Mechanical Behaviour and Testing of Materials 812034250X, 9788120342507

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MECHANICAL BEHAVIOUR AND TESTING OF MATERIALS

MECHANICAL BEHAVIOUR and

TESTING OF MATERIALS

A.K. BHARGAVA and C.P. SHARMA Department of Metallurgical and Materials Engineering Malaviya National Institute of Technology Jaipur

PHI Learning [;)u1ffiG@ llilwlBG@dl Delhi-110092 2014

MECHANICAL BEHAVIOUR AND TESTING OF MATERIALS A.K. Bhargava and C.P. Sharma

© 2011 by PHI Learning Private Limited, Delhi. All rights reserved. No part of this book may be reproduced in any form, by mimeograph or any other means, without permission in writing from the publisher. ISBN-978-81-203-4250-7

The export rights of this book are vested solely with the publisher. Second Printing

August, 2014

Published by Asoke K. Ghosh, PHI Learning Private Limited, Rimjhim House, 111, Patparganj Industrial Estate, Delhi-110092 and Printed by Mohan Makhijani at Rekha Printers Private Limited, New Delhi-110020.

To The Almighty and Our Parents

Contents Preface Acknowledgements Nomenclature

1.

Nature of Materials 1.1 1.2 1.3 1.4 1.5

2.

xv xvii xix

1-31

Introduction 1 Interatomic and Intermolecular Bonding 7 Classification and Combination of Elements Atomic Arrangement 12 Engineering Materials 14 1.5.1 Steel 14 1.5.2 Cast Irons 18 1.5.3 Aluminium and Its Alloys 20 1.5.4 Magnesium and Its Alloys 20 1.5.5 Titanium and Its Alloys 20 1.5.6 Copper and Its Alloys 21 1.5.7 Nickel and Its Alloys 22 1.5.8 Cobalt and Its Alloys 24 1.5.9 Ceramic Materials 25 1.5.10 Polymeric Materials 26 1.5.11 Composite Materials 30

32-44

Crystal Imperfections 2.1

Introduction

JO

32 vii

viii

Contents

2.2

3.

45-56

Mechanical Properties 3.1 3.2

3.3

3.4

4.

Imperfections 37 2.2.1 Point Imperfections 37 2.2.2 Line Imperfections 40 2.2.3 Surface Imperfections 41 2.2.4 Volume Imperfections 44

Introduction 45 Static Mechanical Properties 47 3.2.1 Tensile Strength 47 3.2.2 Compressive Strength 49 3.2.3 Ductility 49 3.2.4 Malleability 50 3.2.5 Stiffness 50 3.2.6 Toughness 51 3.2.7 Creep Strength 52 3.2.8 Hardness 52 Dynamic Mechanical Properties 53 3.3.1 Impact Strength 53 3.3.2 Fatigue Strength 53 3.3.3 Hardness 54 Structure-Mechanical Property Relationship

54

Dislocation Theory 4.1 4.2 4.3

4.4 4.5

4.6

4.7 4.8

Introduction 57 The Shear Strength of Ideal and Real Crystals 59 Geometry of Dislocations 60 4.3.1 Edge Dislocation 61 4.3.2 Screw Dislocation 63 Burgers Vector, Burgers Circuit and Dislocation Loop 64 Movement of Dislocations 67 4.5.1 Concept of Slip 67 4.5.2 Dislocations and Slip 70 4.5.3 Slip Plane 72 4.5.4 Cross-Slip 72 4.5.5 Dislocation Climb 73 Elastic Properties of Dislocations 74 4.6.1 Stress Field and Energy of a Dislocation 74 4.6.2 Forces on Dislocations 77 4.6.3 Line Tension 78 Forces between Dislocations 80 Unit Dislocations and Partial Dislocations 84 4.8.1 Dislocations in FCC, BCC and HCP Crystals 85 4.8.2 Dislocations and their Reaction in FCC Crystals 86

57-103

Contents

4.9 4.10 4.11 4.12

5.

94

Deformation of Metals 5.1 5.2 5.3

5.4 5.5 5.6

6.

4.8.3 Frank Partial Dislocations 91 4.8.4 Lamer-Cottrell Dislocations 92 Peierls-Nabarro Stress and Dislocation Width Dislocation Multiplication 96 Dislocation Intersection 98 Dislocations in Ceramics 101

6.5

6.6 6.7

6.8

104-138

Introduction 104 Elastic Deformation 104 5.2.1 Significance of Elastic Modulus 106 Plastic Deformation 107 5.3.1 Deformation by Slip 107 5.3.2 Type of Loading for Plastic Deformation 109 5.3.3 Potential Slip Planes and Directions in Crystals 110 5.3.4 Critical Resolved Shear Stress 113 5.3.5 Strain Hardening in Single Crystal 119 5.3.6 Structural Changes in Cold Worked Polycrystalline Metals and Alloys 123 5.3.7 Annealing of Cold Worked Metals 128 Deformation by Twinning 134 Deformation Behaviour in Ceramics 136 Deformation Behaviour in Polymers 136

Strengthening Mechanisms in Materials 6.1 6.2 6.3 6.4

ix

Introduction 139 Grain Boundary Strengthening 141 Solid Solution Strengthening 145 Second Phase Particle Strengthening 153 6.4.1 Precipitation Hardening 154 6.4.2 Dispersion Hardening 168 Strain Hardening 169 6.5.1 Properties Affected by Strain Hardening 171 6.5.2 Industrial Importance of Strain Hardening 172 Martensitic Strengthening 174 Composite Strengthening 175 6.7.1 Fibre Strengthened Composites 176 6.7.2 Dispersion Strengthened Composites 188 6.7.3 Particle-Strengthened (or Simply Particulate) Composites Strengthening of Plastics 190 6.8.1 Strengthening by High Average Molecular Weight 191 6.8.2 Strengthening by Crystallinity 193 6.8.3 Strengthening by Bulky Pendant Atomic Group 195

139-205

190

X

Contents

6.8.4

6.9 6.10

7.

Strengthening Thermoplastics by the Presence of Polar Atoms or Groups 196 6.8.5 Strengthening Thermoplastics by Introducing Non Carbon Atoms in the Main Carbon Chain 196 6.8.6 Strengthening Thermoplastics by Introduction of Aromatic Groups in the Main Chain 197 Strengthening of Ceramics 197 Applications of Strengthening Mechanisms to Obtain High Strength Materials 201

Fracture 7 .1 Introduction 206 7.2 Ductile Fracture 207 7.3 Mechanism of Ductile Fracture 209 7.4 Brittle Fracture 209 7.5 Mechanism of Brittle Fracture 210 7.6 Factors Affecting the Type of Fracture

206-212

212

8.

Tensile Behaviour 8.1 Introduction 213 8.2 Tension Test and Stress-strain Curves 214 8.3 Tensile Properties 219 8.3.1 Modulus of Elasticity and Stiffness 219 8.3.2 Yield Strength 221 8.3.3 Tensile Strength 221 8.3.4 Modulus of Resilience 222 8.3.5 Ductility 224 8.3.6 Toughness 225 8.4 True Stress-strain Curve 226 8.5 Plastic Instability in Tension 232 Discontinuous Yielding (Yield Point Phenomenon) 8.6 233 8.7 Important Variables Affecting Tensile Properties 239 8.7.1 Effect of Gauge Length 239 8.7.2 Effect of Size of the Specimen 240 8.7.3 Effect of Form of the Specimen 241 8.7.4 Effect of Strain Rate 243 8.7.5 Effect of Temperature 243

213-245

9.

Hardness Testing 9.1 Introduction 246 9.2 Scratch Hardness 247 9.3 Indentation Hardness 247 9.4 Brinell Hardness Test 249 9.4.1 Precautions 252

246-270

Contents

9.5

9.6

9.7 9.8

9.9

9.4.2 Advantages and Applications of Brinell Hardness Test 9.4.3 Disadvantages of Brinell Test 254 Vickers Hardness Test 254 9.5.1 Derivation of Vickers Formula 255 9.5.2 Sources of Errors 256 9.5.3 Advantages and Applications 257 9.5.4 Disadvantages 257 Rockwell Hardness Test 258 9.6.1 Principle of Operation 261 9.6.2 Advantages of Rockwell Hardness Test 263 9.6.3 Precautions 263 Superficial Rockwell Hardness Test 263 9.7 .1 Precautions 264 Microhardness Test 264 9.8.1 Precautions 266 9.8.2 Applications 266 9.8.3 Comparison of Macrohardness and Microhardness Tests Dynamic Hardness Testing 267 9.9.1 Shore Hardness Testing 267 9.9.2 Poldi Hardness Test 270

xi

253

266

10. Ductile-Brittle Transition Behaviour and Fracture Toughness Test 10.1 Introduction 271 10.2 Ductile-Brittle Transition Behaviour 272 10.3 Transition Temperature and Its Significance 274 10.4 Notch-bar Impact Test 277 10.5 Variable Affecting Impact Values 279 10.6 Behaviour of Polymers under Impact Loading 285 10.7 Fracture Toughness 286 10.7.1 Fracture Stress Test 291 10.7.2 Hardness Indentation Method 292 10.7.3 Importance of Fracture Toughness Determination 10.8 Toughening in Ceramics 294 10.8.1 Crack Deflection Toughening 296 10.8.2 Transformation Toughening 297 10.8.3 Crack Bridging (or Wake) Toughening 299 10.8.4 Microcrack Toughening 302

11. Fatigue Behaviour 11.1 11.2 11.3 11.4

Introduction 304 Stress Cycles 306 Macrography of Fatigue Fracture Fatigue Test (S-N Curve) 309

271-303

294

304-325

308

xii

Contents

11.5 11.6

11.7 11.8

Fatigue Behaviour in Iron and Steel 311 Mechanisms of Fatigue 312 11.6.1 Orowan's Theory of Fatigue 312 11.6.2 Wood's Theory of Fatigue 315 11.6.3 Fatigue Crack Growth 317 Low Cycle Fatigue 322 Variables Affecting Fatigue 322

326-356

12. Creep Behaviour 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9

Introduction 326 Creep Curve 327 Design Curves 331 Andrade's Analysis of Creep 333 Creep at Lower Temperature 334 Activation Energy for Steady-State Creep 335 Creep at High Temperature 336 Equicohesive Temperature 336 Deformation at Elevated Temperature 338 12.9.1 Deformation by Slip 338 12.9.2 Grain Boundary Deformation 339 12.10 Mechanisms of Creep Deformation 339 12.10.1 Dislocation Glide 339 12.10.2 Dislocation Creep 343 12.10.3 Diffusion Creep 345 12.10.4 Grain Boundary Sliding 346 12.11 Metallurgical Factors Affecting Creep Behaviour 347 12.11.1 Effect of Lattice Structure 347 12.11.2 Effect of Prestrain 348 12.11.3 Effect of Soluble Impurities and Alloying Elements 12.11.4 Effect of Second Phase Particles 349 12.11.5 Grain Size 350 12.12 Creep Resistant Materials 350

13. Non-Destructive Testing 13.1 13.2 13.3 13.4

Introduction 357 Visual Inspection 359 Liquid Penetrant Inspection (LPI) 360 13.3.1 Procedure 361 Magnetic Particle Inspection (MPI) 363 13.4.1 Basic Principle 363 13.4.2 Magnetization 364 13.4.3 Magnetization Techniques 366 13.4.4 Procedure for MPI 370 13.4.5 Applications of MPI 372

348

357-386

Contents

13.5

13.6

13.7

Eddy Current Inspection (ECI) 372 13.5.1 Basic Principle 373 13.5.2 Operating Variables 375 13.5.3 Applications 377 Ultrasonic Testing 377 13.6.1 Basic Principle 378 13.6.2 Ultrasonic Waves 378 13.6.3 Ultrasonic Transducers 380 13.6.4 Probes 381 13.6.5 Interaction of Sound Waves at the Interfaces 13.6.6 Methods of Ultrasonic Inspection 383 13.6.7 Advantages of Ultrasonic Inspection 385 Radiographic Inspection 385

xiii

382

Appendix A

Hardness Testing

387

Appendix A1

Brine/I Hardness Test

388-391

Appendix A2

Vickers Hardness Test

392-394

Appendix A3

Rockwell Hardness Test

395-397

Appendix B

Tensile Testing

398-405

Appendix C

Impact Test

406-409

Appendix D

Fatigue Test

410-412

Appendix E

Sheet Metal Formability Test

413-414

Appendix F

Bend Test

415-417

Appendix G

Mechanical Properties of Some Representative Polymer Materials

418-419

Appendix H

Table of Hardness Conversion

420-421

Appendix I

SI Units

422

Appendix J

Conversion Factors

423

Appendix K

Unit Conversion

Appendix L

SI Prefixes

427

Appendix M

Greek Alphabets

428

Appendix N

Table for Conversion of Temperature

424-426

429-431

Glossary

433-466

Bibliography

467-468

Questions Bank

469-546

Index

547-562

Preface

Materials have always been the major attraction for the human beings. Significance of materials is self-evident by the familiar terms-Stone Age, Bronze Age and Iron Age. It is the effective use of the materials that has been, and is still in use, the criterion for the better living and economy of a country. Any material prior to its end use is subjected to many processes and treatments. A large number of materials are known to man and the numbers in the list are increasing gradually with newer and newer arrivals. This makes the task of selection of the materials very difficult. Widely differing physical, chemical and mechanical properties, typical processing characteristics such as castability, machinability, weldability, etc., and the response to various manufacturing methods further complicate the task of materials selection. The success of selected material is largely determined by its conformity to the service conditions and the reliability. Material testing and critical interpretation of the test data play a key role for selection, designing and manufacturing of a material for end use with a minimum of desired reliability. Based on this concept, this book has been presented to engineering students and to technical personnel dealing with materials. The prime aim of the book is to present the subject matter in most concise, coherent, logical and lucid manner. This book provides an insight into the mechanical behaviour and testing of metals, polymers, ceramics and composites which are widely employed for structural applications under varying load, temperature and environments. The book is designed primarily as a text for the undergraduate and postgraduate students of Metallurgical and Materials Engineering. Additionally, it will be useful for the undergraduate and postgraduate students of Mechanical Engineering, Production Engineering, Industrial Engineering, Automobile Engineering, Chemical Engineering, Polymer and Ceramic Engineering, Civil Engineering and Structural Engineering. Much care has been taken to cater the needs of students appearing in the examinations of various professional bodies such as

xv

XVi

Preface

The Institution of Engineers (India), Institute of Metals, etc. Besides, the practising engineers and technical personnel dealing with the materials in general, and dealing with destructive and non-destructive testing in particular, will also get benefit of the information provided in the text. The book is organized in thirteen chapters. While Chapter 1, at first, introduces readers to the fundamentals of materials starting from their basic building units, it gradually rises through atomic bonding, crystal structure, different classes of engineering materials and their salient features to some commonly used industrial materials and their engineering applications. Chapter 2 and Chapter 3 describe role of imperfections on the behaviour of metals and alloys, and various properties of engineering materials. Chapter 4 deals with dislocation theory in a simplified, but analytical manner. Chapter 5 speaks about the plastic deformation of the materials primarily in the light of dislocation theory. Various mechanisms for enhancing strength of all classes of engineering materials have been discussed in Chapter 6. Chapter 7 has been exclusively devoted to common aspects of fracture. Out of next six chapters, first five chapters (Chapters 8-12) describe in detail about destructive tests, whereas Chapter 13 explains commonly used non-destructive testing methods of materials. Whereas, both theoretical and practical aspects of destructive/non-destructive testing are covered in these Chapters, the practical manual is also given at the end in the form of Appendices A to N. A large number of questions, with solutions, have been incorporated as Question Bank at the end of the book. It covers about 200 objective type questions appeared in GATE examinations. For quick reference, glossary of terms has been incorporated in the book. Every effort is made to avoid repetition in the text. However, readers may find some repetition which was a compulsion to maintain the coherency of the text. Authors not only will welcome any constructive suggestion from the readers but also will acknowledge them in future editions.

A.K. Bhargava and C.P. Sharma

Acknowledgements

Gratitude is the hardest of all emotions to express. There is no word capable of conveying everything one faces until we reach the world where thoughts can be adequately expressed in words. It gives us immense pleasure to put on record our profound sense of indebt to Hon'ble Prof. T.V. Rajan, Shri Subodh Bhushan Gupta jee, Prof. Surendra Kumar (Department of Chemical Engineering, IIT Roorkee) and Prof. A.N. Tiwari (Department of Metallurgical Engineering and Materials Science, IIT Bombay) for their benevolent guidance, constant encouragement and support in odds. Special thanks to Mrs. & Dr. Ravindra Padalkar, Mrs. Manju, and Nakul-Taru (daughter's parents-in-law, wife, son-in-law and daughter A.K. Bhargava) and to Mrs. Usha, Anand-Avantika, Ayam-Sunita and Avni-Aarini (wife, sonin-law & daughter, son & daughter-in-law and granddaughters - C.P. Sharma) who not only maintained pleasant atmosphere during the period of successful completion of this project but also provided all the cooperation and moral support. Special thanks are due to Mr. Nakul for visualizing the design of the cover page of the book. Authors are highly thankful to teachers for their blessings, colleagues and friends for their constructive suggestions and students for their frequent questions within and outside the classroom which nucleated the idea of this book. Thanks are due to highly energetic and committed team of PHI Leaming, New Delhi, for chasing us and bringing the book in short period. Last but not the least, we acknowledge each and everyone who directly or indirectly motivated, helped, and inspired us from time to time.

A.K. Bhargava and C.P. Sharma xvii

Nomenclature

Area of cross-sectional plane (4.5. l) Constant (6.5) Surface area of indentation (9.4) Lateral area of indentation (9.5) Projected area of indentation (9.8) Rockwell scale (9.6) Area of cross-section of composite (6.7.l) Area of cross-section at fracture (8.3.5) Area of cross-section of fibre (6. 7. l) Instantaneous or true area of cross-section (8.4) Area of cross-section of matrix (6.7. l) Original area of cross-section (8.2, 8.3.2) Cross-sectional area of the specimen at notch (10.4) Area of slip plane (5.3.4) Axial dimension ( 1.4) Shear displacement Interplanar spacing (4.2) Lattice parameter (4.5, 4.8, 5.3.3, 6.3, 6.4. l/frequently used) Side of the projected square indentation (9.5) Spacing between slip planes (4.9) Surface crack length or half the interior crack length (7.5, 10.5, 10.7, 10.8, 11.6.2) Allowable flaw size (10.7.2) Critical size surface crack (10.5, 10.8) xix

XX

a a a a B B B b b b

b b1 b2 b3

/3 /3 /3 /3 C C Cv c c c D D D D D Dgb

Dv d d d

d* dE dE

dl ds ds d0 dW ~

M

Nomenclature

Shear angle (5.2) Constant (6.2) Local order parameter (6.3) Interaxial angle (1 .4) Constant (6.9) Critical thickness (10.7) Rockwell scale (9.6) Interatomic spacing (4.2) Axial dimension (1.4) Magnitude of Burgers vector (4.6.1) Burgers vector (frequently used) Burgers vector (4.7, 4.8.1, 4.11) Burgers vector (4.7, 4.8.1, 4.11) Burgers vector (4.8.1) Compressibility (5.2) Constant (12.4) Interaxial angle (1 .4) Load transfer function (6.7.1) Constant ( 11.6.2) Rockwell scale (9.6) Fracture energy (10.3) Axial dimension (1.4) Height of the unit cell (5.3.3) Concentration of solute atoms (6.3) Average grain diameter (6.2) True diameter (8.4) Diameter of ball indenter (9.4) Rockwell scale (9.6) Self diffusion coefficient (12.11.1) Grain boundary diffusion coefficient (12.10.3) Volume diffusion coefficient (12.10.3) Diameter of fibre (6. 7 .1) Grain diameter (6.2, 12.10.3) Diameter of indentation (9.4) Critical grain diameter (10.5) Change in energy (4.6.1) Increase in energy (4.6.3) Small distance or displacement (4.6.2) Equilibrium spacing between partial dislocations (4.8.2) Small segment of dislocation line (4.6.2) Angle subtended at the centre of curvature (4.6.3) Work done (4.6.2) Deformation (11.6.1) Increase in energy (4.7)

Nomenclature

Ml 11Uc E E E

E' E0 e e e e t: 1

tdiff dis!

SFE tgbs 81

emisfit

e0 t:1

ec 11t:P

er eu ~· F F(R) F(a) f f f G

r r r

rm

'l'P

rs rs rs

xxi

Activation energy (12.6) Interaction energy (6.3) Elastic modulus (5.2, 6.7.1, 7.5, 8.3, 10.5, 10.8, 12.10.2) Elastic strain energy of dislocation (4.6.1) Energy associated with dislocation (4.8) Elastic modulus of the discontinuous and randomly aligned fibre composite (6.7.1) Core energy of dislocation (4.6.1) Average tensile strain, nominal strain (6.7.1, 8.2, 8.3.1) Shear strain (5.3.4) Tensile strain (6.7.1) Creep strain (12.4) The fatigue ductility coefficient (11.7) Strain rate (8.6) Creep rate (12.4, 12.5, 12.8) Diffusion creep rate (12.10.3) Dislocation creep rate (12.10.4) SFE dependent creep rate (12.11.1) Grain boundary sliding (GBS) creep (12.10.4) Dislocation glide creep rate (12.10.1) Steady-state creep rate (12.10.3) Misfit parameter (6.3, 6.4.1) Instantaneous strain (12.4) Strain at fracture (8.7.1) Measure of modulus difference between solute and solvent (6.3) Plastic strain range (11.7) True strain (8.4) Uniform strain (8.7.1) Strain corresponding to yield stress (8.3.4) Force (4.6.2, 5.3.4) Force of repulsion (4.7) Force of attraction (4.7) Frequency of alternating current (13.5.1, 13.5.2) Volume fraction of precipitate phase (6.4.1) Limit frequency (13.5.2) Shear modulus (4.1, 4.2, 4.6.1, 4.9, 4.10, 5.2, 6.3, 6.4.1, 10.5, 12.10.1,12.10.2) Interaxial angle (1 .4) Shear strain (4.2, 5.2) Surface energy (10.8) Plastic work done around a crack (10.5) Energy required for plastic deformation per unit area (7 .5) Stacking fault energy (4.8.2, 12.11.1) Surface energy per unit area (7.5, 10.5) Precipitate-matrix surface energy (6.4.1)

xxii YAPB

rez H HAc HEc h h h' K K K K K K Kie

K' KR* Kth

K,. k k

kt

Xo X;

Nomenclature

Antiphase boundary energy (6.4.1) Elastic shear strain (4.6.1) Vickers hardness (10.7.2) Alternating magnetic field/primary magnetic field (13.5.1) Secondary magnetic field (13.5.1) Constant (9.6) Height of the hammer from its lowest point before its release (10.4) Height of the hammer from its lowest point after its release (10.4) Bulk modulus (5.2) Constant (7.5, 12.4) Constant called strength coefficient (8.4) Load factor (9.4) Major energy shell (1.1) Stress intensity parameter (10.7, 11.6.2) Critical stress intensity or fracture toughness (10.7) Constant called fibre efficiency parameter (6. 7 .1) Critical stress intensity factor (10.8) Threshold stress intensity value ( 11.6.2) Measure of extent to which dislocation pile up at barriers (6.2, 10.5) Constant (6.2) Boltzman's constant (12.10.3) Stress concentration at the crack tip (10.7) Angle that slip plane makes with respect to stress axis before stressing (5.2.4) Angle of reorientation of slip plane with stress axis at any instant after plastic deformation (5.3.4) Inductance (13.5.1) Length (6.2) Length of diagonal of projected square shaped indentation (9.5) Length of longer diagonal of Knoop indentation (9.8) Length of the specimen at time t (12.4) Major energy shell (1.1) Gauge length before plastic deformation (5.3.4) Length of the specimen just after the load is applied (12.4) Original gauge length of specimen (8.2, 8.7.1) Gauge length at any instant after plastic deformation (5.2.4) Length at fracture (8.7.1) Azimuthal quantum number ( 1.1) Length of cylindrical crystal (4.6.1) Length of dislocation line segment (4.6.3, 4.10) Distance between particles (4.6.3, 6.4.1) Spacing between planes (5.2) Critical fibre length (6. 7 .1) Angle between applied force and slip plane normal (5.3.4) Constant of proportionality (9.4)

Nomenclature

A-0

A; M m1

ms M

µ µ, N N N n n n n n

v m P P

Pc P1 Pm Pu Py PAB

fc.

where, 0, and a'm represent, respectively, the fracture strength of the fibre and the stress in the matrix when the composite fails. A comparison of Eqs. (6.34) and (6.46) shows that discontinuous fibres will always produce less strengthening than continuous fibres . As llle increases the strength of the composite also increases. Equation 6.41 shows that the greater the critical aspect ratio the larger will be the maximum stress in the fibre (i.e. 0,). In the limit, the stress of the discontinuous reinforcement will approach that of continuous reinforcement as llle tends to infinity (i.e. llle ➔ oo ). In other words, if llle is large enough, the difference is unimportant. Practically speaking, this will usually occur as llle ~ 10. At this value the strength of discontinuous fibre reinforced composite is ~ 95% that of the continuous fibre reinforced composite. The critical aspect ratios for most fibres range from 20 to 150. Since a typical fibre diameter range between 10 to 30 µm, critical fibre lengths are of the order of 0.2 to 4.5 mm. In most cases the fibre length is much larger than le. Fibres for which l >> le are called continuous.

188

Mechanical Behaviour and Testing of Materials

If the fibre length is less than the critical fibre length (i.e. l < le), the longitudinal strength of the discontinuous and aligned fibre composite is given by,

(6.47) If l < le and the applied stress is a. 20

E

2 C

0

:~ C !!!

0

1--20 -40 4

5

6

7

8

9

10

ASTM Grain size no.

FIGURE 10.6

Effect of grain size on transition temperature in a typical steel.

