Multifunctional Composites [1, 1 ed.] 151680452X, 9781516804528

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Multifunctional Composites

Other notable work from the Author • Introduction to Composite Materials Design–Second Ed., CRC Press (2011). ISBN: 978-1-4200-7915-9. • Workbook for Introduction to Composite Materials Design, CreateSpace (2014). ISBN: 978-1-5075-5195-0. • Finite Element Analysis of Composite Materials Using AbaqusTM , CRC Press (2013). ISBN: 978-1-4665-1661-8. R , Sec• Finite Element Analysis of Composite Materials Using ANSYS

ond Ed., CRC Press (2014). ISBN: 978-1-4665-1689-2. • Book Series: Composite Materials: Analysis and Design, CRC Press. • Computer Aided Design Environment for Composite Materials (CADEC) software, on the Web at http://cadec-online.com • Further information is available at the author’s Website: http://barbero.cadec-online.com

Multifunctional Composites

Ever J. Barbero (editor) West Virginia University, USA

Cover photo by Don Cochrane Multifunctional Composites c (2016) Ever J. Barbero. All rights reserved Copyright REVISION D ECEMBER 9, 2015 ISBN-13: 978-1516804528 ISBN-10: 151680452X Imprint by CreateSpace 4900 Lacross Rd, North Charleston, SC 29406 CreateSpace is a DBA of On-demand Publishing LLC, part of the Amazon group Book and cover design created by the editor. Graphics created by the editor or available in the public domain. No claim to original U.S. government works. Product or corporate names, which may be trademarks or registered trademarks, are used only for identification and explanation, without intent to infringe. This book contains information obtained from authentic and highly regarded sources but the chapter authors, editor, and publisher do not assume responsibility for the validity of all materials or consequences of their use. If any copyrighted material has not been acknowledged, please contact the editor so that we can rectify any omission as soon as possible. Except as permitted under U.S. copyright law, no part of this book may be reprinted, reproduced, transmitted, translated, or distributed in any form, by any means, in any media, without written permission from the editor. To obtain permission to reproduce artwork or any portion of this work, please contact the editor. Posting on websites, blogs, peer-to-peer networks, or any other publicly accessible distribution media is forbidden.

Dedicado a la memoria de mi madre, Sonia Eulalia Phillpott de Barbero (1935–2014)

Contents Aims and scope

xv

Acknowledgments

xviii

Errata

xviii

Contributors

xix

1 Electromagnetic effects, Ernest K. Condon III and Paul J. 1.1 Major design areas for electromagnetic effects . . . . . . 1.1.1 Electromagnetic compatibility . . . . . . . . . . . 1.1.2 Electromagnetic interference . . . . . . . . . . . 1.1.3 Electrical bonding and grounding . . . . . . . . . 1.1.4 Direct effects of lightning . . . . . . . . . . . . . 1.1.5 Indirect effects of lightning . . . . . . . . . . . . 1.1.6 Precipitation static . . . . . . . . . . . . . . . . . 1.1.7 High intensity radiated field . . . . . . . . . . . . 1.1.8 Power distribution . . . . . . . . . . . . . . . . . 1.1.9 Electrostatic discharge . . . . . . . . . . . . . . . 1.1.10 Nuclear electromagnetic pulse . . . . . . . . . . . 1.1.11 Atmospheric radiation . . . . . . . . . . . . . . . 1.1.12 Antenna performance . . . . . . . . . . . . . . . 1.2 Primary physical characteristics affecting EME . . . . . 1.2.1 Conductivity/resistivity . . . . . . . . . . . . . . 1.2.2 Shielding effectiveness . . . . . . . . . . . . . . . 1.2.3 Contact resistance . . . . . . . . . . . . . . . . . 1.3 Test/analysis methods . . . . . . . . . . . . . . . . . . . 1.3.1 Conductivity/resistivity . . . . . . . . . . . . . . 1.3.2 Shielding effectiveness . . . . . . . . . . . . . . . 1.4 Specific impacts to EME and mitigation approaches . . 1.4.1 Electromagnetic compatibility . . . . . . . . . . . 1.4.2 Electromagnetic interference (EMI) . . . . . . . . 1.4.3 Electrical bonding and grounding . . . . . . . . . 1.4.4 Direct effects of lightning . . . . . . . . . . . . . 1.4.5 Indirect effects of lightning . . . . . . . . . . . . vii

Jonas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1 1 2 2 3 3 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 9 9 9 11 12 13

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Multifunctional Composites 1.4.6 Precipitation static . . . . . . 1.4.7 High intensity radiated field . 1.4.8 Power distribution . . . . . . 1.4.9 Electrostatic discharge . . . . 1.4.10 Nuclear electromagnetic pulse 1.4.11 Atmospheric radiation . . . . 1.4.12 Antenna performance . . . . 1.5 Conclusions . . . . . . . . . . . . . . Bibliography . . . . . . . . . . . . . . . .

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2 Lightning strike protection systems, Gasser F. Abdelal 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Experimental verification . . . . . . . . . . . . . . . . . 2.3 Virtual verification . . . . . . . . . . . . . . . . . . . . . 2.4 Free electric arc model . . . . . . . . . . . . . . . . . . . 2.4.1 Formulation . . . . . . . . . . . . . . . . . . . . . 2.4.2 Electric module (ec) and Magnetic module (mf) 2.5 Similitude modeling . . . . . . . . . . . . . . . . . . . . 2.6 Numerical simulation . . . . . . . . . . . . . . . . . . . . 2.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . .

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25 25 31 33 46 48 48 50 53 54 57

3 Toughening for impact damage, Timothy L. Norman and 3.1 Low velocity impact . . . . . . . . . . . . . . . . . . . . 3.2 Low velocity impact testing . . . . . . . . . . . . . . . . 3.3 Impact damage characterization . . . . . . . . . . . . . . 3.3.1 Impact surface inspection . . . . . . . . . . . . . 3.3.2 X-ray analysis . . . . . . . . . . . . . . . . . . . 3.3.3 Ultrasonic c-scan . . . . . . . . . . . . . . . . . . 3.3.4 Cross sectional analysis using photomicrographs 3.4 Modes of failure in low velocity impact . . . . . . . . . . 3.4.1 Matrix cracking and transverse shear cracking . . 3.4.2 Delamination . . . . . . . . . . . . . . . . . . . . 3.4.3 Fiber breakage . . . . . . . . . . . . . . . . . . . 3.5 Post-impact residual properties . . . . . . . . . . . . . . 3.5.1 Residual compressive strength . . . . . . . . . . . 3.5.2 Residual tensile strength . . . . . . . . . . . . . 3.6 Approaches to reduce low velocity impact damage . . . 3.6.1 Enhancements to fiber, matrix, and interphase . 3.6.2 Nanoparticles/Nanotubes . . . . . . . . . . . . . 3.6.3 Self-healing fiber reinforced composites . . . . . . 3.6.4 Hybridization . . . . . . . . . . . . . . . . . . . . 3.6.5 Textile composites . . . . . . . . . . . . . . . . . 3.6.6 Stitching . . . . . . . . . . . . . . . . . . . . . . 3.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . .

C. T. Sun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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61 61 65 66 66 66 66 68 68 68 69 70 70 72 72 72 73 76 79 80 81 83 89

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Table of Contents

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Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4 Erosion resistance, Edmond Tobin, Aidan Cloonan, and Trevor Young 4.1 Liquid droplet erosion . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Erosion mechanism . . . . . . . . . . . . . . . . . . . . . . . . 4.1.2 Test methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.3 Theoretical models . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Solid particle erosion . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 SPE performance of neat polymers . . . . . . . . . . . . . . . 4.2.2 Effects of particulate and fibrous components . . . . . . . . . 4.2.3 Solid particle erosion mechanisms . . . . . . . . . . . . . . . . 4.2.4 Design considerations for composites subjected to SPE . . . 4.2.5 SPE test methods . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Other degradation mechanisms . . . . . . . . . . . . . . . . . . . . . 4.4 Application examples . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1 Surface protection for wind turbine blades . . . . . . . . . . . 4.4.2 Surface protection for propellers and helicopter rotor blades . 4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

99 99 100 104 109 113 113 114 115 117 118 121 122 122 123 124 125

5 Acoustic and vibration damping, Edith R. Fotsing, Annie Ross, and Edu Ruiz 133 5.1 Introduction and definitions . . . . . . . . . . . . . . . . . . . . . . . 133 5.2 Aircraft engine acoustic damping . . . . . . . . . . . . . . . . . . . . 138 5.2.1 Porous materials . . . . . . . . . . . . . . . . . . . . . . . . . 141 5.2.2 Impedance tube . . . . . . . . . . . . . . . . . . . . . . . . . 142 5.3 Damping of composites in aerospace . . . . . . . . . . . . . . . . . . 145 5.3.1 Structural passive damping . . . . . . . . . . . . . . . . . . . 145 5.3.2 Active vibration damping . . . . . . . . . . . . . . . . . . . . 148 5.4 Viscoelasticity principles . . . . . . . . . . . . . . . . . . . . . . . . . 148 5.4.1 Damping materials . . . . . . . . . . . . . . . . . . . . . . . . 151 5.4.2 Recent developments in damping materials . . . . . . . . . . 151 5.5 Viscoelastic material characterization . . . . . . . . . . . . . . . . . . 153 5.5.1 Dynamic mechanical analysis . . . . . . . . . . . . . . . . . . 153 5.6 New trends in passive damping . . . . . . . . . . . . . . . . . . . . . 155 5.6.1 Viscoelastic layers embedded into composite laminates . . . . 155 5.6.2 Analytical modeling of structural damping . . . . . . . . . . 158 5.6.3 Embedded damping elements into composites . . . . . . . . . 160 5.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 6 Viscoelastic damping treatments, Rui A.S. Moreira 169 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 6.2 Viscoelastic damping treatments . . . . . . . . . . . . . . . . . . . . 170 6.2.1 Unconstrained layer damping treatments . . . . . . . . . . . . 171

