 0  G  G max C G max  G  GF

(2)

B. A. Gama and J. W. Gillespie Jr.

1256

Where, the impact-contact force is assumed to be constant in the hydrostatic compression 1

phase and to have a G behavior in the other penetration phases. This QS-Penetration model provided the concept of a QS-PST-Envelope [3] curve, which represents the total energy absorbed by material damage, and is about 80% of the total ballistic energy. TABLE 1. Energy Absorption in QS- & B-PST.

It is also known that at ballistic limit, the projectile is arrested, and the total energy of impact is transferred to the composite plate. If one assumes that the projectile forms a moving cone of the plate with a velocity profile, 9 r >V C / 1  * [ @1  [ / r ,the conservation of momentum and energy principles yields the following relation for the rest kinetic energy of the projectilePL

laminate system, E KE .

: PL

Where, / C

P -L E KE EI

VC / V I

ª ­° *[2 *[ ½° º / 2C «1  * 0 ® ln *[  ¾» 2 *[  1 °¿ » °¯ *[  1 «¬ ¼

>1  *

(3)

/ 2 *[  1 @ , V is the maximum cone velocity. * 0 is the C 1

0

areal-density ratio of the laminate to projectile, and * [ is the cone to projectile diameter ratio. The energy absorption at ballistic limit then can be expressed in terms of the QS-PST-Envelope Envelope

E Material / 1  : . A good correlation between QS-PST and B-PST energy as: E I QS  PST experiments is obtained using these models. Damage

References 1.

Mines, R.A.W., Roach, A.M., Jones, N., Int. J. Impact Engng, vol. 22, 561-588, 1999.

2.

Gama, B.A., Rahman, M., and Gillespie Jr., J.W., In CD Proceedings of SAMPE 2004, Long Beach, California, 2004, 909-921.

3.

Gama, B.A., Islam, S.M.W., Rahman, M., Gillespie Jr., J.W., Bogetti, T.A., Cheeseman, B.A., Yen, C-F., and Hoppel, C.P.R., In CD Proceeding of SAMPE 2005, Long Beach, California, 2005.

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REPEATED IMPACT BEHAVIOUR AND DAMAGE PROGRESSION OF GLASS REINFORCED PLASTICS G. Belingardi, M. P. Cavatorta and D. S. Paolino Politecnico di Torino, Dipartimento di Meccanica Corso Duca degli Abruzzi 24 – Torino – Italy [email protected], [email protected], [email protected] The paper investigates the response of glass fibre reinforced plastics subjected to repeated low velocity impact loading. The loading condition of repeated impacts is of particular relevance for industrial applications, especially when intended for motor vehicle or naval applications. Recently few papers addressed the problem [1-3]. Experimental tests are performed according to ASTM 3029 standard using an instrumented free-fall drop dart testing machine. Specimens are 100 x 100 mm square plates, mechanically constrained over a circular 76.2 mm diameter edge. The impactor has a total mass of 20 kg, its head is hemispherical with a radius of 10 mm. Static indentation and dropweight impact tests were performed; the comparison of quasi-static and impact curves shows that the material, under the stated loading conditions, has no sensitivity to strain-rate effects. Four falling heights were considered (125 mm, 250 mm, 500 mm, 750 mm) and four specimens for each height were subjected to ten repeated impacts. By means of a piezoelectric load cell, force-time curves were acquired and, with a double integration, force-displacement and deformation energy-displacement curves were obtained [4]. From the force-displacement curves, the actual value of the bending stiffness was calculated. The variation of the plate bending stiffness was chosen as the indicator for the progression of the structural damage within the laminate. Fig.1 shows the mean peak load as a function of the impact number. As visible, for the 125 mm and the 250 mm specimens the peak load slightly increases in the first impacts as compaction of the different layers is achieved. Analysis of the impacted surfaces shows delamination damage from the first impact; however, no penetration is achieved even at the tenth impact. For the 500 mm and the 750 mm specimens, the peak force reaches a maximum and then decreases. The maximum in the peak force seems to correspond to penetration of the first unidirectional ply. For these specimens, delamination and fibre breakage are observed. For the 750 mm specimens, perforation of the laminate plate occurs at the ninth impact. The peak force at the first impact increases almost linearly with the falling height (i.e. the impact energy). The linear relationship continues to exist at higher impact numbers only for the 125 mm and the 250 mm specimens, for which the penetration threshold is not reached even at the tenth impact [5].

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FIGURE 1. Peak impact load as a function of impact number. Fig. 2 on the left end side plots the mean stiffness against the impact number. As visible, the stiffness-impact plot shows a monotone decreasing trend, with the maximum stiffness loss concentrated in the first impact. The overall stiffness reduction increases for increasing falling heights. Fig.2 on the right end side reports both the mean stiffness and the total delamination area plotted against the impact number for the 500 mm specimens. Correlation between the area of delamination and the stiffness reduction is evident.

FIGURE 2. Stiffness vs. number of impact (left) Correlation between stiffness reduction and delamination area - h=500 mm- (right).

References 1.

Azouaoui, K., Rechak, S., Azari, Z., Benmedakhene, S., Laksimi, A. and Pluvinage, G., Int J Fatigue, vol. 23, 877-885, 2001.

2.

Roy, R., Sarkar, B.H. and Bose, N.R., Composites: Part A, vol. 32, 871-876, 2001.

3.

Baucom, J.N. and Zikry, M.A., Composites: Part A, vol. 36, 658-664, 2005.

4.

Belingardi, G. and Vadori, R., Composite Structures, vol. 61, 27-38, 2003.

5.

Liu, D., J. Composite Materials, vol. 38, 1425-1442, 2004.

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IMPACT BEHAVIOUR MODELLING OF A COMPOSITE LEADING EDGE STRUCTURE G. Labeas and Th. Kermanidis Laboratory of Technology and Strength of Materials Department of Mechanical Engineering and Aeronautics, University of Patras, 26500 Rion, Greece [email protected] A methodology for the numerical simulation of bird impact on a novel Leading Edge (LE) structure of a Horizontal Tail Plane is presented. The innovative LE design is based on a ‘tensor skin’ structure, which is an efficient impact resistant design, comprising one or more folded composite sub-laminates, which unfold during the bird impact, providing the required high-energy absorption efficiency. The simulation technique is based on the non-linear dynamic Finite Element PAM-CRASH code and is performed in two steps. The first step deals with the development of suitable material damage models for the composite fabric materials of the LE skin. The developed damage models are capable to describe the material behaviour at the high strain rate conditions, which occurr during the high velocity bird strike event. Different material damage modelling approaches were considered, resulting to a successful and innovative solution for the representation of the composite fabric materials stress – strain behaviour. The second step of the numerical methodology deals with the numerical simulation of bird strike experiments on representative LE structures. Critical issues of the modelling, such as, the damage model of the bird impactor, which is considered as flexible in the current analysis, the mesh density of the highly impacted areas and the methods to represent the actual contact phenomenon of the structural interfaces, are presented. The validation of the methodology is performed by comparisons between numerical and experimental results. Assessing the optimal set of parameters in the numerical model, such as, mesh density, contact thickness and anti-crossing force parameter of the Smooth Particle Hydrodynamics (SPH) bird model, required a thorough examination of the way each parameter affects the numerical results. A comparison between the experimentally and numerically predicted bird strike sequence of the Leading Edge structure is presented in figure 1. Comparisons between measured and calculated test rig reaction force histories were also performed, in order to evaluate the model efficiency (see fig. 2). The numerical predictions for an 80 m/s bird strike indicate that the structure could survive the impact with minimum laminate damage. These simulations are found to be in good agreement with test results. The measured and calculated reaction loads are also found to be in a good agreement, signalising that the numerical model with the optimised material damage model and the bird impactor modelled as a flexible body reaches a high level of success in predicting the loads and damage of the impacted structure. It can be concluded that a simulation methodology for the bird strike on a composite LE was developed, which comprises a useful tool for the analysis of the high velocity impact of a large object on an anisotropic thin shell structure with complex geometry. The work is part of BRITE EURAM Project “CRAHVI” (“CRashworthiness of Aircraft for High Velocity Impact”) supported by European Union. The authors wish to acknowledge financial support from the CEC FW5 Research Program and the CRAHVI Partners for their scientific contributions.

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FIGURE 1: Comparison of experimentally and numerically predicted bird strike sequence of a Leading Edge structure

FIGURE 2: Comparison between experimentally measured and numerically predicted test rig reaction forces during bird strike

References 1.

Gallard JP. Report on Composite Commuter Leading Edge Bird Strike Tests. CRAHVI internal report, CEAT, 2002

2.

PAM-CRASHTM Solver notes and reference. ESI Group, 2001

3.

Johnson AF, Pentecôte N, Kraft H and Weissinger H. Measurement of Dyneema/epoxy composite Mechanical Properties, CRAHVI internal report, DLR IB 435-2002/15, 2002

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BENDING STRENGTH OF SANDWICH PANELS WITH DIFFERENT CORES AFTER IMPACT W. Goettner and H. G. Reimerdes Institut für Leichtbau, Aachen University Wüllnerstr. 7, D-52062 Aachen, Germany [email protected] In this paper results of low velocity impact tests on sandwich panels are presented. All investigated panels have the same quasi isotropic CFRP-face sheets. Goal of this work was to investigate the impact behaviour of panels having different cores. Besides Nomex honeycomb core, slotted Nomex honeycomb core, and slotted Aramid honeycomb core, foam cores with embedded CFRPpins (X-core and K-core, see Fig. 1 from [1]) are investigated. The pins are connected to the top layers to reinforce the panels mechanical properties.

FIGURE 1. X-core and K-core structures [1]. The tests are performed using a drop tower with an impact body which has a ball-shaped head of one inch diameter. Various impact energies are used to generate different damage mechanisms in the panels. During the tests the reaction force, the displacement and the impact velocity are measured. After impact, the achieved damage sizes in the upper face sheets and in the core are measured by means of ultrasonic scanning. Selected specimens with impact damage are cut out of the panels and analyzed by use of a scanning-electron microscope.

FIGURE 2. Wrinkling failure of sandwich panel in the four-point bending tests. The bending strength of undamaged and of impacted panels was measured in four-point bending tests. In most cases the specimen failed in wrinkling of the upper face sheets (FIG. 2). This was confirmed by simple analytical investigations of the problem.

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In parallel, the impacts were simulated numerically using LS-DYNA (FIG. 3). By use of material data achieved by measurement a good agreement between tests and numerical investigations was reached (FIG.4).

FIGURE 3. FE-model of the X-core panel.

FIGURE 4. Impact force versus time.

References 1.

AZTEX Inc. http://www.zfiber.com/x-cor.php

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ENERGY ABSORBING ABILITY OF SANDWICH COMPOSITE STRUCTURES J. P. Dear, W. Maruszewska, S. T. Oh and H. Lee Imperial College London South Kensington Campus, London, SW7 2AZ [email protected] There is increasing interest in the impact energy absorbing ability of lightweight sandwich and similar materials. This is for reducing the unladen weight of transporters to achieve improved operational performance with better fuel economy and lower other direct operating costs. These requirements very much relate to the increasing demand for more transportation systems and the need for increased safety as traffic congestion rises. Two safety needs are to reduce the risk of penetration into the cabin space when impacts occur and to lower the deceleration rate for the occupants. The aim of this study was to investigate the impact energy absorbing ability of sandwich materials that have different skin and honeycomb cores. This was for different impact conditions as simulated by drop-weight and constant velocity impact experiments. These studies assess the energy absorbing damage at all stages of the impact and relate this to the impact conditions in terms of size and shape of impact contact surface and closing velocities. Also, determined were the retained integrity of the sandwich materials at different stages of the impact up to and after it has been penetrated. Examples of some of the sandwich materials evaluated [1-4] are given in Table 1. TABLE 1. Examples of sandwich material.

For the drop-weight impact experiments, an impactor mass of 1.55 kg was used with drop heights of 0.2 to 1.0 m (up to 4.4 m s-1). Honeycomb sandwich material specimens were 150 mm square with support diameter of 100 mm. Force-time and energy absorption data were correlated to highspeed photography as well as c-scan and sectional damage assessments. Fig. 1 shows the behaviour of a Fibrelam sandwich panel for 0.2, 0.6 and 1.0 m drops with the force-time trace for a 1.0 m drop annotated with frame numbers from a high-speed sequence. Fig. 2 shows that Fibrelam panels exhibit the highest peak loads and this is for the lowest maximum displacement of the impactor. The c-scan damage data show that the Fibrelam and H620 front skins spread the impact deformation process more than the skins of H220 and H640 reducing the depth of sectional damage.

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FIGURE 1. Fibrelam: (a) Force-time and (b) Energy absorption for 0.2, 0.6 and 1.0 m drops; (c) Force-time and (d) High-speed sequence for 1.0 m drop.

FIGURE 2. Impact response and damage: (a) For different sandwich panels; (b) Example of c-scan related to sectional damage for Fibrelam panel for a 1.0 m drop.

References 1.

Dear, J.P., Lee H. and Brown, S.A., Int. J. Impact Eng., In Press for 2005.

2.

Lee, H., Drop-weight and ballistic impact of honeycomb sandwich structures, PhD Thesis, Imperial College London, University of London, 2004.

3.

Maruszewska, W., Failure processes in composite sandwich structures for automotive and similar applications, PhD Thesis, Imperial College London, University of London, 2005.

4.

Oh, S.T., Impact response and damage to composite pultruded beams, PhD Thesis, Imperial College London, University of London, 2005.

36. Impact Failure of Laminated and Sandwich Composite Structures

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IMPACT BEHAVIOUR OF METAL FOAM CORED SANDWICH BEAMS S. McKown and R. A. W. Mines University of Liverpool, Department of Engineering, Brownlow Street, Liverpool, L69 3GH, UK [email protected], [email protected] Previous work on the drop weight impact behaviour of polymer composite sandwich beams subject to three point bending has been concerned with beams with polymeric cores (Divinycell H100, H200) and pre-preg UD glass epoxy skins (SP Systems SE84) laid up in a cross ply form [1,2]. In the work, a mass of 1.49 kg was dropped from a height of 2 metres giving an impact velocity of 5.9 m/s and an impact energy of 26 J. The beam span was 200mm and the core depth was 10mm. The impact energy was enough to cause failure of the upper skin, and some progressive collapse of the core. The failure of the upper skin was due to in-plane compression. In references [1,2], the experimental tests were simulated using the implicit finite element code, ABAQUS Standard. In the simulation, the failure of the upper skin was modelled using a user defined field, in which the stiffness of the skin was degraded as a function of strain and the skin then completely failed at a given strain. The multi-axial crush behaviour of the core was modelled using critical state theory (i.e. the *FOAM model), and both uniaxial and hydrostatic foam crush data was used as input into the simulation. Good agreement was shown between experiment and simulation. It was shown that strain rate effects for skin and core damage were secondary, and so these effects were not included in the analyses. This work has now been extended to three point bend beams with metal foam cores (Alporas) and UD glass reinforced polypropylene skins (Plytron). The skin lay up was similar, i.e. crossply. This paper describes some experimental tests, in which a mass of 1.83 kg is dropped from a height of 2 m, giving an impact velocity of 5.9 m/s and an impact energy of 32 J. The beam span was 200mm, and the core depth was between 20 and 40mm. It is shown that the mode of beam failure is similar to the polymeric foam cored case, i.e. upper skin compression failure and stable crushing of the core. However, an additional complication is core shear failure at large beam deflections, after the upper skin has failed. Experimental tests are simulated using the explicit finite element code, DYNA. As the focus of this study was the progressive collapse of the metal foam core, a simple damage model was employed for the skin. This was based on the Hashin criterion [3] for initiation and a constant damage stress to a specific failure strain for post failure behaviour (Mat54 in DYNA). The simulation of the crush behaviour of the core was achieved with a continuum model (Mat63 in DYNA). A comparison of the available continuum metal foam crush models in DYNA has been given by Hanssen et. Al. [4], and they conclude that all the available models have their advantages and disadvantages. It was decided here to use the simplest continuum model in DYNA. Hydrostatic core crush and core and skin strain rate effects were not included in the model, as these were thought to be secondary. However, the shear failure of the metal foam core after upper skin failure was modelled, and a maximum principal strain criterion was used. This criterion will be compared with other failure criteria in the literature. A problem with using an explicit finite element code is the modelling of quasi static tests. Quasi-static conditions were modelled by using increased materials densities and adjusted force time input.

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The static and impact numerical simulations compare well with experiment, from the points of view of remote force and beam displacement data, as well as overall beam deformation profiles. The beam numerical simulation raises some interesting issues relating to the modelling of the progressive collapse of composite sandwich structures. Firstly, the applicability of a continuum model to the foam core is discussed. Typically, cell sizes in the Alporas foam are of the order of 3mm, and this size can vary by up to 100%. This means that the core depth in the sandwich structure needs to be at least 20mm, and preferably 40mm, for a continuum approach in foam core modelling to be valid. Also, continuum models become inaccurate for shear stress cases and for progress damage cases. These issues were investigated using an Arcan testing technique for foams [5], in which simultaneous tensile and shear stresses can be imposed on a block of foam. Experimental data from foam Arcan tests were simulated using DYNA, and the limitations in continuum modelling defined. This work goes some way to defining the limitations of continuum modelling for the progressive collapse of composite sandwich beams. The paper briefly discusses the alternative approach of micro mechanical modeling for the metal foam, as a way of more accurately modelling shear and progressive metal foam failure, in the context of the given structure.

References 1.

Mines, R.A.W. and Alias, A., Comp. Part A, vol 33,11-26,2002

2.

Mines, R.A.W. and Alias, A. In Progress in Structural Mechanics, edited by F Paris and J Morton, Seville University Press, 2000, 11-21.

3.

Hashin, Z., J. Appl. Mech., vol. 47, 329-334, 1980

4.

Hanssen, A.G., Hopperstad, O.S., Langseth, M., and Ilstad, H., Int. J. Mech. Sc., vol 44, 359406, 2002

5.

Chen, C., and Fleck, N.A., J. Mech. Phys. Sol., vol. 50, 955-977, 2002

37. Mesofracture and transferability

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STRESS GRADIENT AT NOTCH ROOTS USING VOLUMETRIC METHOD H. Adib and G. Pluvinage Post-doctorant, Laboratoire de Fiabilité Mécanique (LFM) Full professor, Laboratoire de Fiabilité Mécanique (LFM) Université de Metz-ENIM, Ile du Saulcy, 57045 Metz, France [email protected] The hot spot methods exhibit few defects to appraise flawless fatigue life prediction. The mentioned methods suffer from a real maximum stress location and magnitude, elaborated plastic zone features at notch tips or welded toes [G. Pluvinage, Fracture and Fatigue Emanating from stress concentrators, Dordrecht: Kluwer Academic Publishers, 2003. ] and stress gradient [A. Buch, Analytical approach to size and notch effects in fatigue of material specimens, Material Science and Engineering, Vol. 15, 7585, 1974.][A. Brandt, Calcul des pièces à la fatigue par la méthode du gradient, Editor CETIM, 1980.]. According to the finite element elastic-plastic stress distribution along notch tips, the peak stress does not appear at notch head and it requires certain distance to attain maximum stress value. Moreover, the fatigue mechanism needs to be considered as a physical volume according to fatigue tests large scatters based on Weibull‘s distribution method, specimen size and stress gradient dependence of experimental fatigue results [G. Pluvinage, Fracture and Fatigue Emanating from stress concentrators, Dordrecht: Kluwer Academic Publishers, 2003. ]. The stress gradients around notch tips are also significant according to the weight influence on extracted stresses along notch tips [G. Qylafku, Z. Azari, N. Kadi, M. Gjonaj, G. Pluvinage, Application of a new model proposal for fatigue life prediction on the notches and key-seats, International Journal of Fatigue,21, 753-760, 1999.][H. Adib, G. Pluvinage, Theoretical and numerical aspects of volumetric approach for fatigue life prediction in notched components, International Journal of Fatigue, 25(1), 67-76, 2003.]. In the present study, the role of relative stress gradient for fatigue life assessment using volumetric method is highlighted. The polynomial volumetric method point of view has been proposed which satisfies weight function conditions, removes numerical derivation errors, elucidates effective stress terms as subtraction of average stress and relative stress gradient based phrase. According to the elastic-plastic finite element outcomes for considered notched specimens, Stress Peak Trajectory Path “SPTP” and Effective Stress Trajectory Path “ESTP” have been proposed. The “PSTP” represents linear characteristics in logarithmic diagram and it can be applied to avoid more excessive mesh density generation refinement around notch roots for low applied loading magnitudes. The “ESTP” yields the effective distance-effective stress curve and effective stress-applied loading magnitude curves which can facilitate the calculation of effective stress and effective distance due to the parabolic shape configuration of mentioned curves.

FIGURE 1. a) Maximum principal stress distribution including Peak Stress Trajectory Path b) Effective Stress Trajectory Path versus applied loading magnitude and effective stress.

H. Adib and G. Pluvinage

1268

The volumetric method and Stress Field Intensity method are compared for the weight functions and corresponding stresses at notch roots. The comparisons exhibit that polynomial volumetric weight function completely satisfies all necessary requirements and the volumetric effective stress is lightly greater than Stress Field Intensity stress. The current phenomenon concludes less number of cycles to failure relative to the Stress Field Intensity method which overestimates it. In the present study, volumetric method is investigated and compared to the stress field intensity method. The main outcomes can be summarized as: 1

The stress gradients near notch roots play an important role in fatigue life prediction of notched bodies and the non-gradient based methods can not perfectly assess fatigue life duration of multi-notched specimens.

2

The stress concentration values near notch ahead are not solely main object and it is necessary to be accompanied by stress gradient considerations.

3

The polynomial volumetric method notation for effective stress, effective distance resolves the numerical derivation errors which arise due to truncation and round off errors.

4

The polynomial notation significantly prepares more complete physical ideas about the average stress and role of stress gradient in weight function and effective stress computations.

5

The volumetric weight function displays interactive response as a function of distance along notch roots and it has not been restricted to the notch ahead like Yao’s weight function [Yao Weixing, Xia Kaiquan, Gu Yi, On the fatigue notch factor kf, International Journal of Fatigue, 17(4), 245251,1995.].

6

The polynomial weight function completely satisfies smooth specimen consideration fact, whereas, the Yao’s weight function does not exactly fulfill this requirement [Yao Weixing, Xia Kaiquan, Gu Yi, On the fatigue notch factor kf, International Journal of Fatigue, 17(4), 245-251,1995.].

7

The proposal of Stress Peak Trajectory Path “SPTP” as one useful tool to avoid mesh density variation along notch roots and corresponding linear behavior in logarithmic diagrams.

8

The proposal of effective distance-effective stress curve and effective distance-applied loading magnitude curve based on Effective Stress Trajectory Path “ESTP” concept for evaluating of effective distance and effective stress in parabolic shape graphs.

References 1.

G. Pluvinage, Fracture and Fatigue Emanating from stress concentrators, Dordrecht: Kluwer Academic Publishers, 2003.

2.

A. Buch, Analytical approach to size and notch effects in fatigue of material specimens, Material Science and Engineering, Vol. 15, 75-85, 1974.

3.

A. Brandt, Calcul des pièces à la fatigue par la méthode du gradient, Editor CETIM, 1980.

4.

G. Qylafku, Z. Azari, N. Kadi, M. Gjonaj, G. Pluvinage, Application of a new model proposal for fatigue life prediction on the notches and key-seats, International Journal of Fatigue,21, 753-760, 1999.

5.

H. Adib, G. Pluvinage, Theoretical and numerical aspects of volumetric approach for fatigue life prediction in notched components, International Journal of Fatigue, 25(1), 67-76, 2003.

6.

Yao Weixing, Xia Kaiquan, Gu Yi, On the fatigue notch factor kf, International Journal of Fatigue, 17(4), 245-251,1995.