Equation (10.2) shows that as the grain size decreases yield strength increases. A higher yield strength means a higher stress will be required to nucleate a crack by slip on intersecting planes. If a crack is nucleated under sufficiently high stress conditions, it will traverse on either

Ductile-Brittle Transition Behaviour and Fracture Toughness Test

281

side up to the grain boundaries. If the grain diameter is small, the length 2a of the crack is limited to this diameter. The grain boundaries will stop the crack to propagate in the adjacent grains. In order this crack to enter the adjacent grain it has to search of the most likely propagation plane which in tum needs large expenditure of energy. Further, a crack is able to propagate only if its length 2a is above a critical size. If the grain size itself is less than the critical length of the crack, the crack is unable to propagate, and hence, the brittle fracture is prevented. The critical fracture stress ( Gj) corresponding to this critical size crack (a*) is given as: CT

£)

2 - ( _1__

f -

1 2 '

tra *

(10.3)

In Eq. (10.3) yis the surface energy per unit area, and Eis the elastic modulus of the material. This equation clearly indicates that smaller the crack length larger will be the stress required for fracture . Just as yield strength is a function of grain diameter, fracture strength is also a function of grain size. Using dislocation models, Cottrell and Petch have developed a relationship between fracture strength and grain size which is expressed as: 4ymG k_,,

CT!=--

d-112

(10.4)

where, Ym is the plastic work done around a crack as it moves through the crystal, and G is the shear modulus of the material. The other terms being the same as defined above. Equation (10.4) shows that the fracture strength increases with decreasing grain size. This equation also shows the dependency of fracture strength on Ym· Higher the value of Ym, higher will be the stress required to propagate the crack. The value of Ym will be enhanced by increasing the number of unpinned dislocation sources, increasing test temperature and decreasing the crack velocity. A large number of the unpinned dislocation sources will generate more number of dislocations at the crack tip, and therefore, more blunting of the crack. Increasing temperature results in lowering d2 < d1 of Peierls stress and increase in dislocation velocity. Both Ym and CTJ will be low if dislocation sources are pinned by interstitial solutes, such as carbon and nitrogen u1(d1) in steels or highly immobile, as in ionic or t, covalent materials. The magnitude of Ym ui also get reduced by strengthening '' ' !!! : ~ To : u5 mechanisms such as solid solution, preci~ ' pitation, dispersion and strain hardening as these mechanisms reduce number of mobile dislocations. This also results in T0 (2) To(1) increase of CT;. For a given value of CT; and Transition temperature, T Ym, decreasing grain size results m FIGURE 10.7 Effect of grain size on ay, a, and decreasing transition temperature as is transition temperature for a given a; evident from Figure 10.7. and Ym· !::. T0 is the decrease in T.

f

1/)

282

Mechanical Behaviour and Testing of Materials

Figure 10.8 shows the effect of grain size on yield and fracture stress and fracture strain. The two curves for fracture stress and yield stress are intersecting at a critical grain size, d*. For larger grains (greater than the critical size) the fracture is controlled by the yield stress. Some microscopic yielding is necessary to nucleate a crack. This will happen only when yield stress approaches the fracture stress, i.e. when, a= 0 = a". Once a crack is nucleated, its propagation is rapid enough to cause brittle type failure. For grains smaller than the critical size, yielding occurs first before any fracture to take place. The amount of plastic deformation, before fracture, increases with decreasing the grain size below the critical value. In other words, the ratio of GJIG" increases with decreasing the grain diameter. This in turn leads to improvement in toughness as is evident from the transition curve (strain to fracture) superimposed in Figure 10.8. - - - Fracture stress - - - Yield stress - - - Strain to fracture

e s\(ess ,, r(ac\l.l(

/ / / / /

/ / / / /

d* Grain diameter, d- 112 (mm _, ,2 )

FIGURE 10.8

-

Effect of grain size on yield strength, fracture strength and fracture strain. Decreasing grain size results in not only increase of ay but also a, and strain to fracture.

Thus, fine grained materials have a lower transition temperature as compared to coarse grained materials. Therefore, it is beneficial to either adopt the lowest possible finishing temperature in hot working or normalize the steel after hot working. Figure 10.9 illustrates that decreasing the grain size not only results in improvement in strength but also ·-e in toughness. Ductility is slightly improved while 2i. Wedability e weldability remains unaffected. From the forgoing a.. discussions it is clear that among the various Ductility strengthening mechanisms grain refinement is the only one which results in not only improvement in Decreasing grain size strength, but also improvement in toughness. In all other strengthening mechanism, on the other hand, FIGURE 10.9 Effect of grain refinement on various properties. toughness gets reduced with the increase in strength. 1/)

Q)

Ductile-Brittle Transition Behaviour and Fracture Toughness Test

283

Composition Effect of composition on impact transition temperature has been discussed with reference to steel as these are widely employed in the manufacturing of components of structure and machines involving impact loading conditions. Of all the major alloying elements present in steel, chromium has little effect while carbon and manganese have a great effect on Ductile Brittle Transition Temperature (DBTT). Carbon which is invariably present in steels and which is also the principal alloying element, raises the DBTT. This effect is counteracted by manganese, but to a lesser extent. For example, an increase of carbon content by 0.1 % increases the DBTT by about 15°C, whereas an increase in Mn content by 0.1 % lowers this temperature by only about 5°C. So for a satisfactory notch toughness Mn:C ratio must be maintained to be a minimum of 3: 1. This ratio may be increased to as high as 3: 1. When this ratio is still higher and Mn content is greater than about 11 % , manganese tends to stabilise austenite. Phosphorous and silicon also raise the DBTT of steel. An increase in phosphorous content by 0.1 % over the nominal limit, raise DBTT by about 7°C. Molybdenum also behaves in the same way as carbon. Oxygen also raises the DBTT of steel. An increase of oxygen content by about 0.001 % raises this temperature by 5°C. Nitrogen also has detrimental effect on notch toughness of steel. Aluminium, which is used for deoxidation of steel to produce semi-killed or killed steel, is beneficial as it not only lowers the oxygen content in steel but also combines with the dissolved nitrogen to produce aluminium nitride. Thus, aluminium not only increases notch toughness by reducing oxygen content but also improves strength by forming aluminium nitride. A reduction in dissolved N also eliminates yield point phenomenon in steel. Aluminium increases rate of nucleation during solidification of steel, and thus, refines the grain structure, and hence, lowers DBTT. In HSLA ferritic steels, small amounts of columbium or vanadium also improve impact toughness of steel. Carbides of these elements raise the yield strength and restrict the grain coarsening, thereby lowering the DBTT. Nickel also lowers DBTT of steel. Nickel in steel lowers the lower critical temperature, and thus, produces a fine pearlitic structure which is responsible for improved toughness of steel.

Effect of microstructure and heat treatment In case of rolled or forged products, impact strength (or impact toughness) varies with the directionality of orientation of grains. Impact strength is higher along longitudinal direction, i.e. when the impact force is tensile with respect to the direction of orientation of grains (Figure 10.10). Similar observations are made with banded structure of ferrite and pearlite. Both quench ageing and strain ageing raise the DBTT and reduce tensile ductility and notch bar toughness of low carbon steel. Low carbon steels containing less than 0.1 % carbon when quenched after holding for some time, from about 923 K to 993 K (650°C to 700°C), results in highly supersaturated ferrite phase. The high temperature phase is retained at room temperature. This supersaturated solid solution of ferrite is unstable even at room temperature. This is because interstitial carbon atoms tend to diffuse out of the BCC lattice of iron over a period of time in the temperature range of 293 K-573 K (20°-300°C). Over the period of time, i.e. on ageing, precipitation of iron carbide takes place. This carbide precipitate reduces ductility and impact toughness of low carbon steels. If ageing occurs up to about 473 K (200°C), Fe2.4C carbide having hexagonal close packed structure precipitates out in sub-microscopic form. If the ageing temperature is raised to about 300°C, cementite will form.

284

Mechanical Behaviour and Testing of Materials

Direction of orientation of grains

A

B

"C

i

0 (/)

..c ~

Cl>

C

w Temperature -

FIGURE 10.1 O Effect of orientation of grains with respect to impact load on impact strength.

The phenomenon of blue brittleness is closely associated with dynamic strain ageing and results in decrease of impact toughness in low carbon steels if these deform in the temperature range 373 K-623 K (l00°-350°C). Plastic deformation of low carbon steels, in this temperature range, results in interaction between the solute atoms and dislocations produced. Under thermal conditions, the solute atoms are able to diffuse in the material at a faster rate than the speed of dislocations and catch and pin them. The consequent effect is the increased density of locked dislocations which reduce ductility as well as impact resistance. This phenomenon is accelerated at about 473 K (200°C) or more. The phrase blue brittleness is a misnomer. The name blue is derived from the colour of the oxide film formed on the surface of steel when oxidized in the temperature range 473-573 K (200°-300°C). The name is 'misnomer' as the steel does not become brittle in the normal sense of brittleness. Rather the steel shows minimum elongation at this temperature as well as decreased notched impact resistance. The tensile fracture does not show brittle characteristic. Tempered martensitic structure provides the best combination of tensile strength and impact toughness. In case of some low alloy steels, tempering within certain temperature range (in particular, 623-873 K (350°-600°C) results in embrittlement popularly known as temper embrittlement. The major consequence of temper embrittlement is found to be an increase in ductile-brittle transition temperature, and hence, the reduction of the impact value of steel to a great extent. The temper embrittlement has been thought to arise due to precipitation of certain impurities such as P, As, Sn and Sb at the prior austenite grain boundaries without the formation of observable precipitate. This has been verified by some investigators using Auger electron spectroscopy (a technique by which the chemistry of the first few atomic layers of a material's surface is analyzed). The segregation of these impurities reduces the cohesive energy of the grain boundary which, in tum, lowers the local stress necessary to generate an accelerating microcrack leading to brittle type fracture. The effect of temper embrittlement can be minimised

Ductile-Brittle Transition Behaviour and Fracture Toughness Test

285

in three ways: by cooling relatively fast during this tempering temperature range so that enough time is not available for unwanted precipitation of impurities to occur, by adding a small amount of molybdenum which seems to raise the temperature range of impurity precipitation and tempering can be carried out below this temperature range without the danger of embrittlement effect; small additions of a lanthanide metal (a group of rare earth metals with atomic number from 57 to 71 inclusive are referred to as lanthanide metals) reduces the temper embrittlement effect. A lanthanide metal combines with the embrittling impurities such as P, As, Sn, and Sb and form harmless compounds in the matrix, thereby preventing the impurities segregation at grain boundaries.

10.6 BEHAVIOUR OF POLYMERS UNDER IMPACT LOADING Like many metals that are tough when tested at slow strain rate (as in tensile test), it tend to fracture in a brittle manner under sudden loading, many polymers also follow this trend. In metals this impact energy is dissipated to cause plastic deformation of the material, whereas in polymers this energy is accommodated through atomic vibration and/or molecular movements (such as rotation and small translations) and heat. Polymer materials that do not allow such modes of movements fail by the brittle mode of fracture because the impact energy is confined within a small localized area, and is enough to cause direct rupture of bonds. The movements in polymer molecules cause deformation or strain. Polymer materials that exhibit large deformation or strain display good toughness under impact loads in particular when they have good tensile strength. However, such polymer materials tend to have low elastic modulus. Thus, polymer materials with high elongation and low modulus but high tensile strength are called tough and those with high modulus and low elongation are said to be brittle. This trend is also apparent from the tensile curves shown in Figure 5.25. Polymers that are highly crystalline and those which have high degree of cross-linking (such as thermosets) have restricted molecular movements, and are therefore, brittle in nature. Semicrystalline thermoplastics having high molecular weight and narrow molecular weight distribution display good toughness because such plastics have an optimum combination of high strength and plasticity. In such semicrystalline plastics, energy of impact is dissipated in causing vibrations, rotation and stretching of atoms and molecules. Here crystallites (the regions in which the polymer molecules have high degree of order or molecular orientations) impart high strength and the amorphous part is responsible for molecular movements. Figure 6.30 is a schematic representation of crystallite in polymer. Impact strength of many polymers is raised by introducing reinforcements in them. Toughness of many plastics is also improved by the addition of rubber (also called elastomer) material in them. These additions are called toughness modifiers. The rubber particulate material is mixed thoroughly with a rigid plastic and imparts additional molecular movements when the plastic is impacted. Thus, the modified plastic is able to absorb the energy of impact and has good toughness. Amorphous polymers with large bulky side groups exhibit brittle behaviour. Unoriented crystalline polymers tend to be tough if tested above or near glass transition temperature. However, at still higher temperature impact strength tend to decrease because of the softening of the polymer material. Just as with many metals that tend to show brittle behaviour at low temperatures and

286

Mechanical Behaviour and Testing of Materials

high strain rates, many polymer materials also display this trend. Both amorphous and crystalline polymers are brittle at low temperatures and have low impact toughness. Both display ductile-brittle transition behaviour over a narrow temperature range just as many steels show. Both Izod and Charpy tests can be used to measure impact toughness of polymer materials. In the test, a notched standard specimen is subjected to impact blow and the energy at fracture is measured as impact strength. In the Izod test, the specimen is rigidly held vertically and notch is facing the striking hammer. In Charpy test, the specimen is held loosely as a beam and notch is opposite to the striking hammer. Izod test is more common for plastics.

10. 7 FRACTURE TOUGHNESS Impact test can be used to determine the temperature range for the transition from ductile to brittle behaviour in metals and alloys as the temperature is lowered. An impact test gives quantitative comparative useful data with relatively simple test specimen and equipment. However, these tests do not provide property data for design purposes for material sections containing cracks or flaws. Discipline of fracture mechanics provides the property data for design purposes. Fracture mechanics involves the theoretical and experimental analyses of fracture of structural materials containing preexisting cracks or flaws. Generally, fracture of a material initiates at a location having the highest stress concentration. The tip of a crack is one such location. To illustrate this let us consider a plate sample containing an edge (or surface) crack [as shown in Figure 7.2(b)] and is subjected to a uniaxial tensile load as shown in Figure 10.1 l(a) and (b)]. When there is no flaw in a material, the load is supported by several atomic bonds over a uniform area [Figure 10.1 l(a)], i.e. the applied stress is said to be uniformly distributed. In presence of a surface crack the stress is redistributed such that the load that was supported by several bonds is now carried by only a few bonds at the crack tip as shown in [Figure 10.1 l(b)]. That is, the presence of a flaw will locally amplify the applied stress at the crack tip and is maximum there than anywhere else around the crack tip, as illustrated in [Figure 10.1 l(c)]. There are three fundamental modes of loading that result in different crack surface displacement. These modes are illustrated in Figure 10.12. Mode I is a crack opening (or tensile) mode, whereas modes II and III are sliding and tearing types respectively. In mode I, the applied stress is tensile in nature and acts normal to the faces of the crack (y-direction) thereby leading to its opening. Mode II refers to the shear mode in which the stress applied normal to the leading edge of the crack but lie in the plane of the crack. Mode III is the parallel shear mode that arises when shearing stresses are applied to the leading edge of the crack as shown by arrows. Mode I loading is the most common and important situation associated with most of the structural components. Consequently, considerable attention has been paid to both the analytical and experimental methods designed to quantify mode I stress-crack relations. Mode II is found less frequently and is of little engineering importance. Mode III is also a rare situation in practice. Mode II and mode III in combination with mode I are operative in crack propagation in reinforced composites.

Ductile-Brittle Transition Behaviour and Fracture Toughness Test

(a) Load

287

(b) Load

y

en en ~

"'iii ~

·u; C: Q)

I-

z

\

Distance------

X

Crack tip (c)

FIGURE 10.11

(a) Schematic atomic two-dimensional model of a crystal without a crack, (b) The same crystal with a crack showing breakage of many bonds and redistribution of stress. The stress is supported now by only few bonds, and (c) Variation of tensile stress ahead of the crack tip.

(a) Mode I

FIGURE 10.12

(b) Mode II The sliding mode

(b) Mode III The tearing mode

Modes of crack surface displacement. (a) Mode I, the opening or tensile mode, (b) Mode II, the sliding mode, and (c) Mode III, the tearing mode.

288

Mechanical Behaviour and Testing of Materials

For mode I configuration, the stresses acting on an element of the material at distance r and the angle 0 with respect to the tip of an advancing crack (Figure 10.13) are expressed by:

K 0 a" =--cos. ✓2m2

(l . 0

. 30) +sm-·sm2 2

(10.5)

K 0( . 0 . 30) ax = ✓ 2m- cos 2 1 - sm 2 ·sm 2

(10.6)

r x_, = ~ (cos ~ · sin ~ · cos 30 ) ✓ 2m" 2 2 2

(10.7)

y r -- -

- -------,,,,

0 X

z

FIGURE 10.13

Stress distribution on a small element of the material at a distance rand an angle 0 with respect to the tip of a crack.

Equations (10.5-10.7) are also called field equations and show that the local stresses at the crack tip could rise to extremely high levels as r approaches zero [Figure 10.13(c)]. In Eqs. (10.5-10.7), K is a parameter that measures the magnitude of the stress field in the crack tip region and is called stress intensity parameter. In effect, it describes the extent of stress amplification resulting from the flaw . All the crack tip stresses (as indicated from Eqs. (10.5-10.7) are proportional to K. There are two extreme cases for the mode I loading (i.e. the crack opening mode) depending on the thickness of the plate. If the plate is thin relative to the dimensions of the crack then

-CJ

FIGURE 11.7

Occurrence of yielding in weak crystal A while surrounding material is still elastic under cyclic loading of constant stress amplitude.

-l,

FIGURE 11.8

+l>

Illustration of progressive strain hardening in the weak crystal under cyclic loading.

Fatigue Behaviour

315

in crystal A continues until the overall deformation arrives at -Li 1• As the loading cycle continues the above process is repeated with each subsequent cycle of deformation. Each time the stress reverses, crystal A yields a little more. And each time it yields, it gets strain hardened a little more. Even though slip is in opposite directions during successive cycles, strain hardening is additive because it simply involves the interaction of dislocations from processes like multiple slip, which are not greatly affected by the direction. As a consequence the deformation cycle loops become narrower and narrower (as shown in Figure l 1.8) until that the stress in crystal A increases with each cycle and approaches the perfectly elastic stress for elongation Li 1• As a result of localised yielding and work hardening of crystal A, a crack of submicroscopic size nucleates locally.

11.6.2

Wood's Theory of Fatigue

-

When a polycrystalline moderately ductile material is r loaded under static load it is likely to deform plastically by the process of slip when the stress is enough to move dislocations. When the direction of load is reversed, the direction of slip in the material is also reversed. The contours developed at the free surface of polycrystalline material as a result of slip produced under static loading is shown in Figure 11.9. Under cycling loading conditions a material deforms on the same set of atomic planes and ~ in the same directions as in unidirectional loading . FIGURE 11.9 Slip produced under According to W.A. Wood, microscopic slip bands (or static stress. microscopic deformation) are produced during fatigue cycling as a result of systematic build up of fine slip movements. These fine slip movements are on the order of l nm rather than steps of 100 to 1000 nm, as observed in static slip bands. Such a mechanism is believed to allow for the accommodation of the large total strain (summation of the microstrain in each cycle) without causing appreciable strain hardening. The microdeformation during fatigue leads to the formation of slip band intrusions and extrusions on the surface of the material (as shown in Figure 11.10). These slip band intrusions and extrusions are the stress raisers with a notch root of atomic dimensions and are responsible for the initiation of a fatigue crack. This mechanism

(a)

(b)

Intrusion

Extrusion

FIGURE 11.1 O Slip band intrusion and extrusion produced under cyclic loading.

316

Mechanical Behaviour and Testing of Materials

for the initiation of a fatigue crack is in support with the well-known fact that fatigue cracks commonly start at surfaces of components and that cracks have been found to initiate at slipband intrusions and extrusions. A.H. Cottrell and D. Hull explained the mechanism of formation of slip band intrusions and extrusions on the surface of a polycrystalline metal under reversible cycling loading. To explain this mechanism, they considered a crystal (or the so called individual grain, in terms of microstructural feature) located on the free surface of the metal which is favourably oriented with respect to the applied shear stress. Figure 11.11 illustrates such a surface crystal with a stable internal dislocation configuration. The dislocations are lying on the two parallel slip planes designated as A and B [Figure 11.l l(a)]. The dislocations lying on these planes are of opposite kind (i.e. positive and negative edge dislocations) and offer some kind of barriers (such as dislocations on the intersecting plane or a second phase precipitate particle) at the inner end of the respective plane. This situation might have occurred after many stress cycles. When the tensile part of the applied cyclic stress exceeds the critical resolved shear stress on slip plane A, dislocation l moves to the free surface of the metal and creates a slip step on it [Figure 11.11 (b)]. Dislocations on slip plane B are unable to move as they are resisted by barriers in the direction of shear stress, r. During compressive part of the cyclic stress, dislocation 2 is free to move on slip plane B and it moves to the surface and creates a second slip step, but in the opposite sense, as shown in Figure 11. l l(d). An intrusion is thus produced on the surface of the metal. An intrusion acts as the origin for a fatigue crack.

A B

FIGURE 11.11

(a)

(b)

(c)

(d)

Mechanism of fatique crack initiation proposed by Cottrell and Hull.

Fatigue Behaviour

317

However, the size of this intrusion or nanocrack is of the order of a Burgers vector (i.e. of the order of 0.3 nm). Both this nanocrack and the change in shape of the metal are not detectable. Though a permanent change in the surface crystal or a grain has occurred, yet the overall strain is considered to be elastic or reversible. The above situation may even arise during first cycle of stress and if the cyclic stress is withdrawn, the effects of the emergence of dislocations 1 and 2 shown in Figure 11.11 are negligible. The infinitesimal crack formed at the surface of the polycrystalline metal becomes significant only if it grows through continued stress cycles. If stress cycle is continued, the next stress cycle causes dislocations 3 and 4 to move to the surface in the same way as discussed above, the crack length will increase. If by chance, dislocation 3 encounters an impurity atom and sets blocked, then this dislocation will move only after some number of cycles elapsed when local stresses are sufficient to move it, and continue the process. If this process continues for large number of stress cycles, a detectable microscopic crack will be produced. Suppose this detectable crack is of 10 µm in one surface crystal, this will require some 10/0.3 nm 30,000 cycles at least. (It would also require a dislocation generation mechanism to create the large number of dislocations required to produce this crack). Thus, in order to create a tiny fatigue crack, a large number of stress cycles are required. This initial crack formation during fatigue is called Stage I fatigue. Stage I fatigue usually extends 2 to 5 grains from the origin, which required slip in several adjacent grains in a polycrystalline metal. Stage I crack is sometimes called a microcrack. In case of FCC metals, slip generally occurs on close packed planes of the kind { 1 1 1 } and accordingly these are the fracture surfaces under static stress conditions. However, in addition to slip on { 1 1 1} planes, slip on { 1 1 0} and { 1 0 0} planes which contain ( 1 1 O) directions, has also been observed in aluminium. Thus, fatigue initiation processes are not as simple as in static loading.

=

11.6.3

Fatigue Crack Growth

Once a fatigue crack of microscopic size is nucleated, its growth to finite size is controlled by progressively larger scale effects than operated in its earliest stages. That is, the rate of propagation of a crack in stage I is generally very low, on the order of nanometer per cycle, compared with crack propagation rates of microns per cycle for stage IL This stage of crack growth is commonly called Stage II fatigue. In stage I, slip band crack growth involves the deepening of the initial crack on planes of high shear stress, and therefore, the crack growth is slow. In Stage II, crack growth on planes of high tensile stress involves growth of well-defined crack in direction normal to maximum tensile stress. Stage II fatigue can be described with the help of Figure 11.12. The status of the crack at the end of stage I is shown in Figure 11.12(a) where the slip induced crack has been extended to three grains. It is apparent from this figure that as the crack passes from one grain to another it takes a different orientation and produces a zigzag path. Up to this point the crack has attained a critical length which is enough to develop a stress concentration during next tensile cycle so that local yielding occurs over a small region ahead of the crack tip as shown by a shaded circle in Figure l l.12(a). The local yielding causes strain hardening in the shaded region which eventually lead to sudden cracking in the transverse direction under the tensile part of stress cycle, as shown in Figure ll.12(b). It is important to

318

Mechanical Behaviour and Testing of Materials

recall at this stage that a microscopic crack is able to propagate only if it attains a critical size. This critical size depends on the level of stress concentration at the tip. Low stress levels produce fine cracks and the critical crack length is longer as compared to the critical crack length of a crack with higher stress level. In many instances, the stress level varies with speed of the machine. The growth of this crack is limited to the width of the shaded region during this cycle. Under cyclic stresses the crack growth can occur only when the stress intensity factor K arises when the applied stress exceeds a critical stress intensity factor Kc (Kc is the critical stress intensity factor required for a crack to propagate through the material under cyclic loading. Kc is lower than K 1c, the fracture toughness of the material). In the shaded region of Figure l l.12(a), K has exceeded Kc, so that the crack grows, but it stops as soon as it comes out of the region of localised yielding and enters the undamaged region. The crack gets blunted due to yielding (plastic deformation) as stress concentration is relieved. This results in a decrease of K below Kc in this localized undamaged region. So the propagation of the crack is checked momentarily. Still the stress concentration at the crack tip is enough to create a new, small strain hardened region (shown as shaded) and then stops. The crack opens and propagates during the tensile part of the stress cycle. During second quarter cycle of stress when tensile stress decreases or during the third quarter cycle when stress reverses, the crack partially or cr

cr

Stage I

cr

cr (a)

cr

(b) cr

~ Stag e II

FIGURE 11.12

cr

cr

(c)

(d)

Propagation of a fatigue crack during stage II fatigue.

Fatigue Behaviour

319

almost completely closes up. In fact the complete closing up of the crack is prevented due to local strain hardening that occurs ahead of the new crack tip. Thus, there is marked difference between the stage I and stage II of fatigue fractures. As the crack advances in the undamaged region, its direction changes slightly [Figure l l.l2(d)]. The ultimate crack propagation takes place in the transverse direction.