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Multifunctional Composites 6.2.2 Constrained layer damping treatments . . . . . . . . . 6.2.3 Integrated layer damping treatments . . . . . . . . . . 6.3 Viscoelastic materials . . . . . . . . . . . . . . . . . . . . . . 6.3.1 Experimental characterization of VEMs . . . . . . . . 6.3.2 Experimental data analysis and constitutive model . . 6.3.3 Experimental characterization of VEMs – case study . 6.4 Numerical simulation of viscoelastic damping treatments . . . 6.4.1 Spatial model of layered structures . . . . . . . . . . . 6.4.2 Viscoelastic constitutive models . . . . . . . . . . . . . 6.4.3 Analysis method . . . . . . . . . . . . . . . . . . . . . 6.5 Multilayer and multi material damping treatments . . . . . . 6.6 Optimization of viscoelastic damping treatments . . . . . . . 6.6.1 Partial damping treatments . . . . . . . . . . . . . . . 6.6.2 Optimized multilayer damping treatments . . . . . . . 6.6.3 Special spatial configurations . . . . . . . . . . . . . . 6.6.4 Hybrid damping treatments . . . . . . . . . . . . . . . 6.7 Design of viscoelastic damping treatments: fundamental rules 6.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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172 172 172 173 177 178 180 181 184 185 188 189 189 190 191 192 193 197 199

7 Self-healing in polymers and structural composites, Kathryn Mireles and Micheal R. Kessler 205 7.1 Introduction to self-healing polymers . . . . . . . . . . . . . . . . . . 205 7.2 Self-healing systems: background and design . . . . . . . . . . . . . . 207 7.2.1 Transport assisted self-healing . . . . . . . . . . . . . . . . . 207 7.2.2 Homogeneous self-healing . . . . . . . . . . . . . . . . . . . . 212 7.2.3 Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 7.3 Self-healing structural polymer composites . . . . . . . . . . . . . . . 217 7.3.1 Background and applications of fiber reinforced composites . 217 7.3.2 Self-healing ‘smart’ composite systems . . . . . . . . . . . . . 221 7.4 Evaluation of self-healing effects . . . . . . . . . . . . . . . . . . . . . 221 7.4.1 Effect on structural properties . . . . . . . . . . . . . . . . . 221 7.4.2 Self-healing efficiency and mechanical properties . . . . . . . 222 7.4.3 Theoretical considerations . . . . . . . . . . . . . . . . . . . . 226 7.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 7.5.1 Summary of challenges . . . . . . . . . . . . . . . . . . . . . . 227 7.5.2 Current state and future directions . . . . . . . . . . . . . . . 229 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 8 Microvascular transport, Christopher J. Hansen 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Biological inspiration . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.1 System approach to microvascular transport . . . . . . . . 8.2.2 Structural biocomposites with embedded microvasculature 8.3 Engineering design of microvascular transport . . . . . . . . . . .

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Table of Contents 8.3.1 Physics of microfluidic transport . . . . . . 8.3.2 Mechanics of embedded vasculature . . . . 8.3.3 Network design . . . . . . . . . . . . . . . . 8.3.4 Pump considerations . . . . . . . . . . . . . 8.3.5 Tools for optimized design . . . . . . . . . . 8.4 Composites processing . . . . . . . . . . . . . . . . 8.4.1 Discrete fluid reservoirs . . . . . . . . . . . 8.4.2 Subtractive manufacturing processes . . . . 8.4.3 Additive manufacturing processes . . . . . . 8.4.4 Non-woven fiber-based processes . . . . . . 8.4.5 Woven textile-based processes . . . . . . . . 8.5 Measurement of microvascular-based functionality 8.5.1 Fluid transport . . . . . . . . . . . . . . . . 8.5.2 Mechanical effects . . . . . . . . . . . . . . 8.5.3 Thermal profile . . . . . . . . . . . . . . . . 8.6 Embodiments of microvascular composites . . . . . 8.6.1 Self-healing . . . . . . . . . . . . . . . . . . 8.6.2 Thermal regulation . . . . . . . . . . . . . . 8.6.3 Structural health monitoring . . . . . . . . 8.6.4 Structural fluid storage . . . . . . . . . . . 8.6.5 Recovery of macroscale mass loss . . . . . . 8.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . Bibliography . . . . . . . . . . . . . . . . . . . . . . . .

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241 242 245 246 247 248 248 248 249 250 252 252 253 253 253 254 254 258 260 260 261 261 263

9 Permeation, Shaokai Wang and Ayou Hao 271 9.1 Introduction to gas permeation . . . . . . . . . . . . . . . . . . . . . 271 9.2 Gas permeation through polymeric materials . . . . . . . . . . . . . 273 9.3 Structure and properties of barrier nanoparticles . . . . . . . . . . . 274 9.3.1 Silicate clay . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274 9.3.2 Graphene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274 9.3.3 Other fillers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276 9.4 Theoretical analysis of gas permeation . . . . . . . . . . . . . . . . . 277 9.5 Fabrication process of polymer nanocomposites . . . . . . . . . . . . 280 9.5.1 Conventional approaches for uniformly dispersed nanocomposite281 9.5.2 Preparation for nanolaminate structure . . . . . . . . . . . . 282 9.6 Influence factors and enhancement of barrier properties . . . . . . . 283 9.6.1 Geometric factors of barrier nanoplatelets . . . . . . . . . . . 283 9.6.2 Influence of swelling in humid environments . . . . . . . . . . 284 9.6.3 Alignment of nanofillers . . . . . . . . . . . . . . . . . . . . . 286 9.6.4 Influence of hydrophilic or hydrophobic nature . . . . . . . . 287 9.6.5 Enhancement of tortuosity . . . . . . . . . . . . . . . . . . . 288 9.6.6 Barrier properties of typical polymer nanocomposites . . . . 292 9.7 Multifunctional characteristics of barrier materials . . . . . . . . . . 292 9.8 Application of barrier materials . . . . . . . . . . . . . . . . . . . . . 294 9.8.1 Fiber-reinforced composites . . . . . . . . . . . . . . . . . . . 294

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Multifunctional Composites 9.8.2 Electronics industry . . 9.8.3 Food packaging . . . . . 9.8.4 Anti-corrosion coatings 9.9 Conclusions . . . . . . . . . . . Bibliography . . . . . . . . . . . . .

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10 Fire safety, Ning Tian and Aixi Zhou 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 Mechanisms of ignition and fire growth . . . . . . . . . . 10.3 Fire safety objectives and strategies . . . . . . . . . . . 10.4 Fire properties of PMC materials . . . . . . . . . . . . . 10.4.1 Fire reaction properties . . . . . . . . . . . . . . 10.4.2 Fire resistance properties . . . . . . . . . . . . . 10.5 Mechanisms for improving the fire performance of PMCs 10.5.1 Halogen-based fire retardants (HFRs) . . . . . . 10.5.2 Phosphorus-based flame retardants (PFRs) . . . 10.5.3 Intumescent flame retardants (IFRs) . . . . . . . 10.5.4 Mineral filler flame retardants (MFRs) . . . . . . 10.6 New developments . . . . . . . . . . . . . . . . . . . . . 10.6.1 Nanofiller fire retardants . . . . . . . . . . . . . . 10.6.2 Synergy with traditional FRs . . . . . . . . . . . 10.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . .

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305 305 307 308 310 311 315 316 317 318 319 321 322 322 323 327 327

11 Thermal protection systems, Maurizio Natali, Luigi Torre, and Jos´e Maria Kenny 337 11.1 The hyperthermal environment . . . . . . . . . . . . . . . . . . . . . 337 11.2 Non-ablative TPS materials . . . . . . . . . . . . . . . . . . . . . . . 339 11.2.1 NA-TPS on the Space Shuttle . . . . . . . . . . . . . . . . . . 339 11.2.2 SSO reusable surface insulation . . . . . . . . . . . . . . . . . 341 11.2.3 Conclusion remarks on non-ablative TPS materials . . . . . . 342 11.3 High temperature composites as polymeric ablatives . . . . . . . . . 342 11.4 Testing facilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348 11.4.1 The oxy-acetylene torch testbed - OATT . . . . . . . . . . . 349 11.4.2 The simulated solid rocket motor - SSRM . . . . . . . . . . . 349 11.4.3 Plasma jet torches . . . . . . . . . . . . . . . . . . . . . . . . 351 11.4.4 Recession rate sensing techniques for TPSs . . . . . . . . . . 352 11.5 PAs as thermal insulating materials . . . . . . . . . . . . . . . . . . 356 11.5.1 Rigid HSMs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356 11.5.2 Flexible HSMs for TPSs . . . . . . . . . . . . . . . . . . . . . 356 11.5.3 Elastomeric HSMs for SRMs . . . . . . . . . . . . . . . . . . 357 11.6 Phenolic impregnated carbon ablators . . . . . . . . . . . . . . . . . 359 11.7 Differences between FRPAs and LCAs . . . . . . . . . . . . . . . . . 360 11.8 Nanostructured ablative materials . . . . . . . . . . . . . . . . . . . 360 11.8.1 Nanosilica as filler for traditional and nanostructured ablatives 363

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11.8.2 Carbon nanofilaments based NRAMs . . . . . . . . . . . . . . 366 11.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369 12 Magnetoelectric composites, Tomas I. Muchenik and Ever J. Barbero 12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1.1 Electrostatics . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1.2 Magnetostatics . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1.3 Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1.4 Direct magnetoelectric effect . . . . . . . . . . . . . . . . . . 12.1.5 Historical review . . . . . . . . . . . . . . . . . . . . . . . . . 12.1.6 ME effect in composite materials . . . . . . . . . . . . . . . . 12.2 Particulate ME composites . . . . . . . . . . . . . . . . . . . . . . . 12.3 Laminated composites . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.1 Materials selection . . . . . . . . . . . . . . . . . . . . . . . . 12.3.2 Layer thickness . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.3 Bonding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.4 Orientation of the electric and magnetic fields . . . . . . . . . 12.3.5 Resonance frequency . . . . . . . . . . . . . . . . . . . . . . . 12.4 ME thin films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.4.1 ME thin films characterization . . . . . . . . . . . . . . . . . 12.5 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.5.1 Magnetic sensors . . . . . . . . . . . . . . . . . . . . . . . . . 12.5.2 ME harvesters . . . . . . . . . . . . . . . . . . . . . . . . . . 12.6 Constitutive equations . . . . . . . . . . . . . . . . . . . . . . . . . . 12.7 Geometric configurations . . . . . . . . . . . . . . . . . . . . . . . . . 12.8 Intrinsic properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.8.1 Summary of intrinsic properties . . . . . . . . . . . . . . . . . 12.9 Extrinsic ME properties . . . . . . . . . . . . . . . . . . . . . . . . . 12.9.1 Extrinsic ME voltage coefficient . . . . . . . . . . . . . . . . . 12.9.2 Extrinsic ME charge coefficient . . . . . . . . . . . . . . . . . 12.9.3 Extrinsic ME coupling factor . . . . . . . . . . . . . . . . . . 12.10Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

377 377 377 379 379 380 380 381 385 389 390 391 392 392 393 394 394 395 395 396 398 401 402 406 407 409 412 415 417 418

Index

425

xiv

Multifunctional Composites

Aims and scope Multifunctional composites refer to composite materials that are specifically made, or modified, to provide more than one enhanced property, or functionality. Composites’ main traditional functionalities have been high structural stiffness and strength with the lowest possible weight. Although polymer matrix composites have other advantages such as corrosion resistance, they also bear shortcomings such as relatively poor acoustic damping, damage under impact, and vulnerability to erosion. Multifunctional composites transcend these weaknesses by providing added functionalities without adversely affecting the signature high stiffness and strength densities of composites. For example, carbon nanotubes incorporated into composites enhance electrical conductivity. Added functionalities can be active, such as active vibration control or passive ones such as constrained layer damping. By the very nature of their processing and fabrication, multifunctional composites can not only enhance properties, but include functionalities which do not exist at all in classical composites, such as self-healing and microvascular transport. From ameliorating relative weaknesses to providing functionalities that do not exist in classical materials, the study of multifunctional composites has become a vibrant area of research and development. The aim of this book is to provide researchers and practitioners with a comprehensive introduction to the subject, from which they can advance to performing state-of-the art research or translate current advances into commercial products. After studying this book, the reader will have a broad understanding of the challenges and opportunities afforded by various functionalities that affect the application of composite materials to aircraft and other weight sensitive structures. Prepared by this solid understanding of the field, the reader will then be ready to tackle further technical papers specifically related to individual properties of interest. Each chapter deals with a different functionality. To achieve the aim of this book, the scope entails a full and instructive description of each. Each chapter therefore includes: (a) a brief description of the physics of the function or property that is being added or improved; (b) a brief description of testing and analysis methods used to quantify that functionality; (c) a review of contemporary approaches that implement or improve the functionality, which may include new process and materials development. The relative emphasis within these sections varies from chapter to chapter, as the current state of understanding, characterization, and materials development varies greatly among the functionalities addressed in this book. Furthermore, each chapter draws on the unique expertise of its author. As subject xv

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expert, each author is best suited to determine the most fitting presentation of the chapter’s subject matter. Composites are commonly utilized in aircraft, and are routinely subjected to a variety of electromagnetic effects, including static precipitation, high intensity radiated fields, electrostatic discharge, nuclear electromagnetic pulses, atmospheric radiation, and others, as described in Chapter 1. These effects are especially threatening to composites, which have lower conductivity and higher contact resistance than aluminum. This complicates efforts to provide shielding, grounding, and other features protecting the aircraft from electromagnetic phenomena. In addition, lighting strikes on aircraft cause both direct effects (Chapter 2) and indirect effects (Chapter 1). Alternative materials which mitigate both classes of effects are described in detail in Chapters 1 and 2. Despite their outstanding in-plane strength, laminated composites are susceptible to damage when subject to low velocity/low energy impact normal to their surfaces, as discussed in Chapter 3. The main property affected is compression after impact (CAI), which is the controlling design property in many applications. Although there are many ways to toughen a laminated composite (described in Chapter 3), these solutions tend to degrade some of the in-plane strengths. Therefore, careful consideration should be given during material selection and structural design. Erosion of polymer matrix composites (PMC) is a very complex problem involving removal of surface material by repetitive impact of raindrops or sand, as described in Chapter 4. The result is a roughened surface that may compromise aerodynamic performance, optical and radiation transmission, and even compromise the structural integrity of the part. Aircraft, rotorcraft, windmills, and missiles are among the applications negatively affected by erosion. Multifunctional composites can meet the crucial challenge of protecting against erosion or increasing the erosion resistance of PMCs. Composites have conquered aerospace markets due to their high strength to weight ratio, but their subsequent high stiffness to weight ratio facilitates the spread of acoustic and mechanical vibration. This disadvantage causes passenger discomfort and even mechanical damage. Despite the inherent damping capacity of the polymer matrix, energy dissipation in composites may be insufficient for high performance applications. Therefore, new materials, manufacturing processes, and design methods continue to be developed to improve the damping performance of composite structures. Chapter 5 introduces the problem, emphasizing materials, solutions, and design. Chapter 6 further discusses viscoelastic damping treatments and their design, numerical simulation, and optimization. Healing is no longer a power exclusive to live organisms, but an ability that has been thoroughly implemented in various composites which are now able to selfrepair many types of damage, including distributed intralaminar cracking, large delaminations, erosion damage, and damage to anti-corrosion coatings. These and other fascinating aspects of this innovative technology can be seen in Chapter 7. Early in their development, self-healing ingredients were incorporated into the composite during fabrication, in a process similar to interleaving tough layers be-

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xvii

tween laminas to improve impact resistance (Chapter 3). The problem with that approach is that the self-healing agent is eventually depleted. To circumvent this obstacle, microvascular transport technology was created to deliver healing agents, and eventually many other fluids, throughout the composite. This technology mirrors the microvascular systems present in living organisms (Chapter 8). Since polymers are more permeable to gases than metals, PMCs have faced challenges as materials for gas storage tanks, requiring metal liners that introduce their own problems, or polymer liners that themselves must be highly impervious. Other products such as food packaging, anti-corrosion coatings, fire resistance (Chapter 10), and thermal protection systems (Chapter 11) also benefit from lower gas permeability. Nanotechnologies applied to composites can solve these challenges, as discussed in Chapter 9. Vulnerabilities to fire such as ignitability, flame spread, heat release, smoke opacity, and toxicity, and consequent fire resistant properties including thermal insulation, structural integrity, and residual bearing capacity, are crucial factors determining whether a material can be used in any application where human life is at risk. These applications encompass the wide fields of transportation and architecture among others. Chapter 10 thoroughly investigates the problem of measuring composites’ fire safety, as well as new approaches for improvement. Chapters 9 and 10 provide a natural introduction for Chapter 11: Thermal protection systems (TPS), concerning design of materials that protect an underlying structure such as a spacecraft from the tremendously harsh environment of atmospheric re-entry. TPS are also widely applicable in other situations that pose simultaneous challenges of thermal gradient and load that no classical material can meet. Finally, Chapter 12 introduces a new type of composite able to generate a physical response that is completely absent from any of its constituents. The specific example illustrated involves composites that produce electricity when excited by a magnetic field; a peculiar response that neither of the two constituents (a piezoelectric and a magnetostrictive phase) could produce alone. This is in stark contrast to classical additive composites, in which added components amplify existing attributes. For instance, a fiber might increase the stiffness already present in the matrix. This new class of composites, termed product composites, opens up new possibilities for previously unimagined material responses.