37. Mesofracture and transferability

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LOCAL APPROACH USE AT SOLUTION OF FRACTURE PARAMETERS TRANSFERABILITY L. Jurasek, M. Holzmann and I. Dlouhy Institute of Applied Mechanics, Veveí 95, 611 00 Brno Institute of Physics of Materials ASCR, Žižkova 22, 61662 Brno, Czech Republic, [email protected] A number of works have been published demonstrating that the pre-cracked Charpy (PC) specimens can be, after meeting the validity conditions and/or adjusting the raw data, successfully used for specification of fracture toughness characteristics corresponding to standard (1T) specimens. The procedures showing how to adjust the fracture toughness data determined from PC specimens for fracture resistance characterisation of full scale component include the probabilistic methods, toughness scaling models, introduction of other methods for constraint loss correction, master curve methodology etc. There are boundary cases when no direct fracture toughness characteristics adjustment is necessary and only the validity conditions have to be carefully checked. Typically this is the case of pearlitic steel EN7 (commonly used for wheelset production) having Lüders plateau and higher strength properties. In order to explain the deformation and fracture processes 3D FE simulation of the PC specimen quasistaticaly loaded in three point bending has been performed. The aim of the paper can be seen in explanation of the local behaviour at the crack tip of PC specimens being affected by Lüders flow. Relation of the measured and calculated characteristics of the material behaviour should be analysed giving corresponding explanation. The standard EN7 steel cut from exactly defined locations of railway wheelsets was used for the investigation. Deformation and strength properties and true stress/true strain curves were generated from standard tensile tests. Standard fracture toughness values were determined by using CT specimens, as prescribed by EN 13262. PC specimens were tested at room temperature and at 0 °C. The results are summarized in rank probability diagrams shown in Fig. 1.

FIGURE 1. Rank probability diagram a) left: PC specimens at 0 and 20 °C, b) right: CT specimens at 21.5 °C

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Two types of fracture behaviour have been observed: Several specimens having fracture force Ffr at the point of instable cleavage fracture less than net section yielding force Flim and the other part of specimens with the fracture force at onset of cleavage greater than Flim. For specimen with Ffr < Flim the fracture toughness was calculated using Linear-Elastic Fracture Mechanics but the initial crack length was adjusted for crack tip plasticity effects (Irwins approach, Kec fracture toughness values). For specimens with Ffr > Flim elastic plastic fracture toughness KJc was calculated from Jc evaluated at the point of cleavage. There is a gap in fracture toughness data of PC specimens between the value of 60 and 90 MPam1/2 (Fig. 1a). The phenomenon that is caused by great increase of deflection, which occurred due to plastic hinge in net section of “small” PC specimens loaded by bending to the point when the applied load attains closely Flim forces. At the same, time this phenomenon is also connected to several times steeper increase of crack driving force J; following the Flim force small increment of applied force F above Flim causes great increase of J. 3D FEM simulation have shown that the distribution of maximum principal stress 1 ahead of the crack tip in PC specimen loaded into fully plastic regime (J = 72.4 kN/m) have been identical with that of reference stress-strain field in plane-strain SSY condition (Fig 2a). There is no constraint loss. It is believed that this deformation behaviour of PC specimen is related to the real deformation properties of steel EN7 used as input into numerical study (true stress/true strain curve with Lüders flow). Fig. 2b shows the plot of local peak, 1max, of maximum principal stress near the crack tip for PC specimen and the reference stress-strain SSY field as a function of applied J, for two radii (R) simulating the crack tip in numerical computation. It is again observed the agreement of the magnitude of 1max for the two stress-strain states.

FIGURE 2. Stress distribution below the crack tip (having radii R of 0.01) for PC specimens (a) and development of the maximum stress with J values compared to SSY field (b). It has been found that for steel having at onset of yielding the Lüders plateau the deformation of PC specimen is different from those having continuous onset of plastic flow. Hence, when evaluating the fracture toughness values for the purposes of fracture resistance characterisation (e.g. for determination of reference temperature T0) this phenomenon has to be accounted for. Authors gratefully acknowledge to Grant Agency of the Academy of Sciences (GAAV 200410502 and 1QS200410502) for their financial support.

37. Mesofracture and transferability

1271

DAMAGE IN RUBBER-MODIFIED POLYMERS : EXPERIMENTAL, MODELLING AND COMPUTATIONAL ASPECTS Naïma Belayachi, Fahmi Zaïri, Noureddine Benseddiq and Moussa Naït Abdelaziz Laboratoire de Mécanique de Lille (UMR CNRS 1441), Université de Lille 1 Polytech’Lille, Cité Scientifique, 59655 Villeneuve d’Ascq cedex [email protected] Microstructural modification of materials is a well known technique which is used to enhance their mechanical properties. Examples of such materials are polymer blends, polymer composites, metal matrix composites, alloy systems and most of the natural materials, such as bone and wood. This heterogeneous aspect acts as an important factor on their macroscopic mechanical behaviour response. Relationships between the micro structural phenomena and the macroscopic deformation behaviour are required when predicting macroscopic properties from the microstructure of a material. Homogenisation methods are one of the way which can be followed to obtain a quantitative relation between the two scales. Here, the heterogeneous material is effectively replaced by an equivalent homogeneous one that represents the real material in an averaged sense. The fundamental assumption in these methods is the existence of a unit cell that is representative for the microstructure of the material under consideration, the so called representative volume element (RVE). In this work, a numerical homogenisation method has been adopted to model the mechanical behaviour of an heterogeneous solid material of which the microstructure typically consists of a continuous matrix material (here polymetylemethacrylate) with distributed rubber particles. In general, macroscopic quantities are formulated as averages of the corresponding microscopic state variables. The average of a quantity is taken over the region occupied by the unit cell [1, 2]. Furthermore, attention will be focused on the modelling of the mechanical behaviour of solid polymers. To account for both the large strains, time and history dependent material behaviour of the studied material, an hyper-elastic-viscoplastic description was adopted. The behaviour of rubber particles is described by a Mooney-Rivlin energy density function as formulated by Peric et al [3] , while the perfectly viscoplastic behaviour of the matrix is described by the model of Perzyna [4]. The Mooney Rivlin strain energy density function is written as :

c10 ( I 1  3)  c 01 ( I 2  3)  c1 1 ( I 1  3)( I 2  3) 

W

1 ( J  1) 2 d

(1)

where I1and I2 are the invariants of the right Cauchy-Green deformation tensor C, J the Jacobian, cij and d are material constants The history and time dependent nature of polymethylemethacrylate has been taken into account by Perzyna’s viscoplastic yield stress model [4] in which the viscoplastic strain rate is expressed as: 1

D

vp

§V ·m J ¨  1¸ ©V0 ¹

(2)

N. Belayachi et al.

1272

In equation 1, m and J defines respectively the strain hardening and the viscosity parameters (i.e. the sensitivity strain rate parameters).

V

is the material yield stress, and V 0 the static yield

4 1 stress of the material ( i.e. when strain rate does not exceed 10 s ).

In order to perform numerical simulations, the constitutive model has been implemented in a finite element code. A cell containing a cavitated particle has been modelled and the influence of surface tension has been analysed. The method has been validated by comparing results of homogenised simulations with experimental data. Figure 1 shows as an example, a comparison between experimental and finite elements results. A good agreement is highlighted.

Figure1 : Influence of strain rate (a) and particle volume fraction (b) on the strain-stress relationship of an RT-PMMA

References 1.

R. Hill, (1963), J. Mech. Phys. solids, 11, p. 357, 1963

2.

O. Van Der Sluis, P. J. Schreurs, H. E. H. Meijer, Mech. Mater. , 33, p. 499, 1999

3.

D. Peric, D. R. J. Owen, M. E. Honnor, Comput. Methods Appl. Mech. Engrg. , 94, p.35, 1992

4.

P.Perzyna, , plasticity today-modelling, methods and applications, A. Sawczuk (Eds) p. 657679, 1985

37. Mesofracture and transferability

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FAILURE ASSESSMENT DIAGRAMS BASED ON THE CRITERION OF AVERAGE STRESS Y. G. Matvienko Mechanical Engineering Research Institute of the Russian Academy of Sciences 4 M. Kharitonievsky Per., 101990 Moscow, Russia [email protected] The cohesive zone model and the failure criterion averaging the local stress over the cohesive zone ahead of the crack tip have been suggested for solids with a crack or a notch to develop the failure assessment diagram approach. A simple Dugdale-Barenblatt type cohesive zone model is employed to describe the deformation and failure process ahead of the crack (or notch) tip. The fracture criterion has been employed in the form of the average stress limitation in the cohesive zone ahead of the crack tip, i.e. the normal elastic stress ahead of the crack tip is averaged over the cohesive zone length. The stress distribution on the crack extension line has been described for a body with a finite crack by exact elastic solution according to the well-known form. In contrast to a classical cohesive model, the cohesive stress V coh is treated by Matvienko [1] according to von Mises yield criterion as a property of both the material and the applied stress. Failure curves have been obtained for an infinite plate with a finite crack under two simple mode of loading, namely, an uniform remote tensile stress V and an uniform internal stress applied to crack’s faces (Matvienko [2, 3]). The results clearly show that the failure curves are dependent on mode of loading and stress conditions (plane strain or plane stress). It is seen that opposite to the case of uniform remote loading the failure assessment curve decreases with the decreases of normalized applied stress (Fig. 1). Moreover, the failure assessment diagram becomes raised above the failure assessment diagram for a crack under remote uniform loading. The cohesive model and the local failure criterion of the average stress have been successfully adopted for a solid with a notch as well as a crack. In this case, the stress distribution at the notch tip is simplified considerably on the continuation of the notch (e.g. Creager and Paris [4]). The

fracture criterion for a solid with a finite notch is presented as K 1notch

K 1C

§ V 1  ¨¨ © V coh

2

2 · ª § V coh · 1 º ¸¸ «1  ¨ ¸ 2 » ¹ «¬ © V ¹ K t ¼»

1 / 2

(1)

The failure curve of a solid with a crack falls below the failure curve of a solid with a notch. The difference between these failure curves increases with decreasing the elastic stress concentration factors K t (Fig. 2). The present approach has been spread to describe failure curves in terms of the CTOD and the J-integral. When the requirements of the standard SSY state, or the J-dominant stress state are met, the J-integral and the CTOD are equally valid crack tip characterizing parameters. When the crack tip conditions are no longer characterized by the value of J, the J-CTOD relation becomes dependent on the applied critical stress, i.e. the crack tip constraint effect appears.

1274

Y. G. Matvienko

FIGURE 1. Failure assessment diagrams for a crack under uniform remote and internal tensile stresses (plane stress).

FIGURE 2. Failure assessment diagrams for specific elastic stress concentration factors K t (an infinite plate with a notch under an uniform remote tensile stress).

References 1.

Matvienko, Yu.G., Int. J. Fracture, vol. 98, L53-L58, 1999

2.

Matvienko, Yu. G., Int. J. Fracture, vol. 124, 107-112, 2003

3.

Matvienko, Yu. G., Int. J. Fracture, vol. 131, 309, 2005

4.

Creager, M. and Paris, P.C., Int. J. Fracture, vol. 3, 247-252, 1967

38. Damage in Composites

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MATERIAL MODELS FOR DAMAGED COMPOSITE LAMINATES J. Varna Dept of Applied Physics and Mechanical Engineering Lulea University of Technology, SE 97187, Lulea, Sweden [email protected] In long fiber composites with unidirectional or multidirectional orientation of the reinforcement several damage modes develop during the service life. The most typical and first damage mode is related to intralaminar crack formation in off-axis layers of prepreg laminates or in off-axis bundles in case of Non-Crimp Fabric (NCF) or woven composites. Accumulation of individual fiber fractures in layers oriented parallel to the main loading direction is also typical. More unusual are breaks of fiber bundles oriented in the loading direction observed recently in NCF composites. Part of the bundle interface can be debonded from the rest of the composite. Some examples are given in Fig.1. Common for these damage entities is that each damage mode is usually localized in a certain phase (in a fiber, matrix, at the interface, inside a bundle of a given orientation, inside a layer) and is characterized by a distinct orientation and size. This simplifies the damage characterization and model development.

a) intralaminar cracks in cross-ply laminate

b) broken bundle and intralaminar cracks in NCF composite FIGURE 1. Typical damage modes in long fiber composites. In this paper a unified approach for thermo-elastic properties reduction due to the described damage is presented. Exact closed form expressions are derived which contain constituent properties, composite architecture parameters and density of damage entities belonging to particular mode. Very robust local characteristics of the micro-damage – normalized average crack face opening (COD) and crack sliding (CSD) displacements also enter these expressions. Their dependence on constraining material stiffness and geometry is described by simple power laws which are obtaining in result of numerical parametric analysis using FEM. For example, stiffness matrix of the damaged composite may be expressed in the following form

J. Varna

1276

§ U kn ¨ >I @  ¦ V ¨ k E Tk ©

>Q @RVE

k

>Q @ >T @ k

T k

>U @k >Q @k >H @k >T @Tk >S 0 @RVE 1

> @

· ¸ Q 0 ¸ ¹

RVE

(1)

Here > Q @ k is a layer stiffness matrix in symmetry axes, > T @k is the stress transformation matrix,

V k is the volume fraction of the constituent (bundle, layer, fibers, matrix etc.), matrixes with index 0 represent undamaged composite compliance and stiffness, U kn is normalized crack density in the damaged constituent, >U @ k is the matrix of normalized crack face displacements described by power law, ETk is transverse modulus of the constituent. The > H @ k -matrix defines the relationship between k-th element boundary averaged strains and the strains applied to the RVE. In this work the relationships for > H @ k are developed based on results of FEM parametric analysis. In the local system of coordinates coupled with the material symmetry or with the local geometry the relationship is ba

­° H L ½° ® HT ¾ °¯J LT °¿ k

ª H 11 « « H 21 ¬« 0

H 12 H 22 0

½° ¾ ¯ LT °¿ RVE

º ­ HL » ° 0 » ® HT » k °J H 66 ¼ 0

(2)

The H-matrix dependence on geometrical and mechanical parameters of constituents has been analyzed using FEM and dependence is described by power laws. In case of laminate the constituent is a unidirectional layer with a certain orientation and the H-matrix is identity matrix. The accuracy of the developed predictive tool is high and the model has been validated by comparing with direct calculations using FEM as well as with numerous experimental data.

References 1.

Joffe, R., Mattsson D. and J. Varna, Proceedings of CANCOM 2005 conference, Vancouver, 2005, 10p.

2.

Highsmith, A.L. and Reifsnider, K.L., Damage in Compos. Mater., ASTM STP 775, American Society for Testing and Materials, 1982, 103-117.

3.

Varna, J. and Berglund, L.A., J. Compos. Technol. Res., 16, 1994, 77-87.

4.

R. Joffe, A.Krasnikovs and J. Varna, Composites Science and Technology, 61(2001), 637656.

5.

J.Varna, Proceedings of ECCM-10, Brugge, 2002, 7 p.

6.

Lundmark P. and Varna J., International Journal of Damage Mechanics in press 2005.

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RAMAN SPECTROSCOPY ASSESSMENT OF STIFFNESS REDUCTION AND RESIDUAL STRAINS DUE TO MATRIX CRACKING IN ANGLE – PLY LAMINATES P. Lundmark1, D. G. Katerelos2, J. Varna1 and C. Galiotis2,3 1Department of Applied Physics and Mechanical Engineering, Lulea University of Technology, SE 971 87, Lulea, Sweden 2Foundation Of Research and Technology Hellas/Institute of Chemical Engineering and High Temperature Processes, Stadiou str, Platani, Patras, PO Box 1414, GR-265 04, Greece 3Materials Science Department, University of Patras, Rio University Campus, Patras, GR–265 04, Greece [email protected] Off – axis ply cracking in composite laminates and especially its effect on composites thermomechanical behaviour has been extensively studied in the case of cross – ply stacking sequence; see Katerelos and Galiotis [1], Joffe and Varna [2], and Katerelos et al. [3]. During the last decade, the extension of this research to more complex composite systems used in practice has been addressed and is still under development; see Crocker et al. [4], Katerelos et al. [5], Lundmark et al [6]. In the presented work a detailed analysis of the effects of evolved damage on the behaviour of a [0/45]s laminate under uniaxial tension is presented. Laser Raman Spectroscopy has been applied for the experimental measurements of the strain state variations due to damage within the specimens. Residual strain and stiffness reduction were derived using experimental Raman data, as a function of crack density increase and the results were compared with theoretical predictions using the model presented in [6]. Indicative conclusions on viscoelastic phenomena affecting the behaviour of angle – ply laminates were extracted. A glass fibre reinforced epoxy system was used for experimental investigation of the damage developed in a [0/45]s composite laminate. It was selected due to the special mechanical properties that it exhibits in addition to the ability of manufacturing translucent specimens useful for the Raman spectroscopy inspection. The use of an embedded Aramid fibre – sensor within the 0° ply and near the 0°/45° interface was necessary due to the poor Raman signal for a glass. This technique has been extensively applied in the case of cross – ply laminates. The derivation of macroscopic quantities from Raman data is explained in [1] and [2]. One of the main problems arising when dealing with model laminates different than cross – ply is that the common shear – lag analyses and variational models are not applicable, for example, if the laminate is non – balanced (i.e. [0/45]s laminate) . The model used in this work does not have this problem. It gives exact closed form expressions for all thermo-mechanical properties of a general symmetric laminate with cracks in arbitrary layers. The properties are expressed in terms of laminate lay-up, layer properties and crack density. Parameters characterizing the crack shape: average crack face opening and crack face sliding displacements also enter the stiffness expressions. For a given laminate configuration these robust parameters can be calculated using simple power laws. The derived constitutive relationships can be used also to determine the dimensional changes due to evolution of the damage state. For this task they are applied for a zero mechanical load case. The residual strain development is caused by release of thermal tensile stresses in the cracked layer due to crack development.

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Residual strain and stiffness reduction as a function of crack density derived from experimental Raman data as well as the theoretical model predictions are presented in the following comparison charts of Fig. 1a and b.

(a)

(b)

FIGURE 1 (a) Residual strain variation with increasing crack density. (b) Longitudinal modulus reduction as a function of increasing crack density in 45-layer The stiffness reduction is predicted with a high accuracy whereas the measured residual strains are larger than predicted. The good agreement of elastic modulus reduction proves that the power law expression for crack face displacements, which is the only approximation in the model, is accurate. However, the same values of displacements used in residual strain do not fit the experiment. We explain the difference by viscoelastic – viscoplastic behavior of the off axis layer in shear which increase the “apparent” residual strain. The two curves in Fig 1.b correspond to two possible boundary conditions in the load application area.

References 1.

Katerelos, D.G., McCartney, L.N. and Galiotis, C., Acta Mater, accepted for publication (DOI: 10.1016/j.actamat.2005.03.045).

2.

Joffe, R. and Varna, J., Comp Sci Tech, vol. 59, 1641 – 1652, 1999.

3.

Katerelos, D.G. and Galiotis, C., App Phys Lett, vol. 85, 3752 – 3754, 2004.

4.

Crocker L.E., Ogin S.L., Smith P.A. and Hill P.S., Comp A: App Sci Man, vol. 28A, 839 – 846, 1997.

5.

Katerelos D.G., Galiotis C., Ogin S.L. and Whattingham R.D., In Proceedings of the ECCM – 9 Composites – From Fundamentals to Exploitation, Proceedings on CD – ROM, 2000.

6.

Lundmark P. and Varna J., Int Jrnl Dam Mech in press, 2005.

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PHYSICAL MODELLING OF FAILURE PROCESSES IN COMPOSITE MATERIALS P. W. R. Beaumont University of Cambridge Department of Engineering, Trumpington Street, Cambridge CB2 1PZ, United Kingdom [email protected] Despite the acquisition of vast collections of mechanical property data, our ability to predict the structural integrity of a damaged composite subjected to mechanical and thermal stresses and hostile environment remains restricted. This is because our understanding of problems of composite failure is based almost entirely on this store of information being empirical in nature with limited knowledge of the structural changes taking place in the material over time. Lack of mastery in combining the design of the architectural features of composite materials at the atomistic and micron level of size, and elements of the engineering structure metres in length, has led to the opening of a gap in our knowledge of composite failure. This weakness can be traced to the changing nature of fracture as size increases from the sub-micron level of structure to the metre level of component failure. This size (or length) scale, which spans several orders of magnitude, provides a framework for understanding the failure characteristics of material on the one hand and performance limitation of the component on the other (Fig. 1). Coming to terms with these differences in behaviour as size changes appears to be a key source of design difficulty because at some point on this lengthscale the material problem becomes a structural one. Difficulty arises, however, when conditions become stringent, so that more properties are involved in the design process. We need constitutive equations for design that include all of the design variables including the material properties that in turn depend upon the geometry of the laminate and microstructure of the individual ply. A description of the material's response to a new set of circumstances requires a completely new set of experiments from which new continuum rules must be distilled. Modelling techniques are described, which quantify the accumulation of damage in the composite material in terms of the important structural features of the composite material, applied stress, time, temperature, and environment. Particular emphasis is placed on the internal state variable method. This is to take the path of “physical modelling”. Examples of physical models will be given. One case study is of fatigue cracking in carbon fibre-strengthened polymers. The physical model is based on the coupling mechanisms of splitting and delamination, microscopic processes controlled essentially by the properties of the matrix material. Another physical model is based on a micro-mechanical theory of stress-corrosion cracking in glass fibre-strengthened polymers. In this case study, the time-dependence of composite strength is explained in terms of the structural features of the composite, applied stress and environment. This physical model is based on stable crack growth by fibre fracture and matrix bridging in the crack wake.

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FIGURE 1 Hierarchy of structural scales ranging from the micron to the metre (and greater) level of size, from the single ply to the final structure, and discrete methods of analysis ranging from micro-mechanics to the continuum levels of modelling.

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NCF CROSS-PLY LAMINATES: DAMAGE ACCUMULATION AND DEGRADATION OF ELASTIC PROPERTIES R. Joffe and D. Mattsson Division of Polymer Engineering Lulea University of Technology SE-971 87 Lulea, Sweden [email protected], [email protected] Traditionally high performance composite parts (for instance structural parts used in aerospace applications) are made by lamination of prepregs. However, multi-axial warp knitted fabric (noncrimp fabric (NCF)) proved to be a good alternative. NCF composites combine fairly good mechanical properties with low production costs, high deposition rates and unlimited shelf life. Additionally to these benefits, NCF composites have also been reported to show increasing out-of plane fracture toughness and damage tolerance [1,2]. NCF composites are manufactured from preforms with multiple layers of straight fiber bundles with different orientations stitched together by a warp knitting procedure [3] (see Figure 1a). The main difference between prepreg-tape based laminates and NCF composites is that the former has an internal structure consisting of continuous fibers that are rather homogeneously dispersed; whereas NCF composite has continuous fibers combined in fiber bundles with well defined geometry (see Figure 1b).

(a)

(b)

FIGURE 1. NCF: (a) schematic picture (from Vectroply) and (b) micrograph. In this study, the response of Non-crimp fabric cross-ply composites to tensile loading is investigated. Tensile tests revealed that carbon fiber based NCF cross-ply laminates with different lay-up demonstrated large difference in damage tolerance. It was found that laminates of type A ([0/90/0/90]S) showed 40% reduction of Young’s modulus before final failure, whereas a laminate of type B ([90/0/90/0]S) showed a reduction in modulus of only 5%. These results are presented in Figure 2.

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FIGURE 2. Degradation of elastic modulus as a function of applied strain for carbon fiber based NCF cross-ply laminates with different lay-ups. Analysis of micrographs showed that damage in form of broken and delaminated bundles oriented in the loading direction were present in the laminates of type A, whereas laminates of type B only contained cracks in layers transverse to applied load. Numerical modeling (FE calculations) and ply discount model predicted results within the experimentally measured decrease of modulus (40%) due to a combined effect of both failure and delamination of 0°-bundles and transverse cracks in the 90°-bundles. Results presented in Figure 3 show normalized elastic modulus (normalized with respect to the modulus of undamaged laminate) as a function of extent of damage in 0°-layer (number of failed bundles).

FIGURE 3. Modulus reduction in a cross-ply NCF composite (due to failure and delamination of 0°-bundles) as a function of number of failed bundles.

References 1.

Dransfield, K., Jain, L. and Mai, Y-W., Compos Sci & Techno, vol. 58, 815-827, 1998

2.

Jain, L., Dransfield, K. and Mai, Y-W., Compos Sci & Techno, vol. 58, 829-837, 1998

3.