Mathematical analysis of fatigue crack growth Fatigue crack growth rate (da/dN) most often increases with the number of stress cycles N. That is, as the crack grows longer it grows at a faster rate. This is also because of the fact that a longer crack usually associated with a higher value of applied stress intensity factor K at the tip of the crack which in turn depends on the applied average stress. The changes in stress intensity factor at the crack tip (dK) are determined by the changes in stress dCT = ( CTmax - CTmin)The rate of crack growth da/dN is thus a function of !),,K and it is mathematically expressed by P.C. Paris and F. Erdogan as: (ll.l) where,

a = Length of the surface crack (as it starts at the surface), N = The number of cycles of fatigue, !),,K

=

Kmax - Kmin,

the range of stress intensity factor and can be determined from the

relation !),,K = dCT Jiui C and n are constants depending on the material and various conditions affecting fatigue process. The empirical relationship shown by Eq. (l l.l), commonly known as II III Paris-Erdogan relationship which was originally developed to predict fatigue crack growth rates in metals, is also applicable for some polymers and log!!.§_ ceramics. Figure 11.13, which is a log-log dN plot, shows variation in da/dN as a function of the range of stress intensity factor !),,K resulting from the cyclic variation in the stress for a structural alloy. The curve is sigmoidal in shape and Kth log !lK comprises of three regions. Region I K1h represents the threshold value of stressshows that there exists a minimum value intensity factor below which fatigue crack does not propagate or grow. of !),,K below which the nucleated crack is of non-propagating nature, i.e. it merely FIGURE 11 _13 Log of crack growth rate (daldN') as opens and closes without growing a function of log of stress-intensity forward . This lowest value of stress factor (LlK) showing fatigue crack propagation behaviour. intensity factor below which the nucleated

320

Mechanical Behaviour and Testing of Materials

crack is unable to grow is commonly called the threshold stress intensity value (i.e. the lowest value of ~K below which the crack is unable to propagate) and is designated by the symbol Kth. The rate of crack growth in the threshold region (where stresses are less than the threshold stress intensity) is so slow (of the order of 0.25 nm/cycle or less) that it cannot be detected. The region I is known as the region of non-propagating fatigue crack. The magnitude of ~K is lower for high strength brittle materials than that for low strength tough materials. The value of Kth depends on the mean stress am. As the mean stress is increased in the tensile direction, Kth will be lower. The region I thus, corresponds to the nucleation period; crack growth decreases rapidly approaching the lower limiting value of the stress intensity factor Kth. Therefore, Eq. (11.1) is not applicable in region I. The region II represents an essentially linear relationship between log (daldN) and log ~K in accordance with the empirical Eq. (11.1). This is also called steady-state region of fatigue crack propagation. The slope of this linear curve is constant and equal to n. The constant C can be determined by extrapolating the straight line to the value of ~K = 1 MPa m 112• Thus, log C = log (daldN). Equation (11.1) is valid only within the steady-state region. The value of n is about 3 for steel and in the range 3-4 for aluminium alloys. However, the Paris-Erdogan equation is applicable to certain range of values in the region IL The Stage III is not much related to fatigue process. This is the region of accelerated crack growth. Here ~Kmax approaches the fracture toughness K 1c. Near the fracture toughness the crack growth rate becomes so rapid that only a limited number of cycles can be accumulated before the component fractures suddenly. Alternatively, for ductile material, when the Stage II fatigue crack becomes so large that the remaining cross-section of metal can fail by tensile overload, the component fails suddenly by a ductile mode. Thus, in either case, Stage III fracture occurs without prior warning. In addition to metals, the above mechanism of crack growth involving plastic deformation is also applicable to many thermoplastic materials which exhibit some plasticity. In non-ductile materials such as ceramics, glasses, brittle metals, thermoplastics at temperatures below their glass transition temperature and thermosetting plastics, little, if any, plastic deformation occurs ahead of a crack tip, it makes the crack blunt. When the local stress at the crack tip exceeds the fracture strength of the material, the interatomic bonds get broken leading to fast brittle fracture. Though many micromechanical models have been proposed to explain the micromechanics occurring at the crack tip in ceramic materials, none of these is successful to explain all fatigue data generated for ceramics. Ceramics appear to be fundamentally different from metals where crack propagation results from dislocation activity at the crack tip. Ceramics which exhibit R-curve behaviour (R-curve behaviour refers to a fracture toughness which increases as the crack grows) appear to be most susceptible to fatigue, indicating that cyclic nature of the loading somehow diminishes the effect of crack-tip shielding mechanism. For instance, in case of fibre- or whisker-reinforced ceramics, it is believed that unloading induces fracture or buckling of the whiskers in the crack wake zone (the zone of the crack behind the tip), which in turn reduces their shielding effect. A majority of plastics do not fail by crack propagation alone. This is because most plastics exhibit viscoelastic behaviour, i.e. they exhibit both elastic and a viscous response against

Fatigue Behaviour

321

externally applied forces. Such materials show a hysteresis loop during loading and unloading cycle. Such behaviour is shown in Figure 11.14. The initial loading cycle is represented by the path OPQ while the unloading cycle is shown by the path QL. OL is the permanent set. The curve LM is traced on loading to reverse direction. Reverse loading removes the permanent set OL. As reloading is done in the initial direction at point M, the hysteresis loop completes at Q by tracing the path MNQ. The area under the hysteresis loop is a measure of the energy dissipated as heat. If this heat is not readily dissipated to the surrounding, the temperature of Stress

Compression

M Contraction ----- -------- Extens ion Strain

FIGURE 11.14

Stress-strain hysteresis loop of a plastic material experiencing reversed axial stress.

the material will rise. This is likely to occur with plastics as these are bad conductors of heat and unable to dissipate heat easily to the surrounding. The temperature of the material may rise to its softening point thereby reducing its load bearing capacity and eventual fatigue failure. Polymers do not cyclically harden as do metals. The rise in temperature per unit time in polymer sample increases with increasing cyclic frequency, thickness of the material, the stress amplitude and loss compliance factor (the reciprocal of stiffness). It is also affected by specimen configuration. For example, a high surface to volume ratio favours low temperature rise, and therefore, improved fatigue life of the sample. Rigid polymers like cross-linked phenolics and epoxies show very low loss compliance and fail primarily by crack propagation, because the little heat generated is readily dissipated to the surroundings. Those with medium value of loss compliance such as PMMA, acetal, and polycarbonate fail by both hysteric heating and crack propagation. Finally, the third group of polymer materials such as nylon, polyethylene, propylene, fluoroplastics having high loss compliance tend to fail predominantly by thermal failure. In composite materials, fatigue damage begins at an early life stage in the form of interface debonding, which may lead to the initiation and subsequent growth of microcracks.

322

Mechanical Behaviour and Testing of Materials

11.7 LOW CYCLE FATIGUE Many structures have a total number of service cycles less than 106 , and therefore, they can operate at higher allowable stress than the fatigue limit. It is apparent from the S-N curve that the smaller the number of cycles, the higher the allowable stress. When the local maximum tensile stress around the crack tip are above the yield stress, fatigue usually occurs with less than about 10 4 or 105 cycles. This behaviour is called Low Cycle Fatigue (LCF). LCF conditions are frequently created where the cyclic stresses are of thermal origin. Thus, LCF is an important consideration in the design and operation of high temperature systems subjected to thermal transients. The systems that undergo thermal transients include aircraft gas turbines, nuclear pressure vessels, steam turbines, heat exchangers and fuel elements; and many of the components of power plant. In addition to thermal transients, these structures are also subjected to steady state loading conditions. For example, heat exchanger components in a power plant undergo thermally induced strain cycles during start-up and shut-down or during variation in operating conditions. Thermal stresses arise from the thermal expansion of the material. Therefore, it is easy to consider that in this case fatigue results from cycle stress. Under LCF conditions, the fatigue life can be predicted from Coffin-Manson law, which states as:

~e _P

2

=e/(2Nt

(11.2)

A log-log plot between the plastic strain range ~e,, against the number of fatigue cycles yields a straight line as shown in Figure 11.15. In Eq. (11.2), ~eµf2 is the plastic strain amplitude (the plastic strain range of the cycle), 4' is the fatigue ductility coefficient defined by the strain intercept at 2N = 1. 4' is approximately equals Cf (the true fracture strain = ln AofA1) for many metallic materials. 2N is the number of strain reversal to failure (one cycle in two reversals). The fatigue ductility exponent x, varies between -0.5 and -0.7 for many metals. A smaller value of x results in log2N larger value of fatigue life. FIGURE 11.15 Low cycle fatigue curve.

11.8 VARIABLES AFFECTING FATIGUE The following are the variables that affect the fatigue property of metallic materials: (i) (ii) (iii) (iv) (v)

Alloy composition Stress concentration Size of the specimen Surface condition Metallurgical structure

Fatigue Behaviour

323

Alloy composition Those alloying elements which increase the tensile strength are found to increase the fatigue strength of a metal and alloy. Steels are the most widely used materials for applications involving cyclic stresses. Carbon in steels has been found to have the maximum effect on fatigue strength. Carbon increases the fatigue strength of steels not only through solid solution strengthening but also by strain ageing effect.

Stress concentration The points of stress raiser in the fatigue specimen greatly affect the fatigue strength. The points of stress raiser such as keyways, holes or notches on a component are the preferential sites for the initiation of a fatigue crack. In addition, the changes in the section size and surface irregularities such as machine markings, porosity, inclusions, decarburised regions, etc., also influence the fatigue life of a material to a considerable extent. A surface irregularity, in fact, acts as a notch. The stress concentration at the root of the notch causes the gradient of stresses from the notched region towards the axis or center of the specimen. Many of the surface irregularities can be eliminated by polishing the surface.

Size If the stress cycle is simple reversal type, the stress changes from a tension peak to compression

peak. The effect of such stress cycle is more on a thin section than in case of thick section. The distance between surface and center (axis) will be more in thick section than in thin section. Thus, in a thicker section the gradient of stress or strain from surface to centre will be more than that in a thin specimen. Also the volume of the material deformed is more in thick section. In addition, increased size results in an increased surface area. Thus, there is more likelihood that a thicker section will fail.

Surface characteristics A fatigue crack is generally initiated at the surface, therefore, the nature of surface has great influence on fatigue life of a component. One of the characteristics of the surface is its finishing. For the same material variation in surface finishes will result in variation in fatigue strength. Smoother the surface, longer will be the fatigue life of the component. It has been observed that fatigue life increases with the decrease in extent of surface roughness. In general, a buffed surface is regarded as a smooth surface, whereas an ordinary machined surface as rough. Another importannt surface characteristic of the material experiencing cyclic stress is the surface hardness. It has been observed that the fatigue strength of a material is greatly increased if its surface is made harder. A hard surface tends to resist initiation of a crack. This is because a hard surface is difficult to yield. Any delay in the initiation of a fatigue crack will result in improved fatigue life. Steels are case hardened to improve not only surface hardness, and hence, the wear resistance but also to improve fatigue life of the component. Electroplating, in general, results in lower fatigue strength of the metal.

Residual stresses The stresses that are left behind in an object after the process of manufacturing is finished are called residual stresses. Though these stresses are of very low magnitude, but may be

324

Mechanical Behaviour and Testing of Materials

dangerous when they are tensile in nature. We have seen that the tensile part of the cyclic stress assists crack opening and its propagation. Residual stresses may arise due to the following possible ways: (i) (ii) (iii) (iv) (v) (vi)

Plastic deformation during which the material flow is not uniform throughout Improper and insufficient tempering after quenching Improper and insufficient annealing or normalising after plastic deformation Quenching Some finishing operations such as machining, threading, boring, etc. Sudden heating and cooling or excessive momentary loading, leading to improper recovery during the service.

Residual compressive stresses have been observed to be beneficial from the point of view of fatigue strength of the metal or alloy. It is therefore desirable to introduce compressive stresses in a component experiencing cyclic loading so that fatigue life of the component can be increased. Shot peening appears to be the best and most effective method of introducing compressive stresses in the surface. The other method is heat treatment at the appropriate stage in manufacture. For instance, heat treatment of gear after machining.

Metallurgical structure Fatigue strength of steel is near 50% of its tensile value, Fatigue ratio (the ratio of fatigue strength to tensile strength) for most non-ferrous metals .s::: g, such as Ni, Mg, Cu, etc. is around 0.35 while ~ that for ferrous materials is nearly 0.50. 1i5 ::, Metallurgical structures that improve tensile .Ql strength are also likely to improve the fatigue ~ ratio of a material. However, the correlation between fatigue strength and tensile strength fails as the strength increases above a certain level as is illustrated in Figure 11.16. This failure Tensile strength depends on the type of strengthening mechanism FIGURE 11.16 Relationship between fatigue used to improve the tensile strength of the strength and tensile strength. material. In case strengthening is carried out by second phase particles, the size, shape and distribution of these particles will affect the fatigue life of the material. Among the metallurgical factors that affect the fatigue properties include microstructure, stacking fault energy, grain size, heat treatment, presence of soft surface spots caused by decarburization, formation of retained austenite or the formation of non-martensitic phase. The type of non-metallic inclusions and their orientation with respect to maximum tensile stress also affect the fatigue limit of the material. In general, the microstructures that improve tensile strength are also expected to improve the fatigue limit. However, in some instances it violates. For example, in case of plain carbon steels, two microstructures, namely, lamellar pearlitic and globular pearlitic developed for the same tensile strength possess markedly different fatigue limits. The former structure shows a significantly lower fatigue limit due to the higher notch effect of the carbide lamellae. Q)

Fatigue Behaviour

325

Materials with high Stacking Fault Energy (SFE) allow dislocations to cross-glide easily past obstacles and lead to the formation of slip bands. These slip bands under alternating stress conditions turn into intrusions or extrusions which are the centres for nucleation of a fatigue crack. Materials with lower SFE, on the other hand, make cross slip difficult and dislocations are restricted to move in a planar fashion to a limited extend. A limited local concentration of plastic deformation delays the formation of intrusions or extrusions, and hence, the nucleations of a fatigue crack. A low SFE coupled with a fine grain structure also results in improvement in fatigue properties. Here, grain boundaries control the rate of cracking. In steels, the type of heat treatment affects the fatigue properties. In quenched and tempered steels, the fatigue limit is found to improve as the tempering temperature is lowered to obtain hardness in the range Re 45 to Re 55, depending on the kind of steel. When the quenched and tempered microstructure of steel is compared with austempered structure for the same hardness it is found that the latter imparts much superior fatigue properties than the former.

Creep Behaviour

12.1

INTRODUCTION

A large number of articles around us are made up of metallic materials. These articles may be from kitchenware to aircraft jet engine turbines. Once fabricated, it is generally presumed that the finished articles whether made of metallic or non-metallic material, while under steady load, maintain their shape and dimensions forever. Blades of a turbine rotor, plastic mountings for parts of electrical devices, timber beams in roof of building, filaments in vacuum tubes, steel cables, concrete in a prestressed concrete beam and lead sheaths on telephone cables, are some examples of engineering components which are subjected to steady loads for long periods of time. Usually a slight change in shape is hardly noticed because such changes do not affect the function of the article. However, there are some critical applications in engineering field where even a slightest change in dimensions with time may affect the function of the article (for instance, loosening of flanged joints in the connecting bolts over a period of time and undesirable changes in clearance of steam turbine blade) or may cause even its breakdown. Therefore, such changes in dimensions of the articles are of great concern to materials engineers and designers. Most of the metals and alloys (except a few such as Pb, Zn, Sn and their alloys) working at normal temperature under stress over an indefinite period of time, are capable of maintaining their mechanical strength. However, at high temperature, especially near the recrystallisation temperature of a material, the duration of stress becomes an important factor. A prolonged stress, at elevated temperature, reduces the mechanical strength properties of metals and alloys. It has been pointed out in Chapter 8 that increase in temperature reduces the modulus of elasticity as well as yield and ultimate tensile strength of metals and alloys. In addition to it, the degree of strain hardening, that result due to plastic deformation, also gets reduced at elevated temperatures. For instance, when maintained at about 500°C under stress for long period of time, plain carbon steel has been found to deform permanently even when applied stress is below its elastic limit. 326

Creep Behaviour

327

The critical applications involving high operating temperatures and stresses include parts of internal-combustion engine and jet engine, high pressure boilers and steam turbines, blades of turbine rotor, and cracking stills as used in chemical industries. With increase in operating temperature and applied stress, the deformation may be considerable. This continuous plastic deformation under constant stress that occurs over a long period of time is known as creep. A static load which may not cause any instant permanent deformation, but may cause creep in this material over a long period of time. Deformation that occurs due to creep phenomenon increases with time. The increase of deformation with time is known as creep rate. If the material under stress is heated, the creep rate increases with time and eventually results in rupture of the material. For most materials, creep deformation at room temperature is negligible. At any given temperature, creep rate may be rapid or slow depending on the applied load. Creep rate decreases rapidly as the applied load is lowered. Creep becomes significant in highly stressed components (as mentioned above) operating at elevated temperatures. It is for this reason that creep test is commonly thought of as a high temperature test. If jet turbine blades creep a lot while operating, it is very likely that they get jammed in the turbine leading to costly breakdown. Creep is important not only for the critical applications (cited above) but also is important for such applications as lead pipes, white metal bearings used at or near room temperature, steam and chemical plant components operating in the temperature range 723 K823 K (450°-550°C). The most important properties used in the design of materials for elevated temperature applications are the creep strength and creep rupture strength. Creep strength (also commonly called creep limit) is defined as the stress that a material can withstand for a specified period of time without excessive deformation. The creep rupture strength or simply the rupture strength is defined as the limiting stress that a material can sustain for a specified period of time without rupture. In an alternative way, creep strength can also be defined as the constant stress that will produce a specified magnitude of strain (or creep) in a material over a given period of time at a constant temperature. For instance, for a steam turbine blade, the stress required to produce a creep of 0.2% over a period of 105 hours at 1073 K (800°C) is referred to the creep strength of the material used. The term excessive deformation used in the definition of the creep is the maximum permissible strain or deformation at elevated temperature that a component can tolerate without losing its function. This excessive deformation varies with the type of application and with the service conditions. For example, maximum permissible strain in a jet engine is only about 0.01 % in 2000 hours due to close dimensional tolerances involved, whereas in pressure vessels the tolerable strain is as high as 2% without rupture. Creep strength of a material is highly sensitive to temperature. It decreases considerably as temperature of the material increases. As creep strength decreases, the load carrying capability of the material decreases with the increase of temperature.

12.2 CREEP CURVE It is evident from the discussions done in the previous section that though creep is basically a

time dependent phenomenon, it is also a function of stress level and operating temperature. For metals tested under the suitable conditions of stress level and temperature over a period of time

328

Mechanical Behaviour and Testing of Materials

until fracture occurs, the creep behaviour is described by a graph plotted between strain and time. Such a graph is popularly known as a creep curve. Creep is normally observed by placing a load on a standard specimen at constant temperature and the deformation produced with time is measured. Creep curves obtained for different materials under the given conditions of load and temperature exhibit some common features as illustrated in Figure 12. l. These features are described as follows: '

: Tertiary creep c_______..

Stage III Primary or transient creep or Stage I

Secondary or viscous creep or Stage II or

F

Fracture

Steady-state creep

E D

At elevated temperature

C - - - - - - - - - -,- - - - - - - - - - - - - - - - - - -,- - - - - - - - - __,/ A t - - - - ~ : ~ - - - - - ~ :_ _ _ _ At room B temperature

o~--~~-----~------------

t An ideal creep curve showing three stages of creep. Time,

FIGURE 12.1

(i) If a stress below the proportional limit is applied to a specimen at room temperature, an elastic strain OA will immediately (or instantly) be produced upon application of load. Now whatever will be the duration of loading the strain will remain constant. The strain characteristic under this condition can be described by the path OAB (Figure 12.1). If the same load is applied at an elevated temperature, a strain OC occurs instantaneously. Clearly this strain OC is greater than the strain OA. This increase of strain at elevated temperature under the same loading condition may partly be due to decrease in elastic modulus of the material with increased temperature and partly due to a small amount of plastic strain in addition to elastic strain. Thus, the strain OC may be entirely elastic or elastic plus plastic, depending on the material, temperature and stress. (ii) As the time of loading at elevated temperature is increased, in the beginning, the creep rate increases somewhat rapidly and soon start decreasing with time. The creep corresponds to this segment CD of the creep curve is called primary creep, or the first stage of creep. This stage of creep is also called transient creep. This stage of creep is important for designers in that it is the part of the total creep strain reached in a given time and may affect clearances. Primary creep occurs at all temperatures.

Creep Behaviour

329

(iii) Following the end of primary creep, creep occurs at constant rate with time (curve from D to E). This stage of creep is commonly called secondary or steady-state creep. This creep is also referred to as viscous creep. During this stage, creep rate is reduced to a constant minimum rate. This second stage of creep is very useful in most of the elevated temperature applications. (iv) As the steady-state creep continues with time, a point is reached where creep rate starts increasing rapidly until finally rupture occurs at point F (Figure 12. l ). This stage of creep from E to F in the creep curve is called tertiary, or third stage of creep. Because of the rapid rise in creep during this stage, this creep is also sometimes called as accelerating creep. The rapid increase in creep rate during tertiary stage is due to the increased stress associated with a reduction in crosssectional area of the specimen as it elongates during creep under a constant load. The way in which creep rate varies with time is illustrated in Figure 12.2. It can be seen that the creep rate decreases rather rapidly with time in the beginning and becomes minimum during secondary stage of creep. This minimum creep rate remains constant for a sufficiently long period of time. This minimum creep rate is the criterion for evaluating many materials. At the end of this stage, the creep rate rises again at a faster rate. Under sufficiently high stress and/or temperature conditions, the straight line portion of the curve may be only a point of inflection between the primary and tertiary stages, i.e. the second stage of creep does not exist. Stage I

Stage II

Stage III

Time at constant load and temperature -

FIGURE 12.2

Variation of creep rate with time during various stages of creep.

The varying response of a material with time under the given conditions of load and temperature can be correlated to two opposite processes, namely, the strengthening due to strain hardening and softening by recovery processes. Strain hardening at elevated temperature is believed to be associated with the formation of a subgrain structure. A subgrain structure results due to the rearrangement of dislocations to low angle grain boundaries. The recovery processes involve the thermally activated cross slip, edge dislocation climb and vacancy diffusion. Based on these recovery processes, it can be said that the decrease in strain rate during first stage of creep can be correlated to the formation of subgrain structure that increase the overall resistance to the motion of dislocations. The only recovery process during primary creep is the cross slip of thermally activated screw dislocations. Rate of strain hardening is therefore greater than the rate of softening during primary creep.

330

Mechanical Behaviour and Testing of Materials

Gradually, the subgrain structure tends to stabilise during the steady state creep. A dynamic balance between strain hardening and recovery processes results in a steady state or minimum creep rate. That is recovery occurs simultaneously with strain hardening resulting in a balance between the two rates. As the prolonged secondary creep continues, a point is reached when the balance between hardening and softening processes is lost. This leads to accelerating or tertiary stage of creep. During this stage, recovery processes predominate over strain hardening. As a result, softening occurs faster than strain (work) hardening. In addition to the increased stress associated with reduced cross-section of the specimen (mentioned above), microstructural changes also result in faster rate of recovery, and hence, softening of the material. Among the microstructural changes are the localised necking, microvoid formation, precipitation of a brittle second phase, corrosion/oxidation at/on grain boundaries, intercrystalline fracture and resolution of second phase precipitate that originally contributed towards strengthening of the alloy. Recrystallisation of originally cold worked material also destroys the balance between strain hardening and softening processes. The creep curve, as discussed above and derived under constant loading and temperature conditions is commonly called conventional or engineering creep curve. This is not a true creep curve as true stress increases with increasing tensile strain (increasing tensile strain results in decreasing crosssection, and therefore, load per unit cross-section is increased at any given instant). A true creep curve should therefore be distinguished from the conventional creep curve. In order to derive the true strain-time curve, the load on Engineering F curve the sample is lowered progressively with decreasing specimen cross-sectional area. This is done either manually or by incorporation of a device which automatically lowers the load on the creep stand load train. Usually the tertiary part of the creep does not exist in this curve (refer Figure 12.3). For design purposes, however, the conventional creep curve is important, whereas the true Time, t creep curve is important in the fundamental FIGURE 12 _3 Superposition of true creep curve studies of creep involving the formulation of on engineering creep curve. mathematical creep theories. The creep response of metals depends on many variables. Stress and test temperature are the two important variables which affect the shape of the creep curve. Figures 12.4 and 12.5 illustrate the creep curves obtained for the same material by varying the test temperature and keeping the stress constant or by varying the stress and maintaining the constant temperature. It can be seen that the magnitude of instantaneous strain increases when either the temperature or the stress is increased. The same is true for primary creep also. At low stress for a given temperature or at low temperature at a given stress, the creep curve is characterised by a prolonged steady-state creep with creep rate tends to be negligibly small. Further, it can be noted that creep at low stress or low temperature may not exceed secondary stage up to the duration of the test. The level of creep rises with increasing temperature or stress. As a consequence, the creep rate during secondary stage increases with a decreased duration at t,,)

Creep Behaviour

/ffe..::::-------Creep curves for various tempatures at constant stress.

0"1

Time

Time

FIGURE 12.4

331

FIGURE 12.5

Creep curves for various stress levels at constant temperature.

sufficiently high temperature or stress. This stage no longer exists on the creep curve. The creep curve is characterised by only two stages, namely, the initial decelerating creep rate followed by an accelerating creep rate leading to fracture .