Ever J. Barbero Morgantown, WV

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Acknowledgments This book is the result of the dedicated effort of twenty four authors for twelve chapters. I wish to thank all of them for their distinguished contribution. Also, I wish to thank all of the reviewers, including J. C. Quagliano Amado, A. M. Barbero, E. Barbero Pozuelo, Hyonny Kim, R. Velazco, and R. Zaera, who contributed invaluable comments and suggestions. c and typeset in LATEX (MikTeX implemenThe book is typed with TeXstudio c . Tables are converted from tation). The bibliography is managed with JabRef Excel into LATEX using excel2latex. Illustrations are standardized using encapsulated postcript (eps). Many thanks to the developers and contributors to these free software. Ever J. Barbero Morgantown, WV

Errata An ERRATA for this workbook is available and frequently updated on this Website: http://forum.cadec-online.com/viewtopic.php?f=4&t=278 If you wish to contribute a comment, question, or correction to this workbook, please do so by submitting your contribution to the forum: http://forum.cadec-online.com/viewforum.php?f=4 or contacting the author. The Website for this book is: http://barbero.cadec-online.com/Multifunctional/

xix

Contributors

Contributors Chapter 1

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 6

Chapter 7

Chapter 8

Chapter 9

Chapter 10

Chapter 11

Chapter 12

Electromagnetic effects Ernest K. Condon III and Paul J. Jonas Wichita State University, National Institute for Aviation Research, Wichita, KS, USA Lightning strike protection systems Gasser F. Abdelal Queen’s University Belfast, Belfast, UK Toughening for impact damage Timothy L. Norman Cedarville University, Cedarville, Ohio USA, and C. T. Sun Purdue University, West Lafayette, IN, USA Erosion resistance Edmond Tobin, Aidan Cloonan, and Trevor Young University of Limerik, Republic of Ireland Acoustic and vibration damping Edith R. Fotsing, Annie Ross, and Edu Ruiz ´ Ecole Polytechnique de Montr´eal, Montr´eal, Canada Viscoelastic damping treatments Rui A.S. Moreira University of Aveiro, Aveiro, Portugal Self-healing in polymers and structural composites Kathryn Mireles and Micheal R. Kessler Washington State University, Pullman, WA, USA Microvascular transport Christopher J. Hansen University of Massachusetts Lowell, Lowell, MA, USA Permeation Shaokai Wang Beihang University, Beijing, China, and Ayou Hao Florida State University, Tallahassee, FL, USA Fire safety Ning Tian University of Ulster, Newtownabbey Co, Antrim, UK, and Aixi Zhou University of North Carolina at Charlotte, Charlotte, NC, USA Thermal protection systems Maurizio Natali, Luigi Torre, and Jos´e Maria Kenny University of Perugia, Perugia, Italy Magnetoelectric composites Tomas I. Muchenik and Ever J. Barbero West Virginia University, Morgantown, WV, USA

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Chapter 1

Electromagnetic effects Ernest K. Condon III and Paul J. Jonas Wichita State University National Institute for Aviation Research Wichita, KS, USA Abstract This chapter provides an overview of the various electromagnetic effects design areas involved in design, test, and operation of vehicles and equipment built with composite materials. These design areas determine how well composite materials perform in electromagnetic energy fields and any indirect effects to any systems and equipment on or within. Specifically, the focus will be on the effects that the use of composite materials has on the various electromagnetic effects design areas. The various material properties that contribute to the effects will be addressed from the standpoint of quantification early in a design phase through testing and analysis, design/mitigation choices, and current material and mitigation trends related to these properties. The terminology in this chapter relates the application to aircraft. However, the concepts are also directly applicable to any other complete systems, such as wind turbines and buildings. Note that many of these design areas are interrelated. Be sure to consider all the design areas and their effects in order to get a system-wide view of the interactions.

1.1

Major design areas for electromagnetic effects

The name electromagnetic effects (EME) is typically used to describe all the design areas related to electromagnetic effects on an aircraft. The use of the acronym EME, as well as others such as EMC and EMI, varies somewhat across the industry. The uses of the terms in this chapter are the most common forms. For the purpose of this chapter, the following major design areas of EME will be considered. The specific definitions of these terms follow. • Electromagnetic compatibility (EMC) 1

2

Multifunctional Composites • Electromagnetic interference (EMI) • Electrical bonding and grounding • Direct effects of lightning (DEL) • Indirect effects of lightning (IEL) • Precipitation static (P-Static) • High intensity radiated field (HIRF) • Power distribution • Electrostatic discharge (ESD) • Nuclear electromagnetic pulse (NEMP) • Atmospheric radiation • Antenna performance

1.1.1

Electromagnetic compatibility

The term EMC is typically used to describe a test on a complete aircraft, where one system is operated (as a source) to see if it interferes with the operation of a second system (the victim). This type of testing is called source/victim testing. This testing is usually done on the completed aircraft, near the end of a program. Discovering problems at this stage is costly. Consequently, bench levels testing as well as vehicle level analysis are done earlier in the program in order to reduce the risk.

1.1.2

Electromagnetic interference

The term EMI refers to bench level testing of components or systems. This typically falls into these broad categories: • Emissions: – Conducted (on wiring) – Radiated (electromagnetic fields) • Susceptibility: – Conducted (on wiring) – Radiated (electromagnetic fields)

Electromagnetic effects

3

Setting emissions and susceptibility requirements so that there is a safety margin between them helps ensure there are no EMC issues at the aircraft level. These bench-level EMI tests are currently the primary area of defense against EMC related issues. The EMC test is usually used as a secondary/cursory check for system level verification. These bench-level tests are also typically the final means of showing performance related to the indirect effects of lightning (IEL). Full-threat IEL testing is seldom done on a complete aircraft.

1.1.3

Electrical bonding and grounding

Electrical bonding and grounding are similar but not the same. Grounding is connection of a circuit to a common reference point, typically assumed to be zero volts. This common reference is typically the aircraft primary structure, and is called ground. Ground is typically used as a power return for electrical power, and sometimes used as a zero-voltage reference for signals. Bonding is making good, low impedance electrical contact between two conductors. This connection can be to ground, or can be between any two conductors. In the existing design methods used for systems, both of these items are very important for the control of EMI/EMC. Two very important aspects in electrical bonding include eliminating non-conductive materials from the contact areas, and long term prevention of corrosion in the contact area.

1.1.4

Direct effects of lightning

When a lightning strike attaches directly to an aircraft, the point of attachment experiences extremely high currents and voltages. The energy involved can cause a number of physical/thermal effects: • Melting • Blasting • Burning • Holes • Dents • Magnetic pinching • Sparks • Exploding wires • Welding

4

Multifunctional Composites

These effects are called direct effects of lightning (DEL) (see Chapter 2 for more details). Some secondary effects can include ignition of fuels, jammed control surfaces, structural degradation, etc. Usually, DEL can be distinguished from indirect effects by assuming that anything that addresses voltages and currents on wiring is considered indirect effects. However, in the cases where lightning attaches directly to a wire on the exterior of the aircraft, or an arc-over to a wire occurs inside an external antenna/probe/light, it is usually considered direct effects.

1.1.5

Indirect effects of lightning

When a lightning strike attaches directly to an aircraft, the high currents and voltages involved and the rapid rise times generate large magnetic fields (H-fields), electric fields (E-fields), as well as currents and voltages on the structure. All these can induce voltages and currents on internal wiring, which in turn appear at the connected systems/equipment. These are called indirect effects of lightning (IEL). The E-fields and H-fields can penetrate into the interior of the aircraft and induce voltages and currents on aircraft wiring, which is then seen by the equipment attached to the wiring. The currents on structure and internal conductors can also generate H-fields that couple onto wiring. The current flowing through the resistance of the aircraft structure can also result in voltages (V = I R) seen on the structure/ground. Since ground is then no longer zero volts, the equipment grounded to the structure can be affected.

1.1.6

Precipitation static

When two items rub together, they can transfer charge to each other by rubbing off electrons. This is what happens when you drag your feet in carpet on a cold or dry day and you get a spark. An aircraft charges in the same way when it flies through any liquid or solid particles (rain, haze, snow, ice, sand, dust, etc.). The particles rubbing on the aircraft transfer electrons between the particles and the aircraft. This effect is called P-static. Another name for it is triboelectric charging. Without proper design, the aircraft can charge to hundreds of thousands of volts and start arcing into the surrounding air (corona), between parts of the aircraft (arcing), or across the surface (streamering). When this discharge is visible, it is sometimes referred to as St. Elmo’s Fire. This discharge interferes with aircraft radio receivers, making them unusable. These discharges can also be a hazard to flammable mixtures such as at fuel vents. Static wicks are placed on the wingtip and tail trailing edges to dissipate this charge without interfering with radio receivers. This typically requires that all external surfaces are conductive and make electrical contact with each other and the static wicks. Inlets and ducts that are exposed to airflow from outside can also experience static charging and must be properly grounded.

Electromagnetic effects

5

A related area is static from fluid flow. Fluid flowing in any tube or tank can cause static charge to build up. Proper grounding is needed to prevent sparkgenerated fires in fuel lines/tanks, hydraulic lines, etc.