Steggall, P., In Proceedings 31 st International SAMPE Technical Conference, October 2630, 1999, Chicago, IL, USA

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MATRIX CRACK INITIATION AND PROPAGATION IN LAMINATES WITH OFF-AXIS PLIES N. Vrellos, S. L. Ogin and P. A. Smith School of Engineering, Guildford, Surrey, GU2 7XH [email protected], [email protected], [email protected] Matrix cracking damage in composite laminates is a generic type of damage, common to carbon, glass and aramid fibre composites fabricated using unidirectional plies, as well as more complex fibre architectures (e.g. textile reinforced composites). For such a common type of damage, it is perhaps surprising that currently proposed failure criteria are unable to predict matrix crack development, especially for off-axis plies. Previous work on GFRP laminates by Crocker et al. [1] suggested that matrix crack propagation in off-axis plies is governed by the transverse normal stress. The overall aim of the present work is to provide validated constitutive relations for crack accumulation in off-axis plies of CFRP under mixed mode loading. In this paper, results on crack initiation and crack propagation are presented for a range of multi-layer angle-ply laminates. A number of laminate configurations have been tested, providing both different off-axis ply angles and different off-axis ply thicknesses. The laminates were (a) four unbalanced laminates of the type (02/4)s, where is 45o, 60o, 75o and 90o; (b) a (0/90)4s laminate, which also provides (±45)4s coupons; and (c) quasi-isotropic laminates with configurations (0/90/r45)s, (02/902/r452)s and (02/r602)s. For the (02/4)s specimens with off-axis plies at angles of 45o, 60o or 75o, oblique end-tabs have been used to accommodate extension-shear coupling at the ends of the specimen. The angle for the end-tabs was calculated using a modification of a procedure developed initially by Sun et al. [2] in work on unidirectional composites. Coupons have been tested both with polished edges and with machined-in defects. The edges of all coupons were polished to a 1 µm finish using a Struers Pedemax-2 grinding/polishing machine. For the crack initiation experiments, coupons were tested with polished edges, whereas crack propagation experiments, which have been carried out only on the (02/4)s coupons, required the off-axis central plies to be notched. A 0.8 mm drill bit was used to drill holes, 3 mm deep, parallel to the direction of the fibres in the (off-axis) centre plies, without damaging the outer 0o plies. The tests were carried out to progressively higher strains by loading the coupons to a specific strain level, unloading, and then re-loading to a higher strain. Edge microscopy and X-radiography was used to monitor the crack accumulation during the strain increments. An example of crack development in a (02/454)s coupon containing notches is shown in Fig.1. The figure show six notches drilled into each edge of the 45-ply; matrix cracks can be seen which have developed from the notches after an applied strain of 1%. Data were obtained for crack density as a function of applied stress/strain and the reduction in laminate properties (Young’s modulus, Poisson’s ratio). Fig. 2 shows results for both unnotched and notched (02/4)s coupons. The transverse normal stress 2 value corresponding to initial cracking from notches is similar for the (02/904)s, (02/754)s and (02/604)s samples. Similarly, the stress for crack development in unnotched coupons is similar for these three laminate configurations, and about 20 MPa higher than for crack propagation from notches. The behaviour of the (02/454)s laminates is somewhat different, since there appears to be a significantly reduced value of 2, suggests that there is an interaction between the transverse normal and shear stress components in this case.

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FIGURE 1. Dye-penetrant X-radiograph of a notched (02/454)s coupon subjected to a strain of 1.0 %, showing cracks which have developed from the notches

FIGURE 2. Transverse normal stress as a function of shear stress for crack development in notched ( ) and unnotched ( ) coupons Data from the other multi-layer angle-ply laminates show consistent behaviour with the data from the (02/4)s laminates when the effects of ply thickness and neighbouring ply interactions are considered.

References 1.

Crocker, L.E., Ogin, S.L., Smith, P.A. and Hill P.S., J Compos Mater, 28A, 839-846, 1997

2.

Sun, C.T. and Chung, I., J Compos Mater, 24, 619-623, 1993.

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STRESS OSCILLATION AND INSTABILITY OF YIELDING IN POLYMERS AND NANOCOMPOSITES D. E. Mouzakis, G. Kandilioti, S. Tzavalas and V. Gregoriou Foundation for Research and Technology-Hellas, Institute for Chemical Engineering and High Temperature Chemical Processes, (FORTH-ICE-HT) Patras, GR-26504, Hellas. Tel : +30 2610 965205, Fax: +30 2610 965223 [email protected] Stress Oscillation (SO) is a yielding related-phenomenon known for polymers since the 1970’s. Some polymers exhibit periodic fluctuations of yield stress in the post yield phase of neck propagation. These periodic fluctuations correspond to the formation of opaque zones in the specimen necking area. The overall result is a striation pattern of alternating opaque and transpanent zones perpendicular to the drawing direction. SO has been confirmed for several types of polymers like amorphous copolyesters and poly(ethylene terephtalate) (PET)[1], high density polyethylene [2] and syndiotactic polypropylene (sPP) [3]. It has been also shown that it can appear at both semi-static [1] and impact loading conditions [2]. The appearance of this phenomenon and initiation mechanisms are still somewhat vague. Though, it has been successfully shown that the result of the phenomenon, are local changes in the polymer crystallinity and conformational order [3]. The purpose of our study was to study this phenomenon in nanocomposites based on sPP and a nanoclay, namely montmorrilonite. The phenomenon appeared in several compositions of the nanocomposites in montmorrilonite when the strain rate of tensile loading was changed. Structural changes in the SO zones of the nanocomposites samples were studied by means of scanning electron microscopy. Fourier transformed infrared spectroscopy (FT-IR) was employed in order to determine the exact changes in the nanocomposites microstructure and matrix conformational order. Nanocomposite thin films (200 m) films were manufactured by melt mixing of an organically modified montmorillonite (Cloisite®20A) with the sPP matrix and subsequent hot pressing and quenching at 0 oC. sPP nanocomposites with several compositions of montmorillonite, 0,1,3,5,7 and 10wt% were manufactured in this way. Tensile testing was performed on a H20K-W Hounsefield frame. Tests were run at different crosshead speeds varying from 5 to 40 mm/min, in order to determine the SO envelope of the nanocomposites. Specimens were cut by scissors in dumbbell shape. Finally, Fourier Transform Infrared Spectroscopy was performed with a Nicolet 850 FT-IR spectrometer equipped with an MCT/A detector. 128 scans were accumulated for each spectrum at 2 cm-1 spectral resolution. Figure 1 shows the Force-Displacement (F-X) curve of a sPP matrix specimen. SO was obtained at two different crosshead speed transitions 5 to 40 mm/min and 40 to 30 mm/min respectively. SO transition A was unstable whereas SO transition B held up to specimen rupture. So, it should be concluded here that the SO phenomenon is indeed dependent on the loading conditions and its stability is a function of the testing speed.

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FIGURE 1. Stress Oscillations in the sPP MATRIX. A:5 to 40 mm/min and B:40 to 30 mm/min crosshead speed transitions respectively

FIGURE 2. SEM micrographs showing the stress oscillated surface (A) and fracture surface (B) of a pure s-PP specimen As seen in Figure 2 SEM scans, the SO phenomenon produced a surface undulation on the sPP matrix seen in frame A on the left. Also, different fracture morpfologies are seen for the SO exterior and interior of the same specimen in frame B resulting in a skin-core structure of the SO zone. FT-IR scans have showed [3] a significant difference in the sPP matrix at the SO area: the helical form I is transformed to the metastable trans-planar from III marking a crystal crystal transformation for the SO bands.

References 1.

Karger-Kocsis, J. Benevolenski, O.I. Moskala, E.J., J Mater. Sci., vol 36, 3365 – 3371, 2001

2.

Mouzakis, D. E. Karger-Kocsis, J., J App. Polym. Sci., vol. 68, 561–569, 1998

3.

Gregoriou, V.G., Kandilioti, G. and Gatos, K.G., Vibr, Spectroscopy, vol 34, 47–53, 2004

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PREDICTION OF CYCLIC DURABILITY OF WOVEN COMPOSITE LAMINATES V. Tamuzs and K. Reifsnider Istitute of Polymer Mechanics Pratt&Whitney Chair for Reliability and Design Aizkraukles 23 St, Riga LV-1006, Latvia, 244 Weaver Road Unit 5233, Storrs, CT 06269-5233, USA [email protected], [email protected] It is well known that nonhomogeneous materials (such as composites), under cyclic loadings, change their properties because of damage accumulation. The classical approach to the lifetime prediction based on the damage concept involves an assumption that, at the end of durability, the damage level reaches a critical value. The term "damage" actually is not physically defined and obtains a physical meaning only through the parameters measured during a test. More often, the damage is identified with the density and orientation of microcracks or with the change in the stiffness or damping properties of a material [1]. For a woven composite, under a cyclic loading in the principal direction of orthotropy, the lifetime prediction by monitoring the damage kinetics through the change in compliance and the linearly increasing selfheating temperature was verified experimentally a long time ago [2]. In the present investigation [3] the behavior of a wowen orthotropic composite laminate in fatigue off-axis loadings was studied. In our program, the monitoring of changes in the modulus and hysteresis loop was carried out in all tests. It was found that the final critical damage level before failure, measured as a reduction in the cyclic modulus, did not depend on the durability and was invariant with respect to the loading direction too. Such an invariance of reduction in the final modulus allows one to predict the cyclic durability of materials with a reasonable accuracy for any testing angle. A satin-weave glass fiber-epoxy matrix composite was tested. A fiberite 934 epoxy was used for the matrix. A four-harness satin woven glass-fiber cloth was used for the reinforcement. The panels were cured for 2h at 180qC. The plate consisted of six plies — four plies in the 0º direction and two in the 90º direction. The thickness of the plate was 0.58-0.63 mm. The samples were cut out from plates in directions 0º, 15º, 30º, 45º, and 90º to the material symmetry axes. The width of the specimens was 18-20 mm, and the length between tabs was 100-120 mm. The tests were carried out on a MTS test rig. The strain was measured by an attached strain clip gage, and for data collection and processing of measurements, a Spider 8 device having eight channels and a maximal frequency of 9600 records per second was used. In static loading, at least two samples were tested for each direction. The V – H curves obtained were shown on Fig. 1, and revealed an essential nonlinearity. The cyclic loading was performed at a constant stress level. The loading frequency was 10 Hz, with an R-ratio of r = 0.1. The strain and stress values were registered at 120 points during one cycle, repeating these measurements 15-20 times during the experiment. These measurements allowed us to obtain the change in the cyclic modulus during the test. In Fig. 2 the S–N curves for all tested directions are shown. The experimental values are marked by dots; the continuous straight lines are approximations by the leastsquares method. The dotted lines are results of prediction, which is discussed below.

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The mean damage rate during the lifetime is defined as the final (registered in the last measurement) change in the modulus E divided by the corresponding number of cycles to failure

N:  D !  'E N , which is a function of durability, the stress applied, and the loading direction.

FIGURE 1. The stress-strain curves for specimens cut in five directions

FIGURE 2. S-N curves for all the directions tested

FIGURE 3. Mean damage rate as a function of durability for all test angles

FIGURE 4. Changes in the elastic modulus before failure for all test angles and durabilities

It is remarkable that the graph of the mean damage rate as a function of durability does not depend upon the angle of specimen orientation to the symmetry axis (Fig. 3). Independence of this curve on the angle T means that the final reduction of modulus 'E does not depend on the orientation of specimen and the final reduction of modulus does not depend on the durability N. In Fig. 4, the measured final change in the modulus as a function of durability for all test angles is shown in logarithmic coordinates. Having at our disposal the damage accumulation rate as a function of applied stress and the invariant isotropic value of the final damage level expressed in terms of the final reduction in the modulus, the cyclic durability of the woven composite investigated can be calculated. The predicted S-N curves are shown in Fig. 2 by dotted lines for all test angles. In the second part of paper the results for other loading asymmetries are reported.

References 1.

Kuksenko, V., Tamuzh, V., Martinus Nijhoff Publ., 1981.

2.

Oldyrev, P., Tamuzh, V., Polymer Mechanics, vol. 3(5), 571-576, 1967.

3.

Tamuzs, V., Dzelzitis, K., Reifsnider, K., Applied Composite Materials vol. 1(5), 259-293, 2004.

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REPAIR OF CORRODED AEROSPACE ALUMINIUM PANELS USING ULTRASONIC IMPACT TREATMENT C. A. Rodopoulos1, S. Pantelakis2, M. Liao3 and E. Statnikov4 1Structural Materials and Integrity Research Centre, Materials and Engineering Research Institute, Sheffield Hallam University, City Campus, Howard Street, S1 1WB, Sheffield, UK, 2Laboratory of Technology and Strength of Materials, Department of Mechanical Engineering & Aeronautics, University of Patras, Patras 26 500, Greece. 3Structures, Materials and Propulsion Laboratory, Institute for Aerospace Research, National Research Council Canada, M14, 1200 Montreal Road, Ottawa, ON. K1A 0R6, CANADA. 4Applied Ultrasonics, P.O. Box 100422, Birmingham, Al. 35210, USA. [email protected], [email protected], [email protected], [email protected] The practise of identifying corrosion damage, air-blasting to remove loose material, grinding to remove corrosion, shot peening to increase the fatigue properties and finally back assembly onto the aircraft for many years has governed aircraft operators under the term "find and fix". This empirical practise inevitably causes thickness and hence load bearing reduction while can locally overstress components. To avoid that a rule of thumb is implemented making sure that no more than 10% of the initial thickness of the material has been lost. Otherwise, the component should be replaced. It is not difficult to understand that such practise primarily lies within the expertise of the person performing the repair as well as the geometric complexity of the damage. If the corrosion damage is situated at a location which is difficult to grind or, and to peen then most certainly the quality of the repair will vary. The problem can have significant implication under cyclic loading considering that the residual stresses induced by shot peening will undergo continuous redistribution as part of their relaxation process, while irregular thicknesses can transform the design philosophy used for that component from safe life to fatigue damage tolerance. Herein, such repairs can start fatigue cracks following local stress raisers, due to stiffness loss especially when close to stiffeners or by redistributing shear strains when close to joints. The Ultrasonic Impact Treatments process is employing continuous ultrasonic vibrations at the ultrasonic transducer output end strengthened with hard materials (carbide-containing alloys, artificial diamonds etc.) and being in direct and generally continuous contact with the treated surface. During impact the near surface of the material experiences high strain rates as well as heating. The first is responsible for plastically deforming the material. The induced compressive residual stresses are significantly more stable than those induced by shot peening due to the fact that high rate straining of aluminium alloys generates energetically stable dislocation cells. Heating, on the other hand is responsible for reimbursing the loose material by melting the corrosion oxides. Hence, the final repair does not produce thickness reductions. The table below shows the results from exposing aluminium alloy 2024-T351 under ASTM exfoliation conditions for 36,48 and 72 hours prior to static testing. The results indicate that after exfoliation, all the measured mechanical properties experience degradation with time. Yet, after UIT the yield and ultimate tensile strength showed significant value recovery while in the case of the 36h registered values higher than the original uncorroded material. Microhardenss measurements, prior and after UIT, exhibited that the process can fully recover the corroded layer.

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TABLE 1. Experimental Results Material: Al 2024 T351 Direction/Number of Corrosion 0.2% Ultimate Elongation to Energy specimens exposure prior Yield tensile failure density to test strength strength A50 [%] W [MJ/ Rp0.2 Rm [MPa] m3] [MPa] L2 None 376.12 488.90 15.35 71.90 LT2 None 349.80 484.50 15.20 70.30 L2 Exfoliation 318.30 392.65 6.34 24.60 corrosion 36h LT2 Exfoliation 300.15 369.15 3.95 14.70 corrosion 36h L1 EXCO 36h + 407.30 479.00 6.85 29.00 Ultrasonic treatment LT1 EXCO 36h + 413.70 462.60 4.65 18.65 Ultrasonic treatment L2 Exfoliation 330.80 403.50 5.95 23.75 corrosion 48h LT2 Exfoliation 314.90 375.25 2.90 11.30 corrosion 48h L1 EXCO 48h + 391.75 459.65 5.10 28.40 Ultrasonic treatment LT1 EXCO 48h + 383.15 426.50 2.95 24.90 Ultrasonic treatment L2 Exfoliation 299.60 354.00 4.20 14.90 corrosion 72h LT2 Exfoliation 313.05 372.80 2.80 10.90 corrosion 72h L1 EXCO 72h + 362.50 433.45 4.40 16.40 Ultrasonic treatment LT1 EXCO 72h + 417.10 461.70 3.25 16.90 Ultrasonic treatment

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FATIGUE CRACK INITIATION IN STRESS CONCENTRATION AREAS C. Schwob, F. Ronde-Oustau and L. Chambon EADS CCR/ENSTIMAC, ENSTIMAC, EADS CCR 12 rue Pasteur, 92152 Suresnes Cedex, FRANCE [email protected] The fatigue life of structural components is determined by the sum of the elapsed cycles required to initiate a fatigue crack and to propagate the crack up to the critical dimension. The relative importance of these two phases depends on the level of loading. In the case of aeronautical structure, the loads are supposed to be far enough below the elasticity limit to consider that most of the fatigue life is expanded initiating the crack. Prediction of fatigue crack initiation is commonly achieved through the use of criteria. Although numerous criteria exist in the literature, few of them take into account stress-gradient effect, due to their local formulations. As a consequence they do not predict the well known difference which is observed in all metallic materials between traction and bending fatigue experiments, and are therefore of limited use for the analysis of structures where stress concentrations exist. To alleviate this limitation the basic idea is to use a non local formulation of these criteria. This is usually done either by introducing gradient dependent terms in their formulation (see Papadopoulos and Panoskaltsis [1]) or by averaging their values over a given volume (see Fouvry et al. [2], Banvillet et al.[3]). The latter approach has been retained in our model, since it appears to be consistent with experimental observations (Vivensang and Gannier [4]): before specimen failure, a damaged volume is observed where micro cracks develop. This fact is well illustrated by Fig. 1 which represents an observation of a specimen subjected to cyclic loading. The observation has been captured at 3.104 cycles before the specimen’s failure which occurred around 105 cycles. It can be seen on this figure that fatigue damage occurs in a widespread area.

FIGURE 1. Damaged area on the edge of the central hole of the specimen (Cracks are highlighted in red on the right) Since these micro cracks are initiated by micro plasticity at the level of the grain, a mesoscopic criterion has to be used in order to define this damaged volume: Vd

^M , mesoscopic _ criterion( M ) t 0`

(1)

To define this mesoscopic criterion, we propose to follow the developments of Papadopoulos [5], who introduced a material constant which will be noted G. The new criterion is then defined by the following equation:

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1

³³³ Vd V d



2 Ta



 DPmax dM d E

(2)

where and are material parameters which has to be identified on fatigue tests. Although G might have a physical meaning, we will identify it by using an additional fatigue test. This identification has been carried out for an aeronautical steel - for which enough data were available in the literature - and for an aluminium alloy for which a dedicated test campaign has been done. The predictive capabilities of the criterion has been evaluated by computing Haigh’s diagram for several kind of loadings and confronting the results with experimental data. The influence of the choice of the tests chosen to identify the three parameters of the model has been studied, and found to be reasonably limited.

References 1.

Papadopoulos, I.V., Panoskaltsis, V.P., Multiaxial Fatigue and Design, Mechanical Engineering Publications, London, UK, 1996.

2.

Fouvry, S., Elleuch, K., Simeon, G., The Journal of Strain Analysis for Engineering Design, vol. 6, 549-564,2002

3.

Banvillet, A., Palin-Luc, T., Lasserre, S., International Journal of Fatigue, vol. 25, 755-769, 2003

4.

Vivensang, M., Gannier, A., Recent Advances in Experimental Mechanics, Balkema, Rotterdam, Netherlands, 1994.

5.

Papadopoulos, I.V., High-Cycle Metal Fatigue, Springer, Berlin, Germany, 1999.

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HYDROGEN TRAPPING: DEFORMATION AND HEAT TREATMENT EFFECTS IN 2024 ALLOY H. Kamoutsi, G. N. Haidemenopoulos, V. Bontozoglou, P. V. Petroyiannis and Sp.G. Pantelakis Department of Mechanical & Industrial Engineering University of Thessaly, Volos, Greece, [email protected] Departmernt of Mechanical and Aeronautical Engineering University of Patras, Rio, Greece. [email protected] Corrosion is a major concern to the structural integrity of aging aircraft structures. The effect of corrosion on the damage tolerance ability of advanced aluminum alloys calls for consideration of the problems associated with the combined effect of corrosion and embrittling mechanisms. In recent work [1,2] the authors have shown evidence of corrosion-induced hydrogen embrittlement in aluminium alloy 2024. Hydrogen is produced during the corrosion process and is being trapped in distinct energy states, which correspond to different microstructural traps. These traps are activated and liberate hydrogen at different temperatures. In alloy 2024, four traps T1 to T4 were identified. Trap T1 is considered to be a reversible trap, which liberates hydrogen continuously at low temperatures. Traps T2, T3 and T4 saturate with exposure time and are considered to be irreversible with critical evolution temperatures of 200, 410 and 500oC respectively. The hydrogen front advances with the corrosion front, so hydrogen penetrates in the material through the intergranular paths generated by the corrosion process. Then hydrogen diffuses further in the material establishing a hydrogen affected zone beneath the corrosion zone.

FIGURE 1. Total quantity of hydrogen for 2024 alloy in the solution treated and quenched condition and in the aged condition. (in EXCO for 6 and 12 hours). Removal of the corrosion layer (equal to the depth of attack) leads to complete restoration of yield strength and partial restoration of ductility. Removal of the corrosion layer and heating above the T4 activation range for hydrogen desorption (to activate all traps) leads not only to complete restoration of strength but also to complete restoration of ductility. Although some indications of the trapping states exists [3], the exact nature of trapping sites is not known. The present work makes a contribution towards the identification of the microstructural characteristics of trapping sites. Two series of experiments were performed. In the first series the 2024 alloy was solution treated and quenched, in order to obtain a supersaturated solid solution by dissolving the S phase. Immediatelly after quenching, the alloy was exposed in

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the EXCO solution for 6 and 12 hours. The hydrogen trapped was measured by a thermal desorption technique described in [3]. The results are shown in Fig.1. A significant decrease of trapped hydrogen is documented for the solution treated material relative to the standard aged material of the T351 temper. This result indicated that the T4 state is related to hydrogen trapping by the S phase. In the second series of experiments the alloy was subjected to plastic deformation prior to corrosion exposure in order to alter the dislocation structure of the material. Tensile tests were interrupted at specified plastic strains. Then the specimens were exposed in the EXCO solution for 24 hours and the hydrogen trapped was measured.

FIGURE 2. Total quantity of hydrogen versus plastic deformation. The total quantity of hydrogen trapped is shown as a function of prior plastic strain in Fig.2. The results indicate a decrease of trapped hydrogen at high plastic strains, indicating a potential "dislocation shielding" of the S phase to hydrogen.

References 1.

Kamoutsi, H., Haidemenopoulos, G.N., Bontozoglou, V., and Sp.G. Pantelakis, In Proceedings of the 11th International Conference on Fracture (ICF11), Turin, Italy, 2005.

2.

Kamoutsi, H., Haidemenopoulos, G.N., Bontozoglou, V., and Sp.G. Pantelakis, accepted for publication in Corrosion Science, 2005

3.

Charitidou, E., Papapolymerou, G., Haidemenopoulos, G.N., Hasiotis, N., and Bontozoglou, V., Scripta Materialia, vol. 41, 1327-1332, 1999.