12.3

DESIGN CURVES

Creep strength of a material can be determined in several different ways. One of the simplest ways is to perform the test on various specimens at different temperatures and find out the stress levels g:i ~ for allowable minimum creep rate. The u5 curves can be plotted between stress and per cent creep rate per specified number of hours as illustrated in Figure 12.6. Another most common method to express the strength of a material is to Steady-state creep rate, % per fixed period of hours plot a graph between stress and FIGURE 12.6 Variation of stress with steady-state temperature for specified minimum creep creep rate for various temperatures. rates (Figure 12.7). From such a plot one can express the creep strength as stress for a specified minimum creep rate at a given temperature. For example, the point P in Figure l 2. 7 shows the stress corresponding to the temperature Q for a strain rate of l % in l 000 hours. The most common creep rate corresponds to which the creep strength is specified is l % in l 0000 hours. In many instances, the operating temperature and life time of a component are fixed and it is required to know allowable stress that must prevent the part from fracture or from deformation beyond a certain limit. In such cases, tests are performed to obtain a plot between stress (the conventional stress expressed as logarithm) and time (also expressed as logarithm)

332

Mechanical Behaviour and Testing of Materials

for various strains and rupture as illustrated in Figure 12.8. The creep 1% per hr strength can be determined by drawing en vertical line for a given life time along the en 1% per 1000 hr !.1: abscissa (the x-axis). The intersection of u5 this vertical line with the proper curve gives the allowable stress called the creep strength of the material. The design stress will be this stress less a suitable factor of safety. Along with the data points at rupture, per cent elongation and per cent Q Temperature reduction in area are also determined which provide a measure of ductility of the FIGURE 12.7 Stress as a function of temperature for various creep-rates. material. The rupture curve shown in Figure 12.8 is useful only when the component is not required to fracture, no matter how much strain is produced prior f3 to fracture. That is, there is no limit on the tolerable strain. In such cases, a number of en f2 en !.1: such curves are obtained at various ti temperatures and gathered on a single Ol f1 .2 diagram as shown in Figure 12.9. Such curves are popularly known as stressE4 > f3 > f2 > f1 rupture curves. These curves show the Temperature = Constant variation in stress as a function of rupture log time time at several constant temperatures and these are used accordingly. FIGURE 12.8 Creep-rupture curves showing effect of stress at constant temperature on For many applications, the life of a the time to rupture or to specific part is so long (for example life time is of strain. the order of l 0 years or so) that it is practically not possible to perform the creep test for such a long period of time. In such cases, creep test is performed up to the steady state regime, and the required allowable deformation is determined from the product of minimum creep rate and the life time (e.g. 10,000 hours). Life time can be the time corresponds to rupture of the component or it can be the time which produces a tolerable strain. Generally, creep tests are performed to determine log tR minimum creep rates at various loads for a FIGURE 12.9 Stress-rupture curves at various fixed period of time which may range from temperatures, a : stress and tR: rupture life (time to rupture) . 1000 hours to 10,000 hours (i.e. between

Creep Behaviour

333

40 days to 14 months). These creep rates can be used to estimate the deformation that would result after continuous running for about 100,000 hours (about eleven- and a-half year). The creep rate is determined by dividing the total allowable deformation by the life time and the stress corresponds to this minimum creep rate is determined. This stress is the creep strength of the material. Figure 12.10 shows the creep rupture curves (the solid lines) for various temperatures on which minimum creep rate b curves (the dashed lines) for corresponding temperatures are projected. The intersection of the solid curves with the dashed curves gives the creep strength at a given temperature. The significance of such curves is to decide such log tR (solid curves) low stress and temperature under which the part should neither fracture nor it should log emin (dotted curves) enter the tertiary stage of creep. On the basis FIGURE 12.10 Stress-rupture curves showing of these plots a designer can decide a stress the effect of stress on the time to under which the rupture life of the rupture and minimum creep rate component is far from the service life. (emin) at various temperatures.

12.4 ANDRADE'S ANALYSIS OF CREEP Andrade stated that the true creep curve (the constant stress curve) is a superposition of two separate creep processes which occur after the instantaneous strain, eo produced when a load at certain temperature is applied. The first part of the creep curve is called the transient creep during which creep rate decreases with time. After the transient creep the creep rate becomes constant. This part of the creep curve during which creep rate remains constant is known as viscous creep. The superposition of two creep processes constitutes a whole creep curve. Andrade represented such a creep curve by an empirical equation shown below.

e = e0 (1 + /3t 113 ) exp Kt

(12.1)

In terms of length of the specimen at time t, the Eq. (12.1) can be expressed as (12.2) = L 0 (1 + /3t 113 ) exp Kt where L is the length of the specimen at time t, eo, /3 and K are constants. L 0 is the length of the specimen just after the load is applied. The constants /3 and K represent, respectively the

L

transient creep (or /3-flow) and viscous creep (or K-flow). When viscous creep is absent, i.e. when K = 0, Eq. 12.2 becomes, L = Lo(l + f3tl/3)

or or or

L = Lo + L - Lo Lo

Lo/3t113

= /3tlt3

e=

f3tl/3

(12.3)

334

Mechanical Behaviour and Testing of Materials

This is the Andrade' s equation for Transient creep, and is applicable to metals as well as some plastics. The transient creep rate can be given as:

C ~

ci5

ECT Temperature

FIGURE 12.11

Illustration of equicohesive temperature (ECT). GB: Grain boundary.

.c

O> C ~

ci5

--· GB

ECT range

Temperatur

FIGURE 12.12

Equicohesive temperature range.

GB,, :5

Cl

' ' ---- ---' ' -------- ---..............................

C

'

i

(/)

ECT1 ECT2 Temperature

FIGURE 12.13

Effect of strain rate (£) on equicohesive temperature (ECT).

338

12.9

Mechanical Behaviour and Testing of Materials

DEFORMATION AT ELEVATED TEMPERATURE

The principal deformation processes at elevated temperature include slip, subgrain formation and grain boundary sliding . In addition to these principal deformation processes some secondary deformation processes such as multiple slip, the formation of extremely coarse slip bands, kink bands, fold formation at triple points of the grains and grain boundary migration have also been observed during creep studies. A brief discussion of these processes is given in subsequent paragraphs.

12.9.1

Deformation by Slip

At low temperature (below 0.5Tm) plastic deformation by slip generally occurs on close packed atomic planes. However, at elevated temperature, slip may also result on other non-close packed planes. For instance, in aluminium, {1 1 1} planes are the only active slip planes at low temperatures. Above about 250°C, the planes {1 0 0} and {1 1 2} also become active and provide slip. Similarly, in zinc, non-basal planes of the type {l O 1 0} also become active for slip above its recrystallization temperature. Similar effect has been shown by magnesium. Coarse slip bands are also observed at elevated temperatures. The tendency of slip band formation increases with increase of temperature. Fine slip lines between coarse slip bands are also shown by some metals like aluminium. Slip band spacing has been found to increase with increasing temperature and lowering stress. Deformation by thermally activated cross slip of screw dislocations also results at high temperatures. Creep deformation has been found to be quite inhomogeneous. As a consequence lattice bending, kink bands, deformation bands, and local bending near grain boundaries tend to occur at high temperatures. Lattice bending results in the introduction of an excess number of dislocations of one sign. These dislocations are randomly distributed on bent-glide planes [Figure 12.14(a)]. At high temperatures and stresses, these dislocations are quite mobile and tend to rearrange themselves in a low energy configuration of low angle grain boundary [Figure l 2. l 4(b)]. Dislocation climb also aid to this process. The resulting structure appears as a polygon network of low angle grain boundaries. The size of subgrains depends on the stress and temperature. Low stress and high temperature conditions favour large subgrain formation. Increased number of low angle grain boundaries act as barriers to the motion of dislocations, and thus, results in significant increase in strength. This is why decreasing creep rate is observed during primary creep. The strengthening caused by substructure is counterbalanced by recovery processes during secondary creep . ...L

...L

...L ...L

x Bent glide planes

FIGURE 12.14

>-:

_l....

...L

(a )

_l_

..L ..L ..L ...L

..L

_l_ _l_ _l_

j_ j_ j_

(b)

Distribution of dislocations in a crystal deformed by bending , (a) Before polygonisation, (b) After polygonisation (low angle boundary configuration).

Creep Behaviour

12.9.2

339

Grain Boundary Deformation

Under high temperature creep conditions, the grains in a polycrystalline metallic material tend to slide past each other. Grain boundary sliding refers to the process in which, in response to the imposed shear stress, one grain slides over another grain with the movement occurring at or in a zone immediately adjacent to their common boundary. Grain boundary sliding is thus a shear process which occurs along grain boundaries. In general, this effect is enhanced by increasing the temperature and/or decreasing strain rate. Grain boundary shearing is therefore a significant process at high temperatures. Grains may be thought of as cemented together by an amorphous or liquid layer of atoms which is incapable of supporting a shear stress at high temperature, and therefore, they tend to slide over each other. The rate controlling step becomes the diffusional accommodation of shear strain at macroscopic defects such as triple points (the grain corners) and ledges. Some investigators believe that grain boundary shear is not only simply sliding of one grain over another, but rather as plastic deformation which occurs in the material along grain boundaries. According to Zener, if a grain boundary under shear stress were to shear, then a sufficiently high stress concentration might develop at triple points and other obstacles along grain boundaries. If the stress concentration is sufficiently large to exceed the cohesive strength of the grain boundaries, a microcrack can develop at these obstacles. The nucleation of microcrack can be prevented if the stress concentration at the end of the relaxed boundary (i.e. at the grain corner or triple point) is relieved by plastic flow in the grain ahead of the boundary. There are two ways to relieve this stress concentration. In one case the stress can be redistributed to cause slip on properly oriented planes in the grain ahead of the boundary resulting in lattice bending which accommodates the shear strain along the boundary. A fold usually forms at the triple point. Grain boundary migration is another mechanism to relieve this stress concentration in the grain boundary. Grain boundary migrates at certain angle with respect to original grain boundary and away from the point of stress concentration. It may be considered to be stress induced grain growth. Grain boundary migration is a creep recovery process which is important as it allows the distorted material adjacent to the grain boundary to undergo further deformation.

12.10 MECHANISMS OF CREEP DEFORMATION Creep deformation mechanisms can often be conveniently presented by deformation maps. A typical deformation mechanism map is shown in Figure 12.15. A deformation mechanism map displays the range of stress and temperature in which each deformation mechanism is dominant. A point on the map identifies the dominant mechanism for a particular stress and temperature. Based on this map the major mechanisms of creep deformation include Dislocation glide, Dislocation creep and Diffusion creep (Coble and Nabarro-Herring creep). In addition to these mechanisms there is another important mechanism named Grain boundary sliding.

12.10.1

Dislocation Glide

Dislocation glide involves dislocations moving along slip planes within the grains and overcoming barriers by thermal activation. Thermal fluctuations assist the applied stress and creep can occur at relatively low stresses. Figure 12.15 shows that dislocation glide dominates

340

Mechanical Behaviour and Testing of Materials

100 Theoretical shear stress ---------------------------------------------

G' l5 (/) (/)

10- 2

-

10- 4

-

Dislocation glide

~

\:slocatioc

ti ~

·;;; C

$

creep

"O (I)

.!!? 'iii

Coble creep

E

0

z

10- 6

NabarroHerring creep

-

I

I

I

I

0.2

0.4

0.6

0.8

Homologous temperature, T!Tm

Deformation mechanism map.

FIGURE 12.15

at all temperatures but above the normalised stress ( a/G) of 10- 2. Here a is the applied stress and G is the shear modulus. The applied stress for dislocation glide is higher than the stress level normally existing in creep deformation. Part of the applied stress has to overcome the inherent resistance of the crystal lattice against dislocation motion. This inherent resistance of the lattice is called Peierls-Nabarro stress. Theory suggests that Peierls-Nabarro stress is low for dislocation motion on slip planes in FCC and HCP single crystal metals, but it may be high for more open lattice of BCC metals. In addition to the Peierls-Nabarro stress (also called lattice frictional stress), a dislocation has to overcome other obstacles as it moves through the crystal lattice. These obstacles introduce internal stress. The applied stress has to overcome this internal stress also for dislocation glide to take place and cause creep strain. Thermal fluctuations assist the applied stress in overcoming the obstacles to plastic deformation. That is, the plastic deformation is considered to be thermally assisted and that it could be described by an Arrhenius type equation

.

e= vexp

e

[Q(a)] RT

(12.10)

where, is the tensile strain rate; v is the frequency factor that includes the frequency of vibrations, the strain per successful fluctuations, the entropy term and the structure of the material. Q( a) is the activation energy which decreases with the applied stress. R is the universal gas constant. Two types of obstacles have been recognised. (i) Those which possess long range stress fields of the order of 10 atomic diameters or greater, and (ii) that possess short-range stress fields of the order of less than 10 atomic diameters. (The Peierls-Nabarro stress may also be considered as this type of obstacle). The energy required to overcome the former type of obstacle may be so large that thermal fluctuations cannot assist the applied stress in the temperature range under consideration. Thus, thermal activation plays no role in overcoming

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341

these long range obstacles, and therefore, these obstacles are called athermal obstacles. The typical examples of athermal obstacles include other dislocations lying on parallel slip planes and large incoherent precipitate or second phase particles. Thermal fluctuations can assist the applied stress in overcoming the short-range obstacles and they are therefore termed as thermal obstacles. It is these obstacles (including PeierlsNabarro stress) that are responsible for the dynamic (time dependent) aspects of plastic deformation. Some common thermal obstacles or mechanisms in pure metals are the PeierlsNabarro stress, forest dislocations (the dislocations threading the glide plane), cross-slip of screw dislocations, the motion of jogs in screw dislocations and climb of edge dislocations. The Peierls-Nabarro stress, forest dislocations and jogs represent resistance to the motion of dislocations in the slip plane, while cross-slip and climb represent resistance to motion out of the slip plane. The interaction of glide dislocations with forest dislocations on the glide plane and crossslip of extended screw dislocations in FCC metals involve dislocation glide creep. As a glide dislocation faces (i.e. encounters) forest of dislocations, it is unable to travel far before it intersects other intersecting dislocations lying in the slip plane at various angles (Figure 12.16). There are two consequences of this intersection in the creep deformation. First, the forcing of a dislocation through the stress field of another dislocation which in tum involves work to do. The second effect is that the gliding dislocation once intersects the forest dislocation can receive a jog, the movement of which through the lattice is again a thermally activated process. Formation of jogs on dislocations becomes important when the intersecting screw dislocation receives jog which is edge in orientation. Forest dislocations

---~\

-

------~

~~ ~

FIGURE 12.16

Glide dislocation

Intersection of forest dislocations with glide dislocation, I is the dislocation segment between two forest dislocations.

In FCC metals, a moving dislocation tends to dissociate into a pair of partial dislocations connected by a layer of stacking fault. Figure 12. l 7(a) shows an extended screw dislocation. As this dissociated dislocation glides on primary slip plane of the kind {1 1 1 } and if its leading partial encounters the intersecting slip plane {1 1 1 }, cross-slip on the cross-slip plane cannot occur with ease. In order cross-slip of extended screw dislocation is to occur, a constriction must result in it. The partials must unite to form a unit dislocation of certain length l as shown in Figure 12. l 7(b ). However, this needs thermal activation. At creep temperature this activation energy is available. Once the unit dislocation is formed by constriction, it cross-glides on the cross-slip plane under relatively high resolved shear stress [Figure 12. l 7(c)]. After cross-

342

Mechanical Behaviour and Testing of Materials

gliding, the constricted dislocation again dissociates into a pair of partial dislocations as shown in Figure 12. l 7(d). In the presence of a sufficiently large shear stress on the cross-slip plane, the extended dislocation glides further to produce creep strain. Partial dislocations

Stacking fault---r---i:...

(a)

(b)

Extended dislocation in cross-slip plane

(c)

FIGURE 12.17

Primary-slip plane (f 1 1) (d)

Sequence of steps in the cross-slip of an extended screw dislocation. (a) Extended dislocation, (b) Extended dislocation containing constriction, (c) The constricted dislocation cross glides on cross-slip plane and dissociates into a pair of partials, (d) The dissociated dislocation moves on cross-slip plane under the applied stress.

The creep rate associated with dislocation glide and which applies to both transient and steady-state creep is expressed as: (12.11)

where, Pm is the density of mobile dislocations which is defined as the number of dislocations free to move under an applied stress with a mean velocity v, b is the Burgers vector. The density of mobile dislocations depends on the internal stress field which in turn varies with position in the crystal lattice. Internal stress thus averaged out as direction parallel to the wire axis or the drawing direction. Flaw.

A flaw is a fault or mistake that may arise due to error in design or manufacturing.

Flexural Strength.

Failure stress of a material, as measured in bending.

Flexural Modulus.

Stiffness of a material, as measured in bending.

Fluctuating Stress. The stress which frequently varies in magnitude, especially from one extreme to another as for example, between two positive limits the peak values of which are dissimilar in magnitude.

Glossary

445

Force. An external agency capable of altering the state of rest or motion in a body; measured in Newton (SI units). Forest Dislocations (or Dislocation Forest). The dislocations that intersect or thread the active slip plane are popularly known as forest dislocations. Fracture.

Separation of a material into two or more parts.

Fracture Appearance Transition Temperature (FATT). is 50% fibrous and 50% cleavage or brittle type.

Same as DBTT at which fracture

Fracture Toughness. Quantitatively it is the critical value of stress-intensity factor (Kc) at a crack tip necessary to produce catastrophic failure under an applied tensile stress. Qualitatively it is the ability of a material to resist the propagation of a crack (may be a preexisting crack or nucleated under stress) of known length leading to fracture. In other words, it is the inherent resistance of a material to failure in the presence of a crack or crack-like defect. Fracture Transition Plastic Temperature (FTPT). The temperature above which the fracture shown by a material is about 100% fibrous (zero per cent cleavage) but the mode of fracture changes from totally ductile to substantially brittle on decreasing the temperature. Frank Partial Dislocations. A Frank partial dislocation is formed in a FCC array of closepacked planes by removal of part of one of the close-packed planes or by insertion of an extra part plane. In either case the central part is a stacking fault. The Burgers vector of the dislocation is perpendicular to the faulted plane. Frank partial dislocation is a sessile dislocation. Frank's Rule. It states that the strain energy of a dislocation is proportional to the square of its Burgers vector. Frankel Defect. A defect created due to the formation of a vacancy-interstitial pair. Such a pair is formed when an atom jumps from its normal lattice position to an interstitial position giving rise to a vacancy. Frank-Read Source. A pinned dislocation in a material that generates many dislocations when the material is subjected to external stress. Free Electrons. Loosely bonded valence electrons that are capable of moving freely under the influence of an applied voltage. Free Surface. The outermost planes (external surfaces) of a material separating it from other materials. Gamma Iron. The allotrophic form of iron, with face centred cubic crystal structure, having a stability range varying from 910°C to 1401°C. Gas Porosity. Presence of pores in a casting caused due to entrapment of gases when the metal is in the molten state. Gauge Length. The length with minimum cross-sectional area in a standard tensile specimen. Sometimes, two marks are made along minimum cross-sectional length of the specimen and the length between these marks is taken as gauge length. This length is taken as

446

Glossary

original or initial length in calculating percentage elongation and is reported with the result.

Glasses. Non-crystalline engineering materials having short-range ordering between the atoms. Glide Plane.

The plane over which slip occurs by dislocation motion.

Glissile Dislocations. The dislocations which can move (or glide) under the influence of an applied stress as their Burgers vector lie in the slip plane. G.P. Zones. These are the small regions in which the solute atoms cluster by precipitating out from the non-equilibrium matrix and have the same structure as the matrix. This structure develops in the early stages of precipitation during precipitation hardening. Grain. The part of a solid material within which atoms are not only arranged in a well-defined manner but also oriented in one direction only. It is an individual crystal in a polycrystalline material. Grain Boundary. The boundary separating the two grains having different crystallographic orientations. It is a surface defect (or imperfection) in crystals. Grain Boundary Migration. It is a motion of the grain boundary in a direction which is inclined to the grain boundary. Grain Boundary Sliding. It is a process in which two adjacent grains slide along their common boundary under the action of shear stress. Grain Boundary Strengthening. One of the strengthening mechanisms for crystalline materials, mainly for metallic ones. Grain size is made finer to have more and more grain boundaries which hinder the movement of dislocations. As a consequence, plastic deformation becomes difficult and strength gets enhanced. Grain Growth. The increase of average grain size of a polycrystalline material involving atomic diffiusion across the grain boundaries. Grain size. The average grain diameter of a polycrystalline material determined from a random cross-section of microstructure. Granular Fracture. If the fractured surface of an impact tested sample appears granular and bright the fracture is said to be granular and it is charactrizing the brittle kind of fracture. Grey Cast Iron. Cast iron having all or most of the carbon in free form as graphite flakes. Griffith Criterion. The criterion laid down by A.A. Griffith for brittle fracture. According to this criterion, a crack will propagate when the decrease in elastic strain energy is at least equal to the energy required to create the new crack surface. Griffith Theory. Theory put by Griffith for describing the behaviour of brittle materials by assuming that these materials possess numerous tiny cracks. Hadfield Steel. A high carbon, high manganese wear resistant steel having single phase austenitic structure on water quenching. Hall-Petch Equation. (i) Relationship between yield strength and grain size of a given material. (ii) O:v = a0 + k,. cr 112 , with usual notations.

Glossary

44 7

Hardness. The ability of the material to resist abrasion, wear, plastic deformation, machining or cutting. To a metallurgist or a material's engineer, hardness is the resistance of a material to plastic deformation by indentation. Hardness Test. The test performed to determine the hardness of a material. Hastelloys. Nickel base alloys having molybdenum up to 30%, around 5% iron, and tungsten and chromium in appreciable amounts. Heat Treatment Defects. Defects developed in the heat treated materials due to faulty heat treatment process and/or faulty heat treatment practice. Heisenberg's Uncertainty Principle. It is impossible to determine with accuracy both the position and the momentum of a particle simultaneously. The more accurately the position is known, the less accurately the momentum is determined. Herringbone Pattern. Same as Chevron Pattern. Hexagonal Close Packed Crystal Structure. A crystal structure having atoms at all comers and at centers of two basal planes of the unit cell and three atoms within the unit cell located above the interstices of the atoms in the basal planes. High Alloy Steel. Alloy steel having total alloy content exceeding 10 per cent. High Angle Grain Boundary. Grain boundary having large orientation difference, usually more than 10°, between adjoining crystals or grains. High Carbon Steels. Carbon steels having more than 0.60% carbon. High-Cycle Fatigue. If the strain cycles are largely confined to the elastic range then lower load and higher number of stress cycles are required to cause fatigue failure. This kind of failure is called high-cycle fatigue failure. High Strength Low Alloy Steels. Family of specially developed high strength steels based on thermomechanical processesing. High-Speed Steels. A number of high carbon-high alloy steels containing tungsten, chromium, vanadium and molybdenum as the major alloying elements mainly used for manufacturing cutting tools. High Temperature Creep. The steady-state or viscous creep is referred to as high temperature creep which occurs above recrystallization temperature (about T,,,12). Homogeneous Material. A material exhibiting identical features at each and every point within the mass. Homologous Temperature. The ratio of ambient temperature to melting point temperatures is called homologous temperature. Hooke's Law. The law which states that the stress is proportional to strain in the elastic region of deformation, i.e. the ratio of stress to strain is constant within elastic limit. Hydrogen Bond. A kind of secondary bond in which hydrogen atom is shared between two strongly electronegative atoms such as 0, N, Cl or F. Ideal Crystal. Crystal in which every atom is occupying its well-defined position in the crystal structure lattice with respect to other atoms, i.e. the regularity and periodicity of atomic arrangement are maintained in all the three directions over infinite distance.

448

Glossary

Immobile Dislocation.

The dislocation which is unable to move freely on active slip plane.

Impact Strength. It is the ability of a material to withstand impact loading (sudden loading) without fracture. It is also defined as the ability of the material by virtue of which it is able to absorb energy when subjected to standard impact load. The unit is expressed in terms of energy as Joules or kilogram meter. Impact Test. Test performed for determining the ability of a material to withstand sudden loading without undergoing fracture. Impact Toughness.

Same as Impact Strength.

Imperfections. Deviations from the well-defined arrangement of atoms at several localized regions in the structure of a crystalline material. Incoherent Interface. When two crystal structures are very different from each other with little matching of atomic planes across the interface. The interface is said to be incoherent. Inconels. Alloys of nickel, with 14-17% chromium and 6-IO% iron having small amounts of titanium, aluminium and niobium, well-known for their superior resistance to creep, corrosion, hot corrosion and oxidation at elevated temperatures. Indentation Hardness. Ability of the material to resist indentation under standard load. It is expressed as load divided by surface area or depth of indentation. Indentation Hardness Test. An indenter of specified geometry is forced into the specimen under a standard load to produce an indentation. The hardness is expressed on the basis of the depth or the size of the indentation and the load applied. Indenter. A tool of specified geometry and hardness, but is harder than the material under test, used to impress a specimen for its hardness measurement. Insert. A component phase having discontinuous nature and is embedded in a matrix phase for support. Instantaneous Strain. The strain produced in a specimen immediately when it is loaded. It is time independent. lnteratomic Bonding. The term used to express bonding between atoms of a material or the net force between the atoms that is responsible to hold the atoms together. lntergranular Fracture. The fracture that occurs as a consequence of propagation of a crack along the grain boundaries of a material. Generally occurs at high temperatures and also called intercrystalline fracture. Intermolecular Bonding.

Bonding present between molecules of a material.

Interstitial Defect. A defect created when an atom of impurity elements or of alloying elements, i.e. an atom other than the parent metal's atom occupies interstitial site in the lattice of parent metal. lnterstitialcy. A defect in which an atom of the parent lattice occupies an interstitial site in the lattice which otherwise is not its normal position. lntragranular Fracture. The fracture that occurs due to propagation of a crack through or across the grains. This is also called transgranular fracture.

Glossary

449

Intrusion. Inverse of extrusion which are narrow crevices at the surface produced by slip band (see Figure 11.10). Ion.

A charged atom or molecule due to gain or loss of one or more electrons.

Ionic Bonding. Interatomic bonding between atoms of two different elements arising as a result of transfer of electron/electrons from one atom to another atom. Isobars. Nuclei of different elements having same atomic mass number, i.e. the sum of number of protons and neutrons are same. Isoprene Rubber (IR). An elastomer popularly known as synthetic natural rubber. It is processed like natural rubber and its properties are quite similar to natural rubber with somewhat higher extensibility. Isotopes. Atoms of same element having same atomic numbers, but different atomic mass numbers. Isotropic Materials.

Materials having their properties same in all the directions.

Izod Impact Test. A standard impact test on specially prepared notched specimen of the material. In this test the specimen is loaded vertically such that the notch is facing to the hammer. Jogs.

These are the steps created in dislocations either when they undergo intersection or when an edge dislocation climbs.

Knoop Hardness. The ratio of load applied to the projected area of indentation produced by Knoop indenter under a small load of the order of grams. Knoop Indenter. The indenter used to measure microhardness. It is pyramidal with a rhombic base with diagonals in the ratio 7: 1 and the angles between opposite edges of the pyramid are 172°30' and 130°. Laminar Flow. Lap.