1.1.7

High intensity radiated field

Many transmitters/antennas exist in the world that radiate high levels of electromagnetic energy, for example: • Television/radio stations • RADAR (airport, weather, military) • Communication systems • Military systems Aircraft encounter these electromagnetic fields. On board systems are exposed to some or all of the field energy, and the fields also induce voltages and currents onto wiring in the aircraft. These effects are called HIRF.

1.1.8

Power distribution

Power Distribution simply refers to getting power from an electrical power source (generator/alternator or battery) on the aircraft to the systems that need/use the power. Also included are means of monitoring and controlling this electrical power. Often the airframe is used as a power return (typically called ground, negative, or zero volts) The power distribution system can conduct noise from system to system, and can also radiate noise into systems.

1.1.9

Electrostatic discharge

ESD is similar in cause to p-static in that rubbing two items together in dry air builds up a charge. ESD is used to describe the charge that builds up on a person, and then discharges onto/into systems on the aircraft, or to parts during assembly and handling.

1.1.10

Nuclear electromagnetic pulse

A high altitude nuclear explosion causes a strong electromagnetic pulse that propagates downward through the atmosphere. As with HIRF, the on board systems can be exposed to the electromagnetic fields, and the fields can induce voltages and currents on wiring. An aircraft that encounters this pulse can have damage/upset to its electrical/electronic systems.

6

Multifunctional Composites

1.1.11

Atmospheric radiation

Cosmic rays are high-speed particles in space that come from the sun and sources outside the solar system. When colliding with the atmosphere, they cause a cascade of high-energy particles and photons. These particles can penetrate an aircraft and impact semiconductor devices, occasionally causing upset or damage to electronics systems. This is called Atmospheric Radiation [1]. This radiation is strongest at high altitudes. As aircraft fly higher and semiconductor components grow smaller, this radiation is more of a concern.

1.1.12

Antenna performance

Some of the primary characteristics of antenna performance are gain and radiation pattern over the desired frequency range, and a suitable matching to the radio and transmission line. Also of consideration are preventing re-radiation and noise, as well as operating in the other EME related effects such as p-static and lightning. Many antennas rely on a ground plane for proper performance. The aircraft skin often provides this ground plane.

1.2

Primary physical characteristics affecting EME

This section provides an overview of the primary characteristic of composites that are 1) different from aluminum, and 2) affect EME in a significant way. These characteristics fall into three categories: • Conductivity/Resistivity • Shielding Effectiveness • Contact Resistance The impact that each of these has on specific EME design areas will be discussed in later sections in this chapter.

1.2.1

Conductivity/resistivity

Aluminum is one of the most-conductive / least-resistive materials currently available. Composites usually do not share this trait. At this point, it should be noted that when it comes to conductivity, there are two broad classes of composites: conductive and non-conductive. Conductive composite (carbon fiber in particular) are typically 1000 times more resistive than aluminum. Non-conductive composites are just that: non-conductive, and are actually insulators. Also, aluminum is essentially isotropic in resistance – the resistance is the same in all directions. Aluminum is essentially electrically homogeneous – the same throughout the material. This is not true of composites. The resistance from ply to ply is higher than across a ply. The resistance along the direction of the fibers is less than off axis to the fibers. And, composites are not isotropic [2].

Electromagnetic effects

7

When performing analyses, these non-isotropic and non-homogeneous characteristics should be considered. In many cases, such as when modeling skins, an isotropic/homogeneous approximation can be quite good.

1.2.2

Shielding effectiveness

Aluminum, being highly conductive, provides very good shielding from all electric fields (E-fields), and for magnetic fields (H-fields) higher than roughly one megahertz. This means that if high electromagnetic fields are applied to an aluminum panel, little or none of the energy penetrates through the aluminum to be seen on the other side. However, the energy can go around aluminum or through holes/apertures in the aluminum, and this energy is often orders of magnitude higher than any fields penetrating the aluminum itself. Conductive composites, though they are not nearly as conductive as aluminum, provide fairly good shielding for most applications. For low frequency applications (such as lightning), some penetration can be expected, especially on non-cylindrical bodies. Non-conductive composite provide essentially no shielding. The electromagnetic energy will propagate through the material as if it was not there.

1.2.3

Contact resistance

Electrical bonding to aluminum, if done properly, usually results in a contact resistance (the resistance between the conductor and the aluminum) of around one milli-Ohm. Industry specifications typically require a maximum of 2.5 milli-Ohms. For conductive composites, the contact resistance is typically in the range of 80 to 120 milli-Ohms, which is significantly higher than aluminum. Industry specifications typically require a maximum of one Ohm. This wide range of values (80 milli-Ohms to one Ohm) can make design analyses and assumptions difficult. For non-conductive composites, contact resistance is not applicable. The material itself is non-conductive.

1.3

Test/analysis methods

This section discusses the methods for testing/analyzing the material properties of the composites. Analysis and testing for various EME design areas are discussed in the next section.

1.3.1

Conductivity/resistivity

Being able to determine the resistivity of different materials is important for proper design and analysis. For aluminum, the properties are well known. Resistivity (or conductivity, which is simply the reciprocal of the resistivity) for the various alloys are available [3]. However, for composites it is much more difficult because of the wide variety of layup processes and the fact that the material is non-homogeneous

8

Multifunctional Composites Joint to be measured

Measure voltage (V) here Apply current (I) here Resistance = V/I

Figure 1.1: Four-wire resistance measurement. and non-isotropic. In these cases, it is better to measure the resistance of a sample of the material/layup and calculate the resistivity from there. For non-conductive composites, measurement of resistivity is not typically of value in most applications (only if it is being used as an insulator in a special application), and the process will not be described here. For conductive composites, as well as aluminum, the resistance of the material may be so small that the use of a two-wire resistance measurement (such as a handheld multi-meter) will not produce accurate results. The reason for this is that with a two-wire method, the resistance at the contact points is included in the measurement and may be much greater than the resistance of the sample material itself. To get around the contact resistance problem, a four-wire method is used (Figure 1.1). Two of the wires provide a constant current through the test sample. Two separate wires then measure the voltage across the sample (not including the contacts for the current carrying wires). The resistance R is the voltage divided by the current (R = V / I). Since no current flows in the voltage measuring wires, the contact resistance of those wires will not affect the voltage reading. Most modern electrical bond meters (also known as milli-Ohm meters or micro-Ohm meters) work this way, having two electrical contacts each of two measurement probes. Measuring the contact resistance itself can be accomplished using a similar fourwire process. The current is passed through the contact, and voltage is measured on either side of the contact.

1.3.2

Shielding effectiveness

For non-conductive composites, shielding effectiveness is essentially zero, and measurement is only needed when the material is being used as a radome. Then it is usually called transmissivity instead of shielding. For conductive composites, as well as aluminum, the apertures, windows, seams, etc., in the structure or enclosure contribute much more to reducing the shielding effectiveness than does the material itself. The measurement of the shielding

Electromagnetic effects

9

effectiveness of the material is usually only needed and effective when designing enclosures requiring extremely high shielding effectiveness. Various methods are available [4–6], such as placing a sample of the material between two attached shielded rooms. Electromagnetic energy is supplied in one room, and the amount penetrating through the material to the other room is measured.

1.4

Specific impacts to EME and mitigation approaches

The previous sections discussed the various material properties related to composites that affect EME. This section discusses the specific effects these material properties have on the various EME design areas.

1.4.1

Electromagnetic compatibility

Most of the aspects that impact EMC are actually addressed more specifically in the EMI and the Power Distribution descriptions included in Sections 1.4.2 and 1.4.8, which are done as preparatory steps for the final EMC test. From a requirements hierarchy point of view, EMC is a higher system-level requirement, and is met by allocating much of the requirements to the lower subsystem/component levels in these other sections.

1.4.2

Electromagnetic interference (EMI)

When determining the proper emission and susceptibility requirements for box-level and system-level design, some assumptions are made as to the amount of shielding (or its inverse, coupling) there is between systems. For radiated emissions and susceptibility, a carbon fiber shell provides essentially the same amount of shielding as an aluminum shell. Most of the coupling is through apertures, such as windows and seams. For a non-conductive composite shell, all of the airframe-provided shielding is lost. This must be adjusted for in one (or a combination of) the following methods: • Add conductive material to the airframe/shell to gain back some of the shielding. Expanded metal foil is a common material for this purpose • Add shielding requirements at the box/wiring level • Decrease the allowable emissions from a box/system • Increase the susceptibility levels a box system must withstand If a carbon fiber structure is used as a ground for a box or system with the intent of grounding wire shields or box grounds, the resistance of the carbon and the contact resistance will reduce the shielding effectiveness. This needs to be considered when performing bench level testing; that is, the resistance of the ground structure and the contact resistances need to be included in the bench test setup. It is common for this issue to be mitigated to some degree by providing an aluminum grounding

10

Multifunctional Composites

system for which to ground all boxes and wire shields to. If this aluminum grounding system in contiguous, it provides a low resistance path and zero voltage reference for all systems, and the aluminum provides for a low-contact resistance grounding point locally. The effects described in electrical bonding and grounding (Section 1.4.3) and in power distribution (Section 1.4.8) also contribute to successful EMI design and testing. All these effects should be considered during the design/analysis stage, and when defining the bench test setup. Predictive modeling Predictive modeling tools for the coupling between systems have been available for some time [7], with limited widespread use for certification. The primary reasons for the limited use have been: • The geometry and impacting variables are very complex. • Computing power has been inadequate to efficiently run the complex analysis. • The established bench-level requirements have proven adequate for meeting the overall system needs for EMC. Computing power has increased, and so has the use of computer models for designing the aircraft. Since the computer models already exist for design purposes, they do not have to be created just for EME analysis. Still, the success of the existing bench level requirements has not driven a need for predictive analysis for EMC alone. This is even more true now that certification to HIRF is required, because this raises the susceptibility requirements even higher, increasing the margin for EMC. Predictive analysis for emissions at the box level is more common using frequency domain techniques [8], but is still not very widespread for civil aircraft applications. These methods typically involve: • A digital model of the hardware. • Defined energy sources. • Defined measurement points. • Discretizing (meshing) of the model (usually a tetrahedral mesh or a cubic/rectangular mesh) • Applying a time-domain solver such as finite difference time domain (FDTD), or a frequency-domain solver such as finite element method/method of moments (FEM/MoM).