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AN INTEGRATED METHODOLOGY ASSESSING THE AGING BEHAVIOUR OF AIRCRAFT STRUCTURES G. Labeas and I. Diamantakos Laboratory of Technology and Strength of Materials, Department of Mechanical Engineering and Aeronautics, University of Patras, 26500, Rion, Greece [email protected] Institute of Structures and Advanced Materials Patron-Athinon 57, 26441 Patras, Greece [email protected] The term ‘Ageing aircraft’ indicates an aircraft structure that is about to reach its original design goal. At this stage, the light alloy structures used in commercial aircraft are susceptible to Widespread Fatigue Damage (WFD) and possibly other deteriorating effects, such as corrosion damage. One typical form of WFD is Multiple Site Damage (MSD), which refers to the simultaneous existence of multiple interacting fatigue cracks at different sites of the same structural component (Fig.1). In the presence of MSD, critical crack sizes are greatly reduced, thus decreasing the residual strength of the structure below critical levels [1, 2] and leading to catastrophic failures due to the sudden cohesion of such interacting cracks [e.g. 3].

FIGURE 1. Typical aircraft joint under MSD condition. Assessment of the aging behaviour aircraft structures under MSD condition is a very demanding task to fulfil, as it requires suitable tools for the estimation of all different phenomena involved in MSD. Firstly, models for the prediction of crack initiation and the calculation of crack propagation are necessary. In addition, link-up criteria for the prediction of the coalesce of interacting cracks and the assessment of the residual strength of the structure are required. On the other hand, the physical background of the WFD and MSD processes needs deeper understanding. Furthermore, the computational effort for calculating MSD fatigue behaviour of an aircraft structure is usually huge and depends on the complexity of the structure and the number of interacting propagating fatigue cracks. In the present work an integrated methodology for assessing the aging behaviour of aircraft structures in the presence of MSD is presented. The methodology combines several modules for the prediction of crack initiation, crack growth, crack link-up and residual strength of the structures, as well as an effective technique for the necessary stress analysis. In order to keep the amount of computing effort low, an incremental approach for calculating crack initiation and crack propagation has been adopted.

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Estimation of crack initiation scenarios is based on a probabilistic approach, as the phenomenon exhibits a quite stochastic nature. The number of fatigue loading cycles required for the evolution of a new crack has been experimentally observed to follow a normal distribution, the variables of which are depended on the local stress level at the initiation site. These variables and their relationship with stress are calculated from simple experiments and are defined as a local material property. Coalesce of interacting cracks and residual strength of the structure is predicted using a strain energy based criterion. This criterion is based on the quantity of the ‘specific’ strain energy increase, i.e. the strain energy change (because of the ligament failure) divided by the ligament area and has a similar physical background to the energy release rate (J-integral) concept. The ‘specific’ strain energy change, which is the critical quantity for ligament fracture is dependent on both the plastic deformation of the ligament, as well as, on its fracture toughness. For stress analysis and computation of Stress Intensity Factors a numerical model utilizing the sub-structuring technique of the Finite Element Method is used, in order to reduce the computing effort due to the large model size and the FE discretization difficulties appearing in crack propagation calculations. The applied methodology is based on the development of suitable superelements used for the numerical analysis of aircraft structures susceptible to MSD. All above modules are combined in an integrated methodology capable to assess the evolution of MSD at aging aircraft structures from the stage of cracks development to the final failure of the structure. Numerical results obtained by the proposed methodology are compared to experimental results concerning typical aluminium joints used in aircraft structures under the presence of MSD, and very good agreement is observed.

References 1.

Schijve, J, Fat & Fract of Eng Mat & Struct, vol. 18, 329-344, 1995.

2.

Smith, B.L., Saville, P.A., Mouak, A. and Myose, R.Y., J. of Aircraft, vol. 37, 325-331, 2000.

3.

Hendricks, W.R., In Structural Integrity of Aging Airplanes, edited by Atluri, S.N., Sampath S.G. and Tong, P., Springer-Verlag Berlin, Heidelberg, 1991, 153-165.

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NUMERICAL INVESTIGATION ON THE TENSILE BEHAVIOUR OF PRECORRODED 2024 ALUMINIUM ALLOY P. V. Petroyiannis1, G. Labeas1, Sp. G. Pantelakis1, E. Kamoutsi2, V. Bontozoglou2 and G. N. Haidemenopoulos2 1Laboratory of Technology and Strength of Materials Department of Mechanical Engineering & Aeronautics University of Patras Panepistimioupolis Rion, 26 500 Patras, Greece 2Laboratory of Materials Department of Mechanical & Industrial Engineering University of Thessaly Pedion Areos, 38 334 Volos, Greece 3Transport Processes & Process Equipment Laboratory Department of Mechanical & Industrial Engineering University of Thessaly Pedion Areos, 38 334 Volos, Greece [email protected] The synergetic effect of corrosion and corrosion induced hydrogen embrittlement damage processes which occur at local scale has been found to result in a dramatic macroscopic tensile ductility loss of the 2024 aluminum alloy [1,2]. To make a realistic simulation of the mechanical behaviour of the corroded 2024 alloy manageable, a diligent consideration of the underlying corrosion and hydrogen embrittlement mechanisms is required. From the microstructural viewpoint the corrosion attack of the alloy is not uniform. The corrosion damage evolution and the development of a hydrogen diffusion zone associated to it are extensively discussed in [2-4]. As shown in [3,4], corrosion in the 2024 alloy starts in the form of pits mainly located at intersections of cracks in the protective surface oxide layer. With increasing exposure time pits become deeper and connect through channels of intergranular corrosion paths. This process leads to clustering and coalescence of pits. From that point on, corrosion does not penetrate much deeper but instead spreads beneath the surface and causes exfoliation of surface layers. The described process facilitates the transport of corrosion solution deep into the material. Thus, the corrosive solution attacks the uncorroded material at the front of the corrosion layer (e.g. at the bottom of pits or corrosion notches) and produces hydrogen. The hydrogen generated at the front of the corrosion layer spreads to the adjacent unaffected material creating a hydrogen diffusion zone below the corrosion zone. Recall that the described damage processes occur in atomic scale. To model these complex damage processes in atomic scale in order to estimate their effect on the macroscopic tensile behaviour of the material, is extremely difficult. In the present work it is proposed to simulate the tensile behaviour of the degraded specimen due to corrosion and hydrogen embrittlement with the tensile behaviour of an uncorroded specimen involving microscopic cracks of proper length. In the present work, the tensile behaviour of corroded 2024 T3 tensile specimens has been estimated on the basis of FE analysis by taking into account the local material properties in the damaged areas. A parametric study is involved to account for the effect of thickness and maximum depth of attack in the results.

P. V. Petroyiannis et al.

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To simulate the above mentioned behaviour of the pre-corroded specimen, uniform corroded layers of 200 up to 350 m width evolving from the free specimen edges, as shown in Fig. 1(a), have been assumed. Below the corroded layers lie uniform embrittled zones of 150m thickness and below them undamaged material. Since the corroded zones are expected to have a much lower tensile strength compared to the tensile strength of the undamaged material, they are expected to fail already at low tensile loads. Taking the above into consideration, the initial model may be replaced by a specimen out of undamaged 2024 T3 material with one edge crack or two symmetric edge cracks, with the latter being the most severe case and hence representing a conservative prediction, Fig. 1(b). Calculated tensile properties obtained with the analysis agree well with experimental data. The FE analysis results are supported by metallographic and fractographic analyses.

(a)

(b)

FIGURE 1. (a)Tensile specimen configuration and (b) proposed model of the pre-corroded specimen.

References 1.

Pantelakis, Sp.G., Vassilas, N.I., and Daglaras, P.G., Metall., vol. 47, 135-141, 1993.

2.

Petroyiannis, P.V., Kermanidis, Al.Th., Kamoutsi, H., Pantelakis, Sp.G., Bontozoglou, V., and Haidemenopoulos, G.N., Fatigue Fract. Engng. Mater. Struct., vol. 28, 565-574, 2005.

3.

Kamoutsi, H., Haidemenopoulos, G.N.. Bontozoglou, V., and Pantelakis, Sp.G., accepted for publication in Corrosion Science, 2005.

4.

Kamoutsi, H., Doctoral Thesis, Dept. of Mechanical & Industrial Engineering, University of Thessaly, Volos, Greece, 2004.

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ASSESSMENT OF DEFECTS UNDER COMBINED PRIMARY AND RESIDUAL STRESSES A. H. Sherry and M. R. Goldthorpe Materials Performance Centre University of Manchester Manchester M60 1QD United Kingdom [email protected] Residual stresses can provide a significant element of the crack driving force for defects in welded components. Structural integrity assessment methods are available, such as the R6 defect assessment procedure [1], which provide detailed guidance for the assessment of such defects under the combined influence of primary and residual stresses. However, in some circumstances these methods may be unduly conservative due, in part, to an over-estimation of the crack driving force due to the residual stress, KJs. This over-estimation can lead to a pessimistic view of actual safety margins for welded components and premature replacement or repair strategies. This paper describes a programme of experimental and analytical work undertaken to better characterise the influence of residual stress levels on KJs for fatigue cracks in a high strength, low toughness aluminium alloy, AL2024-T351. A compact specimen has been designed in which a highly tensile residual stress field is mechanically induced through a compressive preload prior to fatigue pre-cracking. The residual stress field generated by this method was characterised using a combination of surface strain mapping using Electronic Speckle Pattern Interferometry (ESPI), and 3-D elastic-plastic finite element modelling, Figure 1.

FIGURE 1. Comparison between ESPI and 3D FEA surface strains in a preloaded notched compact tension specimen

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FIGURE 2. Comparison of crack opening displacement data with numerical data for simultaneous (solid lines) and progressive (dashed lines) cracks Following pre-cracking, a combination of metallographic examination and modelling has provided an accurate characterisation of the crack-opening displacement close to the crack-tip at the centre and surface of the specimen. This gives a set of reference data against which both instantaneous and progressive approaches for introducing cracks into finite element models can be critically assessed. As shown in Figure 2, for the fatigue pre-cracks introduced into the residual stress fields, the progressive approach yields good agreement with experimental data, particularly close to the crack tip. Based on the results of this work, and using enhanced approaches for calculating the J-integral for cracks located in regions of residual plastic strain [2], practical guidance is provided regarding the suitability of alternative approaches for characterising KJs with greater accuracy. The influence of these approaches on the reliability of defect assessments is discussed.

References 1.

R6: Assessment of the integrity of structures containing defects, British Energy Generation Limited, Revision 4, 2001.

2.

D W Beardsmore and A H Sherry, “Allowance for residual stresses and material interfaces when calculating J in and close to welded joints”, ASME Pressure Vessels and Piping, Vol. 464, pp. 11-21, 2003.

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EFFECT OF RESIDUAL STRESSES ON THE CRACK GROWTH IN ALUMINUM B. Kumar and J. E. Locke National Institute of Aviation Research & Wichita State University 1845. N Fairmount St, Wichita KS 67260, USA [email protected] [email protected] Shot peening is a cold working process in which the surface of a part is bombarded with small spherical media called shots. This process results in a hemisphere of cold-worked material that is highly stressed in compression. Fuchs [1] and several other researchers have reported that the values of the compressive stresses are at least as high as 50% of the ultimate strength of the material. In the open literature there is little information of crack growth data through the residual stress fields generated by shot peening. Kocada et al [2] suggested that this is probably due to the fact that the observation of short crack initiation and propagation in a heavily deformed surface layer is very difficult to monitor. The focus of this investigation is on the fatigue crack growth rates of short cracks in the shot peened aluminum alloys. To assess the effects of residual stresses on fatigue crack growth, testing is being conducted on specimens fabricated from the 7050-T7451 and 7075-T7351 aluminum alloys. The material was obtained from Alcoa in the form of 0.25-inch thick sheets. To produce specimens with short cracks several specimen geometries proposed by Suresh & Ritchie [3] were used. After several specimens were tested we found that the double edge notched specimen geometry used by Everett et al [4], was most suitable for the present investigation. The short crack specimens are then shot peened at two locations. The edge containing the short crack is shot peened so that the crack is embedded in the residual stress field. The specimens are also shot peened on the front and back surfaces such that there is a zone on the surface of the specimens which is unpeened. Figure 1 show the region described. Understanding the influence of compressive residual stresses and how it affects the fracture mode is central to any investigation on how it may be utilized to improve fatigue resistance of the material. Further the peening process can modify the topography of the fracture surface at the crack initiation site. Turnbull et al [5] suggest that this is most likely caused by the distortion that the grain structure experienced due to the surface deformation as a result of shot peening. Therefore detailed fractographic analysis has also been undertaken. The results of fractography showed there were numerous crack initiation sites, before the main fatigue crack formed. There was evidence of ratcheting also observed on the specimens. Due to file size constraint’s we are unable to submit photomicrographs of our findings.

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Figure 1 & 2: Residual Stress Profile of the Shot Peened 7050–T7451 Aluminum with 100% and 200% coverage The primary fatigue enhancing effect of any surface treatment is the residual compressive stress field. Thus, quantifying and measuring the residual stress field is necessary to understand its affect on crack growth. We are using the X-ray diffraction technique to determine the residual stresses and results on Al 7050-T7451 with 100 % and 200% coverage’s are shown in figures 1 and Fig. 2. Currently we are analyzing the Al 7075T-7351 alloy. We are currently testing the double edge notch coupons using the ACPD probes and an optical microscope. Detailed results will be provided for the paper.

References 1.

Kocada, D., Kocada, S., and Tomazek, H. “Description of Short Crack Growth in ShotPeened Medium Carbon Steel,” Fatigue & Fracture of Engineering Materials & Structures, vol 21, pp 977-985, 1998.

2.

Suresh, S., and Ritchie, R. O., “Propagation of Short Fatigue Cracks”, International Metals Review, vol. 29, No.6, pp 445-476, 1984.

3.

Everett Jr., R. A., Mathews, W.T., Prabhakaran, R., Newman, Jr., J. C., and Dubberly, M.J., “The Effects of Shot and Laser Peening on the Crack Growth and Fatigue Life in 2024 Aluminum Alloy and 4340 Steel” NASA/TM-2001-210843, ARL-TR-2363.

4.

Turnbull, A., De Ls Rios, E. R., Tait, R. B., Laurant, C., and Boabaid, J.,S., “Improving the Fatigue Resistance of Waspaloy by Shot Peening” Fatigue & Fracture of Engineering Materials & Structures, vol 21:pp 1513-1524, 1998

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EFFECT OF THE CRYOGENIC WIRE BRUSHING ON THE SURFACE INTEGRITY AND THE FATIGUE LIFE IMPROVEMENT OF THE AISI 304 STAINLESS STEEL GROUND COMPONENTS N. B. Fredja, H. Sidhoma and C. Brahamb a Laboratoire de Mecanique, Materiaux et procedes (LMMP ; LAB-STI-03). ESSTT, 5 Av. Taha Hussein Montfleury 1008 Tunis-Tunisie. b Laboratoire Microstructure et Mecanique des Materiaux (LM3 ; CNRS UMR 8006) ENSAM, 151 Boulevard de l’Hopital, 75013 Paris, France. [email protected] In this investigation, ground surface integrity and fatigue behavior improvements of the AISI 304 SS resulting from the application of wire brushing at ambient and low temperatures were investigated.

Quality of surfaces generated under cryogenic wire brushing The formation of plastic induced martensite D’ is favored by the cold work hardening generated by the cryogenic wire brushing. This can be clearly grasped from the X-ray diffraction peaks. On the other hand the wire brushing carried out under dry condition induces an increase of the interface temperature between the steel wires and the brushed surface (about 85°), which is enough high to inhibit any austenitic plastic transformation to martensite. Wire brushing of the AISI 304 SS surfaces induces superficial cold work hardening (depth less 100µm) with a level which is as important as the brushing temperature is low. Brushing under low temperatures results in a higher resistance of the work material to the plastic deformation. Therefore, the material removal by the successive passes of the brush wires on the work surface is minimized under these conditions. Consequently, the initially preexisting grinding groves are partially erased by the steel wires and only a slight total roughness differences between the ground (Ra=2.2µm, Rt=16.5µm) and the cryogenic brushed (Ra=1.95µm, Rt=11.5µm) states are noticed. However, brushing under dry condition significantly deforms plastically the brushed surfaces and therefore, generates a completely different finished surface morphology than the ground one. Wire brushing redistributes the residual stresses fields generated by the grinding process and put in compression the upper layers of the brushed surfaces (figure 1). This redistribution is thought to be very beneficial to the fatigue life of mechanical components subjected to cyclic loading.

Fatigue behavior of cryogenic wire brushed surfaces Near surface cold work hardening associated to the compressive residual stress fields generated under cryogenic wire brushing, improve substantially the resistance of ground components to fatigue crack nucleation and propagation (figure 2). Moreover, the formed plastic induced martensite by cryogenic wire brushing is found to contribute significantly to increase the levels of the compressive residual stresses and therefore, delays the fatigue crack nucleation. On the other hand, the formed plastic induced martensite by the cyclic loading at the tips of the nucleated fatigue crack, contributes to slow down the crack propagation speed and to stop it in some cases.

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Figure 1 Residual stress profiles measured using the incremental hole method

Figure 2 Fatigue life improvements by wire brushing under dry and cryogenic cooling of the AISI 304 SS ground surface Substantial improvement of the fatigue life of the AISI 304 SS ground surfaces could be realized by the application of cryogenic wire brushing (72%). This improvement is thought to be, mainly, the consequence of the high level of the compressive residual stresses induced by both clod work hardening at low temperature and volume change associated to the formation of the plastic induced martensite. These stresses delay the nucleation of fatigue cracks. On the other hand the formation of the plastic induced martensite at the tips of the fatigue cracks was observed to block the propagation of the cracks and therefore, increases the propagation fatigue life.

40. Residual Stress and its Effects on Fatigue and Fracture

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INTERACTION OF RESIDUAL STRESS WITH MECHANICAL LOADING IN FERRITIC STEELS A. Mirzaee-Sisan, C. E. Truman and D. J. Smith Department of Mechanical Engineering University of Bristol Queen’s Building, University Walk Bristol, BS8 1TR, UK [email protected] The paper will present recent results obtained as part of the EU FP5 project “Enpower – Management of Nuclear Plant Operation by Optimised Weld Repair”1 concerning the effect of residual stress load-history on fracture. This paper concentrates on the behaviour of A533B low alloy ferritic steel. A companion paper concentrates on type 316H austenitic stainless steel. The rationale of the research was to validate advanced numerical modelling techniques with an experimental fracture programme. In order to achieve this, a laboratory test specimen was required which contained a well-defined residual stress field. This would enable complementary numerical and experimental fracture programmes to proceed in parallel. The paper therefore begins with a description of the mechanism developed to generate residual stress fields in beam specimens. The paper will then show numerical predictions of the residual stress state in the beam specimens, details of the numerical fracture modelling, the experimental fracture test results, and will conclude by discussing the comparison of experimental results and predictions.

Figure 1. Schematic diagram of in-plane loading. All diamensions are in mm An in-plane compression procedure was developed to generate residual stress fields in A533B ferritic steel single edge notch bend, SEN(B), specimens [1]. An in-plane compressive load was applied to two ‘V’ notches at the two ends of the beam causing a localised zone of plasticity to develop at the root of a shallow notch at mid-length. A residual stress field was subsequently generated when the load was removed. A schematic diagram of the procedure, and specimen dimensions is shown in Fig. 1. ABAQUS was used to model the in-plane compression procedure using room temperature material properties. A notch was then instantaneously introduced into specimens containing a residual stress field generated by in-plane compression. The material properties were then set to 1.ENPOWER was co-sponsored by the Nuclear Fission Safety Programme of the European Commission and the project partners: Institut de Soudure (co-ordinator, F), British Energy Generation Ltd (UK), Mitsui Babcock Energy Limited (UK), Framatome ANP (D), Joint Research Centre (NL), University of Bristol (UK) and Industeel Arcelor (formerly Usinor Industeel) under contract No FIKS-CT-2001-00167.

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those at -150°C, and the specimens then loaded to failure in what was termed a Compress, Unload, Cool, Facture (CUCF) cycle. Two complementary approaches were followed. A ‘global’ approach used a modified J-integral routine to determine KJmod values for test specimens containing combined primary loads and residual stresses. These KJmod values were then used in a Weibull probability model to reflect the observed statistical scatter in the fracture load. In parallel, a ‘local’ approach [2] was also used to predict the cleavage fracture behaviour of the A533B SEN(B)s following in-plane compression. Weibull parameters were obtained by fitting a Weibull probability distribution to as-received experimental fracture data. The same parameters were then used in a local model, along with a Weibull stress component determined by integrating the maximum crack tip principal stress over the crack tip plastic zone.

Figure 2. Probability of failure of SEN(B) ferritic steel specimens in the as-received state and after CUCF Fracture tests were performed on 8 SEN(B) specimens in the as-received state, and 5 SEN(B) specimens following the CUCF cycle. These results are shown in Fig. 2., along with predictions based on the global approach, detailed above. Two predictions are shown. One assumed that the total influence of the in-plane compression procedure could be encapsulated in the parameter Kres, the magnitude of the equivalent stress intensity factor of the residual stress field without primary load. The second set of predictions are based on the values of KJmod determined from the modified J-integral routine.

References

1.

Mirzaee-Sisan, A., Mahmoudi, A. H, Truman, C. E. and Smith, D. J., Proc. ASME PVP conference, Denver, Colorado, USA, 2005.

2.

Hadidi-Moud, S., Mirzaee-Sisan, A., Truman, C. E. and Smith, D. J., Fat. and Frac. Eng. Mat. Struct., 27, 931-942, 2004.

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EVALUATION OF NOVEL POST WELD HEAT TREATMENT IN FERRITIC STEEL REPAIR WELDS BASED ON NEUTRON DIFFRACTION C. Ohms*, D. Neov*, R. C. Wimpory** and A. G. Youtsos* *EC-JRC-IE, High Flux Reactor Unit, PO Box 2, 1755 ZG Petten, Netherlands **Hahn-Meitner-Institute, Glienicker Str. 100, 14109 Berlin, Germany [email protected] The occurrence of cracks in – normally welded – components with safety relevance in, e.g. nuclear installations or in the (petro-)chemical industry, is not an unusual event. In almost all cases such cracking is detected in periodic inspections prior to complete failure of the component. Sometimes a detected defect necessitates repair of the damaged component to facilitate its further operation. Repairing of a crack would in most cases be facilitated by excavation of the material surrounding the crack and subsequent filling of the excavation by welding. However, such a repair welding process leaves the component in a sensitive state in that it generates a complicated residual stress pattern and that the heat affected zone of the weld might become very susceptible to the formation of new cracking [1]. Post weld heat treatment of a repaired component can be an option to mitigate the damaging impact of the welding process. Through heat treatments residual stresses can be severely reduced or redistributed to obtain stress fields around the weld deemed less detrimental. At the same time a heat treatment process could positively influence the HAZ sensitivity for further cracking. In any case, a thorough assessment of the welding process is necessary to ensure a safe continued operation of the repaired component. In this context letterbox repair welds applied to thin ferritic steel plates to simulate repair of postulated shallow cracks have been manufactured. A typical excavation shape is shown in Fig. 1 below [2]. Such an excavation would typically be filled with 20 to 30 welding passes. Components have been made available in the as welded state and after the application of a PWHT. Two different heat treatment processes were analysed: a. a full scale treatment, where the entire component has been subjected to an elevated temperature for several hours in order to significantly reduce the residual stresses, and b. an alternative treatment whereby the heat is applied locally for a short period of time in order to redistribute the stresses in a controlled manner. In this paper the experimental determination of these residual stresses in the as welded and tin the heat-treated states is presented. Such measurements have been performed by neutron diffraction at the High Flux Reactor of the Joint Research Centre of the European Commission in Petten, the Netherlands. The principle of residual stress measurements by neutron diffraction is introduced [3] and the particular considerations for performing such measurements in multi-pass butt welds are briefly outlined [4]. The experimental approach is presented and explained and an outline is given on the data analyses. Results are depicted in the form of comparison between the as received and the heat treated stress states. The derived data facilitate conclusions on the effects and effectiveness of the applied heat treatments and they also demonstrate that neutron diffraction is a very suitable tool for non-destructive analysis of internal residual stress fields in such welded components of considerable thickness. In addition, the method is well suited for the validation of predictive numerical models.

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FIGURE 1. Typical repair excavation geometry.

References 1.

Boucher, C., Bourchard, P.J., Brown, B., Smith, D., Lawrjaniec, D., Hein, H., Truman, C., Smith, M., Ohms, C., Dauda, T.A., Cardamone, D. and Youtsos, A.G., submitted for: Proceedings of ASME Pressure Vessels and Piping Conference 2005, Denver, July 17-21, 2005

2.