Same as easy glide.

A lap is a defect caused by folding a fin of metal onto a surface, without welding. It may arise during forging. A lap always opens to the surface and is irregular in contour.

Lateral Strain. The strain produced in the transverse direction in a bar specimen when loaded in the longitudinal direction. Lattice Parameters. Parameters, usually three axial dimensions and three inter-axial angles, describing a unit cell completely. Leak. Refers to a discontinuity or passage through which a fluid flows or permeates from inside to outside or vice versa. Leakage.

It refers to the flow of fluid through a leak.

Leak Test. A test which involves detecting leaks and determining the rate at which a gas or liquid will penetrate from inside a tight component or assembly to the outside or vice versa as a result of pressure difference between the two regions. Line Imperfections.

Same as dislocations. These are the one-dimensional defects.

Line Tension. Every dislocation is associated with a force which tends to keep it to a minimum length, and hence, have minimum energy.

450

Glossary

Liquid Penetrant Test. A non-destructive testing method for detection of flaws that are opened to the surface by applying a suitable liquid on the surface under examination. The liquid is drawn into the surface discontinuities by capillary action and is exposed by applying a dye or UV light. Load-Elongation Curve. The observations made during tensile testing of a standard specimen are recorded in the form of a curve plotted as load on y-axis and corresponding elongations produced in the specimen on x-axis. Such a plot is called load-elongation curve. Logarithmic Creep. The creep that occurs at low temperature where recovery processes cannot occur and the creep produced follow the logarithmic law, i.e. creep strain (e) = K log t + ei, where K is a constant, tis time ei is the instantaneous strain. Lomer-Cottrell Dislocation. A sessile dislocation produced by interaction of slip dislocations (moving/gliding dislocations) on two identical intersecting planes. Such dislocations cannot move freely. Low Alloy Steel. Alloy steel having total alloy content less than 5 per cent. Low Angle Grain Boundary. An array of dislocations producing a small difference in orientation between the adjoining lattices. The angular mismatch between the lattices on either side of the boundary in case of a low angle grain boundary is usually low and less than 1°. Low Carbon Steels. Carbon steels having less than 0.30% carbon. Low Cycle Fatigue. The fatigue failure that occurs under the condition of relatively high stress so that significant amount of plastic strain is induced during each cycle resulting in failure at low number of cycles. The value of applied stress is such that the local maximum tensile stresses in the region ahead of the crack tip are greater than the static yield strength of the material. The number of cycles of failure may vary from one to 104 or 105• That is, under low cycle fatigue, the life of a material is short while it is much longer under high cycle fatigue. Lower Yield Point. The approximate constant stress at which yield point elongation accompanied with the propagation of Ltiders bands occurs. This stress is lower than the stress at upper yield point. Liiders Bands. These are the discrete bands of deformed metal often visible on the surface of the polished tensile specimen with naked eye and run at approximately 45° to the tensile axis. These bands spread along the specimen during yield point elongation. Machining Faults. The faults introduced on the surface of a component during its machining such as machine markings or rough surface. A machine marking may give rise to notch effect and therefore it is a stress raiser mark. Macrodeformation. The deformation which can be observed by conventional methods is called macrodeformation. Macrohardness. The hardness measured over larger area using loads of the order of kilograms such that indentations are visible by naked eyes and can be viewed with the aid of low magnifying glass for dimensional measurements.

Glossary

451

Magnetic Particle Inspection. A nondestructive testing method that relies on the interruption of lines of magnetic flux by surface and sub-surface cracks. In this method the sample under test is magnetized and dry or wet iron particles in a liquid carrier are sprayed over the surface. For any surface or subsurface discontinuity oriented at approximately 90° to the magnetic field direction magnetic particles are collected. The magnetic bridge so formed indicates the size and shape of surface discontinuity and its location. Magnetic Quantum Number. electron.

The quantum number related to the magnetic moment of the

Malleability. Ability of a material to undergo plastic deformation without rupture under the influence of compressive force. Malleable Cast Iron. A grey cast iron having a microstructure consisting of ferritic or pearlitic matrix and rounded graphite aggregates obtained from the decomposition of cementite of white cast iron as a result of prolonged heat treatment cycle known as malleablising. Maraging Steels. High alloy steels principally containing nickel with cobalt. Basically, they are Fe-Ni alloys with carbon as impurity in which martensite phase can be developed by suitable heat treatment. Subsequent ageing results in dispersion of intermetallic compound in the soft and ductile Fe-Ni martensite. Martensite. A super-saturated solid solution of carbon and alloying elements in alpha-iron with reference to ferrous alloys. In general sense, a non-equilibrium phase obtained by diffusionless transformation of a high temperature phase (usually a solid solution) on rapid cooling. Martensitic Stainless Steels. High chromium steels with relatively higher carbon, wellknown for their high resistance against corrosion, having only martensitic phase stable at ambient temperature. Martensitic Steels.

The steels having only martensitic phase at room temperature.

Martensitic Strengthening. Material.

Method of strengthening steels by the formation of martensite.

Anything that occupies space and has mass.

Matrix. A continuous phase that supports a second phase. Mechanical Fibering. The alignment of inclusions, cavities and second phase inclusions in the main direction of mechanical working. Mechanical Properties. Those properties which describe the behaviour of a material under the application of mechanical force (static or dynamic type) are termed as mechanical properties. Such characteristics as strength, elasticity, plasticity, ductility, hardness, machinability are included under this definition. Since almost all engineering products are subjected to load under service, measurement of these properties is of great importance. Medium Alloy Steel.

Alloy steel having total alloy content between 5 and 10 per cent.

Medium Carbon Steels.

Carbon steels having carbon ranging from 0.30% to 0.60%.

Metallic Bonding. A bonding between the valence electrons and the positively charged ion cores of the atoms of a metallic element or metallic materials such that the valence electrons are free to move.

452

Glossary

Metallic Characteristics. The characteristics shown by the metals such as crystallinity good thermal conductivity, electrical conductivity, malleability, ductility coupled with opacity and typical lustre. Metallic Elements.

Group of elements possessing free electrons.

Metallic Materials.

Materials exhibiting metallic properties.

Metalloids. Group of elements that exhibit some properties of metals and some properties of non-metals, i.e. these elements have properties intermediate between metals and nonmetals. Some examples are C, S, Si and P. Metals. Group of elements possessing free electrons (same as metallic elements). A metal is a crystalline material, in which ions are connected indirectly through the field of free electrons surrounding them. Each ion attracts as many neighbouring ions as it can, giving a close packed structure of short bonds. Meyer's Index. An index or constant expressing some function of susceptibility of a material to work hardening, observed by plotting the load (P) against the diameter (d) of indentation produced from a ball indenter and determining Meyer index using the expression P = M,n_ Here, n is called Meyer's index. Microdeformation. micrometer.

The deformation which is so small that it can only be measured using

Microhardness. The hardness of a material when measured over a very small area by producing a small indentation under a load of less than 1000 grams force, the most common being 1 gm to 250 gms. The indentation is usually not visible by naked eyes. Microvoids. Very small or tiny voids at the fractured surface of a material resulted by the separation of the material either at the grain boundaries or at some other interfaces (as an inclusion and matrix) during ductile fracture. Microvoid can be formed by decohesion at matrix-particle interface or by cracking of brittle particles. Miller-Bravais Indices. Method of representing various planes and directions of interest in a hexagonal close packed crystal structure/unit cell. These are represented by a set of four integers to designate a plane or direction. Miller Indices. Method of representing various planes and directions of interest in a cubic crystal structure/unit cell. Miller indices are represented by a set of three integers that designate a crystallographic plane or direction in cubic crystal. Mixture. A material obtained when two or more elements and/or compounds are in intimate contact with each other. There is no bonding between these elements or compounds on atomic level. Bonding is of simple physical or mechanical nature. They can be mixed in all proportions and their properties are an aggregate of properties of the constituents. A mixture, unlike a compound, does not have definite composition, properties and chemical formula. A mixture can be separated into its constituent elements by simple physical and mechanical means. Modulus of Elasticity. (i) The ratio of engineering stress (tensile or compressive) to engineering strain within elastic range for a material. (ii) The slope of the engineering stress-strain curve in the elastic limit of the material. (iii) A measure of the stiffness of a material.

Glossary

453

Modulus of Resilience. The strain energy absorbed per unit volume when a material is strained to its proportional limit. Modulus of Rigidity. (i) The ratio of shear stress to shear strain within elastic range for a material. (ii) The slope of the shear stress-strain curve within the elastic limit of the material. (iii) A measure of the rigidity of a material. Modulus of Rupture. A means of defining the strength of a brittle material which cannot easily be pulled in tension due to their sensitivity to non-axiality of loading, difficulty in fabricating the specimen of specified geometry and difficulty of applying the tensile load. It is measured by supporting a small bar of rectangular section on two supports and loading it at the centre of the opposite face to produce failure in three-point bend test (Figure Fl, page 416). The stress at fracture using this test is known as the modulus of rupture, flexural strength, or bend strength. Mohs Hardness. The ability of a material to resist surface scratching and abrasive wear is referred to as scratch hardness or Mohs hardness (associated with Mohs scale, after the name of the investigator Friedrich Mohs, well known to mineralogists). Mohs Scale. The scale used to measure the scratch hardness of minerals. It consists of a series of numbers from 1 to 10, in the order of increasing hardness. Each mineral listed in the scale is softer than (i.e. is scratched by) all those below it. The minerals with increasing hardness are: (1) Talc, (2) Gypsum, (3) Calcite, (4) Fluorite, (5) Apatite, (6) Orthoclase, (7) Quartz, (8) Topaz, (9) Corundum and (10) Diamond. Molecule. The smallest stable unit exhibiting all the properties of the material under consideration. Monel.

Nickel-copper alloy containing about 33% copper.

Nabarro-Herring Creep. It is the diffusion creep in which vacancies move along a gradient from grain boundaries experiencing tensile stresses to the boundaries experiencing compression through the grain. In other words, atoms move in the opposite directions leading to elongation of grains and the test bar. Narrow Dislocation. If there is no relaxing displacement of atoms in the adjacent planes surrounding dislocation region, the dislocation is said to be narrow and stiff. Natural Ageing.

A process causing precipitation of coherent particles at room temperature.

Natural Rubber. It is the product derived from rubber latex. The rubber latex is a milky liquid obtained from certain tropical trees such as Hevea braziliensis. The latex is coagulated and smoked to produce a spongy mass. This is then rolled into sheets of crude rubber from which usable elastomer is produced. Chemically, it is the polyisoprene with a series of double carbon bonds along the chain together with one methyl group per isoprene unit. The methyl groups in natural rubber are all on the same side of the molecule. Necking. Localized region of plastic deformation produced in a ductile material during tensile loading. Neoprene Elastomers. It is basically polychloroprene elastomer having the structure similar to polyisoprene except that methyl group attached to the double carbon bond is replaced by chlorine atom.

454

Glossary

Neutrons.

Neutral sub-atomic particles.

Nichrome.

An alloy of nickel and chromium with 20 per cent chromium.

Ni-Hard Cast Irons. Nickel-chromium cast irons (having 3.0 to 7.0% Ni and 1.5 to 11 % Cr) possessing outstanding resistance to wear. Nil Ductility Temperature (NDT). The temperature below which a material breaks while above it does not break. Nimonics. The term represent a family of nickel-chromium alloys developed by modifying the early composition of nichrome (80%Ni- 20%Cr) by adding large proportion of cobalt in addition to appreciable amounts of titanium, aluminium and /or molybdenum. Ni-Resist Cast Iron. Trade name used for a group of high nickel (14-36%) austenitic corrosion resistant grey cast irons. Nitrile Elastomers. Nitrile elastomers are copolymers of butadiene and acrylonitrile monomers with proportion of butadiene ranges from 55% to 82%. These are also termed as buna-N and GR-N. They are outstanding in resistance to oil and aromatic solvents. Nodular Cast Irons. Same as 'Ductile Cast Irons'. Non-Coherent Particles. A precipitate particle having no orientation relationship with the parent phase from which it has originated. Non-Crystalline Materials. Same as amorphous materials. Non-Ferrous Alloys. Metallic materials having any metal, other than the iron, as the base metal. Non-Metallic Elements. Group of elements not possessing free electrons. Non-Metallic Inclusions. These are the nonmetallic impurities such as slag, sand, oxides, or sulphides present in metal castings. Usually these inclusions are irregular in shape. In wrought metals, the inclusions become elongated during hot working and provide permanent evidence of their extent. Non-Metallic Materials. Materials other than the metallic materials. Non-Metals. Group of elements not possessing free electrons. (same as non-metallic elements). Normal Stress. stress.

Stress acting in a direction that is perpendicular (normal) to the surface under

Notch-Bar Toughness. The energy absorbed by a notched test bar of a ductile material under impact load. Notch Sensitivity. The tendency of a ductile material to behave like a brittle material in the presence of notches known as notch sensitivity. Nucleus. Highly compacted central part of an atom comprising of protons and neutrons. Electrons revolve around it. Orange Peel Structure. A manufacturing defect frequently results from mechanical deformation of a metal and appears on the surface. The surface of the metal appears as rough pebbled made of raised or depressed areas corresponding to the centers of the

Glossary

455

individual grains, outlined by a pattern of valleys or ridges which correspond to their boundaries.

Orbital Quantum Number.

Same as Azimuthal Quantum Number.

Overageing. Holding a precipitation hardened alloy for too long a period at a given temperature causes it to lose its hardness due to loss in coherency between the second phase and the matrix. Partial Dislocation. translation.

A dislocation for which Burgers vector is a fraction of a lattice

Partially Stabilized Zirconia. In this material the cubic phase of zirconia is less as compared to totally stabilized zirconia content when an oxide such as MgO, CaO or Y 20 3 is added to pure zirconia. The microstructure consists of a fine dispersion of coherent tetragonal zirconia (a metastable phase) precipitate particles in the cubic zirconia matrix phase. Pearlite. A microconstituent present in steels and cast irons (also in some other ferrous materials). It is an intimate mixture of ferrite and cementite phases in which ferrite and cementite are usually present as alternate lamellae. Peierls-Nabarro Stress. It is the lattice frictional stress which a dislocation must overcome in order to move or displace from one equilibrium position to the next. This stress is minimum for a most densely packed atomic plane and in the close packed direction. Percentage Elongation. The ratio of increase in length of gauge section of a specimen at fracture to the original gauge length expressed in per cent. In other words, it is the percentage increase in the gauge length of the specimen after tensile test. Percentage Reduction in Area. Ratio of the decrease in the cross-sectional area of the tensile specimen at fracture to the original cross-sectional area expressed in percentage. Perfect Dislocation. A full or perfect dislocation is one for which the Burgers vector is an integral multiple of a lattice translation. Periodic Table. The table showing the arrangement of the elements in the ascending order of atomic numbers. Phenolics. Phenolics are the thermosetting plastic materials formed by the reaction between phenol and formaldehyde by condensation polymerization reaction accompanied with the release of water molecules as by product. Pin Holes. The corrosion pits or holes with diameters much smaller than the depth produced by pitting corrosion. Plain Carbon Steels.

Same as 'Carbon Steels'.

Plastic Deformation. The deformation (changes in the dimensions of a material) caused by the application of external forces, but is not recoverable even after the removal of external forces. Plastic Instability. The condition at which localized deformation (necking) begins at maximum load in ductile specimen during tension test. Increase in load or stress is zero at this point, i.e. slope of the tensile curve is zero.

456

Glossary

Plasticity. The characteristic property of a material as a result of which it cannot regain its original size and shape after the removal of external force and the deformation, so occurred, is of permanent nature. Point Imperfections. a few atoms.

Localized deviations in the crystal lattice involving one or possibly only

Poisson's Ratio. The ratio of the lateral deformation to the longitudinal elastic deformation caused by tensile or compressive stress. Poldi Hardness.

The Brinell hardness measured by using Poldi hardness tester.

Poldi Hardness Test. In this test, two indentations are produced simultaneously one on a standard test bar and the other on the specimen under examination by giving a blow of hammer on spring loaded plunger and a 10 mm diameter hardened steel ball. Corresponding to the two diameters Brinell hardness is read from the table. Polyethylenes. Basically polyolifins based on ethylene monomers. Polyethylenes are composed only of carbon and hydrogen atoms with carbon atoms singly bonded and lie in the backbone while all hydrogen atoms are pendant. These are available in different grades depending on density such as low density, medium density and high density polyethylenes. Polygonization. The rearrangement of excess like sign dislocations into low angle grain boundaries with a resultant lowering of the lattice strain energy. The excess edge dislocations form a tilt boundary, whereas the excess screw dislocations form a twist boundary. The regions of the crystals separated by these low angle boundaries are free of dislocations and represent blocks or polygons. Hence, the term polygonization. Polymers. These are principally the organic compounds of carbon and hydrogen, but many of these contain one or more of other elements such as nitrogen, oxygen, chlorine, fluorine or sulphur. Organic non-metallic materials are characterized by low hardness, low strength, low stiffness, low density and poor electrical conductivity. Polymorphism. Similar to allotropy but used in broader sense, i.e. the term is used for characteristic property shown by some materials to exist in more than one crystal structure at different temperature and pressure. Polypropylene (PP). Polyolifin polymer of propylene monomers in which a methyl group is attached as pendant to every alternate singly bonded carbon atom. Polystyrene. An amorphous thermoplastic polymer of styrene monomer. The monomer consists of a carbon-carbon double bond to which a pendant benzene ring and three hydrogen atoms are attached. The polymer is produced by addition polymerization. Polytetrafluoroethylene (PTFE). The polymer produced from tetrafluoroethylene gas by addition polymerization. It is highly crystalline. Only carbon atoms are in the backbone while all fluorine atoms are pendant. Polyvinyl Chloride (PVC). A thermoplastic in which a chlorine atom is attached to every alternate singly bonded carbon atom. The polymer is produced by addition polymerization.

Glossary

457

Porosity. The presence of pores in castings introduced as a result of entrapment of gas in the molten metal. Precipitate. A solid phase formed as a result of rejection of excess amount of an element or elements from the non-equilibrium matrix phase. Precipitation Hardenable Alloys. hardening.

The alloys that can be strengthened by precipitation

Precipitation Hardenable Stainless Steels. precipitation hardening. Precipitation Hardening. precipitate particles.

The stainless steels that are strengthened by

A strengthening mechanism caused by the presence of coherent

Preferred Orientation (or Texture). It is a state of severely cold worked metal in which certain crystallographic planes of the grains orient themselves in a preferred manner with respect to the direction of the stress. This is also called deformation texture. Primary Bondings. Chemical bondings between atoms of elements having bond energy in the range 1-10 eV (or 100-1000 kJ/mole). Principal Quantum Number. electron.

The quantum number related to the main energy levels of the

Prismatic Loop. A dislocation loop having the same orientation at all points. If b is perpendicular to the plane of the loop it is pure edge in character over its entire length. Prism Plane.

The planes of the type {l O 1 0} parallel to the c-axis in HCP crystals.

Proof Stress. The value of stress that permits a predecided plastic strain (deformation) on the gauge length in a material. The common predecided plastic strain varies between 0.1 % and 0.2%. Proportional Limit. from linearity. Protons.

It is the limiting value of stress at which the stress-strain curve deviates

Positively charged sub-atomic particles.

Quantum Numbers.

The numbers assigning electrons in an atom to discrete energy levels.

Radiographic Test. A non-destructive testing method of detecting flaws within a material using X- or r-rays. The technique relies on a difference between the absorption of radiation by the material and the flaws present within the material. R-Curve Behaviour. It refers to a fracture toughness which increases as the crack grows. It is a crack-resistance curve in which toughness is plotted against the crack extension. Rebound Hardness Test.

Same as Shore hardness test.

Recovery. Recovery is the process of annihilation and rearrangement of imperfections to special configuration of lower energy within the deformed material without the movement or migration of high angle grain boundaries as occurs during the initial stage of annealing. Recrystallization. Nucleation and growth of new strain free grains by the migration of high angle grain boundaries.

458

Glossary

Recrystallization Temperature. The temperature at which a cold worked material develops a new set of strain free grains in one hour. (It is not a constant temperature as depends on several factors.) Recrystallization Texture. When extensively deformed polycrystalline metal exhibiting a preferred orientation is annealed, the recrystallized grains also possess a preferred orientation which in many cases is even stronger than the deformation texture. Reinforcement. A material as second phase in the form of a particle, fibre, flake, ribbon, etc., embedded in a matrix material to strengthen the latter is called reinforcement. Residual Stresses. The stresses present in the material even after the removal of external forces. Also referred to as locked-in stresses or internal stresses. Residual stresses may also be present in a material quenched from high temperature or cold worked. Resolved Shear Stress. The actual shear stress ( r) operating on a slip system (that is, in the slip plane and in the slip direction) resulting from the application of a simple tensile stress. The expression is given as r = a cos

with a { 1 1 0} plane lie in the rolling plane and a < 1 1 2> direction in the rolling direction. Rupture. The term rupture is commonly used to a kind of failure in which the fracture of the material is accompanied by considerable plastic deformation. It is often associated with creep failure. Even under simple tensile loading if a ductile material necks down by plastic deformation to the extent that break occurs at the smallest section of the neck, the material is said to be ruptured. This type of failure is termed as ductile tensile failure. Thus, point like and chisel edge type fracture profiles are characterizing rupture behaviour. Rupture Time.

The time taken by a material to fail by creep at a given temperature and stress.

Schmid's Law. The expression that relates the orientation of the crystal and the normal stress to the shear stress at which plastic deformation occurs. Schottky Defect. A typical defect, usually observed in ionically bonded solids, consisting of a pair of vacancies created due to the missing of an anion and a cation from the lattice.

Glossary

459

Scratch Hardness. The hardness measured in the Mohs scale when the material is scratched by a harder mineral. Scratch Hardness Test. In this test, a scale called Mohs scale is used to measure the hardness. This scale consists of ten minerals. The test is based on the ability of a material to be scratched by other. The material which is scratched is softer than the other. For measuring the hardness of a given material its surface is scratched by a testing point of the standard mineral starting with the softest. When the testing point moves on the surface of the material under a testing load, material is removed from the surface. Screw Dislocation.

A dislocation whose Burgers vector is parallel to the dislocation line.

Seams. A seam is a longitudinal (i.e. elongated) crack like surface defect observed in a wrought product such as slab, billet, etc. Secant Modulus. Certain materials show a nonlinear elastic behaviour and only the initial portion of the stress-strain curve follows Hookean behaviour. In such cases, to designate a value for the modulus, a line is drawn from the origin to some convenient point along the stress-strain curve, for example, at 1% strain. The slope of this line is termed as secant modulus, the 1% secant modulus in this case. Secondary Bondings. Bondings between the molecules of materials having bond energy in the range 0.01--0.5 eV (or 1-50 kJ/mole). Segregation. Localized region within a material having different composition than the equilibrium composition of the material. Self-Interstitial. When a host atom is displaced from its equilibrium site in the crystal lattice and occupy an interstitial site. It is called self interstitial. Same as interstititalcy. Sessile Dislocation. A dislocation, which for any reason is unable to move or glide freely (or readily). This is opposite to glissile dislocation. For sessile dislocation the Burgers vector and the dislocation line do not both lie in the same active slip plane. A sessile dislocation acts as a barrier to glissile dislocations. Shear Fracture.

A kind of ductile fracture that occurs by shear.

Shear Modulus.

The ratio of shear stress to shear strain within elastic limit.

Shear Strain.

The strain produced in a body under pure shear stress or force.

Shear Stress.

Stress acting in a direction that is parallel to the stressed surface.

Shockley Partial Dislocations. The partial dislocations produced as a result of dissociation of a unit dislocation having complete lattice translation. These partials were suggested for the first time by Heidenreich R.D. and Shockley W. Shore Hardness.

The hardness measured by Shore Scleroscope. It is called rebound hardness.

Shore Hardness Test. In this test, a diamond-tipped hammer weighing one-twelfth of an ounce (about 2.4 gm) is made to fall vertically down to a glass tube from a standard height on the finished surface of a specimen. The top height of rebound is a measure of rebound hardness expressed in number. This is also called Shore hardness as the device used is naming Shore Scleroscope. Shore Scleroscope.

The device used to measure rebound hardness.

460

Glossary

Shot Peening. A specific process of introducing residual compressive stresses in the surface of a material by blasting its surface with small hard steel shots. Shrinkage Porosity. The porosity that arises when excessive dendritic growth occurs in a casting. Liquid metal is unable to flow even from riser through fine dendritic network to the solidifying metal. As a result, small shrinkage pores are produced throughout the casting. Sialons. An advanced ceramic in which aluminium and oxygen atoms are partially substituted for silicon and nitrogen in silicon nitride when alumina is added to it and giving the structure Si-Al-O-N. Other metal atoms can also be substituted (by adding Y 20 3, MgO, BeO) to produce sialons with three dimensional structure formed by (Si, Mh (0, N) 4 tetrahedra. Here, M stands for Al, Mg, Be, Y, or others. Silicon Carbide. It is a ceramic compound of Si and carbon with chemical formula SiC (also called carborundum). It is a hard black insoluble substance having a melting point of 2700°C and hardness of 9 in the Mohs scale. It has two polymorphic forms, namely, alpha and beta. Alpha SiC has a crystal structure of wtirtzite type (hexagonal) and beta-SiC has a diamond cubic type (zinc-blende) structure. Silicon Nitride. It is a man-made advanced ceramic compound of silicon and nitrogen with chemical formula Si3N 4• The material is dark grey to black in colour. Sinking-In. It is the depression at the rim of the spherical indentation produced by Brinell indenter. The measured diameter of indentation is less than the true value thereby introduces an error in the hardness. This kind of error is observed for very soft metals. Sinking-in effect can also occur in Vickers hardness test. Sintered Aluminium Product (SAP). A dispersion strengthened composite belonging to AlAl2O3 system. Skin Rolling. A small cold reduction, usually 0.25 to 2% in thickness to bypass (or eliminate) the yield point. Slag Inclusions. Particles of slag entrapped in the melt during its pouring from the furnace and exist in subsequent casting. Slip.

Name given to the deformation produced in a material by the movement of dislocations through the lattice.