Electromagnetic effects

1.4.3

11

Electrical bonding and grounding

An aluminum structure typically provides an outstanding ground circuit for noise protection and power distribution. Likewise, aluminum provides a low contact resistance when making electrical connections if done properly. A good resource for describing electrical bonding practices is [9]. The importance of these two items is that any current running through a resistance (either contact resistance or material resistance) will result in a voltage across that resistance. Any devices that share that resistance will then also share the induced voltage. For example, if one device has noisy/varying current that passes through a resistive ground connection, this current will cause a varying voltage across the ground connection. Any other items connected to the same ground point will see this varying voltage as noise on all its interconnection wiring; the noise will be common mode with respect to ground. Clearly, electrical connections to non-conductive composites are not possible. A dedicated conductor or conducting ground plane must be provided if a ground is needed. It is also possible to establish a single-point ground system for the aircraft, where all grounds are brought to a single point on the aircraft at which all electrical systems on the aircraft make contact with. Current equipment design for aircraft do not easily lend themselves to a single-point ground system, but this approach may be more viable for wind generators or other structures. The resistance of carbon fiber material, as well as the contact resistance for carbon fiber, should be considered in design and analysis. Most aircraft do not allow power grounds to carbon fiber because of the resistance (for voltage losses, thermal issues, and for noise coupling), and provide an aluminum ground plane system for this purpose. The ground plane is also used for box grounds and shield grounds. The shields are typically grounded at the box, and the box grounds to the ground plane. There are ongoing studies to investigate providing a highly conductive layer on the carbon fiber shell (metal foil, metalized cloth, nanomaterials [10–20], etc.). This approach could alleviate many of the issues with composites, both conductive and non-conductive. These conductive layers would have multiple uses, such as power return, IEL improvements, DEL protection, EMI noise reduction, etc. Another aspect related to bonding and grounding is corrosion prevention. The industry has much experience in achieving a good electrical bond/ground to aluminum, using chemical conversion coating, sealants, etc. However, carbon fiber has a significantly different galvanic potential that aluminum. This means that if aluminum and carbon are in contact with each other and there is an electrolyte present (such as salt water), corrosion will occur if steps are not taken to prevent it. Common practices includes efforts to avoid the use of aluminum where possible (using copper-based metal foils instead of aluminum-based), or providing electrical isolation between any aluminum and carbon materials.

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1.4.4

Direct effects of lightning

The direct effects of lightning (DEL) are addressed in Chapter 2. However, this section will be used to describe the lightning phenomenon briefly, as the phenomenon also applies to the indirect effects of lightning (IEL). The industry guidance material listed below provides excellent details of all the waveforms, current, levels, and phenomena, so only a cursory explanation is provided here. An overall, very complete encyclopedia concerning the lightning phenomenon is contained in [21]. The Society of Automotive Engineers (SAE) has created a number of specifications that provide guidance for certification of aircraft [22–25]. See also Chapter 2. Lightning begins with convective activity in a thunderstorm. The motion of the particles of rain and ice, as well as condensation and freezing, generates charges on particles. Air convection separates these charges into charge pockets. Typically positive charge pockets accumulate high in the cumulonimbus clouds, and negative charge pockets accumulate low in the cloud. These charge pockets result in electric fields between oppositely charged pockets and between pockets and the ground. Once the electric field becomes high enough, the air ionizes and a leader is formed. This leader advances forward in steps, meters at a time. These steps result in current pulses in the channel. These pulses are referred to as multi-burst. These leaders are typically not visible to the eye. Once the leader from one charge pocket reaches a leader from another charge pocket or from the ground, the first return stroke occurs. This is the bright flash that is easily visible. For design, analysis, and testing purposes, this first return stroke is a double-exponential waveform with a peak current of 200,000 amps. This is referred to as Component A in [22]. Component A is followed by an intermediate current of lower magnitude and longer duration that is referred to as Component B. This is followed by a continuing current of even lower magnitude and longer duration that is referred to as Component C. These are all defined in the industry guidance material and Figure 1.2. It is common for a restrike to occur. This is easily visible when watching lightning strike, as flickering or pulsing. A series of these restrikes is called multi-stroke. Component D is the first of these restrikes. Again, all of these components and patterns are defined in detail in the industry guidance material [22]. They can be summarized as follows: • Component A is the first return-stroke – Short duration (6.4 µs to peak), very high current (200kA peak) • Components B is the intermediate current – Intermediate in current and duration (average 2kA for 5ms) • Component C is the continuing current – Up to one second in length, 200 to 800A

Electromagnetic effects

13

• Component D is the first subsequent strike – Short duration (3.18 µs to peak), high current (100kA peak)

Figure 1.2: Components of a lightning strike. An aircraft can encounter any or all phases of a lightning strike. Different parts of the aircraft can experience different phases of the lightning strike. Extremities of the aircraft are more likely to receive a lightning strike. Because of these effects, the aircraft is divided into lightning strike zones. Refer to [23] and Chapter 2 for more details.

1.4.5

Indirect effects of lightning

Voltages and currents that appear on wiring (and consequently at equipment interfaces) as a result of lightning attachment to an aircraft are called indirect effects of lightning (IEL). These are usually characterized as the open-circuit voltage (Voc) and short-circuit current (Isc) on the wiring, and the overall current on a bundle of wires. Two primary effects drive these voltages and currents: • Electromagnetic fields impinging on the wiring • Ground-conducted voltages

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Multifunctional Composites

Figure 1.3: Magnetic fields generated by lightning. Electromagnetic fields Lightning striking an aircraft creates large electric fields (E-fields) and large magnetic fields (H-fields). Aircraft equipment is typically far more susceptible to Hfields, so most attention is applied there. However, if a circuit has very high impedance, E-field coupling needs to be considered. The largest H-fields are typically caused by current flowing through the fuselage (Figure 1.3). Current flowing through any conductor causes an H-field around that conductor. This field then propagates into the interior of the aircraft through windows, seams, etc. (Figure 1.4). For aluminum and carbon (conductive) composites, little of the fields actually penetrate through the skins themselves (except for noncircular shapes, see Figure 1.5). Once inside the aircraft, H-fields impinging on the wires induce Voc on the wires, which in turn induce Isc on the wires. Because of the resistivity of carbon fiber, any non-circular area (such as a wing) will experience increased coupling of H-fields at later times during the lightning strike (Figure 1.5). This is called diffusion of fields. Likewise, initially during a lightning strike nearly all the current flows on the outer layer of the shell/wing (whether it is circular or not). As time progresses, more and more of this current begin to flow on interior conductors. This is referred to as current redistribution. This effect is proportional to the resistivity of the material; consequently it is much greater for a carbon shell than for an aluminum shell. Diffusion of fields and current redistribution are the time-domain equivalent of skin effect that is seen in the frequency domain. Cable shielding, grounded at both ends, provides a large reduction in the cou-

Electromagnetic effects

Figure 1.4: Fields propagating through apertures.

Figure 1.5: Diffusion of magnetic fields.

15

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Multifunctional Composites

pling from H-fields to wires. Additional protection is sometimes warranted at the box, in the form of transient suppression devices or active suppression techniques. Ground-conducted voltages For an aluminum aircraft the H-field coupling is by far the largest contributor to IEL. Essentially the same H-field coupling levels occur in carbon fiber aircraft. However, for carbon fiber aircraft the ground-conducted voltages are so much greater that they become the primary effect. This is a direct consequence of the increased resistivity of the carbon (as compared to aluminum). Carbon is essentially 1000 times more resistive than aluminum. The nose-to-tail resistance of an aluminum aircraft of any size is typically less than a milli-Ohm. A 200,000 amp current through and aluminum shell may produce an end-to-end voltage of tens of volts. This voltage is seen on the grounds of equipment in the aircraft. A pulse of tens of volts is usually easily designed for. Now compare this to a carbon shell. At 1000 times the resistance, the end-to-end voltage on a carbon fuselage can be 10,000 volts or more. Again, this is seen on the grounds of equipment installed on the aircraft. This is much more of a design challenge. Additionally, traditional shielding practices for H-field coupling (shielded wires, etc.) do not help much when the voltage is ground-conducted. Currently, it is common for expanded metal foil to be added to the shell for direct effects. This affords some reduction in the nose-to-tail resistance and consequently a reduction in IEL. However, the amount of foil is not adequate to reduce the IEL to that of an aluminum aircraft. Studies underway [27] suggest that an increase in the amount of foil (or other conductive material) is warranted. Non-conductive composites The IEL description thus far has focused on carbon and aluminum materials. Nonconductive composites become much more of a challenge because there is no inherent ground plane or shielding provided. Typically most aircraft using this type of material achieve a significant level of protection by adding an expanded metal foil to the outside of the aircraft. The challenge for IEL protection for this type of material still remains a high program risk because of the differences involved. Predictive modeling Moderate success has been achieved recently in modeling of IEL levels on aircraft. This is of greatest benefit on composite aircraft, where the design history is not available to help predict the levels that will be seen on a new design. One of the more successful approaches is described in [27]. The approach involves importing/creating a definition of the aircraft geometry in digital format (Figure 1.6). Each section of the geometry is assigned material properties. This geometry is then discretized (meshed) so that it appears to be constructed of small building blocks called cells (Figure 1.7). Current and voltages

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17

Figure 1.6: Digital model of an aircraft.