Ohms, C., Wimpory, R.C., Neov, D., Lawrjaniec, D. and Youtsos, A.G., submitted for: Proceedings of ASME Pressure Vessels and Piping Conference 2005, Denver, July 17-21

3.

Hutchings, M.T., Krawitz, A.D., editors, Measurement of residual and applied stress using neutron diffraction, Kluwer Academic Publishers, Dordrecht, Boston, London, 1992.

4.

Ohms, C., Youtsos, A.G. and van den Idsert, P., in: Proceedings of Baltica V – International Symposium on Condition and Life Management for Power Plants, edited by S. Hietanen & P. Auerkari, VTT Technical Research Centre, Espoo, Finland, June 2001, Vol. 2, 487-497

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SURFACE CRACK DEVELOPMENT IN TRANSFORMATION INDUCED FATIGUE OF SMA ACTUATORS Dimitris C. Lagoudas1, Olivier W. Bertacchini1 and Etienne Patoor2 1Aerospace Engineering Department Texas A&M University, College Station, TX 77843-3141 [email protected], [email protected] 2Laboratoire de Physique et Mecanique des Materiaux UMR CNRS 7554/ENSAM Metz 4 rue Augustin Fresnel 57078 Metz, France [email protected] Fatigue properties of Shape Memory Alloys (SMAs) have been primarily studied based on the pseudoelastic response of SMAs with some reference work done by Tobushi et al. [1] and Miyazaki et al. [2]. However, thermally induced transformation fatigue is a more recent subject, where the applied level of stress has a major influence on the developed plastic strains and therefore on the fatigue performance of SMA actuators (Bigeon and Morin [3], De Araujo et al. [4]). Recent work on the surface aspects has been carried out and has been demonstrated to be relevant to the fatigue properties (Horbogen and Eggeler [5]). This paper is based on the study of a post mortem analysis of NiTiCu shape memory alloy actuators (SMA) undergoing thermally induced martensitic phase transformation fatigue under various stress levels. In a previous study (Bertacchini et al. [6]), fatigue life results were obtained for both complete and partial phase transformations of SMA wire actuators. In addition to inducing cyclic loading with the transformation cycles, forced fluid convection cooling was utilized to increase the cycling frequency (up to 1Hz), leading to an important corrosion phenomenon due to the temperature variations. These experimental conditions led to the formation of a microcracked structure with a uniform distribution of surface cracks (Fig. 1).

FIGURE 1. Periodic cracks in post mortem SMA wire (crack spacing | 200Pm). In order to understand the stress state in the SMA wires leading to the observed microcracks, a modified shear lag model is developed that accounts for eigenstrains due to corrosion, plasticity and due to the martensitic transformation. Such inelastic eigenstrains were added to an elastic solution previously derived by McCartney [7]. Some results are shown in Figs. 2-3.

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FIGURE 2.Axial stress profile at failure vs. crack spacing: 200Pm in complete transformation (4% strain) External load = 154MPa Thickness of cracked brittle layer = 55Pm. Eigenstrain mismatch = 0.5%

FIGURE 3. Axial stress profile at failure vs. crack spacing: 400Pm in partial transformation (2% strain) External load = 154MPa Thickness of cracked brittle layer = 70Pm. Eigenstrain mismatch = 0.5% Critical values of crack spacing are reached at fatigue failure: spacing of 200Pm for complete cycles and 400Pm for partial transformation cycles. The amount of transformation strain (and therefore the plastic strain accumulation) seems to drive the ultimate crack spacing at failure.

References 1.

Tobushi, H., Hachisuka, T., Hashimoto, T., Yamada, S., 1998. Journal of Engineering Materials and Technology 120, 64-70.

2.

Miyazaki, S., Mizukoshi, K., Ueki, T., Sakuma, T., Liu, Y., 1999. Material Science and Engineering A 273-275, 658-663.

3.

Bigeon, M., Morin, M., 1996. Scripta Materialia Vol.35 (N°12), 1373-1378.

4.

C.J. De Araujo, M. Morin, G. Guénin, Material Science and Engineering. A 273-275 (1999) 305.

5.

E. Hornbogen, G. Eggeler. Materialwissenschaft und Werkstofftechnik, Volume 35, Issue 5 , 255-259.

6.

Bertacchini, O., Lagoudas, D., Patoor, E. In: Proceedings of SPIE. Editors: Dimitris C. Lagoudas, San Diego, CA, 2003, Vol. 5053, 612-624.

7.

L.N. McCartney. In: Local Mechanics Concepts for Composite Material Systems. Eds., J. N. Reddy and K. L Reifsnider, Proc. IUTAM Symposium, Blacksburg, VA, 1991, 251–282.

40. Residual Stress and its Effects on Fatigue and Fracture

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FINITE ELEMENT SIMULATION OF WELDING IN PIPES: A SENSITIVITY ANALYSIS Dimitrios Elias Katsareas1, Carsten Ohms2 and Anastasios George Youtsos3 1Machine Design Lab., Mech. Engg & Aeronautics Dept, University of Patras GR-26010 Rion, GREECE [email protected] 2High Flux Reactor Unit, Institute for Energy, EC-JRC PO2, 1755 ZG Petten, The Netherlands [email protected] 3High Flux Reactor Unit, Institute for Energy, EC-JRC PO2, 1755 ZG Petten, The Netherlands [email protected] Thermal cycling, high heating rates, high temperature peaks and inter-pass and post weld cooling are parameters that largely affect residual stress generation in and around welds. Residual stresses influence considerably nuclear power plant component integrity, by affecting service-induced crack initiation and even crack propagation. This influence can be even more severe under the presence of corrosion mechanisms, like inter-granular stress corrosion cracking in austenitic steel pipes. Such failure mechanisms are common in stainless steel piping used in pressurized water reactors. As early as 1979 [1] residual stresses in pipes due to welding have been investigated experimentally. Faure and Leggatt [2] utilized destructive test methods, like the centre-hole and layering methods, to determine the residual stress fields in austenitic-ferritic pipe welded joints. The common trend in industry, when developing a welding procedure specification, is to base it on a large number of costly and complicated experiments. Computer simulation of welding and finite element prediction of residual stresses present a cost effective and more efficient alternatives to the engineer/designer of welds, as long as these methods have been validated and proven in the field. Finite element simulations are in general supplementing the experimental tests for the evaluation of welding residual stresses. As early as 1978 [3-8] two and three-dimensional models of welds have been used for pipe welded joints. Lindgren [9] has shown that over the last 25 years of recorded weld simulation efforts, FE model sizes have increased by a factor of 104. This dramatic increase was allowed, off course, by a similar increase in computer power and clearly illustrates the continuous effort for model refinement and increase in accuracy. This effort reflects the trend in industry to shift the welding residual stress evaluation from an experimental to a computational based procedure. Fricke et al [10] have developed FERESA, a finite element code based on ABAQUS, dedicated to welding simulation and residual stress predictions and validated it by analysing an austenitic pipe weld using 2-D and 3-D models. It is common practice among researchers to develop in-house finite element codes for weld simulation. Such codes, though, lack the universality of commercially available software, which is favoured by the industry. This is due to the fact that, residual stress analysis procedures based on them can be readily transferred to industrial applications. In the present paper, a multi-pass weld joining two pipes made of different materials and a single-pass benchmark pipe weld, are simulated using 2-D axi-symmetric finite element models. The proposed methodology for weld simulation incorporates the well-known birth of elements technique and follows the prescribed temperature approach for heat input modelling. Predicted residual strains are compared to neutron diffraction measurements. The effect of various aspects of modelling, on the accuracy of predicted residual strains, is investigated through a series of

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sensitivity tests. After examination of the impact of free convection, as the most common cooling method between weld passes, on predicted residual strains, it is derived that the heat transfer coefficient has no significant effect, as long as its value remains within the free convection regime. Radiation also contributes to cooling of a welded structure, but incorporating it into the FE model shows that its effect on resulting residual strains is negligible. The same conclusion is reached when applying two different methods of heat input modelling. The prescribed temperature and the heat generation rate technique are based on entirely different approaches, concerning the FE idealization of weld-induced thermal load. Numerical tests using both these approaches illustrate that the end result of the simulation is insensitive to the choice. Comparison of computed residual strains with and without incorporating phase change (solidification) in the model indicates that its impact is also insignificant. The effect of non-linear material model choice and creep model on the accuracy of results is also investigated, leading to the conclusion that they have to be accounted for during welding simulation. Numerical tests are also performed concerning mesh optimisation as well as procedure optimisation. In the later detailed bead-by-bead simulation results are compared to layer-by-layer and lump-by-lump simulation results. Lumping is simply grouping of weld beads in order to reduce computational costs. The ultimate goal of the present analysis is to determine the level of simulation detail, which can be implemented under a realistic computational cost, but at the same time achieving the industrial requirement of accuracy, regarding residual stress predictions. The proposed simulation methodology is evaluated as a weld-induced residual stress predictive tool and future steps towards this direction are outlined.

References 1.

Ellingson, W.A. and Shack, W.J., Experiment. Mech., vol. 19, 317-323, 1979

2.

Faure, F. and Leggatt, R.H., Int. J. Pressure Vessels Piping, vol. 65, 265-275, 1996

3.

Rybicki, E. and Stonesifer, R., ASME J. Press. Vessel Technol., vol. 101, 149-154, 1979

4.

Brust, F.W. and Rybicki, E., ASME J. Press. Vessel Technol., vol. 103, 226-232, 1981

5.

Rybicki, E. and McGuire, P.A., ASME J. Press. Vessel Technol., vol. 103, 294-299, 1981

6.

Koch, R., Rybicki, E. and Strttan, R., J. Engng. Mater. Technol., vol. 107, 148-153, 1985

7.

Josefson, B.L. and Karlsson, C.T., Int. J. Pressure Vessels Piping, vol. 38, 227-243, 1989

8.

Karlsson, R. and Josefson, B., ASME J. Press. Vessel Technol., vol. 112, 76-84, 1990

9.

Lindgren, L.E., J. Therm. Stress, vol. 24, 141-192, 2001

10. Fricke, S., Keim, E. and Schmidt, J., Nucl. Engng. Design, vol. 206, 139-150, 2001

40. Residual Stress and its Effects on Fatigue and Fracture

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RESIDUAL STRESS PREDICTION IN LETTERBOX-TYPE REPAIR WELDS Loukas Keppas1, Nikolaos Konstantinos Anifantis2, Dimitrios Elias Katsareas3 and Anastasios George Youtsos4 1Machine Design Lab., Mech. Engg & Aeronautics Dept, University of Patras GR-26010 Rion, GREECE [email protected] 2Machine Design Lab., Mech. Engg & Aeronautics Dept, University of Patras GR-26010 Rion, GREECE [email protected] 3Machine Design Lab., Mech. Engg & Aeronautics Dept, University of Patras GR-26010 Rion, GREECE [email protected] 4High Flux Reactor Unit, Institute for Energy, EC-JRC PO2, 1755 ZG Petten, The Netherlands [email protected] Many researchers over the last two decades have paid attention to predict satisfactorily the residual stresses in weldments. Dong et al [1] inferred that residual stresses in weld repairs typically exhibit strong three-dimensional features, depending on both component and repair geometry. Repair welds are a common way in industry of repairing cracks or other forms of defects in steel components and structures. Part of the metal is excavated through machining and with it the crack. The groove, which has usually a letterbox geometry, is filled with weld metal of the same composition as the parent material. Since the welding procedure is of a multi-pass type, a repair weld is considered an extreme case (many passes) of a multi-pass weld. Robinson et al [2] concentrated on practical weld repair procedures for low alloy steels. During the design phase of structures and their components or during evaluation of a potential crack initiation and growth, it is important to have a complete description of the residual stress distribution. Moreover, there is the potential for stress distributions to become even more complicated, when weld repairs are undertaken within regions of components that have been fabricated previously by welding. Indeed, in the construction of new plants and for their continued operation, local repair welds are undertaken, so it is necessary to be able to underwrite these for safe operation. As a consequence, knowledge of the residual stresses and their distribution is an important input to an overall structural integrity assessment. Several researchers have conducted numerical analyses incorporating PWHT and creep effects in their models. The main scope of these studies is the examination of hot-cracking risk during the PWHT or during the operation under real conditions. Hyde et al [3] using a lumped bead 3D finite element model to simulate a pressurized CrMoV pipe. A full PWHT was carried out and the analyses covered a number of initial damage levels, magnitudes of axial loads and repair excavation depths. Weld simulation involves complicated aspects of modelling like metallurgical phase transformation, temperature dependent material properties, creep, phase change, radiation, heat input models, etc. The impact of these on the accuracy of the predicted residual stress has attracted researchers for some time now. Lindgren in his review [4] demonstrates the complexity of weld simulation models if aspects such as solid-state phase transformations and hot cracking are involved in order to achieve a more accurate analysis. The scope of the present work is the determination of the residual stresses in a 2¼CrMo plate, containing a multi-pass repair weld of the same material, including the effects of different post weld heat treatments. The weld simulation procedure is incremental in nature as is the real process

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of weld bead deposition. Each weld bead is descretized in a number of increments and these are “deposited” sequentially. “Deposited” means, in numerical terms, activated and that refers to the elements that constitute the weld bead. The deactivation and activation of elements during the simulation is achieved through the very well known “birth & death of elements” technique, a feature common to many commercial FE codes. Element deactivation or “death”, as it is called, is not achieved by actual removal of "killed" elements, but by multiplying their stiffness, conductivity, etc, by a severe reduction factor. When an element is reactivated, its stiffness, conductivity, etc. return to their full original values. The proposed methodology, for multi-pass weld simulation follows the prescribed temperature approach for heat input modeling. Metallurgical phase transformation effects are not included in the model, although it is general knowledge that its role in the formation of a residual stress field might be quite significant. Such transformations might be introduced in a future model, in an appropriate FE code. Experimental results are used to validate predictions obtained by finite element computer simulation. Specifically, computed temperature and thermal strain histories are compared to measured data, whereas predicted residual strains are compared to neutron diffraction measurements. Results obtained using the aforementioned methodology will be compared with simplified models, in the frame of the sensitivity analysis, in order to establish a balance between acceptable accuracy and computational costs. The overall objective of the present paper is the development of a residual stress predictive tool for repair welds, based on the evaluation of currently developed finite element techniques, as encountered in industrial applications. Emphasis is to be given on the applicability such a tool will have for the industry, in respect of the computational cost of its implementation.

References 1.

Dong, P., Zhang, J. and Bouchard, P., ASME J Press. Vessel Technol., vol. 124, 74-80, 2002

2.

Lant, T., Robinson, D., Spafford, B. and Storesund, J., Int J. Press. Vessels Piping, vol. 78, 813-818, 2001

3.

Hyde, T., Sun, W., Becker, A. and Williams, J., Int J. Press. Vessels Piping, vol. 81, 1-12, 2004

4.

Lindgren, L.E., J. Therm. Stress., vol. 24, 141-192, 2001

40. Residual Stress and its Effects on Fatigue and Fracture

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EFFECT OF REFLECTION SHOT PEENING AND FINE GRAIN SIZE ON IMPROVEMENT OF FATIGUE STRENGTH FOR METAL BELLOWS H. Okada1 , A. Tange1 and K. Ando2 1NHK SPRING CO.,LTD. ,Kanagawa-Pref, JAPAN, 2Yokohama National University, Kanagawa-Pref, JAPAN [email protected], [email protected], [email protected] Generally metal bellows (it is hereafter described as a bellows) are known for a seal to defend a leak being elastic1)The appearance photograph of bellows is shown in Fig.1.Recently small size bore bellows are getting to expect to a seal of pump which was small and can use under the circumstances of high pressureHowever, until now, it would be difficult to achieve the fatigue strength for required specifications in most cases. Meanwhile, in order to increase the fatigue strength of automobile parts, the author proposed the new improvement method on fatigue strength, through the clarification of the process of fatigue fracture and defensive factors2-4). That is: (a)To increase the Vickers Hardness of the component as high as possible.(b)To introduce high compressive residual stress as high as possible.(c)To fine a grain size as fine as possible. In this study, these methods were applied to bellows.The experiment was carried out by using bellows of SUS631 steel and SUS304 steel. Grain diameter was adjusted by changing bright annealing temperature after cold working. It could be realized that fatigue strength increases in proportion with decreasing grain diameter. It was known for that shot peening had an effect on improving fatigue strengthIt can be expected that it is difficult to obtain a large compressive residual stress on the inner surface of small bore size bellows by shot peening processIn order to obtain the effect of shot peening on the inner surface of bellows, a new shot peening processes by using a air peening machine and a reflective plate were developedThe reflection plate shown in Fig.2 installed to the nozzle, in order to apply the shots effectively to the inside surface of bellows5). It was found that this method could apply the shots to the inner surface of bellows effectively, to improve the fatigue life of bellows, comparing with non-shot peening one. The optimum shot peening conditions were decided by the relationship between residual stress, pressure and glass beads size in experiment. Fatigue limit of 107 cycles of SUS631 bellows was improved by 140% from SUS304 bellows when the optimum condition is applied. The reason why was improved fatigue strength by shot peening was considered from the viewpoint of the residual stress, work hardening, surface roughness and grain size.

Fig.1 Appearance photograph of bellows

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References 1.

T.Mitsushiba, a vacuum, 26-10, (1983), 757.

2.

H.Ishigami,K.Matsui,A.Tange and K.Ando,JHPI,Vol.38 No.4,(2000),205-215.

3.

A.Tange and K.Ando,JHPI,Vol.38 No.4,(2000),216-223.

4.

K.Matsui, H.Eto,K.Kawasaki,Y.Misaka and K.Ando, The collection of the Japan Society of Mechanical Engineers papers(A piecies),65-637(1999),1942-4947.

5.

H.Ishigami, K.Matsui, Y.Jin and K.Ando Fatigue and Fracture of Engineering Materials & Structures,23(2000),959-963.

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VISCOSITY EFFECT ON DISPLACEMENTS AND STRESSES OF A TWOPASS WELDING PLAT W. El Ahmar and J. F. Jullien LaMCoS, CNRS UMR 5514, INSA-Lyon INSA-Lyon, 20 Avenue Albert Einstein, 69621 Villeurbanne Cedex, France, [email protected], [email protected] The highly localized transient heat and strongly nonlinear temperature fields in both heating and cooling processes cause nonuniform thermal expansion and contraction, and thus result in plastic deformation in the weld and surrounding areas. Consequently, residual stress, strain and distortion are permanently produced in the welded structures. High tensile residual stresses are known to promote fracture and fatigue, while compressive residual stresses may induce undesired, and often unpredictable, global or local buckling during or after the welding. It is particularly evident with large and thick panels, as used in the construction of nuclear building. These adversely affect the fabrication assembly and service life of the structures. Therefore, prediction and control of residual stresses and distortion from the welding process are extremely important for the nuclear installation’s security. The aim of this study is to investigate the effect of each temperature-dependent material property on numerical results. A three-thermo-mechanical behaviour of 316L stainless steel, during a TIG welding process, with 316L material filler, is adopted and based on an experimental study, which is carried out on an industrial two pass weld benchmark [1]. The proposed simulation analyses, using finite element method, are performed with Code_Aster from EDF. A two-pass weld using the TIG process with 316L material filler is made along the chamfer of the plate (270 x 200 x 30mm) in the long axis direction. The weld begins on the appendix and ends 10mm from the plate edges. The welding parameters used for the trial are U = 9V, I = 155A, and a travelling speed of 0.667mm.s-1. The plate is lying on three points in its lower face. Temperatures are continuously recorded during the welding, using thermocouples (kind K (±15%)) in some points of the plate surface. Welding parameters (Tension, Intensity, travelling speed of the torch) are also continuously recorded during the test. After cooling of the second pass, the residual stresses in the middle section perpendicular to the welding direction of the plates are measured with X-rays (±50MPa). A three-dimensional numerical simulation is adopted. Due to the symmetry of the plate (the role of the thermocouple T4 and the captor D6 is to verify that the symmetry is conserved), only one half was modelled. For the modelling of the heat source, it is of course possible to consider different kinds of mathematical models, from surface, like a Gaussian heat source [2], to volumetric, like the double ellipsoid from Goldak. Different kinds of modelling of the heat source have been considered for the thermal steady state calculation, with an efficiency parameter K fitted so as to adjust the simulated temperatures considering the measured ones (Fig.2). If the net total heat flux KUI is the same, it appeared that, the way of the heat flux geometry density has little effect on the macroscopic simulated temperature field. For that raison, the chosen heat source modelling for the 3-Dimensionnal transient thermal calculation was rather simple: it presents a volumetric heat flux density, with a triangular aspect (Fig.1).

W. El Ahmar and J. F. Jullien

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FIGURE 1. Heat source modelling

FIGURE 2. Thermal adjust

FIGURE 3. Transient displacement

FIGURE 4. Longitudinal residual stress

The main results and conclusions are summarized as follows: •

The transient displacement (Fig.3) is mainly sensitive to the thermal expansion coefficient.

•

The residual stress (Fig.4) is mainly sensitive to the yield stress and hardening model.

References 1.

D.Ayrault, O.Blanchot, A.Fontes, Two-Passes GTA Welding Instrumented Tests as references for both the Round Robins on numerical analysis and measurements of residual stresses, 56th Annual assembly of International Institute of welding, July 6-11, 2003, Bucharest, Romania, paper IIW-X/XIII/XV-RSDP-82-03

2.

L.Depradeux, J-F.Jullien, Experimental and numerical simulation of thermomechanical phenomena during a TIG welding process, J.Phys.IV France 120 (2004) 697-704

3.

Y.Vincent, J-F.Jullien, P.Gilles, Thermo-mechanical consequences of phase transformations in the heat-affected zone using a cyclic uniaxial test, International Journal of Solids and Structures, 42 (2005) 4077-4098.

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SURFACE INTEGRITY IN HIGH SPEED MACHINING OF TI-6WT.%AL-4WT.%V ALLOY Juan David Puerta Velasquez1*, Bernard Bolle1, Pierre Chevrier2 and Albert Tidu1 1 Laboratoire d’Etude des Textures et Applications aux Materiaux (LETAM), UMR CNRS 7078, ISGMP, F-57045 Metz Cedex 01, France 2 Laboratoire de Physique et Mecanique des Materiaux (LPMM), UMR CNRS 7554, ISGMP, F57012 Metz Cedex 01, France CEPGV – Ecole Nationale D’Ingenieurs de Metz (ENIM), F-57045 Metz Cedex 01, France *[email protected] Titanium alloys are very interesting materials for industrial applications because of their elevated mechanical resistance having a low density and their excellent corrosion resistance, even at high temperatures. Despite these features, utilisation of titanium alloys is still limited because of their poor machinability, intimately bound to their thermal and chemical properties [1]. In fact, low thermal conductivity of titanium hinds the evacuation of heat generated during cutting process, leading to temperature rise of the work-piece. Furthermore, the high chemical reactivity of titanium, which increases with high temperature, produces an early damage of the cutting tools, affecting the final quality of obtained surface as well as increases in production costs. High speed machining is widely appreciated in industry for its high quality and surface finishing in the obtained parts. Nevertheless, erroneous selection of cutting parameters can generate poor surface finishing. Surface integrity can be defined as a measure of the quality of a machined work-piece and it includes roughness, crystallographic texture, residual stress and metallurgy of the obtained surface. The presence of residual stresses and residual stress gradients in surface of parts under fatigue conditions are recognised as important factor affecting their life. Generally it is accepted that the presence of compressive residual stresses in surface is beneficial for work-piece lifetime and the residual tensile stresses can lead to crack propagation and final failure of the work-piece. The aim of this work is to study the surface integrity in high speed machining of Ti-6wt.%Al-4wt.%V alloy. Machined material was an (D+E) titanium alloy (tube diameter 77.98 mm, average thickness 5 mm). High speed turning experiments were carried out using orthogonal cutting geometry in a computer numerically controlled lathe (Ernault HS-400). All tests were carried out without lubrication. Machining parameters are given in Table 1. Diamond coated flat top inserts (Sandvik TMCW cutting angle of 0° and a clearance angle of 7°, Balzers Balinit Diamond coating) were used. A new insert was used for each test, in order to avoid negative cumulated wear effects. TABLE 1. Machining parameters Cutting speed (m.min-1):

20, 40, 100, 140, 180, 220, 260, 300, 420, 540, 660

Cutting depth (mm):

0.6

Cutting width (mm):

5

Radial cut depth

(mm.rev-1):

0.12

J. D. P. Velasquez et al.

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Machined surfaces were characterised by X-ray diffraction (XRD). Measurements were carried out on a texture goniometer equipped with a curved position sensitive detector (CPS120, Inel). The XRD patterns, crystallographic texture and residual stresses were obtained using Cu KD (O = 1.5418 Å) radiation emitted by a rotating anode (Rigaku RU300). An isotropic model, socalled sin2\ method, was used to determine residual stress. Detailed explanation of this method can be founded in [2]. Samples were also observed by cross sectional scanning electron microscopy (SEM), using 6500F JEOL FEG-SEM. Microstructural images obtained by SEM shows a turning of grains at the machined surface, in the direction of the cutting tool passage (Fig. 1a). Samples were also evaluated by XRD techniques. An analysis of XRD patterns leads to determinate the effect of cutting tool passage in the obtained surface. Changes in peaks intensity ratios and peaks broadening, depending on the cutting speed, evidences a high plastic deformation and a modification of crystallographic texture in the obtained surface (Fig. 1b).