Slip Bands.

A group of closely spaced slip lines appear on the deformed metal.

Slip Direction.

Direction of movement of dislocation in the lattice.

Slip Lines. The visible markings produced on the surface of a single crystal which has undergone plastic deformation. Slip Plane. Slip System.

Plane swept out by the dislocation during the process of slip. The combination of slip plane and the slip direction lying in that slip plane.

S-N Curve. The presentation of engineering fatigue data in the form of a curve plotted between fatigue stress (S) and the logarithm of the number of cycles of failure (N). Solid Solution. A single phase alloy having uniform chemical composition and the atoms of one element become the part of the crystal lattice of other and vice versa.

Glossary

461

Solid Solution Strengthening. A strengthening mechanism by alloying the material within solid solubility limit. The strengthening produced in a solid solution alloy by solute atoms when the stress field surrounding them interferes with the motion of glide dislocations under the applied stress. Solution Treatment. A process in which a material is heated to above the solvus temperature to get a homogeneous single phase by dissolving any phase other than the matrix phase. Space Lattice. An infinite array of points in three dimensional space, so arranged that each interior point has identical surroundings to that for other. Spring Steels. A general name given to carbon steels containing 0.5 to 0.8% carbon or silicomanganese steels containing 1.75% Si, 0.75% Mn which can be hardened and tempered to give materials of high proportional limit and low mechanical hysteresis. Stacking Fault. Name given to a crystal imperfection (a surface defect) resulting due to an error in the stacking sequence of close packed planes of atoms in the structure. Stacking Fault Energy. The energy required to create stacking fault. Stacking Sequence. The sequential arrangement of close-packed planes of atoms in closepacked crystal structures. The stacking sequences are ----ABCABCABC---- and ABABAB----, respectively in FCC and HCP structures. Static Mechanical Properties. The characteristics of a material displayed under the conditions of steadily applied force. Stainless Steels. Essentially low carbon high chromium or chromium-nickel steels, having a minimum of 12 per cent of chromium, well known for their excellent corrosion resistance. Steel. Essentially an alloy of iron and carbon (less than the maximum solid solubility limit of carbon in gamma-iron, i.e. "" 2%) with or without intentionally added alloying elements. Stellites. A group of cobalt base alloys, having chromium, tungsten, nickel, molybdenum, niobium, titanium and iron as alloying elements, well known for their high temperature properties. (A typical composition of stellite is as Co-0.25% C-27% Cr-3% Ni-5% Mo5% Fe.) Stiffness. Ability of a material to resist elastic deflection under an applied force. Straight Rolling. Rolling in only one direction is called straight rolling. Strain. The term is used to express the accompanying changes in dimensions of a material under stress. Strain Ageing. Changes in mechanical properties of plastically deformed (i.e. strain hardened) metals as a result of ageing at room temperature or moderately high temperature. Steels containing nitrogen or carbon are typical example of alloys exhibit strain ageing effect. Ductility and impact value get reduced after strain ageing. Strain Energy. elastically. dislocation increase in

It is the elastic strain energy stored in any elastic material when it is stressed In terms of elastic strain energy of a dislocation, since atoms around a line are elastically displaced from their equilibrium positions, there is an energy of crystal due to stored elastic strain energy.

462

Glossary

Strain Hardening. The hardening (increase in hardness, yield and tensile strength) produced in a metal as a result of previous strain or cold working. Plastic deformation or strain results in increase of dislocation density. As the dislocation density increases, the stress required to move any dislocation increases due to interfering effect of the stress fields of the surrounding dislocations. Strain Hardening Exponent. It is the slope of the log-log plot of true stress and true strain up to maximum load which is a straight line. Strain Hardening Rate. The slope of the stress-strain curve (either engineering curve or true curve) is referred to as strain hardening rate. Strain Rate.

The rate of deformation of a material under an applied stress.

Stress. The internal resistance offered by the object to external force. Usually expressed as the ratio of the magnitude of the force applied to the magnitude of the original area of crosssection of the object upon which the force is acting. Stress Corrosion Fracture. Fracture of a material caused by the combined effect of stress (including internal stress) and corrosion. Stress Intensity Factor. It refers to a combination of the applied stress and flaw size in accordance with the expression: K = Y crJ tra. It represents the stress distribution in vicinity to a crack tip. Stress Raisers. A small flaw (internal or external) or a structural discontinuity (such as an inclusion) at which applied tensile stress will be amplified and from which a crack may propagate. Stress Ratio. Also called range ratio. The ratio of minimum stress to maximum stress of a cyclic stress. Stress-Rupture Curve. Graph plotted between the applied stress values and the corresponding rupture times obtained by creep testing of a material. Stress-Strain Curve. When a material is loaded under tension or compression until fracture of the specimen, the load is expressed in terms of stress and elongation in terms of strain and a graph is plotted between stress values and strain values. This graph is called a stressstrain curve. Stretcher Strains. A kind of manufacturing surface defect in which surface markings or Ltider lines in relief appear on drawn or stamped low carbon steel sheets. These surface markings (smoke like or flame like pattern) are depressions or irregularities on the surface. Striations. The fatigue fractured surface of stage II crack propagation shows ripple marks. These marks are called striations. Each striation was produced by a single cycle of stress and represents the successive position of an advancing crack front. Structural Steels.

The steels that are used for applications involving structural loadings.

Sub-Atomic Particles.

The particles less than an atomic diameter.

Sub-Boundaries. Boundaries within the grains having small orientation difference on both sides of them.

Glossary

463

Substitutional Defect. An imperfection developed in the crystal structure as a result of substitution of the atom of the parent element from its normal lattice site by the atom of another element, i.e. atom of any element other than that of parent element. A point defect. Subsurface Flaws.

Flaws just below the surface of a material are called subsurface flaws.

Supersaturated Solid Solution. A solid solution having excess amount(s) of solute element(s), i.e. beyond the solid solubility limits permissible for solute elements in the base element at a given temperature, usually at room temperature. Surface Discontinuities. Any break in the continuity of a material at its surface is termed as surface discontinuity. Surface Imperfections. The lattice imperfections of two dimensional in nature are referred to as surface imperfections. TD-Nickel. The name given to thoriated nickel, i.e. thoria (ThO 2) dispersed nickel, a dispersion strengthened composite. Temper Embrittlement. Embrittlement resulting either due to slow cooling of the steel through a particular temperature range or due to holding for reasonably long period of time within this temperature range. Tempering. A stress-relieving heat treatment process to which hardened steels and cast irons are frequently subjected. Tensile Force.

An uniaxial force that tends to stretch or elongate the material.

Tensile Strain.

The strain resulting due to the application of tensile force on the material.

Tensile Strength. Ability of a material to withstand tensile forces without fracture. Also as the maximum tensile stress which a metal can withstand without fracture. Usually measured as the ratio of maximum uniaxial tensile force that can be sustained by the metal to the original cross-sectional area on which tensile force acted. Tensile Stress.

The stress developed in the material as a result of tensile force.

Tensile Test. The test performed on standard specimens of materials to know about their behavior on subjecting to uniaxial tensile loading. Texture. Extensive plastic deformation of a polycrystalline metal results in its crystallites (the randomly oriented individual crystals or grains) to acquire a preferred crystallographic orientation with respect to the direction of deformation. That is, in majority of the crystals a particular direction or plane becomes parallel to the direction of deformation. This is called texture. Thermoplastics. Group of organic nonmetallic materials (polymers) that can be easily formed and reformed into desired shapes by the application of heat and/or load. Thermosets. Group of hard and brittle organic nonmetallic materials (polymers) that once formed by thermosetting reaction cannot be reformed into desired shapes by the application of heat and/or load. Thiokol Elastomers. Chemically these are polysulphide elastomers obtained by the reaction between ethylene dihalides and alkali sulphides. These elastomers are outstanding in oil and solvent resistance and in gas permeability.

464

Glossary

Three-Dimensional Defects. Volume imperfections are also known as three-dimensional defects. Precipitate particles, voids, pores and blow holes are some common examples of volume defects. Similar to other defects, these defects also break the continuity of the crystal structure lattice. Three-Dimensional Imperfections. dimensional imperfections.

Volume imperfections are also known as three-

Threshold Stress Intensity Factor (Kth). It is the lowest value of range of stress intensity ~K (= Kmax - Kmin = ~a~) up to which the pre-existing crack is unable to propagate in a materials subjected to cyclic loading. Here K is stress intensity factor. Tilt Grain Boundary. Boundary between adjacent grains having difference in orientation in a manner that each lattice appears to be tilted with respect to other lattices. Small angle grain boundary comprised of an array of edge dislocations. Torsional Stress. The shear stress produced in a cylindrical bar or in a tube when it is subjected to twisting or torsional moment at one end of the specimen. Toughness. The property of a material which enables it to absorb energy and deform plastically before fracture. Transcrystalline Fracture. Another name of 'Intragranular Fracture'. (Fracture of a material across the grain or individual crystal). Transgranular Fracture. Another name of 'Transcrystalline Fracture'. (Fracture of a material through the grains.) Transient Creep.

The initial part of the creep curve during which creep rate decreases with time.

Transition Temperature. The temperature below which an otherwise ductile material starts behaving as a brittle material under conditions of impact (sudden) loading. Triaxial Stress. A stress state in tension in which the material is loaded in such a manner that all the three principal stresses are effective such as at notch. True Creep Curve. The experimental creep curve obtained when the stress on the specimen is maintained to be constant. True Strain. It is defined as the natural logarithm of the instantaneous length (l) divided by the original length 10 , i.e. In (l/l 0 ). True Stress. The ratio of the applied load on a material at any instant to its instantaneous cross-sectional area. True Stress-Strain Curve.

Graph plotted between true stress and true strain.

Twin Boundary. The boundary between the two parts of the crystal, one undergone deformation on application of shear stress and the other non-deformed part, having symmetry about a plane. (The deformed part looks like a mirror image of the nondeformed part.)

Twinning Direction. the crystal.

The direction in which the atoms are displaced in the twinned region of

Twinning Plane. The plane of symmetry between the twinned and untwined portions of the crystal undergoing twinning is called the twinning plane. This is the crystallographic plane about which twinning takes place under the action of shear stress.

Glossary

465

Twist Grain Boundary. Boundary between adjacent grains having difference in orientation in a manner that each lattice appears to be twisted with respect to other lattices. Small angle grain boundary comprised of an array of screw dislocations. Ultimate Tensile Strength.

Same as 'Tensile Strength'.

Ultrasonic Testing. It is a NOT technique specially used to detect internal flaws within a material. It makes use of high frequency acoustic waves produced by piezoelectric transducers. A highly directional sound wave is transmitted to the test piece through a suitable couplant, usually oil or grease like material. The wave propagates effectively through the test piece if no flaw is present within it, but reflected by inhomogenities or discontinuities. The signal is displayed on a cathode ray oscilloscope. Uniaxial Stress. A stress state in which the material is loaded in such a manner that only one of the principal stresses is in tension and the remaining two principal stresses are zero. Unit Cell. The smallest unit of the lattice which on repeating in all the three directions gives rise to crystal structure lattice. Unit Dislocations. A dislocation with Burgers vector equals one lattice spacing in the direction of slip. Upper Yield Point. Some of the materials when loaded display abrupt yielding with a drop in stress. The peak stress is then called as upper yield point. Vacancy.

An empty atomic site in the crystal structure lattice. A point defect.

Valence Electrons. The electrons in the outermost orbit that are relatively loosely bonded with the nucleus. van der Waals Bond. Secondary bond arising from the fluctuating dipole nature of an atom with all occupied electron shells filled or from a weak electrostatic attraction between polar molecules. Vicalloy. The name given to a cobalt base alloy having a nominal composition as Co-14% V-34% Fe. Vickers Hardness.

The hardness of a material measured by Vickers hardness test.

Vickers Hardness Number. The number showing only the magnitude of the Vickers hardness for an applied load. Vickers Hardness Test. The indentation hardness test, performed by pressing a square based diamond pyramid indenter having an included angle of 136° between opposite faces into the surface of the material under consideration by applying a load ranging from 1 kg to 120 kg. Viscous Creep.

The regime of the true creep curve during which creep rate remains constant.

Visual Examination. An NOT method in which the examination of a component or structure is carried out with the aid of naked eyes. Sometimes, a magnifying glass is also used for this purpose. Vitallium. Trade name of cobalt base alloy having chromium (:==30%) and molybdenum (:==5%) as the main alloying elements. Void.

A volume defect that does not have any mass within its region.

466

Glossary

Volume Defects.

Same as 'Three-dimensional Defects'.

Volume Imperfections.

Same as 'Three-dimensional Imperfections'.

Weathering Steels. These are low carbon steels containing small amount of copper and other elements such as silicon and phosphorous that enhance atmospheric corrosion resistance, solid solution strengthening and some refinement in grain structure of ferrite. These steels initially corrode at the same rate as plain carbon steels, but soon exhibit a decreasing corrosion rate. After a few years continuation of corrosion is stopped. Welding Defects. Defects developed in the welded materials as a consequence of faulty welding process, practice and/or faulty design. Whiskers.

Specially developed single crystals almost free of dislocations.

White Cast Irons.

Cast irons having all the carbon in combined form as cementite/carbide.

Work Hardening.

Same as 'Strain Hardening'.

Y-Alloy. An alloy of aluminium, containing 4% copper, 2% nickel and 1.5% magnesium, suitable for high temperature applications. Yielding. It is the beginning of plastic deformation in which some of the atoms in the material will, under tension, slip to new equilibrium positions at which they can form new bonds, thus, permitting an elongation in excess of that produced by simple elastic separation of atoms. Yield Point.

The distinct point on the stress-strain curve where yielding begins.

Yield Point Elongation. The elongation that occurs at approximately constant stress or load corresponding to lower yield point is called yield point elongation. Yield Point Phenomenon. Many metals, particularly low carbon steels show a localized, heterogeneous type of transaction from elastic to plastic deformation which produces a yield point in the stress-strain or load elongation curve. In the load-elongation curve, load increases steadily with elastic deformation, drops suddenly, fluctuates about some constant value and then rises with further strain. The load at which sudden drop occurs is called the upper yield point. The approximate constant load at which yielding occurs is called the lower yield point, and the elongation which occurs at constant load is called yield point elongation. Yield Strength. The minimum applied stress that produces permanent (plastic) deformation in a material. Young's Modulus.

Same as 'Modulus of Elasticity'.

Zero-Dimensional Defects. zero dimension.

Same as 'Point Defects'. The defects which have approximately

Zirconia Toughened Alumina (ZT A). The alumina ceramic that has been dispersed with metastable tetragonal zirconia particles to impart transformation toughening is called ZT A. Zirconia Toughened Ceramics (ZTC). These ceramics consist of tetragonal or monoclinic zirconia (ZrO 2) particles finely dispersed in other ceramic matrices such as alumina, mullite and spinel.

Bibliography

Askeland, Donald R., The Science and Engineering of Materials, 2nd ed., S.I., Chapman & Hall, UK, 1990. Baldevraj, Jayakumar T. and Thavasimuthu, M., Practical Nondestructive Testing, Narosa Publishing, New Delhi, 1997. Barsoum, Michel W., Fundamentals of Ceramics, International McGraw-Hill, New York, 1997. Bhargava, A.K., Engineering Materials: Polymers, Ceramics and Composites, Prentice-Hall of India, New Delhi, 2004. Chawla, Krishna K., Composite Materials: Science and Engineering, Springer-Verlag, 1987. Clauss, Francis J., Engineers Guide to High Temperature Materials, Addison-Wesley, Massachusetts, 1969. Davis, Harmer E., Troxell, George Earl and Wiskocil, Clement T., The Testing and Inspection of Engineering Materials, 3rd ed., McGraw-Hill, New York, 1955. Davies, D.E., Practical Experimental Metallurgy, Elsevier, 1966. Dieter, George E. Mechanical Metallurgy SI Metric Edition, McGraw-Hill, New York, 1988. Epifanov, G.I., Solid State Physics, English Translation, MIR Publishers, Moscow, 1979. Gorelik, S.S ., Recrystallization in Metals and Alloys, English Translation, MIR Publishers, Moscow, 1981 . Harris, W.J., Metallic Fatigue, Pergaman Press, New York, 1961. Hayden, H.W., Moffatt, William G. and Wulff, John, the Structure and Properties of Materials, Vol. 3, Mechanical Behaviour, Wiley Eastern, New Delhi, 1980. 467

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Hertzberg, Richard W., Deformation and Fracture Mechanics of Engineering Materials, 3rd ed., John Wiley & Sons, New York, 1989. Higgerson, C.A., (ed.), Experiments in Materials Technology, Affiliated East-West Press, New Delhi, 1973. Honeycombe R.W.K., The Plastic Deformation of Metals, Edward Arnold, 1968. Hornbogen, Erhard and Zurn, Gahr Karl-Heinz, "Distribution of Plastic Strain m Alloy Containing Small Particles", Metallography, Vol. 8, pp. 181-202, 1975. Hull, Barry and John, Vernon, Nondestructive Testing, ELBS/Macmillan, 1988. Jastrzebski, Zbigniew D., The Nature and Properties of Engineering Materials, 3rd ed., John Wiley and Sons, New York, 1987. John, Vernon, Introduction to Engineering Materials, 3rd ed., MacMillan, 1992. Lysagt, Vincent E., Indentation Hardness Testing, Reinhold Publishing, USA, 1949. Matthews, F.L. and Rawlings, R.D., Composite Materials: Engineering and Science, Chapman & Hall, London, 1994. McLean, D., Mechanical Properties of Metals, 2nd ed., John Wiley & Sons, 1965. Novikov, I., Theory and Heat Treatment of Metals, Mir Publishers, Moscow, 1978. Raghvan, V., Solid State Phase Transformations, Prentice-Hall of India, New Delhi, 1987. Ranganathan, S., Arunachalam, V.S. and Chan, R.W., (Eds.), "Alloy Design", Indian Academy of Sciences, Bangalore, 1981. Reed-Hill, Robert E., Physical Metallurgy Principles, D. Van Nostrand Company, Toronto, 1964. Schaffer, James P., Saxena, Ashok, Antolovich, Stephen D., Sanders, Thomas H. and Warner, Steven B., The Science and Design of Engineering Materials, International Editions, IRWIN, Chicago, 1995. Schwartz, Mel M., Composite Materials: Properties, Nondestructive Testing and Repair, Prentice Hall, New Jersey, 1997. Shackelford, James F., Introduction to Materials Science for Engieers, 4th ed., Prentice Hall, New Jersey, 1996. Shah, D.N. and Kamat, G.R. "Convener", Proc. National Workshop on Testing and Characterisation of Materials (TACOM-90), IIT Bombay, March 15-16, 1990. Singh Vijendra, Physical Metallurgy, Standard Publishers, Delhi, India, 1999. Smith, William F., Principles of Materials Science and Engineering, 3rd ed., McGraw-Hill, New York, 1996. Suryanarayana, A.V.K., Testing of Metallic Materials, 2nd ed., B.S. Publications, Hyderabad, 2007.

Questions Bank

Objective Type Questions Write the correct or the most appropriate answer to the following objective type questions by writing the corresponding letter a, b, c, or d. Answer key is given at the end of the question bank. 1. The Miller indices of the direction common to the planes (l l l) and (l l 0) in a cubic system is: (a) [l l l] (b) [l l 0] (c) [11 0]

(d) [l l l]

2. The engineering stress-strain curve for a ceramic material is: (a) parabolic (b) exponential (c) logarithmic (d) linear 3. The number of slip systems in an ideal close packed hexagonal structure is: (a) 3 (b) 12 (c) 24 (d) 48

469

470

Question Bank

4. A square of 9 mm 2 area is subjected to simple shear displacement ✓3 mm along x-direction, as shown in Figure l . The shear strain imparted will be: (a) 1/3 (b) 1/✓3

'' '''

'' ''' '

(c) ✓3

(d) 3

FIGURE 1

5. Driving force for grain growth after completion of recrystallization is: (a) stored energy for cold work (b) vacancy concentration (c) dislocation density in the crystal (d) grain boundary curvature 6. In an ideal HCP packing, the c/a ratio is: (a) 1.225 (b) 1.414 (c) 1.633 (d) 1.732 7. The property that cannot be obtained from a tensile test is: (a) Young's modulus (b) yield strength (c) ultimate tensile strength (d) endurance limit 8. Superalloys are: (a) Al-based alloys (c) Ni-base alloys

(b) Cu-based alloys (d) Mg-based alloys

9. Wood is a naturally occurring: (a) malleable material (c) ceramic material

(b) composite material (d) isotropic material

10. The Miller indices of the plane PQRS, shown in the unit cell (Figure 2), are: (a) (l l l) (b) (l

2

l)

(c) (l l 0) y

(d) (l O 0)

11. A defect is bounded by two mirror planes is: (a) twin (b) stacking fault (c) grain boundaries (d) edge dislocation

R X

FIGURE 2

12. X-ray radiography is used to determine the: (a) soundness of casting (b) chemical composition (c) crystal structure (d) phases present 13. Stacking Fault Energy (SFE) plays an important role in determining the work hardening ability of a metal. In this context, the correct logical sequence is:

Question Bank

(a) (b) (c) (d)

471

High SFE ➔ easy cross-slip ➔ low work hardening High SFE ➔ difficult cross-slip ➔ high work hardening Low SFE ➔ easy cross-slip ➔ low work hardening Low SFE ➔ difficult cross-slip ➔ low work hardening

14. During low temperature plastic deformation of an under-aged precipitation hardened alloy, dislocations: (a) climb to completely avoid the precipitate (b) loop around the precipitate (c) cross-slip to completely avoid the precipitate (d) cut through the precipitate 15. The yield point phenonmenon observed in annealed low carbon steels is due to the presence of: (a) silicon (b) chromium (c) phosphorous (d) carbon 16. In a tensile test of a ductile material, necking starts at: (a) lower yield stress (b) upper yield stress (c) ultimate tensile stress (d) just before fracture 17. Fatigue resistance of a steel is reduced by: (a) decarburization (b) polishing the surface (c) reducing the grain size (d) shot peening 18. The NOT technique used to detect deep lying defects in a large sized casting is: (a) liquid penetrant inspection (b) magnetic particle inspection (c) ultrasonic inspection (d) eddy current inspection 19. The stacking sequence of close packed planes with a stacking fault is: (a) ab Cab Cab C (b) ab ab ab ab (c) a b c a c a b c a b (d) a b c a b a c b a 20. The slip directions on a (1 1 1) plane of a FCC crystal are: (a) [1 0 l], [0 1 l], [1 1 0]

(b) [1 0 l],[11 0],[1 0 1]

(c) [1 0 l],[1 1 0],[0 1 1]

(d) [0 1 l], [0 1 l], [1 1 0]

21. The correct statements among the following are: (P) screw dislocations cannot climb (Q) screw dislocations cannot cross-slip (R) edge dislocations cannot climb (S) edge dislocations cannot cross-slip (a) P, R (b) P, S (c) Q, R (d) Q, S 22. A steel bar (elastic modulus = 200 GPa and yield strength = 400 MPa) is loaded to a tensile stress of 1 GPa and undergoes a plastic strain of 2%. The elastic strain in the bar in per cent is:

472

Question Bank

(a) 0 (c) 0.5

(b) 0.2 (d) 2.0

23. The structure sensitive properties are: (P) elastic modulus (Q) yield strength (R) melting point (S) fracture strength (a) P, S (c) Q, R

(b) Q, S (d) P, R

24. The planar density for (1 1 1) plane in a FCC crystal is: (b) 0.74 (a) 0.68 (d) 0.91 (c) 0.85 25. With e = true plastic strain and n = strain hardening coefficient, necking in a cylindrical tensile specimen of a work-hardening metal occurs when: (a) e = n (b) e = 2n (c) e = n°· 5 (d) e = n2 26. A perfectly plastic metal piece, with 4 mm x 4 mm cross-section and 25 mm length, is stretched to 100 mm. What is the deformed cross-section? (a) 1 mm x 1 mm (b) 2mmx2mm (c) 3 mm x 3 mm (d) 4mmx4mm 27. Loading in Mode I fracture refers to: (a) opening mode (c) tearing mode

(b) sliding mode (d) twisting mode

28. Which one of the following alloy systems exhibits complete solid solubility? (a) Cu-Ni (b) Fe-Cu (c) Pb-Sn (d) Cu-Zn 29. A small amount of thoria is doped is because thoria particles: (a) decreases solute diffusivity (b) enhance the mobility of grain (c) increase solute segregation to (d) are effective in limiting grain

into tungsten filament wires used in light bulbs. This

boundary the grain boundary growth

30. In one FCC unit cell, there are: (a) 4 tetrahedral and 8 octahedral sites (b) 8 tetrahedral and 4 octrahedral sites (c) 12 tetrahedral and 4 octrahedral sites (d) 4 tetrahedral and 4 octrahedral sites

31. The [l 0 0] and [l 1 0] directions in a cubic crystal are coplanar with: (a) [l 0 l] (c) [l 2 0]

(b) [0 0 l] (d) [l 1 l]

Question Bank

473

32. The conditions necessary for superplastic deformation in an alloy are: (P) extremely fine and uniform grain size (Q) high homologous temperature (R) high strain rate (S) coarse non-uniform grains (a) P, Q (b) Q, R, S (c) P, Q, R (d) Q, R 33. The atomic packing factor for diamond cubic structure is:

wo~

~o~

(c) 0.34

(d) 0.25

34. A dislocation free single crystal of aluminium has a theoretical strength of about: [Given: shear modulus, G = 28 GPa] (a) 28.0 GPa (b) 4.50 GPa (c) 0.56 GPa (d) 0.07 GPa 35. In a cubic crystal with lattice parameter a, the dislocation reaction that is vectorially correct and energetically feasible and is given by:

a

a

(b)

2 [11 0] + 2 [11 0] ➔ a [11 0]

(d)

-[0ll] ➔ -[211]+-[12

a

a

a

2

6

2

-

l]