Figure 1.7: Meshed model of an aircraft (cell size exaggerated for clarity). sources are applied to the model. Measurement points and parameters are defined in the model. This model is then submitted to a solver; in this case, a finite difference time domain (FDTD) approach using the software package called EMA3D [7]. Maxwell’s Equations are applied to each cell in succession (Figure 1.8), and this is repeated for each time step in successions. An example model can easily have five million cells and a million time-steps applied. Clearly with this many calculations, a cluster computer with parallel processing is a must. Application of these methods for design and certification are still somewhat in the developing stages, and are not currently in widespread use. However, this is rapidly changing with more and more examples of usable accuracy, acceptance/validation of the results, and inclusions in design and certification efforts.

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Figure 1.8: A typical cell for FDTD analysis. Yee cell on right, reproduced from EMA3D Manual #2, Figure 2.1.3, with permission from Electro Magnetic Applications, Inc.

1.4.6

Precipitation static

The typical means for mitigating any p-static effects is to make sure that all surfaces exposed to the air stream are conductive, that the surfaces are all electrically connected to ground, and electrically connected to the static wicks. The number of static wicks depends on the aircraft frontal area and the aircraft speed. The typical layer of paint over the conductive skins does not usually create a problem because charges can bleed through this paint effectively. A few exceptions to this exist. Sometimes is it acceptable to have side windows that are not conductive because they are not forward facing and therefore the particle impingement is greatly reduced. Also, windows with no conductive layers (heater elements, etc.) within them can sometimes be shown to have small enough capacitance that the energy of the discharge is tolerable. This all still holds true for conductive composites. There is slight increase in the amount of charge build-up on the paint surface because the resin in the composite matrix increases the dielectric thickness somewhat. Therefore, for a carbon fiber aircraft, the noise floor due to p-static may be slightly raised, but typically is well within tolerable levels. Once again, non-conductive composites are a completely different case. If not treated with a conductive external layer, then p-static is much more of a concern. If the outer surface is protected with expanded metal foil that is also connected to

Electromagnetic effects

19

the static wicks, this is usually adequate. It is also possible to use anti-static paint as is used on radomes for this purpose. P-static is extremely low current, so the conductivity does not have to be very high to be quite effective. A sheet resistivity of 1.0 mega-Ohm per square is often adequate.

1.4.7

High intensity radiated field

Since HIRF is based on radiated field sources external to the aircraft, shielding effectiveness of the shell is the primary area of interest. Work performed to date indicates that the shielding provided by carbon fiber composite fuselage shells and wing skins provide nearly the same level of shielding as do aluminum counterparts [28]. Consequently, the biggest concern for carbon fiber aircraft would not be in the shielding effectiveness of the shell, but rather the ability to form and connect to a proper ground plane. These issues have been addressed in the other sections in this chapter and will not be repeated here. As in the other sections of this chapter, non-conductive composites are radically different in the attention that must be given to HIRF. If the shell/skins on the aircraft are unprotected, essentially no shielding is provided by non-conductive composites. All the units/systems within the aircraft are consequently exposed to the full external HIRF energy levels, and require increased levels of shielding and filtering. Protecting the shell/skins with a relatively contiguous layer of expanded metal foil is a common approach on non-conductive composites. If this expanded metal foil installation is executed properly, the shielding effectiveness can approach that of an aluminum aircraft. Care should be taken to minimize the number of seams, gaps, and apertures in the foil. The programmatic risks are still higher than with aluminum or carbon fiber, so steps to mitigate this risk are advised (such as early-program shielding effectiveness testing). It is prudent to provide a reminder here: Any bench testing used to demonstrate performance when exposed to HIRF energy should use grounding, bonding, and shielding schemes similar to the actual aircraft installation. For a carbon fiber aircraft, this may mean a deviation from the standard bench test techniques of performing the test with the units bonded to a copper table.

Predictive modeling HIRF is another area where predictive modeling has increased [7]. The numerical modeling tools for HIRF are similar in many ways to those used for IEL. However HIRF more commonly uses frequency domain techniques, while IEL tends to use more time-domain techniques. Using Fourier transform methods to convert between the two, either time- or frequency- domain techniques can be applied to either HIRF or IEL.

20

1.4.8

Multifunctional Composites

Power distribution

Power distribution systems in traditional aluminum aircraft have commonly relied on aircraft structure to provide the current return path. The power wires are considered hot or positive, and the structure is zero reference, ground, return, or negative. In some cases, new aircraft have moved to dedicated ground returns, especially for high power systems, but the majority of aircraft still rely on the structure to carry the return current. For the reason described in Section 1.1.3, this is no longer as easy for carbon fiber aircraft. First, the airframe can be as much as 1000 times as resistive for carbon fiber, and the V = I / R drops across the airframe can be intolerable. Also, the current density at a ground point can cause thermal issues in materials as resistive as carbon fiber. This issue is increased by the contact resistance when connecting to carbon fiber. All this resistance, be it contact resistance or material resistance, greatly increases the noise coupling on the ground system. This type of coupling is where current variations from one box are converted to ground voltage variation by the ground resistance. Any other equipment connected to this ground sees this varying ground voltage as common-mode noise on all the connecting wiring. There are two primary ways to work around this. The most common is to install a separate ground plane structure for electrical power and other EME related needs. This added ground plane sometimes adds little or no structural benefits to the aircraft. The second method is to provide dedicated return lines for all power and signal grounds on the aircraft, sometimes with a single point ground ; that is, one single point in which the electrical systems make contact with the airframe. This method works in theory, but is seldom implemented on modern aircraft because it is such a paradigm shift for box/equipment manufacturers. It may well be the best approach for other systems such as wind generators and buildings. It is clear that for a non-conductive composite aircraft, using the airframe for power distribution is not possible without implementing some variant of the two solutions described above. Studies are underway to create a single integrated solution that answers the issues of all or most EME design areas with a single solution [27]. Most are focused on establishing methods to increase the conductivity of the shell/skin with minimal increase in weight. Significant gains can be achieved with significantly less conductivity than an all-aluminum shell [27].

1.4.9

Electrostatic discharge

The effects of ESD are largely unchanged by the application of composites as structural material. This is because the electric charge generation usually occurs on clothing, upholstery, and personnel, and is discharged to the exposed user-interface portions of the devices. It is possible that an aircraft made entirely of non-conductive composites could tend to be more prone to static discharges than a carbon or aluminum aircraft.

Electromagnetic effects

21

However, this would not change the design or protection requirements. Aircraft systems must be designed for these effects anyway.

1.4.10

Nuclear electromagnetic pulse

Many aspects of NEMP are currently classified for military reasons. Also, commercial aircraft are not currently required to test or certify for an NEMP environment. Consequently, this section will just briefly discuss generalities related to composite materials. Most of the discussion provided in this chapter for IEL and HIRF would be applicable to NEMP as well. NEMP is technically a radiated phenomenon, so the shielding effectiveness discussion applies in that manner, in particular the discussion on IEL. However, the NEMP phenomenon is large enough in magnitude and contains enough low frequency content that significant currents could be seen on the airframe, making it prudent to consider ground currents/voltages as well.

1.4.11

Atmospheric radiation

Atmospheric radiation is another area that is not currently a certification requirement for aircraft, though current regulations do address single-event upsets in electronics. Since atmospheric radiation is a combination of electromagnetic (photon) and particle radiation, it is discussed briefly here. Most or all of the upset and damage from atmospheric radiation is from particle radiation interacting with semiconductor devices. These sub-atomic particles, of various types, penetrate skins and structure to a large extent. No firm data exits currently that indicates that any commonly used material (aluminum, carbon fiber, non-conductive composites) provides any real difference in the amount of penetration and interaction with electronics.