(a)

(b)

Figure 1. Microstructure modification of surface after cutting tool passage (a). XRD patterns of asreceived material and machined surfaces at different cutting speeds (b). Theoretical XRD patterns of Ti D and Ti E phases are given on the top of the figure. Linear correlation between the cutting speed and the residual stress was revealed. Lower cutting speed leads to compressive residual stress. Higher cutting speed causes the residual stress to change from compression to tensile. Surface integrity study of parts obtained by high speed machining was carried out. SEM and XRD techniques reveal microstructural modifications of surface after cutting process. Major influence of cutting speed on crystallographic texture and residual stress has been noticed.

References 1.

Ezugwu, E.O., Wang, Z.M., J. Mater. Process Tech., vol 68, 262-274, 1997

2.

Chevrier, P., Tidu, A., Bolle, B., Cezard, P. and Tinnes, J.P., Int. J. Mach. Tools & Manu., vol. 43, 1135-1142, 2003

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PHASE TRANSFORMATION AND DAMAGE ELASTOPLASTIC MULTIPHASE MODEL FOR WELDING SIMULATION T. Wu, M. Coret and A. Combescure LaMCoS, CNRS UMR 5514, Institut National de Sciences Appliquees INSA-Lyon Bat. Coulomb, 20 avenue A. Einstein 69621 Villeurbanne Cedex, France [email protected], [email protected] The article is dedicated to the study of the introduction of damage concept in the multiphasic behaviour which occurs during by welding process. Attention is paid to coupling between ductile damage, small strain elasticity, finite visco-plasticity and phase transformation. Based on the theory of thermodynamics and continuum damage mechanics (CDM), we built constitutive equations to describe damage growth and crack appearance during and after welding. The thermodynamics of irreversible processes with state variables is used as a framework to develop the phase coupling model. The related numerical aspects concern both the local integration scheme of the constitutive equations and the global resolution strategies. The models are implemented in CASTEM 3M finite element code. Based on the finite element program, some examples and applications are presented to forecast the damage induced by welding and validate the models. In the filed of metal hot process, virtual process is more and more used in many institutes and enterprises in order to forecast the results and adjust the process parameters before implement of the real experiments and manufacture processes. Since welding is an important method of manufacture process, many researchers studied welding numerical simulation and one want to prevent cracks or moreover damage induced by welding process. Simulation should help a lot in order to avoid long test periods. However, now there is no evidence of a model which is able to predict the damage induced by welding process. One observes high spatial and temporal gradients as well as phase transformations. Such situations imply to cope with a diversity of damage models and add complexity to standard constitutive equations. The model contains three main ingredients, continuum damage mechanics, transformation plasticity and multiphase behavior. To model the damage, the strains are assumed small, and the damage isotropic. The article focuses on the coupling of damage with thermal strains as well as visco-elastoplasticity including the mixed isotropic and kinematic nonlinear hardening. The framework used is the thermodynamics of irreversible processes with state variables. The basic work is presented in





Lemaitre & Chaboche [1-2]. The two observable state variables are H , V . The internal variables

 



e & & are H , V , q , g grad (T ) , and their conjugate forces are isotropic damage and its conjugate force.

r , R , D , X . D, Y are the

For multiphase situation, the volumetric proportion of each phase, denoted

zi

, is calculated

from continuous cooling transformation (CCT) diagram obtained by experiments and some models for calculating phase fraction are available and chosen depending on different temperature history such as Waeckel’s model, Koistinen-Marburger’s law and Leblond’s transformation plasticity model. M. Coret and A. Combescure have proposed a model for plastic transformation and behavior of multiphase materials [3-5].

T. Wu et al.

1322

e The Helmholtz free energy < (H , r , D , D , T , z i ) is considered to be the addition of free

energy of each phase

i

of the

n

phases considered and is described by the following equation

(1): e

U< (H , r , D , D , T , zi )

n n p tr e e ¦ U< (H , D , T , zi )  ¦ U< ( r , D , D , T , zi )  U< ( D , T , z ) i 1 i 1

(1)

p e tr In this equation < is the elastic potential, < the inelastic one and < the transformation plasticity one. By introducing the above state potential into the Clausius-Duhem basic inequality, the dual variables

V , R, X , Y can be derived together with the residual or

dissipation inequality. In the inequality thermal dissipations ) )

m

th

and mechanical dissipations

are uncoupled. )

)

m

)

th

t0

(2)

p  & Analysing dissipations ) and potential of dissipations M , flux variables (H , D , D , q T ) will be presented. The idea in this model is to characterise rupture by single common parameter to all phases. This approximation is rather crude but is a first step to a more realistic model which should have a damage evaluation for each phase: this type of model necessitates new models to describe the relationship between these damages (history effects). The constitutive equations and formulae are implemented in CAST3M finite element code. Application examples shall be presented.

References 1.

Lemaitre, J. and Chaboche, J. L., Mechanics of Materials, Cambridge University Press, Cambridge, 1994.

2.

Lemaitre, J., A Course on Damage Mechanics, Springer-Verlag, 1992.

3.

Coret, M., Etude Experimentale et Simulation de la Plasticite de Transformation et du Comportement Multiphase de l’acier de Cuve 16MND5 sous Chargement Multiaxial Anisotherme, These, LMT-Cachan, Paris, France, 2001.

4.

Coret, M., Calloch, S. and Combescure, A., Experimental Study of the Phase

Transformation Plasticity of 16MND5 Low Carbon Steel Induced by Proportional and Nonproportional Biaxial Loading Paths, European Journal of Mechanics - A/Solids, vol. 23, 823-842, 2004. 5.

Coret, M., and Combescure, A., A Mesomodel for the Numerical Simulation of the Multiphasic Behavior of Materials under Anisothermal Loading, International Journal of Mechanical Sciences, vol. 44, 1947-1963, 2002.

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THE PRESENT SANS INSTRUMENT AND THE NEW HFR-PETTEN SANS FACILITY BASED ON A COLD NEUTRON SOURCE O. Ucaa,b, C. Ohmsa, D. Neova and A. G. Youtsosa aHigh Flux Reactor Unit, Institute for Energy, EC-JRC, POs2, 1755 ZG Petten, The Netherlands [email protected] A great deal of the properties of materials is influenced by phenomena taking place in the submicron region. Scattering techniques play an important role for obtaining structural information. Small-Angle Neutron-Scattering (SANS) is one such scattering technique by which one can obtain structural information of the material being studied. Structural information here means size and form of the object under investigation. In a SANS experiment one collects data as a function of the momentum transfer which is proportional to the scattering angle. The probed length scales by SANS varies from a few nanometer to 600 nanometers. The Small-Angle Neutron-Scattering facility at the 45 MW High-Flux Reactor in Petten, the Netherlands, is constructed in the late eighties. It is a medium size SANS instrument covering a q range of 5x10-3 Å-1 to 0.4 Å-1. The instrument has been constructed with a double crystal monochromator consisting of six pairs of Pyrolytic Graphite crystals giving a monochromatic beam of 4.75 Å. The present SANS machine uses the HB3 radial beam tube. The flux at the sample position is for the current case ~104 n/cm2/s. The instrument has a length of 10 meters. The two dimensional position sensitive detector can be moved from 90 to 425 cm, Alf and Zurita [1] and Vlak et al. [2]. After the construction of the facility the scientific activities were stopped due to several non-scientific reasons. In recent years there has been effort to make the facility become operational. This article consists of two parts: a) In first instance, we will show the first preliminary results obtained at the HFR SANS facility from measurement of two different samples. The first sample is a solution of silica particles (SiO2) solved in cyclohexane. The volume fraction of the silica particles is 0.02. The second measured material is a ceramics sample. In both cases one can determine the radius of gyration. Actually these samples are old samples and aging effects cannot be excluded. However, at this stage we are interested in obtaining a signal from the instrument and the question of absolute calibration is not important. Moreover, determination of several characteristics in SANS such as the radius of gyration is independent of absolute calibration. In future we plan to do experiments with accurately defined mono-disperse micro-spheres to absolutely calibrate the instrument. After this, the facility can be used to do scientific experiments on an absolute scale. b) Secondly, we will discuss the possibility of increasing the flux at the sample position of the SANS facility. The main components/characteristics of the instrument are:

1

The initial flux which is extracted from the reactor pool.

2

The moderator.

3

The in-pile collimator

4

The neutron guide

5

Monochromatization of the beam

6

Sample collimator

7

Sample station

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Flight tube

9

The two-dimensional position sensitive detector.

For the purpose of upgrading only points 1, 2, 4 and 5 are important. It is evident that a higher initial flux is favorable. The flux at the entrance of the HB10 radial beam tube is two times higher than the HB3 radial beam tube, which is the present tube for the facility. So moving the facility to the new beam tube will double the flux. At the moment, the instrument uses neutrons of 4.75 Å at room temperature. The neutrons from the reactor follow a Maxwell-Boltzamn distribution. Therefore it is favorable to use a cold source for increasing the flux. The monochromatization of a white beam can be done by several methods. These are: doublecrystal monochromator, velocity selector and polycrystalline BeO filter Aswal, [3]. Although, it is used in SANS facilities, the BeO filter is not a good choice because of the asymmetric wavelength distribution around the mean wavelength. The velocity selector gives a slightly higher flux compared to the double monochromator. However, with a velocity selector one has the choice to continuously tune the wavelength form 2 Å to 25 Å Rosta [4]. The neutron guide will have a transmission of 1 for neutrons above the cutoff wavelength, Oc and for neutrons whose paths are inclined at angles less than the critical angle T c to the nominal beam direction. For 4.75 A and 58Ni, Tc=9.64 10-3 rad Crawford [5] and Baruchel et al. [6]. Therefore, the divergency of the in-pile collimator has to match the divergency of the guides.

References 1.

Ahlf, J. and Zurita, A. (editors), High Flux reactor (HFR) Petten- characterization of the installation and the irradiation facilities, Report No. EUR 15151 EN, 1992

2.

Vlak, W.A.H.M., Dijk C. , Slagter, S., The ECN Small- Angle Neutron Scattering facility, Report No. ECN-PB-89-3

3.

Aswal, V. K.,, Journal of Applied Crystallography 33, 118-125, 2000

4.

Rosta L., Physica B 174, 562-565, 1991

5.

Crawford, R. K. and Carpenter, J.M ., J. Appl. Cryst,. 2, 589-601,1988

6.

Baruchel. J. et al. (editors), Neutron and synchrotron radiation for condensed matter studies, HERCULES, volume 1, p. 125-126

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RESIDUAL STRESS NUMERICAL SIMULATION OF TWO DISSIMILAR MATERIAL WELD JUNCTIONS Philippe Gilles, Ludovic Nouet and Pascal Duranton Framatome-ANP Tour AREVA Paris la Défense 92084, France [email protected] Pascal Duranton ESI-France Le Discover, 84 Bd. Vivier Merle 69485 Lyon France In nuclear reactors such as Pressurized Water Reactors (PWR), heavy section components made in low alloy steel are connected with stainless steel piping systems. The dissimilar material weld (DMW) junctions are performed following a special manufacturing procedure to ensure a good resistance of the joint. However, several experiences from the field confirm sensitivity to fatigue, corrosion or low toughness areas in this type of junction. In the framework of the European Community Research and Development Programme two projects (DG-RTD programmes BIMET, C. Faidy et al. [1] and ADIMEW, C. Faidy [2]) have been sponsored on the fracture behaviour of cracked stainless steel/ferritic steel bimetallic welds. In each of these projects, a task was carried out on of residual stresses evaluation. Residual stress measurements were performed using the neutron diffraction technique (C. Ohms [3]) across the piping thickness in the buttering, weld and the HAZ of the base material. In the ADIMEW project, residual stress measurements were also carried out on the surface by the Hole Drilling method and verifications were also made later by the Cut-Compliance method (H. Schindler [4]). The BIMET tubular mock-ups had a length of 393 mm and outer and inner diameters of 168 and 118 mm (25 mm thick). Two mock-ups were used for fracture testing and one for material characterisation and residual stress measurements. The 308/309SS DMW connects a A508 ferritic steel pipe section to a 304 stainless steel pipe section. A 308/309SS buttering is applied on the ferritic pipe. For the ADIMEW project, two DMW specimens (Fig. 1) have been manufactured of which one has been tested in 4-point bending and one being utilised for the experimental determination of welding residual stresses and for the generation of material property data for input to the analysis procedures. The ADIMEW mock-ups were much larger than the BIMET ones, the diameter and thickness being respectively 445 and: 51 mm. To guarantee the quality of the DMW's, a considerable experience and high degree of quality control has been required within the weld manufacturing process, in accordance with FRAMATOME-ANP basic nuclear specification. This paper presents numerical simulations of the welding process of the BIMET 6” and the 16” ADIMEW Dissimilar Metal Weld mock-ups. The calculations were performed by ESI and FRAMATOME-ANP using different levels of modelling: A simplified analysis, which consists in a cooling down calculation and assumes a stress-free state after the stress-relief heat treatment, A detailed analysis, which simulates each elementary step of the mock-up manufacturing procedure using a lumped element technique. A refined analysis, which simulates each elementary step of the mock-up manufacturing procedure by modelling each of the passes

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FIGURE 1. ADIMEW Dissimilar Weld Metal Junction mock-up The paper compares numerical results with the residual stress measurements to discriminate the different numerical simulation techniques. All o these simulations assume axisymmetry, which is shown to be realistic by reference to another test on butt welded pipes. Comparisons are also made on residual stress fields obtained on the two geometries to put in evidence of their similarity. It is shown that the simplified approach based on a cooling down simulation underestimates the level of residual stresses. The lumped technique gives satisfactory results except in the root weld area. The pass by pass simulation may be considered as the most reliable which is supported by comparison to other simulations of the same type. It should be underlined that for the ADIMEW simulation, the phase transformation process has been modelled in the ferritic part, allowing predicting size and hardness of the Heat Affected Zone.

References 1.

Faidy C. et al., "BIMET: Structural Integrity of Bi-Metallic Components", In Proceedings of FISA 1999 Conference, Luxembourg, 1999.

2.

Faidy C., “Structural integrity of dissimilar welds – ADIMEW project overview” In Proceedings of PVP 2004, ASME Pressure Vessel and Piping Conference, 2004, Ed ASME USA.

3.

Ohms C., Katsareas D. E., Wimpory R. C., Hornak P., Youtsos A. G., “Residual stress analysis in a thick dissimilar metal weld based on neutron diffraction”, PVP Vol. 479, ASME Pressure Vessel and Piping Conference, July 2004, USA.

4.

Schindler, H. J., 2003, 'Residual stress effects on crack growth mechanisms and structural integrity', 9th Conf. on Mechanical Behaviour of Materials, Geneva, Switzerland, 25-29 May.

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IDENTIFICATION OF WELD RESIDUAL STRESS LENGTH SCALES FOR FRACTURE ASSESSMENT P. J. Bouchard and P. J. Withers British Energy Barnwood, Gloucester GL4 3RS, UK [email protected] Manchester Materials Science Centre, University of Manchester Grosvenor Street, Manchester M1 7HS, UK [email protected] It is unlikely that any engineering component is entirely free from residual stress because of the material processing, fabrication and service load history. Residual stresses originate from the elastic accommodation of misfits between different regions in a structure. The interaction between the misfit and the restraint of the surrounding material and structure determines the magnitude of the resultant residual stress and its length scale. In order to assess the influence of residual stress on fracture, it is essential to quantify the residual stress field over the length scales of concern. This paper identifies the residual stress length scales that must be considered in fracture mechanics analyses for welded joints in engineering structures and proposes a new approach for the treatment of short length scale stresses. The findings are illustrated by results from recent weld residual stress finite element simulations and measurement studies. Simplified fracture assessment methods, such as the R6 procedure [1], are widely used by industry to determine the structural integrity significance of postulated cracks, manufacturing flaws, service-induced cracking or suspected degradation of engineering components. The R6 procedure was originally developed for the assessment of macro-cracks in pressurised steel vessels and pipework. For this type of application the length scale (through-thickness extent) of macrocracks often lies within the range 0.5 – 5mm. Such macro-cracks might be based on the largest defect that could have been missed by the inspection method, the size of a weld bead (a lack of fusion defect for example), or an assumed “engineering crack” initiation size. Of course much larger defects in structures are assessed when discovered by service inspection. More generally, the length scale of macro-cracks can be defined as being an order of magnitude greater than the material grain size. Multi-pass welding introduces a very complex residual stress field in a structure. The stresses vary in 3-dimensions over a range of macro length scales [2]. However, for simplified engineering fracture assessments a representative through-wall line stress profile is required that applies across the width of the crack. The R6 procedure provides upper bound (Level 2) residual profiles for various classes of welded joint that can be used, but these are very conservative. Recently, more realistic (Level 3) profiles for pipe butt welds have been introduced into R6. These are based on detailed residual stress measurements and finite element predictions for several welds and it is claimed that they capture the underlying residual stress distribution [3]. However, some marked differences between measurements and the idealised profiles have been noted and this undermines confidence in their use. Rapid advances in the capability of measurement techniques, such as the Contour method and Synchrotron diffraction, now readily allow residual stresses and strains in welded structures to be mapped. Recent experimental and analytical studies have revealed the importance of short length scale residual stress variations arising from weld bead pass sequence effects, weld bead start/stops and stress concentrating features. Measurements at a limited number of points in a structure will

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P. J. Bouchard and P. J. Withers

quantify the local stresses at those points but this may not reveal the underlying stress field characterising the structural behaviour of the joint (i.e. the Level 3 profile). When Level 3 profile stress modulations are significant it is important that they are accounted for in fracture assessments. A criterion is proposed for filtering benign short-range residual stress perturbations from fracture assessments based on the size of the defect relative to the length of the residual stress tensile zone. In addition, it is shown how significant stress modulations might be conservatively treated in fracture assessments by using classical stress intensity factor solutions for self-equilibrating stress fields having appropriate length scales and magnitudes.

References 1.

R6 Revision 4, 2004, Assessment of the Integrity of Structures Containing Defects, British Energy Generation Ltd., Gloucester UK.

1.

Bouchard, P.J., Withers P.J., J Neutron Research,12(1-3):81-91, 2004.

1.

Bouchard, P.J., Bradford R.A.W., In Proceedings of ASME Pressure Vessels & Piping Conference, PVP-Vol. 423, ASME, 2001, 93-99.

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HIGH-RESOLUTION NEUTRON DIFFRACTION FOR PHASE AND RESIDUAL STRESS INVESTIGATIONS P. Mikula and M. Vrana Nuclear Physics Institute and Research Centre Rez, plc. 250 68 Rez, Czech Republic [email protected] In this contribution the authors present attractive properties of an unconventional neutron diffractometer employing a dispersive multiple-reflection monochromator which permits ultrahigh-resolution macro- and microstrain scanning of bulk polycrystalline materials as well as to distinguish individual phases of a multiple phase material having very close structure properties. The latest instrumentation achievements exploiting neutron Bragg diffraction optics permits considerably to improve the resolution properties of the future generation neutron diffractometers. The effects of multiple Bragg reflections in a deformed single crystal can be observed when more than one set of planes are simultaneously operative for a given wavelength i.e. when more than two reciprocal lattice points are at the Ewald sphere. Using bent prefect crystals we determined several strong double reflection processes on several pairs of lattice planes which are mutually in the dispersive geometry (see upper part of Fig. 1). In relation to the value of bending radius, the obtained doubly reflected beam has however a narrow band-width 'OO of 10-4 - 10-3 and 'T-collimation of the orders of minutes of arc. It is clear that in comparison with the conventional single reflect-ion monochromators the monochromatic neutron current is lower proportionally to a smaller 'O and 'T spread. New experimental studies of the multiple reflection monochromator proved its possibility for using for high-resolution mono-chromatization. For our test we used the double-reflection process based on two pairs of 153/1-3-1 and -31-1/513 reflections at O= 0.156 nm which was realized in a cylindrically bent Si-crystal set for diffraction in symmetric transmission geo-metry [1]. Fig. 1 shows D-Fe diffraction profiles taken with a diffractometer performance employ-ing this multiple reflection monochromator (without using any Soller collimators and with a 2 mm wide sample) which demonstrates its re-solution abilities. The profiles were taken by a PSD detector with 1.5 mm spatial resolution and situated at the distance of 1.42 m from the sample. Using only FWHM of the diffraction profiles, the resolution in 'd/d calculated from our results is of about 8x10-4 in the vicinity for 2TS 90o. But an estimation of the contribution coming from the width of the sample together with the detector spatial resolution gives a comparable uncertainty value. Therefore, it is expected that the intrinsic instrument resolution would be better than 5x10-4. Thus, it follows from the obtained results that at the highflux sources the strains can be measured with the sensitivity of 10-5 in a large range of scattering angles. Then, as a first step, the diffractometer equipped with this monochromator we used for investigation of Fe-reflections in an induction hardened S45C steel rod ()=20 mm) having different phase composition at different distances from the rod axis. The gauge volume was determined by 2 mm wide slits in the incident as well as diffracted beam. Fig. 2 displays the diffraction profile obtained at the distance 8 mm from the axis. Similarly, Fig. 3 displays the diffraction profile obtained at the distance 6 mm from the axis. Thanks to the used high-resolution monochromatic beam, after a fitting procedure we could reliably determined contributions of the individual phases.

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Finally, it can be stated that diffractometers employing multiple reflection mono-chromator can provide very high resolution at low monochromator take-off angles. The resolution can be even comparable to back-scattering instruments. They can be efficiently used namely at high-flux neutron sources. For adjustment of optimum parameters (the crystal cut, the thickness and the bending radius) of the monochromator and of the per-formance of the whole scattering device Monte Carlo simulations would be desirable [2]. These studies were supported by the projects AV0Z10480505 and MSM2672244501.

References 1.

Mikula P., Vrana M. and Wagner V., Physica B, vol. 350 , e667-e670, 2004.

2.

Saroun, J. and Kulda, J., 1997, Physica B, vol. 234-236, 1102-1103, 1997.