36. Crack propagation in metallic materials is detected by the NOT method: (a) Eddy current testing (b) Magnetic particle inspection (c) Acoustic emission testing (d) Ultrasonic testing 37. Cross slip is prevalent in materials with: (a) high stacking fault energy (b) high grain boundary energy (c) low stacking fault energy (d) low grain boundary energy 38. Rockwell hardness on the C-scale is measured using an indenter with a: (a) 120° diamond cone with a slightly rounded tip (b) square base diamond pyramid (c) 10 mm diameter steel ball (d) 3 mm diameter steel ball 39. In a rhombohedral crystal structure: (a) a (c) a

=t:-

b =t:- c,

= b = c,

a= a=

r= 90° =t:- /3

/3 = r=

90°

(b) a (d) a

=t:-

b =t:-

C'

= b = c,

a

= /3 = r = 90° /3 = y =t:- 90°

a=

40. Identify the correct statements: (P) c/a ratio greater than ideal in an HCP crystal promotes basal slip (Q) BCC materials are generally more ductile in comparison to FCC materials as they have more number of slip systems

474

Question Bank

(R) (S) (a) (c)

Screw dislocations have greater mobility The Burgers vector of any dislocation is P, R, S (b) P, Q (d)

than edge dislocations always equal to one lattice spacing Q, R, S P, R

41. In fracture control design procedure, NOT plays an important role because it primarily enables to: (a) predict the time it will take for a given defect to grow to a critical size (b) evaluate accurately the defect type, location and size that exist in the material (c) measure the mechanical properties of the design materials (d) measure the grain sizes of the microstructures in the material 42. Identify the statement that precisely describes alloys: (a) it is mechanical deformation carried out (b) it is mechanical deformation carried out (c) it is mechanical deformation carried out (d) it is mechanical deformation carried out

the principle of hot working of metals and above above above below

the the the the

temperature of recrystallization room temperature annealing temperature melting temperature

43. Arrange the following refractory materials in ascending order of their melting point: (P) alumina (Q) silica (R) carbon (S) zirconia (a) R > P > Q > S (b) S > R > Q > P (c) R > S > P > Q (d) P > S > R > Q 44. An Al-4.5 wt.% Cu alloy solutionised at 500°C, quenched to room temperature and aged at 200°C for 2h, is found to exhibit an increase in hardness. The primary mechanism contributing to increased hardness is: (a) martensitic transformation due to quenching (b) soild solution strengthening (c) precipitation hardening (d) point defect strengthening 45. For a dislocation with Burgers vector b, the energy is (a) independent of b (b) proportional to b (c) inversely proportional to b2 (d) proportional to b2 46. If the volume of a material does not change during deformation, then the Poisson's ratio should be: (a) 0.25 (b) 0.50 (c) 0.67 (d) 1.00 47. Under application of stress, when a straight dislocation (radius of curvature, r = oo) tries to bow out around precipitate of spacing L, there is an instability during changing of curvature at: (a) r = L (b) r = L/2 (c) r = L/3 (d) r = L/4

Question Bank

475

48. The indenter used in Vickers hardness test is: (a) 10 mm dia steel ball (b) 120° diamond cone with a slightly rounded point (c) 3.2 mm dia steel ball (d) square base diamond pyramid (included angle 136° between opposite faces) 49. For the same volume fraction, size and size distribution of precipitates, the highest strength in a precipitation-hardened material is obtained when the precipitates are: (a) uniformly distributed in annealed matrix (b) distributed along grain boundaries (c) nucleated on dislocation substructure (d) nucleated at impurities and inclusions 50. Engineering stress-strain curves for a metal under two conditions, A and B, are shown in Figures 3 and 4. Identify the correct statement: (a) the resilience of the material is same in conditions A and B (b) the resilience of material is higher in condition B than in condition A (c) the toughness of material is higher in condition A than condition B (d) the toughness of material is higher in condition B than in condition A

(/) (/)

~

U)

Conditi on A

Condition B

Strain

Strain

FIGURE 3

FIGURE 4

51. Identify the false statement: (a) Burgers vector and the dislocation line are parallel to each other for screw dislocations (b) Burgers vector and the dislocation line are perpendicular to each other for edge dislocations (c) screw dislocations glide parallel to its Burgers vector (d) edge dislocations glide parallel to its Burgers vector 52. A dislocation line in a FCC crystal dissociates into two partials which have their Burgers a

--

a

-

vector as - [2 l l] and - [l l 2] . Indicate the correct statement:

6

6

(a) Burgers vector of the undissociated dislocation line is

~ [l 0 l]

476

Question Bank

(b) Burgers vector of the undissociated dislocation line is ~ [l I 0] 2 2

(c) energy of each partial is proportional to ~ 3 (d) energy of the undissociated dislocation line is lesser than the sum of energies of the two partials

53. A copper sample has been metallographically analysed for determining its mean grain size. It is found to have an ASTM grain size number of 5. The number of grains per mm 2 in the sample will be: (b) 124 (a) 72 (d) 496 (c) 248 54. Choose the correct statements (P) interstitial atoms diffuse slower than substitutional atoms (Q) in pure metals the vacancy concentration increase with temperature (R) martensitic transformation is athermal in nature (S) atoms in the grain boundary diffuse slower than in the bulk at relatively lower temperature (a) P, Q (b) Q, R (c) Q, S (d) R, S 55. To obtain superplasticity, the alloy (P) should have a fine grain structure that is also stable at high temperature (Q) should be deformed at low temperature (R) should be deformed at low strain rates (S) should be deformed at high strain rates (a) P, R (b) Q, S (c) Q, R (d) P, Q 56. Secondary hardening in steels arises out of : (a) the precipitation of fine alloy carbides at high temperatures (b) the refinement of ferrite grain size by working (c) the decomposition of retained austenite upon heat treatment (d) the precipitation of complex intermetallic upon heat treatment 57. The following property can be conveniently measured to monitor the annihilation of point defects during recovery: (a) hardness (b) impact strength (d) electrical resistivity (c) thermal conductivity 58. Ultrasonic testing can be used for (choose the correct combination of the following statements P, Q, R and S) (P) quantitative analysis of phases (Q) determination of elastic constants (R) determination of endurance limit (S) detection of internal defects.

Question Bank

(a) P, R (c) Q, S

477

(b) P, Q (d) R, S

59. The following statements can be made about the flow stress of particle containing material systems. (Choose the correct combination of P, Q, R and S) (P) Monotonically increases with increase in particle size (Q) First increases, then decreases with increase in particle size (R) Increases with increase in volume fraction of the particle (S) Decreases with increase in volume fraction of the particle (a) P, S (b) Q, S (c) P, R (d) Q, R 60. The flow stress may decrease with increasing temperature due to (Choose the correct combination of P, Q, R and S) (P) increasing dislocation width (Q) annihilating dislocation kinks (R) increasing dislocation climb (S) increasing obstacle strength (b) P, S (a) P, Q (c) P, R (d) Q, S 61. Radiographic appearance of inclusions resembles: (a) dark patches as compared to the background (b) bright patches as compared to the background (c) dark or bright patches depending on radiation energy (d) dark or bright patches depending on relative density 62. A truly sessile dislocation in a FCC material is: (a) Shockley partial (b) Lamer dislocation (c) Frank partial (d) Lamer-Cottrell dislocation 63. The hardness of a spheroidised graphite cast iron and that of a case carburized steel is best determined by the following combination of test methods: (a) Brinell and Knoop microhardness respectively (b) Rockwell and Rockwell superfacial hardness respectively (c) Vickers and Vickers microhardness respectively (d) Vickers and Knoop microhardness respectively 64. Hydrogen embrittled steel samples can exhibit (a) only cleavage fracture (b) cleavage, dimple and intergranular fracture (c) both cleavage and dimple fracture (d) only intergranular fracture 65. Identify the test method which cannot be used for estimating nil ductility temperature: (a) Robertson crack arrest test (b) Dynamic tear test (c) Erichson test (d) Dropweight test

478

Question Bank

66. Nabarro-Herring creep and Coble creep are governed: (a) by grain boundary (D 8 b) and volume diffusion (Dv) respectively (b) only by Dgb (c) equally by Dv and Dgb (d) by Dv and Dgb respectively 67. Elastic energy of a dislocation is related to its Burgers vector as follows: (a) directly proportional (b) proportional to the square of the Burgers vector (c) proportional to the square root of the Burgers vector (d) not related at all 68. The fracture toughness of lower-strength ductile material is best measured using the following experimental method: (b) I-integral method (a) K1c evaluation (d) three point bend test (c) dynamic impact testing 69. A pure tilt boundary may be equivalently represented by: (a) an array of jogs on an edge dislocation (b) a cross grid of screw dislocation (c) a dislocation pile up consisting of both edge and screw dislocations (d) an array of edge dislocations perpendicular to the slip plane 70. The fatigue resistance of a material is improved by the following technique: (a) anodizing (b) carburizing (c) ion nitriding (d) shot peening 71. Strain rate sensitivity of flow stress for the occurrence of superplasticity is in the range: (a) 0.40-0.60 (b) 0.01-0.10 (c) 0.10-0.20 (d) -0.10-0.00

72. Perfect dislocations can act as nucleation centres for precipitation primarily because: (a) they locally produce the atomic structure of the precipitate (b) they reduce the interfacial energy (c) they provide additional driving force due to elimination of their own strain energy (d) they provide a fast diffusion path for solute 73. The thermodynamic driving force for precipitate coarsening at high temperature is: (a) increase in diffusivity at high temperatures (b) reduction of interfacial energy per unit volume (c) reduction in the yield stress of the matrix (d) reduction of strain energy due to misfit between precipitate and matrix 74. A tilt boundary consists of the following dislocation arrangement: (a) a cross-grid of screw dislocations on intersecting planes (b) a wall of like sign edge dislocations on parallel slip planes (c) a row of dislocations (d) alternate sign of edge dislocations on parallel slip planes

Question Bank

479

75. A Brale indenter used in Rockwell hardness test has the following geometry and material: (a) square based diamond pyramid with 136° included angle (b) conical shaped steel with 120° apex angle (c) conical shaped diamond with 120° apex angle (d) 10 mm diameter hardened steel ball 76. In which of the following sheet material is springback effect significant: (a) aluminium alloys (b) stainless steel (c) magnesium (d) lead 77. The formation of earing defect in deep drawing is due to the following reason: (a) improper punch and die alignment (b) dynamic strain ageing (c) crystallographic texture (d) faster press speed 78. The appearance of intercrystalline fracture suggests that the following mechanism is responsible for the failure: (b) brittle fracture (a) ductile fracture (c) fatigue failure (d) high temperature creep failure 79. An aluminium block is plastically deformed with large plastic flow. The poisson's ratio is (a) 0.28 (b) 0.33 (c) 0.50 (d) 1.00 80. The Larson-Miller parameter P connecting the temperature T and rupture time t, is given as: (a) P = T (log t, + C) (b) P = log t, - CIT (d) P = T log t, (c) P = (C - nit, 81. In sheet metal forming stretcher strains occur in: (a) duralumin sheets (b) low carbon steel sheets (c) austenitic stainless steel sheets (d) Ni-base alloy sheets 82. The miller indices of the plane containing the direction [l 2 3] is: (a) (1 11)

(b) (1 2 3)

(c) (111)

(d) (1 1 0)

83. In case of close packed structures, octahedral voids have a coordination of: (a) 4 (b) 8 (c) 6 (d) 12 84. Stretcher strains found in a low carbon steel sheet are associated with: (a) texture (b) dislocation density (c) yield point phenomenon (d) thickness of the sheet 85. A high cycle fatigue failure is identified by the presence of: (a) dimples (b) beach markings or striations (c) slip lines (d) glass like fracture

480

Question Bank

86. Often earing defects are found in deep drawing operation because: (a) the surface finish of the sheet is poor (b) the sheet material has been given substantial spring back (c) starting sheet has planar anisotropy due to its texture (d) starting sheet has normal anisotropy due to its texture. 87. A cylindrical rod subjected to a tensile strain within the elastic limit undergoes a volume change. If the volume strain is equal to half the applied tensile strain then the Poisson's ratio of the rod is: (a) 0.00 (b) 0.33 (d) 0.25 (c) 0.44 88. In an annealed metal the density of dislocations is typically of the order of: (a) 10 4 m-2 (b) 10 8 m-2 2 2 (c) 10 m(d) 10 13 m-2 89. Two samples A and B of a brittle material have crack lengths in the ratio 3: 1. The ratio of the tensile strengths (measured normal to the cracks) of A and B will be in the ratio: (a) 1 : 3

(b) ✓ 3:1

(c) 1: ✓ 3

(d) 1 : 9

90. On decreasing the grain size of a polycrystalline material, the property most likely to deteriorate is (a) creep (b) toughness (c) tensile strength (d) fatigue

91. Creep rate used in estimating the life of components operating at high temperatures is: (a) (b) (c) (d)

strain rate in stage I average of the strain rates in stages I, II, III strain rate in stage III strain rate in stage II

92. Elastic strain in copper is due to: (a) motion of dislocations (c) breaking of atomic bonds

(b) stretching of atomic bonds (d) none of the above

93. In the X-ray radiography technique the tube voltage for thicker plates, as compared to thin plates, should be (a) higher as it gives higher wavelength (b) lower as it gives higher wavelength (c) higher as it gives shorter wavelength (d) lower as it gives shorter wavelength 94. For maximum sensitivity in the detection of transverse surface cracks in plain carbon steel, we should use: (a) a.c. and generate the magnetic field in longitudinal direction (b) a.c. and generate the magnetic field in the transverse direction

Question Bank

481

(c) d.c. and generate the magnetic field in the transverse direction (d) any one of the above techniques as sensitivity is independent of the above factors 95. In age-hardenable alloys, maximum ductility is obtained: (a) in as cast state (b) immediately after solution treatment and subsequent quenching (c) after optimum ageing (d) after overageing 96. The swift cup test evaluates the following property of a sheet metal: (a) stretchability (b) drawability (c) bendability (d) none of these 97. A metal having a Poisson's ratio of 0.3 is elastically deformed under uniaxial tension. If the longitudinal strain is 0.8, then the magnitude of the thickness strain is: (a) 0.80 (b) -0.80 (c) 0.24 (d) -0.24 98. The tensile load-elongation curve of a metal does not describe: (a) work hardening (b) yield stress (c) anisotropy index (d) necking strain 99. The most important property of steels for use in automobile bodies is: (a) formability (b) yield strength (c) toughness (d) resilience 100. The yield point phenomenon observed in annealed low carbon steel is due to the presence of the following element: (a) silicon (b) carbon (c) phosphorous (d) chromium 101. The driving force for grain growth is: (a) decrease in dislocation strain energy (b) increase in grain boundary energy (c) decrease in grain boundary energy (d) decrese in vacancy concentration 102. Thoria (ThO 2) is dispersed in nickel-based superalloys because it: (a) provides elevated temperature strengthening by resisting coarsening (b) provides elevated temperature strengthening due to the coherency strains surrounding the particle (c) prevents grain boundaries from sliding at elevated temperature (d) provides enhanced corrosion resistance 103. A mixed dislocation can be characterized by one of the following: (a) the angle between the dislocation line and its Burgers vector is zero (b) the angle between the dislocation line and its Burgers vector is 45° (c) the angle between the dislocation line and its Burgers vector is 90° (d) none of the above

482

Question Bank

104. Which of the following describes a slip system in BCC crystals?

(a) (110),(a/2)[111]

(b) (011), (a/2) [111]

(c) (101),(a/2)[111]

(d) (110),(a/2)[111]

105. The energy of a dislocation is: (a) proportional to b (c) proportional to b3

(b) proportional to b2 (d) independent of b

Where b is the Burgers vector 106. The recrystallized grain size will be smaller, (a) lower the annealing temperature and lower the amount of prior cold work (b) higher the annealing temperature and lower the amount of prior cold work (c) lower the annealing temperature and higher the amount of prior cold work (d) higher the annealing temperature and higher the amount of prior cold 107. The plain strain fracture toughness parameter, K 1c has the units:

(a) MPa.✓ m

(b) MPa.m

(c) MPa.m2

(d) ✓MPa.m

108. Herring-Nabarro creep is prominent in: (a) coarse grained materials at high temperature (b) coarse grained materials at low temperature (c) fine grained materials at high temperature (d) fine grained materials at low temperature 109. Intercrystalline fracture refers to failure of a material where: (a) the crack paths are confined mostly to the interior of the grains (b) the cracks grow along certain well-defined crystallographic directions (c) the cracks propagate mainly along the grain boundaries or interphase boundaries (d) the separation occurs along well-defined crystallographic planes 110. Austenitic stainless steel can be strengthened by: (a) quench hardening (b) deformation hardening (c) irradiation hardening (d) quenching and tempering 111. A fatigue fracture is characterized by: (a) cup and cone fracture (c) cleavage facets

(b) dimples (d) striations

112. Ductility can be represented precisely by: (a) per cent elongation (b) per cent reduction in area (c) true local necking strain (d) true fracture strain 113. Rockwell-F scale corresponds to the combination: (a) 100 kg load, red numbers (b) 60 kg load, Brale indenter (c) 60 kg load, 1/16" ball indenter (d) 150 kg load, black numbers

Question Bank

483

114. The cavity inside a one meter thick steel slab can be best detected by: (a) X-ray radiography (b) ultrasonic testing (c) eddy current testing (d) y-ray radiography 115. Liquid penetrant test can be used to detect: (a) internal porosity in castings (b) corrosion wall thinning in pipes and tubes (c) fatigue cracks in magnesium alloy parts (d) residual stresses in steels 116. A low angle grain boundary occurs when the orientation difference between the adjacent grains is of the order of : (b) 10° (a) 100° (d) none (c) 1° 117. The elastic strain energy of a unit length of an edge dislocation as compared to that of a screw dislocation is: (a) more (b) equal (c) less (d) double 118. Increasing the mean stress influences the S-N curve as follows: (a) shifts upwards (b) keeps unaltered (c) shifts downwards 119. The preferred alloying element for low temperature application of steel is: (a) Cr (b) N (c) Mo (d) Ni 120. Lithium is a useful alloying addition to aluminium because: (a) it is cheap (b) it imparts solid solution strengthening (c) it lowers density and contributes to age-hardening (d) it improves corrosion resistance of aluminium 121. The coordination number in simple cubic structure is: (a) 4 (b) 6 (c) 8 (d) 12 122. The primary strengthening mechanism in 70:30 brass is: (a) solid solution strengthening (b) precipitation strengthening (c) dispersion strengthening (d) order hardening 123. The bulk modulus of a material with poisson's ratio of 0.5 is equal to: (a) 3 x Young's modulus (b) Young's modulus (c) infinity (d) zero 124. Dislocation cross-slip is difficult in those materials which have: (a) large number of slip systems (b) high work hardening rate (c) coarse grain size (d) low stacking fault energy

484

Question Bank

125. The ASTM grain size number for a structural steel which shows 65 grains per square inch at a magnification of lO0x is: (b) 3 (a) 1 (d) 7 (c) 5 126. The strain energy per unit of a dislocation of Burgers vector b is proportional to: (a) b (b) b 112 (c) b 312 (d) b 2 127. The direction of glide motion of a screw dislocation is: (a) parallel to the Burgers vector of dislocation (b) perpendicular to the Burgers vector (c) perpendicular to the dislocation line vector (d) any direction within the slip plane 128. Young's modulus of a material gives an idea about: (a) toughness (b) stiffness (c) hardness (d) electrical conductivity 129. Martensite in steel is: (a) an interstitial solid solution of C in alpha iron (b) a supersaturated interstitial solid solution of C in BCT iron (c) a supersaturated solid solution of C in gamma iron (d) a very finely dispersed lamellar structure 130. Slip plane in copper is: (a) (1 0 0) (c) (1 1 1)

(b) (1 1 0) (d) (0 0 0 1)

131. The best method for determining the average hardness of an aluminium casting is: (a) Rockwell A (b) Rockwell C (c) Knoop (d) Vickers (e) Brinell 132. Yield strength of a polycrystalline metal with an average grain size, d, is proportional to: (a) d1,2 (b) a112 (c) d (d) a 1 133. The typical dislocation density (lines/cm2) of a hot rolled material is: (a) 102 (b) 10 12 ~ 1~ ~l~ 134. The single most important requirement for a turbine blade material is: (a) damping (b) resilience (c) creep resistance (d) DBTT 135. Fatigue strength of a steel can be increased by: (a) increasing tensile surface residual stresses (b) introducing hydrogen in steel (c) increasing the grain size

Question Bank

485

(d) increasing the specimen size (e) increasing compressive surface residual stresses 136. The number of octahedral voids in a FCC unit cell is: (b) 4 (a) 8 (c) 12 (d) 6 137. A metal shows higher ductility during wire drawing through a die than in simple uniaxial tension because: (a) higher tensile stresses are applied during wire drawing (b) lateral compressive stresses are generated due to reaction with die (c) dislocation density increases drastically during wire drawing (d) some lubricants are present during drawing operation. 138. The recrystallization temperature decreases as: (a) the amount of cold work decreases (b) the temperature of cold work decreases (c) the grain size decreases (d) the impurity content increases 139. The method which cannot be used to improve the fatigue life of a steel shaft is: (a) annealing (b) shot peening (c) grain refinement (d) surface hardening 140. The Charpy impact test can be used to determine (a) the ductile-brittle transition temperature (b) yield strength under dynamic loading conditions (c) hardenability (d) ductility 141. As (a) (b) (c) (d)

the grain size decreases: both the yield strength and fracture toughness increases yield strength increases but fracture toughness decreases yield strength as well as fracture toughness decrease yield strength and fracture toughness remain unaffected

142. Plain strain condition exists when: (a) one of the principal stresses, i.e. a3 = 0 (b) 0'1, a2 , a 3 are present but one is of the principal strain, e3 = 0 (c) 0'1, a2 , a 3 as well as e1, ei, e3 are present (d) Only one of the principal strains is present 143. The crystal which shows the maximum yield strength is the one containing: (a) no dislocation (b) very few dislocations (c) a high density of dislocations (d) volume imperfections 144. At room temperature, polycrystalline zinc is brittle because zinc: (a) has a low surface energy (b) requires a high stress to cause slip

486

Question Bank

(c) does not have enough independent slip systems (d) has a number of pre-existing cracks

145. In a polymer with a large quantity of relatively small chains, the mass averaged molecular weight is: (a) greater than the number-average molecular weight (b) smaller than the number-average molecular weight (c) equal to the number-average molecular weight (d) unrelated to the number-average molecular weight 146. The [l 0 0] and [l 1 0] directions in a cubic crystal are coplanar with: (a) [l O l] (b) [0 0 l] (c) [l 2 0] (d) [l 1 l] 147. The mechanical response of an elastomer (such as rubber) is characterized by: (P) an increase in elastic modulus with increasing temperature (Q) large recoverable strains (R) a decrease in elastic modulus with increasing temperature (S) an adiabatic decrease in temperature on stretching (a) Q, S (b) P, S (c) Q, R (d) P, Q 148. Which of the following statements are true about edge dislocations? (P) edge dislocations do not have an extra half plane associated with them (Q) the Burgers vector is perpendicular to the dislocation line (R) edge dislocation can avoid obstacles by cross-slip (S) depending on geometry, parallel edge dislocations of opposite sign can attract or repel one another (a) R (b) P, Q, S (c) Q, S (d) Q, R 149. A suitable technique for monitoring a growing crack in an alloy is: (a) acoustic emission (b) radiography (c) magnetic particle technique (d) liquid penetrant test 150. Scissors used in home cut material by concentrating forces that ultimately produce a certain type of stress within the material. Identify this stress: (a) bearing stress (b) shearing stress (c) compressive stress (d) tensile stress 151. Match the defects given in Group I with suitable from Group IL Group I (P) Cracks in a flat aluminium slab (Q) Subsurface porosity in a bronze casting (R) Surface cracks in a steel tool (S) Internal porosity in a ceramic block

non-destructive evaluation technique

Group II (1) Radiography (2) Eddy current technique (3) Ultrasonic technique (4) Magnetic particle technique

Question Bank

(a) P-3, Q-4, R-1, S-2 (c) P-4, Q-2, R-1, S-3

487

(b) P-2, Q-4, R-1, S-3 (d) P-3, Q-2, R-4, S-1

152. Match the mechanical behaviour in Group I with the terms in Group II: Group I

Group II

(P) low cycle fatigue (Q) creep (R) impact toughness (S) stretcher strains

( 1) (2) (3) (4) (5) (b) (d)

(a) P-2, Q-4, R-1, S-5 (c) P-3, Q-4, R-1, S-2

Charpy test Portvin-LeChatelier effect Coffin-Manson equation Larson-Miller parameter Jominy test P-2, Q-1, R-5, S-3 P-3, Q-1, R-4, S-5

153. Match the alloy in Group I with the main precipitates responsible for hardening in Group II: Group I (P) (Q) (R) (S)

Group II

Al-4.4%Cu-l.5%Mg-0.6%Mn Fe-18.0%Ni-8.5%Co-3.5%Mo-0.2%Ti-0.l %Al Al-l.0%Mg-0.6%Si-0.3%Cu-0.2%Cr Ni-15.0%Cr-2.7%Al-l.7%Ti-l.0%Fe

(a) P-3, Q-5, R-2, S-4 (c) P-4, Q-1, R-3, S-5

Ni 3Mo Mg 2Si CuA1 2 TiA1 3 Ni 3Al (b) P-1, Q-3, R-2, S-4 (d) P-3, Q-1, R-2, S-5 (1) (2) (3) (4) (5)

154. The following fibre has the lowest density: (a) tungsten (b) Kevlar (c) glass (d) graphite 155. The most widely used glass fibre for polymer composites is: (a) R glass (b) S glass (c) E glass (d) C glass 156. A flow curve is also called as: (a) creep curve (c) true stress-strain curve

(b) S-N curve (d) R-curve

157. Ductility of a metallic material after cold working: (a) increases (b) decreases (c) remains unaffected (d) unpredictable 158. The following is the example of precipitation hardenable material: (a) Al-Si alloy (b) Nichrome (c) austenitic stainless steel (d) Cu-Be alloy 159. R-curve behaviour is associated with the following property: (a) tensile strength (b) toughness (c) fatigue strength (d) hardness

488

Question Bank

160. Increasing the crystallinity of polymers results in: (a) increased stiffness, tensile strength, impact strength and ductility (b) increased stiffness and tensile strength but reduced ductility and toughness (c) increased impact strength but reduced strength, stiffness and ductility (d) increased ductility, toughness but reduced stiffness and strength