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SENSITIVITY OF PREDICTED RESIDUAL STRESSES TO MODELLING ASSUMPTIONS S. K. Bate1, R. Charles1, D. Everett2, D. O’Gara1, A. Warren1 and S. Yellowlees1 1Serco Assurance, 2Rolls-Royce 1Walton House, 404 The Quadrant, Birchwood Park, Warrington, Cheshire, WA3 6AT, United Kingdom [email protected] The treatment of residual stresses in welded components is considered in defect assessment procedures such as R6 [1], BS7910 [2] and API579 [3]. R6 considers three approaches for determining the as-welded residual stress distribution. The first approach, Level 1, is a simple estimate of stresses which enable an initial conservative assessment of a defect to be made. The second approach, Level 2, uses a published compendia that characterises bounding profiles for a range of structures. The third approach, Level 3, entails the use of analysis coupled with experimental measurements to define the detailed spatial distribution of residual stress. The assessor should first try to apply Levels 1 and 2, however these may lead to insufficient margins in the assessment. There may also be cases where a more comprehensive understanding of the residual stress field is required and the Level 3 approach has to be used. The use of analytical, mainly finite element, and experimental approaches to characterise weld residual stresses is fairly widespread but the limitations to these methods are not always known and therefore needs to be recognised. However, when the two approaches are combined, and the results corroborate each other sufficiently well, the resulting residual stress distribution can be confidently used for assessment. The use of numerical techniques to simulate the welding process is not new and the increase in computing power has seen the size and complexity of the models increase. Such features mean that in some cases simplifications and assumptions have to be utilised to approximate residual stresses. Thus there is an uncertainty in the accuracy of these methods which has meant that conservative approximations, i.e. upper bound residual stress profiles, have still to be relied upon when carrying out structural integrity assessments. A programme of work is now underway to develop a procedure for residual stress prediction which will account for how the various simplifications and assumptions affect the magnitude of predicted stresses, and to identify the limitations of the various modelling techniques. This will include heat source representation, material behaviour in terms of high temperature annealing, cyclic hardening or softening, creep, and phase transformations. Supporting experimental data is required in order to validate the predictions and a series of mock-ups will be manufactured to enable measurements to be carried out. Use will also be made of benchmarks which are the subject of round-robin exercises which combine analytical predictions with various measurement techniques. Initial work has considered an austentic single weld bead-on-plate specimen, see Fig. 1 below, which is one of the benchmarks being studied within the NET European network.

S. K. Bate et al.

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FIGURE 1. Schematic of NET Benchmark Plate (17mm Thick) This paper describes the analytical work that has been carried out by Serco Assurance which looks at how various assumptions on modelling the bead on plate specimen affect the predicted residual stresses. In each of the cases considered, a 3-dimenensional finite element representation of the plate has been used for the analysis. The cases presented in this paper are: Varying the geometric parameters defining the Goldak [4] heat source model. Varying the weld efficiency. The effect of different material hardening models and annealing.

References 1.

R6 - Revision 4, Assessment of the integrity of structures containing defects, British Energy, September 2000.

2.

BS7910:1999, Guide on methods for assessing the acceptability of flaws in metallic structures, BSI 10-2000.

3.

Fitness-for-Service, API Recommended Practice 579, First edition , January 2000.

4.

Goldak J., Chakravarti, A. and Bibby, M., Metallurgical Transactions, vol. 15B, 229–305, June 1984.

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WELDING EFFECTS ON THIN STIFFENED PANELS T. T. Chau TECHNICATOME (Aix-en-Provence, France) Centre Jean-Louis Andrieu BP34000 13791 Aix-en-Provence, FRANCE Commission SNS / AFM (Paris, France) [email protected] The major problems due to welding effects are the residual stresses and deformations of which the levels affect more or less the resistance and lifetime of welded structure. In steel industry and particularly in shipbuilding, during these last few decades, thin plates are used more and more in ship construction in order to lighten the structure weight. Unfortunately, excessive distortions occurred on these thin stiffened panels and straightening works must be executed in respecting the limit tolerance fixed by the Quality Standard of Ship Construction. These futil works reduce Productivity and Quality, increase Construction Cost and get longer Fabrication Delay. Thus, it is necessary to evaluate, control and minimize the distortion and stress levels of thin welded panels before welding assembly operations.

FIGURE 1 : A Metallurgical Concept for Numerical Simulation of Arc Welding. Carried out from RD studies in France (1991-1995), subsidized by the French Ministry of Reseearch and Industry with the cooperation of French shipyards, a simplified methodology of numerical simulation of arc welding has been developed and validated successively by measurements on 2D and 3D samples [1, 2, 3]. Based on a metallurgical concept (Fig. 1), the Methodology presents interesting advantages for uses: simplicity in modelling, rapidity on computer time within reliable results. In this paper, a short presentation of the methodology is described and its industrial applications, in 1996, on two 3D FE models of thin deck and bulkhead panels of superstructure of a Chemical parcel tanker in fabrication stage are presented. Another application of the methodology has been realized in 2002 for a RD project with the cooperation of the “Chantiers de l’Atlantique” shipyard (CAT). The methodology was successfully applied and validated on a very large thin stiffened “Testing” Panel in full scale (17m x 6m x 6mm).

T. T. Chau

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The "Testing"Panel has been realized under real conditions of fabrication (by automation welding chain) in the shipyard. A 3D FE model was created for calculation according to the Methodology, representing the welded assembly of more than five hundred thousand of volumeelements within more than two million of degrees of freedom . The numerical results due to welding effects so obtained within short computer-time (three hours and half) on a linear FEM software were verified with measured stress values and identified with the buckling state of the “Testing” Panel before and after welding operations by photographies (Photo 1).

PHOTO 1 : Deformed shape of the “Testing” Panel after assembly welding operations.

References 1.

Chau, T.T. & Masson, J.C., Une méthode d’evaluation des contraintes et des deformations residuelles dans les assemblages d’elements métalliques soudes d’epaisseurs moyennes, Proc., ATMA 1992, 207-233.

2.

Chau, T.T., Paradis, A., Masson J.C., A simple method for evaluating the 3D welding effects on thin stiffened panel assemblies in shipbuilding, Proc., 3rd International Conference on Marine Technology, ODRA’99, Szczecin, Poland, Marine Technology III, 1999, 485-530. WIT Press: [email protected]

3.

Chau, T.T., A metallurgical Concept for Numerical Simulation of Arc Welding, Proc. ASME PVP 2005, 17-21 July 2005, Denver, Colorado, USA., paper 71654.

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EVALUATION OF RESIDUAL STRESSES IN CERAMIC POLYMER MATRIX COMPOSITES USING FINITE ELEMENT METHOD K. Babski, T. Boguszewski, A. Boczkowska, M. Lewandowska, W. Swieszkowski* and K.J. Kurzydlowski Division of Materials Design Faculty of Materials Science and Engineering Warsaw University of Technology Woloska 141, 02-507 Warsaw, POLAND [email protected] Composites are complex materials which comprise of multiple phases (components) of different thermal and mechanical properties. By combining such components, especially metals, ceramics, glasses, and polymers, one can produce new functional and construction materials with superior properties which could be tailored for the specific applications. However, due to mismatch in to the properties of their constituents, composite are prone to build-up of residual stresses. This is in particular true to the thermal stresses arising due to mismatch in thermal expansion coefficients. These thermal stresses might be generated either during manufacturing process, more precisely during the cooling from fabrication temperature, or due to thermal cycling in in-service conditions. They, in general, can improve the properties of the composites [1]. However, they can also have detrimental effect on their performance. This calls for their control over manufacturing and inservice conditions. The aim of the study was to evaluate the residual stresses in two types of composites polymer – ceramic composites using the finite element method (FEM). The effect of the composite structure, defined in terms of the volume fraction, size and shape of constituents, on the residual stresses built up was also analyzed. The ceramic - polymeric matrix composites were made of porous SiO2 ceramic infiltrated with urea – urethane elastomer [2]. In the infiltration process liquid mixture of the substrates is incorporated into ceramic pores using the vacuum pressure and temperature of 120oC. Since the thermal expansions of the elastomer and ceramics are different upon cooling to ambient temperature thermal stresses are generated. Moreover, the elastomer shrinks as a consequence of its transformation from the mixture of substrates in the liquid to the solid states. These two phenomena result in buildup of considerable residual stresses. The bis-glycidylmethylmethacrylate (bis-GMA) polymeric matrix with the ceramic fillers, which is used for dental restoration [3], was also investigated. As during the restoration the matrix polymerizes, it shrinks and for large cavities the composite material might be pulled away from the walls. This in turn, leads to restoration failure by de-bonding at the composite-tooth interface. The fillers are added to the polymeric matrix to reduce the material shrinkage. The effect of the fillers size, shape and arrangement on the residual stresses at composite-tooth and resin-ceramic filler interfaces has been evaluated in the present study. Both composite materials were analyzed by the finite element method in the Ansys software. The models were 3D axi-symmetric. The Solid92 elements (which have 10 nodes) were used in the FE analyses. A linear and isotropic properties have been assumed for the ceramic matrix composite [2] as well as for the dental restoration [4]. For infiltrated composite (CMC) the simulations of both thermal and tensile loading of material were carried out. The models were subjected to thermal load simulating the cooling from fabrication (120oC) to room temperature (20oC),

K. Babski et al.

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followed by a tensile straining. For the dental restoration (polymer matrix composite (PMC)) the polymerization shrinkage of the composite was modeled using temperature-dependent expansion. The residual stresses were investigated in the composite itself as well as in the restoration-tooth system. The analysis of distribution of principal stresses in the CMC shows that change of temperature leads to buildup of high tensile stresses in elastomeric phase and both tensile and compressive ones stresses in the ceramic pre-form (Fig.1a). It was found that the thermal stresses present in composite mostly reduce the maximum values of tensile stresses in ceramics. It can be advantageous from the mechanical point of view and result in an increase of toughness. The FE results obtained for the PMC show the effect of the resin shrinkage on the residual stresses at the resin-ceramic filler interface, which can cause de-bonding (Fig.1b). Various fillers have been examined in terms of the efficiency in the reduction of these residual stresses (Fig.1c).

a)

b)

c)

FIGURE 1. Residual stresses in: a) ceramic-elastomer composite, b) resin- ceramic composite and c) composite – tooth system In more general sense, the present studies show the potential application of the finite element method in investigation of the residual stresses in different types of the composite materials. The future work will be concentrated on the experimental validation of the numerical results.

References 1.

Antheunis, V. et al. Dental Materials, 20, 554-564, 2004.

2.

Boczkowska, A. et al. Procced. E-MRS 2004 Fall Meeting, Warsaw, 6-10. X. 2004, p. 225.

3.

Boguszewski, T. et al. e-Polymers, 032, 2005.

4.

Barink, P.C.P. et al . Biomaterials, 24, 1427-1435, 2003.

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TOWARDS DATA-DRIVEN MODELING AND SIMULATION OF MULTIPHYSICS DEGRADING SYSTEMS J. G. Michopoulos and C. Farhat Computational Multiphysics Systems Lab Special Projects Group, Center for Computational Material Science, Code 6390.2 Naval Research Laboratory, Washington DC 20375 USA [email protected] Department of Mechanical Engineering & Institute for Computational and Mathematical Engineering Stanford University, Stanford CA 94305 USA [email protected] Recently it is becoming more and more apparent that research and development (R&D) activities in developed economies are driven by motivations asserted by the various stake holders involved in the production and consumption processes. Producers are interested in tailoring R&D processes to drive various economic metrics such as total cost of ownership and return on investment towards their benefit. Consumers are interested in optimized utility-based metrics such as functionality, reusability, safety and maintainability, thus forcing producers to pay attention into building these properties into their R&D products. Furthermore, today’s cradle-to-grave engineering requirements for validated, safe, economic and maximally functional design, flexible manufacturing, qualification, certification, utilization and maintenance of system products have significantly raised the demand for validated, efficient and quick simulation of the behaviour of complex whole systems. In the particularly complex category of degrading systems that exhibit a time-varying behaviour for the large time scale where aging and maintenance are critical, life extension for usability purposes has become a focal area of interest. On the other hand, simulations inherit all of their utility and economic properties from those of the analytical and computational models they are based upon. Research conducted at NRL for the past forty years within the context of the material constitutive behaviour characterization has been both anticipating and exploiting the computational technologies evolution in a manner that is consistent with the previously mentioned motivational drivers. The present paper focuses on describing the utilization of these ever evolving computational and mechatronic technologies, to automate data-driven model generation for multiphysics degrading systems with emphasis on multi-field excitation of composites [1,2]. A brief exposure of NRL’s data-driven and mechatronically automated method [3] is presented. This method is based on the concept of identifying the constitutive behaviour of degrading composite material via parameter estimation associated with the dissipated energy density function. Its extension to include temperature dependence in a multiphysics context is also presented. The continuum multiphysics formulation for multi-field and multi-domain problems is based upon the experimental determination of an energy density dissipation function that depends on the multiphysics state variables of the system under investigation. The integrated over the volume of the specimen is matched by the experimentally measured dissipated energy of the system computed as the difference between the total energy imparted into the specimen system minus the recoverable energy. This matching is implemented as an inverse problem solved via standard global optimization techniques. The experimental values of dissipated energy are computed from the displacements and tractions measured from the multi-degree of freedom testing

J. G. Michopoulos and C. Farhat

1338

m machines created at NRL. The dissipated energy density function I for a given material constructed according one of three possible combinations, n

I m (T  H jk )

¦c

m i

(T ) F i ( H

i 1

jk

m

is

n

)

I m (T  H

, or

jk

)

¦

c im F i ( T , H

jk

)

, or

i 1

n

¦c

I m (T  H jk )

m i

\ i (T ) F i (H jk )

i 1

,

that encode the decomposition combinations between temperature and strain field variables dependence of the corresponding basis function(s). The corresponding energy balance equation used for each loading step of the pre-programmed loading paths is now extended from the previous forms to be:

³

ur 0

tu q v d q v 

1 tsu tu v  Q 2

³

wV

I m ( T ( x j )  H ik ( x j )) d x j ,

where tu ,uv , are the traction and displacement resultants along the pre-programmed path and Q is the thermal energy imparted into the system. Finally, the field equations for the multi-field and multi-domain problem of aero-thermostructural fluid-structure interaction are given and simulation results resulting from their space and time integration by use of Stanford University’s AERO suite of codes [4] are presented as an example for simulation-based design of a multiphysics degrading system such that of an aircraft.

References 1.

Michopoulos J., Tsompanopoulou P., Houstis E., Farhat C., Lesoinne M., Rice J., Joshi A., “On a Data Driven Environment for Multiphysics Applications”, Future Generation Computer Systems Journal special issue on PSEs, vol 21/6 pp 953-968, 2005.

2.

Michopoulos J., “Mechatronically Automated Characterization of Material Constitutive Respone”, Proceedings of the 6th World Congress on Computational Mechanics (WCCMVI), September 5-10 2004, Beijing China, Tsinghua University Press and Springer, pp. 486491, 2004.

3.

Mast, P.W., Nash, G.E., Michopoulos, J.G., Thomas, R., Badaliance, R., Wolock, I., Theoretical and Applied Fracture Mechanics, vol. 22, 71-125, 1995.

4.

Farhat C., Geuzaine, Brown R and G., “Application of a Three-Field Nonlinear FluidStructure Formulation to the Prediction of the Aeroelastic Parameters of an F-16 Fighter,” Computers and Fluids, vol. 32, pp. 3-29, 2003.

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MATHEMATICAL MODELLING OF PIEZOCERAMIC TRANSDUCER PERFORMANCE IN THE PRESENCE OF MATERIAL DEFECTS Torben Amby Christensen1,2, Niels Lervad Andersen1, and Morten Willatzen2 Center for Product Development and 2Mads Clausen Institute of Product Innovation, University of Southern Denmark, Grundtvigs Alle 150, DK-6400 Sønderborg, Denmark [email protected]

1

We model the influence of air-void imperfections inside a piezoceramic PZT-5H material. Results show that significant modifications of the frequency characteristics are observed with air voids increasing from 0 to 1 mm corresponding to half of the piezoelectric material’s height. Similar conclusions are reached when the width is increased for given height. IMechatronic products become increasingly advanced involving smart materials and smart structures. Piezo-materials are often used as a smart material for sensing and actuating. In addition, piezomaterials are show fast response characteristics but suffer from limited range of motion. This means that practical applications require sensors and actuators to perform near materials-strength limits with the possibility of imperfection formation. In the present work, we examine the influence of air-void imperfections on the signal characteristics of piezoelectric media which can be useful in the quality assessment of such materials. Piezoelectric model: The domain

ȍp is modeled as PZT-5H ceramic including the coupling between mechanical and electric

effects. Stress equilibrium is assumed:  ’ ˜ T  B

0 where T is the stress matrix and B is mass times

acceleration. Furthermore, assuming zero free charge density, Gauss’s law states that ’ ˜ D 0 , where D is the electric displacement. Consider the piezoelectric constitutive laws in stress-charge S E H ik  e ikl S kl , where S, E, c, e, and is strain, electric field, c klmn S mn  e ikl E i and D i form: T kl stiffness, piezoelectric stress constant, and permittivity. Using these, the governing equations can be expressed as functions of strain and electric potential. Neglecting magnetic effects implies that the electric field is

conservative: ’ u E = 0, thus it is possible to express the electric field as the gradient of a electric potential: E S ii

’V . Assuming small displacements, the normal and shear strain can be expressed as w u i w x i and S ji



½ wu i

wx j  wu j

wxi

where ui and xi is the displacement and spatial

variable in the ith-direction. It is assumed that stresses and the electric field in the z direction can be neglected & & iZ t (i.e., Tzz = Tyz = Txz = Ez 0). Using a monofrequency excitation source : V  x , t V  x e all other 2

variables are modulated with the same frequency in a linear approach. Hence, B i  U p Z u i , where U p is the density for the piezoelectric material. Using the symmetries of the hexagonal system class 6mm which PZT-5H belongs to the governing equations become:

 ’ ˜T ’ ˜D

B½ 0

¾ ¿

Ÿ

c~13E v y  c~33E u x  e~33 V x x  c 55E u y  c 55E v x  e15 V y y U p Z 2 u c 55E u y  c 55E v x  e15 V y x  c~11E v y  c~13E u x  e~31 V x y U p Z 2 v e~31 v y  e~33 u x  H~3S V x x  e15 u y  e15 v x  H 1S V y y 0

where:



E 2  c12

E c~11

§¨ c E © 11

e~31

e 31  c12E e 32

E c 22

·¸ , ¹



E c~13

E c 22 , e~33

c13E  c12E c 23E e 33  c 23E e 32



E E c 22 , c~33



E S c 22 , H~3

H

§¨ c E © 33



E 2  c 23



2 S 3  e 32

E c 22

E c 22



·¸ ¹ .

T. A. Christensen et al.

1340

The domain ̛ f is modeled as a fluid with no dissipative effects while assuming acoustic processes with 2

small amplitude. Consider the Linear Euler equation:

UfZ u

’p

where U f u, and p is the fluid density,

displacement vector and the acoustic pressure respectively. Assuming irrotational flow, the displacement vector can be expressed as the gradient of a potential: u 2



’I implying I

2 p Z U f . In addition, the

2

Linear wave equation for fluids: ’ p  U f c Z p , where c is the adiabatic bulk modulus, is employed in the mathematical model framework. The latter equation can be reformulated in terms of the scalar potential 2

2

as follows: c ’ I  U f Z I Boundary conditions

0 .

Numerical values:

Numerical Results: We have modeled the situation where the left-most (right-most) interface faces water (air). In Figure 1, we plot the center velocity of the aperture facing water as a function of frequency for five different heights of the air void inside the piezoelectric medium. The width of the void is 50m for all height cases. The solid line shows the frequency plot corresponding to the case without an air void in the piezoelectric medium. One pronounced resonance peak is observed close to 0.75 MHz. If an air void with height 50m is present, the overall characteristics mimic those of the perfect piezoelectric medium except that two small satellite resonances are found at frequencies 0.94 and 1.4MHz. As the height of the air void increases these satellite peaks increase substantially in their maximum values (note, however, that the maximum value decreases somewhat when the height is approaching 1 mm). Moreover, the main resonance becomes increasingly red-shifted with air-void height. In Figure 2, we show the frequency plot of the center aperture velocity as a function of air-void width all corresponding to the air-void height 0.2mm. Evidently, the presence of a 25 m width air-void does not lead to significant disturbance of the main peak but, again, two satellite peaks show up at higher frequencies. As the width increases further, the frequency of the main peak becomes red-shifted in agreement with the observations in Figure 1. Figure 1

Figure 2

41. Computational Modeling of Multiphysics Degrading Systems (CMMDS)

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A CONTINUUM APPROACH FOR IDENTIFYING ELASTIC MODULI OF COMPOSITES J. G. Michopoulos and T. Furukawa Center of Computational Material Science Naval Research Laboratory, Washington DC 20375 USA [email protected] School of Mechanical and Manufacturing Engineering The University of New South Wales, UNSW 2052 Australia, [email protected] Composite materials can be tailored to meet specific needs such as high strength and stiffness combined with low weight [1], which are not achievable by metallic and other materials. Recent past decades have seen the accelerated use of composite materials in structural components due to cost reductions. The performance of a composite structure is, however, highly sensitive to the mechanical behaviour of the composite material. As the expectation of structural performance becomes more demanding, the need for reliable prediction of the mechanical behaviour of composite materials has become ever more important [2]. Despite a growing need, a basic obstacle to the comprehensive understanding of the mechanical behaviour of composite materials is the complexity of their observed behaviour. Unlike metallic and other isotropic materials where plastic deformation occurs by the slippage between planes of atoms in the crystal grains of the material, the nonlinear mechanical behaviour of composites is caused by a local decrease in stiffness, which results from an accumulation of different types of microscopic damage [3]. Microscopic damage modes such as microcracks in the matrix and debonding between the matrix and the reinforcement are common in all composites. In continuous fibre-reinforced composites, failure can be also caused by the breakage and microbuckling of the fibre and, due to fibre alignment, their mechanical behaviour is directiondependent, i.e. anisotropic. The nonlinear behaviour of laminar composites can further result from delamination. As a consequence, composites fail in an extremely complicated manner [4] (in contrast to homogeneous isotropic materials, the fracture of which occurs by the propagation of a single macroscopic crack [5]), so that classical fracture mechanics is not applicable to modelling failure behaviour in composites. Various macroscopic and microscopic approaches have been proposed for failure modelling [6,7 and references therein] but, due to the complexity of the systems, they mainly focus on simply structured laminates such as unidirectional or cross-ply laminates under a specified set of uni-axial tests, leaving the prediction of failure behaviour of complicated laminates such as angle-ply composites under various loading conditions as a further issue. The approach proposed by the authors, which is to be used for failure prediction of various composites, quantifies the deformation, including damage, developed in a test specimen on a continuum basis. Provided that experimental data from various loading tests, which describe the full-field deformation of a continuum, and associated techniques to handle such a wide variety of experimental data are available, failure behaviour of composites can be predicted irrelevant to the type of composite and design of experiments. As the first step to the prediction of the failure behaviour, this paper presents a technique to determine the elastic moduli of composites from various full-field deformation tests of a continuum. The multi-DoF material testing machine used by the authors enables the measurements of boundary displacement and force of a test specimen. The elastic moduli are identified such that the total energy calculated from the boundary displacement and force is equated with that computed from the stress-strain analysis by finite

J. G. Michopoulos and T. Furukawa

1342

element method. Figure 1 shows some results that compare the total energy simulated with the identified moduli and the corresponding total energy by experiments. Detailed discussion of the numerical analyses will be presented in the final paper.

FIGURE 1. Pareto-optimal solutions in parameter space (left: K  D , right: n  H ).

References 1.

Dowling, N.E., Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue, Prentice-Hall, 1993.

2.

Mast, P.W., Nash, G.E., Michopoulos, J.G., Thomas, R., Badaliance, R., Wolock, I., Theoretical and Applied Fracture Mechanics, vol. 22, 71-125, 1995.

3.

Staab, G.H., Laminar Composites, Butterworth-Heinemann, Boston, 1999.

4.

Badaliance R. and Hill, H.D., STP775 Damage in Composite Materials, edited by K. L. Reifsnider, Philadelphia, PA., 229-242, 1982.

5.

Matthews, F.L., Davies, G.A.O., Hitchings D. and Soutis, C., Finite Element Modelling of Composite Materials and Structures, Woodhead Publishing, Cambridge, England, 2000.

6.

Vinogradov, V. and Hashin, Z., Int. J. Solids Struct., vol. 42, 365-392, 2005.

7.

Rikards, R., Abramovich, H., Green, T., Auzins J. and Chate, A., Mechanics of Advanced Materials and Structures, vol. 10, 335-352, 2003.

41. Computational Modeling of Multiphysics Degrading Systems (CMMDS)

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REGULARIZED IDENTIFICATION OF MATERIAL CONSTANTS USING MULTI-OBJECTIVE GRADIENT-BASED METHOD T. Furukawa and J. G. Michopoulos School of Mechanical and Manufacturing Engineering The University of New South Wales, UNSW 2052, Australia [email protected] Center of Computational Material Science Naval Research Laboratory, Washington DC 20375, USA [email protected] The past decades have seen an increasing complexity of nonlinear material models proposed as scientific interests in materials grow and high performance materials are introduced. One of the core processes in the material modelling is the parameter identification, where constants in a material model are identified such that the model can describe material behaviour accurately. Due to the non-linearity of the material model, the parameter identification problem is most commonly converted into minimisation of an objective function describing errors between the measured and computed outputs using an optimisation method. However, the problem of this iterative technique is that the solution often cannot be obtained if measurement data and/or the model contain large errors [Bard, 1974] as this makes the objective function complex. The most common approach to tackle this problem is to add a regularisation term, which normally consists of a function multiplied with weighting factors such as regularisation parameters, to the objective function. This approach additionally requires a technique to find the best set of weighting factors since the solution obtained depends upon the weighting factors. Such techniques conventionally adopted include Morozov discrepancy principle [Morozov, 1984] and the generalised cross validation [Groetsche, 1984]. Later, Reginska [1996] considered the maximizer of the L-curve as the optimal parameter. Kubo, et al. [1998] also proposed a technique using Singular Value Decomposition, while Zhuang and Zhu [1998] proposed a multi-time-step method for inverse problems involving systems consisting of partial differential equations. Despite their performance to some degree, the fundamental question common in all the techniques is whether the automatic determination of a single solution is necessary, as the solution of the inverse analysis will be never known in nature unlike the forward analysis. In addition, an additional parameter must be often introduced to find the best regularisation parameter, the solution being again dependent on the additional parameter. Meanwhile, multi-objective optimisation methods have been proposed for solving multiobjective design optimisation problems [Coello, 1999]. These methods allow the design parameters to be optimised without weighting factors on design criteria such as weight and energy consumption. The solution of this vector functional formulation is henceforth represented as a space, namely the solution space, rather than a point, and the methods find a set of admissible solutions in the solution space. Due to the derivation of multiple solutions and the possible complexity of the objective functions, the methods are mostly based on the evolutionary algorithms (EAs), which execute robust search from multiple search points for single objective optimisation. Many EAs are, however, very robust at the expense of efficiency in contrast to the conventional calculus-based methods, so that they are not inefficient for parameter identification problems of concern, which have a relatively simple formulation. Moreover, since these algorithms find only a fixed number of solutions in the solution space, the solutions are sparse and not well distributed in the solution space.

1344

T. Furukawa and J. G. Michopoulos

In this paper, a technique for solving a regularised parameter identification problem without weighting factors is first proposed. In this technique, regularisation terms are each formulated as another objective function, and the multi-objective optimisation problem is solved by a multiobjective optimisation method. Furthermore, Multi-Objective Gradient-based Method (MOGM) is proposed as a multi-objective optimisation method to find the solutions for this class of problems efficiently. The algorithm is also formulated such that its solutions can describe the solution space to be derived. Numerical and experimental results will be detailed in the final paper, but FIGURE 1 shows the resulting Pareto-optimal solutions in some parameter spaces when parameters of Chaboche model were identified. The well-distributed solutions obtained by the proposed technique, the results indicate the total solution space of the identification problem. In addition, the resulting Pareto-optimal solutions can be advantageously used to further investigate the sensitivity of the solution space.

FIGURE 1. Pareto-optimal solutions in parameter space (left:

K  D , right: n  H

).

References 1.

Bard, Y., Nonlinear Parameter Estimation, Academic Press, New York, 1974.

2.

Morozov, V.A., Methods for Solving Incorrectly Posed Problems, Springer-Verlag, New York, 1984.

3.

Groetsche, C.W., The Theory of Tikhonov Regularization for Fredholm Integral Equation of the First Kind, Pitman, Boston, 1984.

4.

Reginska, T., SIAM Journal of Scientific Computation, vol. 17, 740-749, 1996.

5.

Hansen, P.C., SIAM Review, vol. 34(4), 561-580, 1992.

6.

Kubo, S., Takahashi, T. and Ohji, K., In Inverse Problem in Engineering Mechanics, edited by M. Tanaka and G.S. Dulikravich, 337-344, 1998.

7.

Zhang, X. and Zhu, J., Inverse Problems in Engineering Mechanics, edited by M. Tanaka and G.S. Dulikravich, Elsevier Science, 299-308, 1998.

8.

Coello, C.A., Int. J. Knowl. Inform. Sys., vol. 1(1), 1999.

41. Computational Modeling of Multiphysics Degrading Systems (CMMDS)

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LOADING AND MATERIAL FEATURES INFLUENCE ON PIEZOELECTRIC MATERIAL PERFORMANCE V. G. DeGiorgi and S. A. Wimmer System Design and Integration Section, Code 6353 Naval Research Laboratory, Washington, DC 20375, USA [email protected] Even though much research has been completed on constitutive relationships for piezoelectric ceramics, there is generally the assumption that material and loading axes are aligned. Current actuator designs focus on alignment of these axes. Natural flaws may occur at any orientation to material and loading axes. The criticality of a flaw may depend directly on its relationship to the primary loading direction. Understanding the interrelationship between flaw orientation, material orientation and loading axes will have multiple benefits. It will allow for evaluation of flawed components based on scientific understanding and it will allow for more diverse and novel designs. The work presented examines the interaction between geometric flaws and misalignment between load and material axes. We examine the relative merit of different geometric features, the effects of material property axes rotation about the main loading axes (3-direction) and the effects of material property axes rotation about the out of plane axes (2-direction). The ASTM E8 test specimen has been customized in order to establish a complex stress state and to increase the amount of data that can be obtained from a single test specimen [1]. A close up of the gage region of the test specimen is shown in Fig. 1. Three types of loads are considered; electrical, mechanical and mechanical followed by electrical. The current work is a computational study using finite element methodology. Follow-on work planned includes experimental verification. The material used in this study is PZT-5A, a commercially available piezoelectric ceramic.

FIGURE 1. Close up of gage region of test specimen. Results of interest are the stress levels and displacement in the test specimen for each loading condition. Detailed examination of these results will begin to provide insight into the interrelationship between flaw size, flaw location, loading axis and material axes. Fig. 2 shows the Von Mises stress levels for electrical, mechanical and combined electrical and mechanical loading. As can be seen from the contours, there are significant differences between the responses for electrical and mechanical loads.

1346

V. G. DeGiorgi and S. A. Wimmer

(a)

(b)

(c)

FIGURE 2. Von Mises stress contour plots for (a) mechanical, (b) electrical and (c) combined mechanical and electrical loadings. The next step is to rotate the material axes: the material is rotated about the 2-axis resulting in a material axes that are rotated in the 1-3 plane with respect to the specimen geometry. The 2direction axis for material and loading path are identical in this case. The second rotation considered rotates the material axes about the 3-axis so that the material is rotated in the 1-2 plane with respect to the specimen geometry. The 3-direction axis for material and loading path are identical in this case. In both cases only the material orientation is rotated, there is no change in specimen geometry or load application. Variations in stress and deformation values are evaluted to determine the impact of the different conditions.

References 1.

Wimmer, S.A. and DeGiorgi, V.G. “Component Based Test Specimen Design”, Small Specimen Test Techniques: Fourth Volume, ASTM STP 1418, p. 251-266, 2002.

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MODELING OF PLASMA CHEMICAL DEPOSITION AND DEGRADATION OF SILICON THIN FILMS Valeria V. Krzhizhanovskaya1,2, Peter M. A. Sloot1 and Yuriy E. Gorbachev2 1Section Computational Science, University of Amsterdam Kruislaan 403, NL-1098 SJ Amsterdam, The Netherlands. {valeria, sloot}@science.uva.nl 2St. Petersburg State Polytechnic University Polytechnicheskaya 29, St. Petersburg 195251, Russia. {lera, gorbachev}@csa.ru Thin silicon films are important semiconductor material widely used in modern microelectronics and solar cells. One of the technologies employed for industrial production of these films is plasma enhanced chemical vapor deposition (PECVD). Modeling and simulation of this industrially important technology is essential for optimizing physical and chemical parameters, reactive chamber geometry and operating regimes of the installation, in order to reduce the costs of film production and to provide a better growth rate and film quality in terms of layer composition and homogeneity. For the latter, spatial processes (convection, diffusion, heat transfer, chemical transformations and plasma non-uniformity), as well as the variation of system behavior in time, play a decisive role. We have developed a 3D transient multiphysics multiscale model taking into account all relevant chemical kinetics, plasma physics and transport processes that occur in the bulk of a PECVD reactor and on the surface of the growing film [Krzhizhanovskaya, V.V., Zatevakhin, M.A., Ignatiev, A.A., Gorbachev, Yu.E., Goedheer, W.J. and Sloot, P.M.A., In Proceedings of the 5th International Bi-Annual ASME/JSME Symposium on Computational Technologies for Fluid/Thermal/Structural/ Chemical Systems with Industrial Applications, ASME PVP-vol. 491-2, 59-68, 2004]. In addition to that we have built an efficient problem solving environment for scientists studying PECVD processes and end-users working in chemical industry [Krzhizhanovskaya, V.V., Sloot, P.M.A. and Gorbachev, Yu.E., Simulation: Transactions of the Society for Modeling and Simulation International, vol. 81, No. 1, 77-85, 2005]. One of the most challenging and least studied topics in modeling a time-dependent film deposition is the process of film degradation at the end of the production cycle, when the plasma is ‘switched off’ and the inflow of the source gases is stopped. Experimental analysis of processes occurring at this stage is very difficult because the processes of plasma recombination, radicals' diffusion towards the surface and their attachment to the film, are much faster than the time needed for film characterization. Moreover, the measurements of the composition and homogeneity are usually done ‘off-line’, after the film is taken out of the reactive chamber. In order to study the film degradation processes computationally, we carried out a series of simulation experiments varying the basic physical and chemical parameters (pressure, temperature, inflow rate, raw mixture composition and chemical reaction rates), as well as the moments in time when the finishing stages occur (plasma switch-off, gas inflow and heating shut-down). In this paper we briefly introduce the previously developed 3D model of plasma chemical deposition emphasizing the dissipative nature of the processes; then we present the latest development for modeling the film degradation processes; describe the problem solving environment created to provide distributed parallel multitask simulation and visualization on computer Grids; and finally present the simulation results. The model presented is an extension of the 1D [Gorbachev, Yu.E., Zatevakhin, M.A., Krzhizhanovskaya, V.V. and Shveigert, V.A., Technical Physics, vol. 45, No 8, 1032-1041, 2000],

1348

V. V. Krzhizhanovskaya et al.

2D [Krzhizhanovskaya, V.V., Zatevakhin, M.A., Ignatiev, A.A., Gorbachev, Y.E. and Sloot, P.M.A., Lecture Notes in Computer Science, vol. 2328, 879-888, 2002] and 3D [Krzhizhanovskaya, V.V., Zatevakhin, M.A., Ignatiev, A.A., Gorbachev, Yu.E., Goedheer, W.J. and Sloot, P.M.A., In Proceedings of the 5th International Bi-Annual ASME/JSME Symposium on Computational Technologies for Fluid/Thermal/Structural/ Chemical Systems with Industrial Applications, ASME PVP-vol. 491-2, 59-68, 2004] models previously developed by the authors, with a new description of chemical processes taking into account oligomer formation [Gorbachev, Yu.E., Technical Physics, in press, 2005.]. The model is based on the numerical solution of the full Navier-Stokes equations for transient laminar flows of viscous compressible multi-component mixtures of chemically reacting gases. The boundary conditions take into account temperature jumps, as well as molecular slipping and sticking processes on the walls. For simulation of capacitively coupled plasma discharge, a fluid model [Nienhuis, G.J. and Goedheer, W.J., Plasma Sources Sci. Technol., v. 8, 295-298, 1999] was used. The electron and ion continuity equations were solved consistently with the Poisson equation for the electric field distribution. We developed a “Virtual Reactor”, generic problem solving environment [Krzhizhanovskaya, V.V., Sloot, P.M.A. and Gorbachev, Yu.E., Simulation: Transactions of the Society for Modeling and Simulation International, vol. 81, No. 1, 77-85, 2005] with an advanced interaction capabilities integrating the basic modules for reactor geometry design, computational mesh generation, plasma, flow and chemistry simulation, as well as editors of chemical reactions and gas properties, databases, pre- and postprocessors, advanced multimodal visualization modules, Web-interfaces and a Grid portal. The first steps in integrating distributed resources through Grid technology promise efficient utilization of the computing power. The model developed has shown a good ability to predict the main characteristics of PECVD processes [Krzhizhanovskaya, V.V., Zatevakhin, M.A., Ignatiev, A.A., Gorbachev, Yu.E., Goedheer, W.J. and Sloot, P.M.A., In Proceedings of the 5th International Bi-Annual ASME/JSME Symposium on Computational Technologies for Fluid/Thermal/Structural/ Chemical Systems with Industrial Applications, ASME PVP-vol. 491-2, 59-68, 2004]. The Virtual Reactor allowed us to study the film degradation processes and to find the featuring trends in system response to the variation of physical and chemical parameters and the operating actions. We were able to indicate the mechanisms responsible for the irreversible deterioration of film homogeneity and degradation of the layer composition at the finishing stage of the film production process. Acknowledgements The research was conducted with financial support from the Dutch National Science Foundation and the Russian Foundation for Basic Research within the projects No 047.016.007 and 047.016.018, and with partial support from the CrossGrid EU project IST-2001-32243 (www.eu-crossgrid.org) and from the Virtual Laboratory for e-Science project (www.vl-e.nl).

References

1.

Krzhizhanovskaya, V.V., Zatevakhin, M.A., Ignatiev, A.A., Gorbachev, Yu.E., Goedheer, W.J. and Sloot, P.M.A., In Proceedings of the 5th International Bi-Annual ASME/JSME Symposium on Computational Technologies for Fluid/Thermal/Structural/ Chemical Systems with Industrial Applications, ASME PVP-vol. 491-2, 59-68, 2004

2.

Krzhizhanovskaya, V.V., Sloot, P.M.A. and Gorbachev, Yu.E., Simulation: Transactions of the Society for Modeling and Simulation International, vol. 81, No. 1, 77-85, 2005

3.

Gorbachev, Yu.E., Zatevakhin, M.A., Krzhizhanovskaya, V.V. and Shveigert, V.A., Technical Physics, vol. 45, No 8, 1032-1041, 2000

4.

Krzhizhanovskaya, V.V., Zatevakhin, M.A., Ignatiev, A.A., Gorbachev, Y.E. and Sloot, P.M.A., Lecture Notes in Computer Science, vol. 2328, 879-888, 2002

5.

Gorbachev, Yu.E., Technical Physics, in press, 2005.

6.

Nienhuis, G.J. and Goedheer, W.J., Plasma Sources Sci. Technol., v. 8, 295-298, 1999

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A FRACTAL APPROACH INTERPRETATION FOR THE INDENTATION SIZE EFFECT A. Carpinteri and S. Puzzi Politecnico di Torino, Department of Structural and Geotechnical Engineering Corso Duca degli Abruzzi 24, 10129 Torino, Italy [email protected] [email protected] Since the 1950’s (Tabor [1]), the hardness measurements have been recognized to be size dependent; a hardness increase with decreasing indentation depth (or indenter size) is always observed. The indentation size effect (ISE) is extensively studied in the literature and research in this field has been continuously growing in the last decades; this is motivated partly by the development of nano-composites and the large-scale application of nanometer-thick films in electronic components, partly by the availability of new methods of probing mechanical properties in very small volumes. Several different mechanisms have been suggested to be responsible for the ISE. Proposed mechanisms include: presence of oxides or chemical contamination on the surface, interfacial friction, increased dominance of edge effects with shallow indents, indenter pile-up or sink-in and loading rate (for a review, see Xue et al. [2]). Recently, several Authors proposed a strain gradient theory, in order to explain the ISE. Among them Stelmashenko [3], Fleck and Hutchinson [4], Nix and Gao [5], Gao and Huang [6], Al-Rub and Voyiadjis [7]. This theory, based on Taylor’s hardening rule, incorporates in the classical plasticity theory the material scale length that is needed to characterize and predict the indentation size effect. This theory, in all its variants, assumes that the material deformation is ruled by the density of statistically stored and geometrically necessary dislocations. The ISE arises since the density of the statistically stored dislocations depends on the effective strain, whereas the density of the geometrically necessary dislocations is a function of the strain gradient. A different theory, that gained some success in explaining the ISE, is based on the surface to volume ratio (S/V) and was proposed almost contemporarily by Gerberich et al. [8] and Zhang and Xu [9]. This theory is based on the remark that the work done by an applied indentation load contains both bulk and surface terms. The surface work, which is related to the surface stress and the size and geometry of the indenter tip, prevails if the indentation depth is shallower than a critical depth, while the bulk deformation prevails when the indentation depth is deeper than the same depth. In this paper, we propose an original interpretation of the ISE in single crystal and polycrystalline metals, which is based on the experimental evidence of the formation of cellular dislocation patterns during the later stages of plastic deformation, in the strain hardening of facecentered cubic metals, both under tensile loading and in compression (Hähner et al. [10], Sžekely et al. [11]). This dislocation patterns have also been explained theoretically by means of a stochastic model for the evolution of the densities of dislocations (Zaiser [12]). When fractal patterns are present, the dislocation cell structures are not appropriately characterized by any regular, periodic or nearly periodic geometry. Thus, the microstructure cannot be characterized at the meso-scale through an average dislocation density. In fact, the dislocation structure, which is the damage domain, is a lacunar fractal of dimension D comprised between 2 and 3. In this case, the same arguments already proposed by Carpinteri [13] to derive the Multifractal Scaling Law (MFSL) for the tensile strength in brittle and quasi-brittle materials can be applied. As a consequence, the hardness of metals, evaluated by micro- and nano-indentation, can be interpreted

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by means of a power-law. Formally, the proposed equation is identical to the one already proposed by Stelmashenko et al. [3] and Nix and Gao [4], but the underlying physical model is completely different. Eventually, some experimental hardness data from micro-indentation on copper have been fitted with the MFSL, showing a very good agreement.

References 1.

Tabor, D., The hardness of metals, Oxford University Press, Oxford, 1951.

2.

Xue, Z., Huang, Y., Hwang, K.C. and Li, M., J. Eng. Mater. Technol. (ASME), vol. 124, 371379, 2002.

3.

Stelmashenko, N.A., Walls, M.G., Brown, L.M. and Milman, Y.V., Acta Metall. Mater., vol. 41, 2855-2865, 1993.

4.

Fleck, N.A. and Hutchinson, J.W., Adv. Appl. Mech., vol. 33, 295-361, 1997.

5.

Nix, W.D. and Gao, H., J. Mech. Phys. Solids, vol. 46, 411-425, 1998.

6.

Gao, H. and Huang, Y., Int. J. Solids Struct., vol. 38, 2615-2637, 2001.

7.

Al-Rub, R.K.A. and Voyiadjis, G.Z., Int. J. Plast., vol. 20, 1139-1182, 2004.

8.

Gerberich, W.W., Tymiak, N.I. and Grunlan, J.C., J. Appl. Mech., vol. 69, 433-442, 2002.

9.

Zhang, T-Y. and Xu, W-H., J. Mater. Res., vol. 17, 1715-1720, 2002.

10. Hahner, P., Bay, K. and Zaiser, M., Phys. Rev. Lett., vol. 81, 2470-2473, 1998. 11. Szekely, F., Groma, I. and Lendvai, J., Mater. Sci. Eng., A, vol. 309–310, 352-355, 2001. 12. Zaiser, M., Mater. Sci. Eng., A, vol. 309–310, 304-315, 2001. 13. Carpinteri, A., Mech. Mater., vol. 18, 89-101, 1994; Internal Report, Laboratory of Fracture Mechanics, Politecnico di Torino, N. 1/92, 1992.

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DESCRIPTION OF MULTI-SCALING POWER LAWS IN FRACTURE AND STRENGTH A. M. Korsunsky Department of Engineering Science University of Oxford, Parks Road, Oxford OX1 3PJ, United Kingdom [email protected] Scaling transitions and size effects in the fracture and strength of materials and structures have particular significance in modern science and engineering, since the boundaries of mechanical phenomena studied and devices exploited are being pushed both out, towards global scale phenomena, and in, towards the nano-scale. These circumstances challenge the conventional wisdom acquired over many decades of laboratory experiments and modelling at the engineering scale (sub-mm to a few meters). More specifically, violations of the accepted scaling laws are observed, requiring new physical deformation mechanisms to be proposed or identified, and new modelling approaches to be developed and validated.

FIGURE 1. The Irwin et al. [2] data for net failure stress as a function of total slit length 2a, plotted in bi-logarithmic coordinates, together with the ‘knee’ function describing the transition.

FIGURE 2. Paris fatigue crack growth diagram (Botvina et al., [3]) described by the ’knee’ function. The power law indicated by the straight line represents an intermediate asymptotic.

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The present study aims to address a fundamental question of the efficient description of size effects and scale transitions. To this end the functional description of multi-scaling power law regimes is considered from first principles, and the functional form suitable for the task is identified (Korsunsky [1]). The newly formulated ‘knee’ function is then applied to a variety of experimental data containing manifestations of the size effect, including instances of two-criteria failure strength (stress and toughness), fatigue crack growth threshold (Kitagawa-Takahashi diagram) and its application in the context of fretting fatigue, Paris fatigue crack growth law, indentation hardness of coated systems, etc.

References 1.

Korsunsky, A.M. Physical Review B, submitted; e-print cond-mat/0508653.

2.

Irwin, G.R., Kies J.A. and Smith H.L., ASTM STP, vol.381,1958.

3.

Botvina, L.R., Yarema S.Ya., Grechko V.V. and Limar L.V. Physico-Chemical Mechanics of Materials, vol.6, 41-50, 1981.

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THE SPALLING FAILURE AROUND DEEP EXCAVATIONS IN ROCK MASSES A. P. Fantilli and P. Vallini Department of Structural and Geotechnical Engineering, Politecnico di Torino Corso Duca degli Abruzzi 24, Torino – 10129 Italy [email protected], [email protected] The process of spalling failure around a deep excavation in a rock mass is one of the main problems in tunnel construction. It consists in a brittle failure, produced by the crushing of compressed rock, during which strain localization appears as a shear crack. Both the tensile damage and the confinement reduction, produced by the excavation of the tunnel, play a fundamental role in the production of the spalling failure [1]. To better understand and to prevent this failure, a plane strain model able to evaluate the structural response of the rock around the excavation is here proposed. In particular, under the hypothesis of circular tunnel (of radius R0 ), within an undefined rock mass having an initial hydrostatic pressure V0 , the stress VT in the tangential direction is evaluated during the progressive reduction of the radial stress Vr (Fig. 1a). This reduction represents the loss of confinement produced by the excavation.

FIGURE 1. Spalling failure of a rock mass after the excavation of a tunnel: a) geometrical properties of the tunnel; b)-c) crushing of compressed rock cylinders. In the proposed approach, the stress-strain VT-HT relationship of Figs. 1b-1c is considered for the rock mass subjected to confinement stress Vr . As Fig. 1c shows, in the softening subsequent to the compressive strength fT , a strain localization and, consequently, a shear crack appear in the rock cylinder (Fig. 1b). Since this phenomenon is similar to that of compressed concrete observed by Jansen and Shah [2], the VT-HT relationship already adopted for the crushing of compressed concrete in RC beams is here considered. By means of this relationship the size effect of ultimate bending moment, both with [3] and without [4] confinement produced by stirrups, has been evaluated. Regarding to a deep tunnel in a rock mass, the proposed model is here applied in two different situations (case_1 and case_2). In case_1 the tunnel does not have any reinforced concrete RC

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cover (R0=RC in Fig. 1a), whereas the cover is present in case_2 (RC/R0=1.1). In both cases, the failure radii Rf , which define the failure zone produced by the tunnel excavation (Fig. 1), are evaluated by changing the tunnel radius R0. Precisely, for R0