Objective Type Questions (One or more than one answer may be correct) 1. Nil (a) (b) (c) (d)

ductility temperature is that below which fracture is 100% cleavage fracture is 50% cleavage and 50% shear energy absorbed will be minimum fracture surface shows fibrous character

2. Increasing the carbon content of steel (a) reduces the upper shelf energy (b) increases the ductility transition temperature (c) decreases brittleness (d) decreases hardness 3. Soft materials are tested on Rockwell: (a) C scale (b) B scale (c) with 1.6 mm steel ball and 100 kg major load (d) with diamond indenter and a 150 kg major load 4. Movement of jogs can produce: (a) vacancies (c) grain boundary sliding

(b) interstitial (d) decrease the impact strength

5. Fine grain size in metallic materials will: (a) increase the yield strength (b) increase the creep strength (d) decrease the impact strength (c) increase the fatigue strength 6. In hot working, dynamic recovery occurs in: (a) metals of low stacking fault energy (b) metals of high stacking fault energy (c) single crystals of Ni-based supperalloys (d) alpha iron 7. The direction(s) of the line of intersection between (1 1 1) and (011) planes is (are) (a) [l 1 l] (c) [l O 2]

(b) [11 0] (d) [2 1 l]

8. Recovery process in cold worked metals can be studied by: (a) hardness (b) resistivity (c) fracture toughness (d) microcalorimetry

Question Bank

489

9. Critical resolved shear stress in single crystal is calculated by applying: (a) Bragg's law (b) Hooke's law (c) Coulomb law (d) Schmid's law 10. Ductile-brittle transition for state depends significantly on: (a) tensile strength (b) strain rate (c) grain size (d) shear modulus

11. The contrast between areas of different thickness in a radiograph could be increased by: (a) higher X-ray tube current keeping the voltage low (b) increasing both the tube current and voltage to higher possible values (c) using a large focal spot size (d) using fine-grained films 12. In a discontinuous fibre metal matrix composite the fibre will fracture in the middle portion if: (a) the length of the fibre is less than half of the critical fibre length (b) the length of the fibre is more than double the critical fibre length (c) the length of the fibre is nearly same as the critical fibre length (d) the fibre surface contains stress raisers 13. Which of the following are considered applications of the ultrasonic testing? (a) determination of elastic constant (b) detection of defects in metals (c) measurement of material thickness (d) none of the above

14. With increase in annealing temperature the following defect density decreases: (a) vacancy (b) dislocation (c) grain boundary (d) all of them 15. The strength of material increases with: (a) increase in dislocation density (c) increase in grain size

(b) decrease in dislocation density (d) decrease in grain size

16. Solute atoms which cause yield point phenomenon in mild steel are/is (a) aluminium (b) boron (c) carbon (d) nitrogen 17. In precipitation hardenable alloy, like duralumin, intermediate precipitates can form due to: (a) difficulty of nucleation of the final precipitate (b) difficulty of growth of the final precipitate (c) ease of diffusion (d) coherency strain 18. Earing is a defect found in steels after the following metal working operation(s): (a) deep drawing (b) rolling (c) extrusion (d) wire drawing

490

Question Bank

19. The technique(s) which can be used for the direct observation of dislocation is (are): (a) scanning electron microscopy (b) transmission electron microscopy (c) field-ion microscopy (d) electron probe micro analysis 20. Which of the following phenomenon/phenomena is/are diffusion controlled? (a) dislocation climb (b) cross-slip (c) twinning (d) recrystallization 21. Springback in sheet metal bending depends on: (a) elastic limit (b) bend radius (c) degree of bend (d) thickness of sheet 22. The stacking fault energy of metal A is greater than that of metal B. Then: (a) width of stacking fault ribbons will be larger in metal A (b) screw dislocations will cross-slip more easily in metal A (c) separation distance between partials will be larger in metal B (d) climb of edge dislocations will be faster in metal A 23. The dislocation reaction, ~ [111] + ~ [l I

2

(a) energetically unfavourable (c) vectorially balanced

2

l] ➔ a[l O 0],

in a crystal is:

(b) energetically favourable (d) likely to occur in Zn

24. A case carburized and hardened steel component has: (a) compressive stresses at the surface (b) tensile stresses at the surface (c) compressive stresses in the core (d) tensile stresses in the core 25. Fatigue life is expected to increase by: (a) increasing the size of the sample (b) smooth polishing of the surface of the sample (c) having compressive residual stresses at the surface (d) having tensile residual stresses at the surface 26. The flow curve for a FCC crystal consists of three stages. Which of the following statements are true: (a) stage I is characterized by high work-hardening rate (b) in stage I slip occurs on one slip system (c) in stage II slip occurs on multiple slip systems (d) in stage II dynamic recovery takes place 27. The springback phenomenon in metal sheet bending can be compensated by: (a) bending the part to a smaller than desired radius of curvature (b) bottoming the punch in the die (c) using low temperature bending (d) using high viscosity lubricant

Question Bank

491

28. In a composite, the matrix (a) is always fibrous (b) transfers the load to the reinforcement (c) separates and protects the surface of reinforcement (d) is usually stronger than the reinforcement (e) is never a ceramic 29. The specific modulus: (a) is given by 1/E where E is the elastic modulus (b) is given by Ep where p is density (c) is given by El p (d) is generally low for polymer matrix composites (e) is generally low for metallic materials 30. Metal matrix composites usually: (a) have a heavy metal for matrix (b) have a poorer ductility than the matrix (c) retain their strength at high temperatures than the matrix (d) have a lower elastic modulus than the matrix (e) are reinforced by polymer fibres

Matching Questions 1. Match the following: (a) stacking fault (b) antiphase boundary (c) martensite (d) tilt boundary

(i) (ii) (iii) (iv)

athermal nucleation edge dislocations ordering partial dislocations

2. Match the following: (a) dislocation multiplication (b) fatigue crack nucleation (c) internal friction (d) Coble creep

(i) (ii) (iii) (iv)

intrusions and extrusions Frank-Read source grain boundary diffusion hopping of interstitials

3. Match the following: (a) precipitation of a phase coherent with the matrix (b) cross slip of dislocations (c) order-disorder transition (d) Brinell hardness (e) Vickers hardness (f) Rockwell C

(i) spheroconical indenter (ii) (iii) (iv) (v) (vi)

interfacial energy spherical indenter elastic strain energy stacking fault energy square based pyramidal indenter

492

Question Bank

4. Match the following: (a) precipitation hardening (b) dispersion hardening (c) solid solution hardening (d) grain size strengthening

(i) (ii) (iii) (iv)

Mott and Nabarro's theory Fleischer's theory Hall-Petch relation Orowan mechanism

5. Match the defects with the most suitable NOT method for examining them: (a) porosity (i) acoustic emission (b) lack of fusion in welds (ii) X-ray radiography (c) surface cracks in aluminium casting (iii) ultrasonic test (d) microcrack initiation in austenitic (iv) dye-penetrant inspection S.S. tubing 6. Match the following: (a) line defect (b) point defect (c) area defect (d) volume defect

(i) (ii) (iii) (iv)

vacancy grain boundary voids dislocation

7. Match the following fractographic features with the types of fracture with which they are associated: (a) striations (i) ductile fracture (ii) brittle fracture (b) separated grain facets (c) dimples (iii) fatigue fracture (d) facets, river patterns (iv) intergranular facture 8. Match the following features in tensile stress-strain curves (a) yield drop (i) strain ageing (b) serrations (ii) superplasticity (c) increase in flow stress with plastic (iii) dislocation pinning deformation (d) 1000% uniform strain (iv) dislocation multiplication 9. Match the following: (a) Rockwell hardness (b) Knoop hardness (c) Vickers hardness (d) Meyer hardness

(i) unrecovered projected area of indentation (ii) surface area of indentation (iii) depth of indentation (iv) projected area of indentation

10. Match the following metals and alloys with their slip planes for room temperature deformation: (i) None (a) austenitic stainless steel (b) molybdenum (ii) (1 1 0) (c) cadmium (iii) (1 1 1) (d) tin (iv) (0 0 0 1)

Question Bank

493

Short Questions and Numericals 1. Explain for difference in the elastic strain energy associated with a unit length of an edge dislocation and of a screw dislocation. Ans. The elastic strain energy associated with a unit length of an edge dislocation is greater (1.5 times) than that associated with a unit length of a screw dislocation. It is because of the fact that strain field of an edge dislocation is not as symmetric as that of screw dislocation. 2. Give slip planes for austenite stainless ( 18-8) steel, molybdenum, cadmium and titanium. Ans. The following table shows the desired planes in respective materials. Material

Crystal Structure

Slip Plane

Austenitic (18-8) stainless steel Molybdenum Cadmium

FCC BCC HCP

{1 1 1} {1 1 O}, {1 1 2}

Titanium (pure)

HCP

{110 O}

(0 0 0 1)

3. How are wavy slip lines formed in iron? Ans. Iron has BCC structure. Slip in BCC metals is found to occur on { 1 1 0}, { 1 1 2} and { 1 2 3} planes, while the slip direction is always of the type . There are in all 48 possible slip systems but non of the slip planes is as close as find in FCC structure. Therefore, a relatively higher critical resolved shear stress is required to produce slip. The all above planes belong to < 1 1 l> zone. Multiple slip in iron on { 1 1 0}, { 1 1 2} and { 1 2 3} planes in < 1 1 1> directions, when viewed parallel to the slip direction could then be straight, but, in any other direction, and, particularly normal to the slip direction, would appear wavy. 4. Under what condition does a screw dislocation need a plane to be defined for its movement? Ans. For a screw dislocation the Burgers vector bis parallel to the tangent vector t, any plane that contains the dislocation line defined by b (or equivalently, t) is a potential slip plane. The movement of a screw dislocation can be confined to those sets of planes that possess a low Peierls-Nabarro stress. But for cross-slip, the screw dislocation should have a definite plane defined for its movement. When a screw dislocation is dissociated into a pair of partial dislocations separated by a stacking fault, its motion is confined on the plane containing the stacking fault [the { 1 1 1} plane of the fault] because the partials are edge in character.

5. Write the dislocation reaction for the dissociation of a perfect dislocation in a fee metal into two Shockley partials. Ans. The dissociation of a perfect dislocation (b 1) into two Shockley partials (b 2 and b3) is energetically favourable only if a

-

bf > bi + bf a

--

a

-

- [l O l] ➔ - [2 1 l] +-[112]

2

6

6

494

Question Bank

6. Explain why an extended screw dislocation cannot cross slip unlike a simple screw dislocation. Ans. While whole screw dislocations are free to move (and cause slip) on any of several planes in which they lie, dissociated screw dislocations (also called extended screw dislocations), since they have edge character, can move only in the planes containing the stacking fault. If a dissociated screw dislocation is to change slip plane, its partials must first recombine. Once cross-slip occurs, it again dissociates into different pair of partial dislocations on new slip plane (Figure 12.17). 7. A screw dislocation, having Burgers vector equal to ~[l 1 l], is moving on a plane 2 ( 1 1 0). Give the Miller indices of some other planes belonging to { 1 1 0} family in which this screw dislocation can move if some hindrance to its motion is there on initial plane. Ans. In case of hindrance in the movement of screw dislocation, dislocation can move on any plane (belonging to same family) that contains it. So, the dot product of any such plane (h k 1) with a direction a[l 11] must be zero. The Miller indices of such planes are

(0 1 1), (101), (10 1) and (110). 8. Name the direction in which a dislocation (in a bee metal) can move in (12 3) plane.

Ans.

The direction in which a dislocation (in a bee metal) can move in (1 2 3) plane is of the kind for which the dot product is zero. In general, a direction [h 1 k1 li] lies in the plane (h 2 k2 12 ) only when h1h2 + k1k2 + 1112 = 0. Hence, the desired direction is [111]. The dot product of this direction and the indices of the given plane will yield in a zero value.

9. Determine the stress required to move a dislocation of Burgers vector 3A through a matrix having stress modulus of 80 GPa and containing incoherent precipitates separated by an average distance of 0.3 µm. Ans. The stress required to move a dislocation between two incoherent precipitate particles is equal to Ghil where G is the shear modulus, bis the Burgers vector and l is the distance between two particles.

80xlO00MPax3x10-10 m so stress () r = 6 0.3x10- m = 80 MPa 10. An edge dislocation lies in the plane (2 2 2). This plane is perpendicular to this page, in an iron crystal. Determine the Miller indices of direction of Burgers vector and its length. The lattice parameter of iron is 0.2836 nm. Ans. Burgers vector is perpendicular to edge dislocation. Therefore, direction of Burgers vector will be perpendicular to (2 2 2) plane. Miller indices of direction of Burgers vector will be [2 2 2] or [l 1 l]. The length of Burgers vector is equal to distance between two adjacent (2 2 2) planes. ao d222

=--;:::====== ..j(h2

+k2 +z2)

Question Bank

495

0.2836 nm

=----;:=====

✓(22 + 22 + 22)

0.2836 =---nm 3.464 = 0.0827 nm 11. Calculate the length of the Burgers vector of an edge dislocation in nickel crystal. Ans. Nickel has FCC crystal structure with a lattice parameter of 0.3156 nm. The direction of Burgers vector will be the close packed direction of nickel, i.e. one belonging to . The plane perpendicular to Burgers vector will belong to (1 1 0). Length of Burgers vector =

0.3156 nm / -v(l2 + i2 + 02)

0.3156 =---nm 1.414 = 0.2232 nm 12. What is the density of dislocation in an annealed metal? Ans. In an annealed metal, density of dislocation is typically of the order of 109 m-2. The dislocation density in an annealed crystal ranges from 109 to 10 10 m-2 or m/m 3 • 13. The stacking fault energy of metal A is greater than that of metal B. Comment on relative ease with which edge or screw dislocation can move in these metals. Ans. For a metal to have higher stacking fault energy (SFE) the separation between the partial dislocations constituting the stacking fault is shorter than in metal with low SFE. For an edge dislocation to climb or for a screw dislocation to cross-slip, the two partials must have to recombine. Less work is required for recombination of partials for less separation and therefore a dislocation can move more easily in metal A having high SFE. 14. The stacking fault energy of metal A is greater than that of metal B. Will this difference have any influence on width of stacking fault ribbons? Ans. Yes. The width of stacking fault ribbons is small for the metal A that possesses greater stacking fault energy in accordance with the Eq. 4.44. 15. As related to Burgers vector, what is the characteristic of a mixed dislocation? Ans. Burgers vector of a mixed dislocation is always at an angle to the dislocation line. Alternately, if Burgers vector at a point lying on dislocation line makes an angle with it, the dislocation is said to be mixed in character at that point. 16. Describe a slip system in BCC crystal. Ans. The combination of a slip plane and a slip direction lying in the plane is called a slip system. In BCC crystal, the slip planes are of the type { 1 1 0}, { 1 1 2} and { 1 2 3}. Each of these planes contain the slip direction of the type . The most common slip systems in BCC crystals are of the type { 1 1 0}. There are in all 48 slip systems in BCC metal crystals as shown in Table 5.2.

496

Question Bank

17. What is the relation between energy of a dislocation and its Burgers vector? Ans. Elastic strain energy of a dislocation (edge as well as screw) is proportional to the square of the Burgers vector. This is in accordance with Eqs. (4.15) and (4.17). 18. A copper crystal has two parallel and straight screw dislocations of opposite sign on a slip plane. Calculate its Burgers vector. If they are separated by a distance of 100 nm, calculate the force acting on each dislocation. What is the nature of this force? (Lattice parameter of copper is 0.3615 nm and shear modulus of copper is 45 GPa). Ans.

The Burgers vector of an individual screw dislocation = ~ [l 1 0] 2 Its magnitude is given as =

~ .J1 2 + 12 + 0 2 2

Ji

= 036

nm = 0.256 nm 2

The force on each dislocation = Gb 2nr

45 X 10 9 Nim 2 X (0.256) 2 X (10-9) 2 m 2 2x3.142xl00xl0-9 m

=---------------

= 45 X 0.256 X 0.256 Nim 2 X 3.142 X 100 = 4.693 x 10-3 Nim Thus, the force per unit length acting on each dislocation is 4.693 x 10-3 Nim and is of attractive type. 19. Cross-slip can occur in BCC and FCC metals, but cannot occur in HCP metals. Explain. Ans. BCC and FCC metals contain non-parallel slip planes and as a result of it a number of intersecting slip systems are available. Consequently, cross-slip is possible in such metals. In HCP metals, in general, cross-slip cannot occur as slip planes are parallel, and hence, intersecting slip systems are not available. 20. The alloying of an FCC metal X with a small amount of Y reduces its stacking fault energy from 200 ergslcm2 to 150 ergslcm2 • Assuming identical Burgers vectors of the partials for an extended dislocation in metal X and alloy X-Y. (a) indicate whether increase or decrease in the equilibrium spacing between the partials would occur by alloying and (b) calculate the percentage change in the equilibrium spacing between the partials by alloying. Ans. (a) Alloying of metal X with small amount of Y will result is increase in equilibrium spacing due to decrease of SFE. (b) The spacing between the partial dislocations is given by Eq. (4.44), i.e. Gb 2 24,r,ys

d =--

s

Question Bank

497

Since G, b and 7r are constant terms, we can write ds

=.!5_ Ys

d -

or

i -

.!5_ - _.!5__ and d 2 - .!5_ = _.!5__ Yi - 200 Y2 150

Per cent change in equilibrium spacing = d 2 - di x 100 di

= 0.0066 K - 0.005 K x lOO 0.005 K = 32 Thus, the per cent change in equilibrium spacing between partials is 32. 21. A straight dislocation in copper has a Burgers vector parallel to [l 1 0] direction and the dislocation line is parallel to [0 1 l] direction. (a) What is character and slip plane of the dislocation? (b) Given the lattice parameter of copper to be 0.362 nm, calculate the magnitude of Burgers vector. Ans. (a) As the Burgers vector is parallel to [l 1 0] direction and dislocation line is parallel to [0 1 1] direction, the angle ( 0) between the Burgers vector and dislocation line is =cos

1 XO + 1 X 1 + 0 X 1

-i

✓i2 + i2 + 02 ✓02 + 12 + i2

= 60° y

we know that when the Burgers vector is at an angle to dislocation line, then the dislocation is mixed dislocation. X The plane containing dislocation line and the Burgers FIGURE 5 vector has been shown in Figure 5. Miller indices of this plane is (1 1 1). The cross product of the dislocation line (i.e. tangent vector) and the Burgers vector gives the indices of the plane containing it. Thus, cross product of [l 1 0] and [0 1 l] yields the indices of the desired plane. (b) Burgers vector for a face centred cubic crystal structure is equal to ~ [110] where 2

a is the lattice parameter. So,

Burgers vector

= 0.362 nm

✓l2 + i2 + 0 2

2

0.362 nm = - ~ - = 0.256 nm ✓ 2

498

Question Bank

22. Explain why an edge dislocation line does not experience any force on it unless subjected to external load. Ans. Atoms, around the both sides of a dislocation line are symmetrically placed (refer Figure 4.6). Due to the presence of equal and opposite forces acting on dislocation line, an edge dislocation does not experience any force. That is the net force acting on the dislocation is zero. Such a state will be disturbed on applying external force and under this state, edge dislocation will experience some net force on itself. 23. A dislocation does not/cannot end abruptly inside a crystal. Why? Ans. A dislocation can end inside a crystal only when Burgers vector value is changing along the dislocation line and is equal to zero at the end point. Since Burgers vector is invariant along the whole length of the dislocation line, a dislocation does not/cannot end abruptly inside a crystal. However, a dislocation can extend from one surface to another surface, one surface to a grain boundary or from one surface to another dislocation. A dislocation can form a closed loop in the crystal. 24. Explain the meaning of the statement "Burgers vector of a dislocation is invariant. Ans. This statement means that for a dislocation, the magnitude and direction of Burgers vector is same throughout the dislocation line. (See Figure 4.10) 25. Explain why dislocations have Burgers vector as small as possible. Ans. Elastic strain energy of a dislocation is proportional to the square of Burgers vector. Therefore, the overall energy of a crystal having dislocation will be minimum only when the Burgers vector will be as small as possible. 26. Explain the significance of close packed planes and direction with reference to process of slip. Ans. For a given crystal structure, the smallest shear distance during the process of slip that maintains the periodicity of the crystal structure is equal to an inter-atomic distance (spacing) between the atoms lying in the close-packed direction in close packed plane. Further close packed planes have lowest lattice frictional stress and are the most widely separated ones. 27. Cross slip is easier in aluminium and not in copper and nickel though all the three have FCC crystal structure. Explain. Ans. Stacking fault energy for aluminium (0.2 J/m2) is much higher than the stacking fault energies for copper (0.04 J/m2) and nickel (0.03 J/m 2). This is why cross-slip is easier in aluminium and not in copper and nickel. 28. A large substitutional atom, in a given material, prefers to accommodate itself in the region where atoms are in the state of tension. Why? Ans. Atoms surrounding the extra-half plane of atoms above the slip plane are in a state of compression while those below the slip plane are in a state of tension. Introduction of extra-half plane raises the internal energy due to elastic distortion created in the crystal in vicinity to the edge of the extra-half plane. A large substitutional atom prefers to accommodate itself in the region where atoms are in a state of tension as it results in lowering of distortional energy. Similarly, substitution of a smaller atom in the region

Question Bank

499

where the host atoms are in a state of compression will lower the distortional energy (i.e. elastic strain energy) of the crystal. 29. What is Cottrell's atmosphere and what is its importance? Ans. Small interstitial atoms tend to occupy positions in the region where atoms are in a state of tension. It lowers the elastic strain energy of the crystal. An interstitial atom that is of larger size than that of the interstitial void, lowers the elastic strain energy by sitting in the core of an edge dislocation (tension side). Such a state (interaction between interstitial solute atom and edge dislocation) is called Cottrell's atmosphere (Figure 8.14). Cottrell's atmosphere explains the mechanisms of phenomenon of yield point, strain aging and solid solution hardening. For details of these phenomena, refer to Sections 8.6, 11.5 and 6.3 respectively. 30. From what experimental measurements can the density of dislocations be deduced? Ans. (a) Measurement of etch pit density (b) Transmission electron microscope (c) Measurements of the stored energy by cold working 31. Describe the etch pit technique of observing dislocations. Ans. In etch pit technique of observing dislocations, a suitable etchant is applied on the surface of the specimen under examination. The etchant produces pits at the points where dislocations intersect the surface. The etch pits are produced at dislocation sites because of the elastic strain field that surrounds them and cause preferential chemical attack.

32. What do dislocation etch pits show? Ans. A dislocation etch pit shows that the material in vicinity to a dislocation is chemically more active than the bulk material in the absence of a dislocation. 33. On what crystallographic systems does slip take place in (i) FCC metals and (ii) HCP metals? Ans. (i) Slip takes place on { 1 1 1} type planes and in type directions in FCC metals. The slip systems are represented as { 1 1 1 }. (ii) Slip in HCP metals takes place on {O O O 1} planes and in < 1120 > directions. The slip systems are represented as {0 0 0 1 } < 11 2 0 > . For other slip systems refer Table 5.2. 34. Distinguish between slip and twinning. Ans. Slip is the parallel motion of two parallel, adjacent crystal planes relative to one another. Twinning is a homogeneous shear which reorients the deformed lattice into a mirror image of the parent lattice with respect to plane of twinning. 35. A zinc single crystal is oriented with the normal to the basal plane making an angle 60° with the tensile axis, and the three slip directions making angles 38°, 45° and 84° with the tensile axis. If plastic deformation is first observed at a tensile stress of 80 MPa, calculate the critical resolved shear stress for zinc. Ans. The critical resolved shear stress is given as: 'l'crss

=

(J' COS

and A are shown in Figure 6. The angle q>

Since

= 60°

so cos q>

= l/2 = 0.5

,1 = 38°

⇒

cos A= 0.788

= 45°

⇒

cos A= 0.707

= 84°

⇒

cos ,1

a=

r

crss

cos q> cos

N

--- Tensile axis

Slip direction

= 0.105

Slip plane

A must be minimum

So cos q> cos A must be maximum Therefore, A = 38° for cos q> cos A to be maximum Then,

cos q> cos A= 80 (0.5) (0.788)

rcrss

=

rcrss

= 31.52 MPa.

(J

FIGURE 6

36. The minimum tensile stress of a series of differently oriented cadmium crystal specimens was found to be 1.8 MPa. Calculate the critical resolved shear stress of the material. Ans. The critical resolved shear stress is given as: rcrss

=

a cos

q> cos A

For minimum tensile stress to initiate plastic deformation cos q> cos A must be maximum. For this, A must be 45° such that cos q> = cos A= cos 45° = 1/2 [ and A as per Figure 6]. For minimum tensile stress of 1.8 MPa, or

rcrss

= l. 8/2

rcrss

= 0.9 MPa

37. Single crystals are very much weaker than they theoretically should be, because dislocations can operate to produce slip at low values of resolved shear stress. In what way can the presence of grain boundaries in polycrystals lead to higher yield strengths than those of single crystals? Ans. A single crystal deformed under tension is usually free to deform on a single slip system for a large plastic deformation and change its orientation by lattice rotation as deformation continues. During deformation, dislocations are able to move over relatively large distances without encountering barrier and eventually escape from the crystal at surface. This is in accordance with stage I of deformation called 'easy glide' of single crystal (Figure 5.15). In a polycrystal, the presence of grain boundaries eliminate stage I of deformation by preventing the dislocations from escaping from properly oriented grains. Since at the grain boundary, the slip plane is no longer continue, dislocation pile-up occurs there in favourably oriented grains. As a consequence a back stress is developed at the dislocation source which raises the stress required for further deformation to take place. The resulting stress distribution caused by dislocation pile-up results in deformation by multiple slip in most grains and produces strengthening (stage II of Figure 5.15).

Question Bank

501

38. The modulus of elasticity of a steel is 200 GPa. What tensile stress is required along the corresponding crystallographic direction in order to increase the interatomic separation distance by 0.07%? Ans.

The elastic modulus is given as: E Given E

= 200 GPa,

=