1.4.12

Antenna performance

There are a wide variety of antenna designs available today, and an ever increasing list of applications. Some of these antennas require a ground plane for proper operation. Others are designed for use without a ground plane, or work as well with or without a ground plane. Many antennas have been shown to work (gain, pattern, etc.) as well whether they are installed on aluminum or carbon fiber structure. Others have shown the need to add a metallic ground plane near the antenna. For this reason, it is wise to use modeling to determine if the resistive nature of carbon fiber in the ground plane, as well as contact resistance, will affect the performance of the antenna, and then to consider testing on an installed application. One issue that needs attention on all antennas installed on a carbon fiber shell is corrosion as a result of dissimilar metals. This was discussed in more detail in the Section 1.1.3 of this chapter. Many aircraft antennas available commercially today have an aluminum base plate. Placing this in contact with carbon fiber in the presence of moisture is likely to result in severe corrosion. In some cases it has

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Multifunctional Composites

been shown that VHF and UHF communication antennas can be installed such that they are DC (direct current) isolated from the skin and still perform as designed (reactive coupling provides the needed interaction with the ground plane). However, this could decrease the protection against lightning direct effects designed into the antenna, as well as P-static protection. Predictive modeling Antenna performance is an area in which predictive modeling tools have been in wide use for a long time [8]. These are typical frequency domain solvers (FEM) as described earlier, although some antennas are simple enough for manual calculations.

1.5

Conclusions

The use of composite materials has an impact in most EME design areas. In some of these design areas, especially lightning protection, the impact can be quite significant. However, these challenges are not insurmountable. This chapter has provided a complete overview of the EME design areas involved, and provides the reader with enough information to address the relevant issues with increased confidence. Methodically addressing each of these issues will significantly reduce program risks. To realize this reduction in risk, addressing these challenges early in the design process is imperative. Future technologies will provide additional mitigation choices, especially in the methods/materials that can be applied to improve the conductivity of the composite materials. The increasing capability and capacity of computers, and the development of new/refined algorithms, will add efficiency and accuracy to predictive modeling, providing additional means for identifying solutions earlier in the design phase of a project.

Bibliography [1] E N A Taber. Single event upset in avionics. IEEE Transactions on Nuclear Science (IEEE, 40(2), 1993. [2] E J Barbero. Introduction to Composite Materials Design–Second Edition, Boca Raton, FL. CRC Press, 2 edition, 2011. [3] C f N Education. Conductivity and resistivity values for aluminum & alloys. accessed 5/6/2015. 2002. https://www.nde-ed.org/GeneralResources/ MaterialProperties/ET/Conductivity_Al.pdf. [4] MIL-STD 285. Method of attenuation measurements for enclosures, electromagnetic shielding, for electronic test purposes, 1956. [5] IEEE STD 299. Standard for measuring the effectiveness for electromagnetic shielding enclosures, 1997. [6] ASTM D4935-10. Standard test method for measuring the electromagnetic shielding effectiveness of planar materials, 2010.

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[7] EMA3D. Electromagnetic applications (ema). accessed 5/6/2015. 2015. http://www. electromagneticapplications.com. [8] Altair. FEKO. accessed 5/6/2015. 2015. https://www.feko.info. [9] SAE ARP1870A. Aerospace systems electrical bonding and grounding for electromagnetic compatibility and safety, 2012. [10] H. M. Kim, K. Kim, C. Y. Lee, J. Joo, S. J. Cho, H. S. Yoon, D. A. Pejakovi, J. W. Yoo, and A. J. Epstein. Electrical conductivity and electromagnetic interference shielding of multiwalled carbon nanotube composites containing fe catalyst. Appl. Phys. Lett., 84(4):589–591, 2004. [11] Chunxia Wu, Haibao Lu, Yanju Liu, and Jinsong Leng. Study of carbon nanotubes/short carbon fiber nanocomposites for lightning strike protection. Proc. SPIE, 7644:76441H–76441H–8, 2010. [12] D.D.L Chung. Electromagnetic interference shielding effectiveness of carbon materials. Carbon, 39(2):279 – 285, 2001. [13] Y. Yang, M.C. Gupta, K.L. Dudley, and R.W. Lawrence. Electromagnetic interference shielding characteristics of carbon nanofiber-polymer composites. J. Nanosci. Nanotechnol., 7(2):549–554, 2007. [14] Y. Yang, M.C. Gupta, and K.L. Dudley. Towards cost-efficient emi shielding materials using carbon nanostructure-based nanocomposites. Nanotechnology, 18(34), 2007. [15] Y. Yang, M.C. Gupta, and K.L. Dudley. Studies on electromagnetic interference shielding characteristics of metal nanoparticle- and carbon nanostructure-filled polymer composites in the ku-band frequency. Micro and Nano Letters, 2(4):85–89, 2007. [16] Y. Yang, M.C. Gupta, K.L. Dudley, and R.W. Lawrence. Novel carbon nanotube polystyrene foam composites for electromagnetic interference shielding. Nano Lett., 5(11):2131–2134, 2005. [17] Y. Yang, M.C. Gupta, K.L. Dudley, and R.W. Lawrence. A comparative study of emi shielding properties of carbon nanofiber and multi-walled carbon nanotube filled polymer composites. J. Nanosci. Nanotechnol., 5(6):927–931, 2005. [18] A. Mehdipour, I.D. Rosca, C.W. Trueman, A. Sebak, and Suong Van Hoa. Epoxy composites with high shielding effectiveness for aeronautic applications. IEEE Transactions on Electromagnetic Compatibility, 54(1):28–36, Feb 2012. [19] Rajeev Kumar, Sanjay R. Dhakate, Tejendra Gupta, Parveen Saini, Bhanu P. Singh, and Rakesh B. Mathur. Effective improvement of the properties of light weight carbon foam by decoration with multi-wall carbon nanotubes. J. Mater. Chem. A, 1:5727–5735, 2013. [20] Parveen Saini, Manju Arora, Govind Gupta, Bipin Kumar Gupta, Vidya Nand Singh, and Veena Choudhary. High permittivity polyaniline-barium titanate nanocomposites with excellent electromagnetic interference shielding response. Nanoscale, 5:4330–4336, 2013. [21] Franklin A Fisher and J. Anderson Plumer. Lightning Protection of Aircraft (ISBN 1478241527). CreateSpace, 2012. [22] SAE ARP5412B. Aircraft lightning environment and related test waveforms, 2013. [23] SAE ARP5414A. Aircraft lightning zoning, 2012.

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[24] SAE ARP5415A. User’s manual for certification of aircraft electrical/electronic systems for the indirect effects of lightning, 2008. [25] SAE ARP5416A. Aircraft lightning test methods, 2013. [26] P Feraboli and M Miller. Damage resistance and tolerance of carbon/epoxy composite coupons subjected to simulated lightning strike. Composites Part A, 40:954–967, 2009. [27] E K Condon. Shell resistivities correlated to indirect effects of lightning. In International Conference on Lighnting and Staic Electricity (ICOLSE). 2013. [28] U.S. Department of Commerce. NIST Technical Note 1549: Electromagnetic Airframe Penetration Measurements of the FAA 737-200 (ISBN 1495965880). CreateSpace, 2014.

Chapter 2

Lightning strike protection systems Gasser F. Abdelal Queen’s University Belfast, Belfast, UK Abstract This chapter presents state of the art numerical and experimental testing procedures to investigate the efficiency of lightning strike protection (LSP) systems. Thus, a coupled thermal-electrical finite element analysis (FEA) procedure is proposed to enable the investigation of the design variables that control lightning strike damage in Graphite/Epoxy composites. The major contribution of this chapter is the formulation and verification of temperature dependent material properties, a key attribute not considered within previous literature. The proposed procedure is applied to a test specimen and the results are verified against published experimental data, illustrating the accuracy and computational cost of lightning strike simulation and the requirement for temperature dependent material properties. The procedure is then applied to a number of practical LSP systems and the simulation results are used to further understand and quantify the physical behavior that minimizes material damage. Further, this chapter investigates using multiphysics (magnetic, electric, heat transfer, and computational fluid dynamics) to model the free burning electric arc (plasma) between the cathode and the anode during lightning strike of a composite, providing an estimate of the damage caused by resistive heating and overpressure.

2.1

Introduction

A lightning strike is a thermal plasma channel, made up of high temperature and fast moving electrons (30,000 C, 5,000 m/sec), conducting significant energy within micro-seconds (40-200 kJoule/Ohm)1 . Striking a metallic lightning strike protection 1

Refers to energy per unit resistance. See Equation (2.2).

25

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Multifunctional Composites

(LSP) layer with such energy leads to a series of coupled physical processes. The metallic surface heats up, melts, vaporizes and once the surface temperature reaches the critical temperature, explosive boiling occurs, which results in an ejection of a mixture of vapor and liquid droplets. Damage from lightning strike is a major challenge when using composites for the construction of aircraft structures. The physical consequences of a lightning strike on an aircraft can be summarized as: (a) Resistive heating at the lightning arc contact point, which decomposes the polymer resin, (b) An overpressure due to the explosion of the lightning channel, which leads to the propagation of a strong shock wave in a radial direction away from the arc. The explosion is due to the fast increase in the arc temperature in the conducting channel, up to 30,000 K within a time interval of a few microseconds, (c) A magnetic force due to fast conduction in any metallic component, including for example a metallic element used as part of a LSP system. Experimental testing of lightning strike on aircraft materials and structures is expensive. Moreover, the large number of design parameters of the composite, plus those associated with an embedded LSP system result in a vast design space, for which purely empirical design and development is very time consuming. Thus, LSP systems are typically restricted to the most feasible design of a few considered, or are limited to a known, previously used design space. Unfortunately, this can result in non-optimum designs being selected, which can in turn cause problems at a later design stage. Reviews of LSP systems for metallic and composite aircraft are available in [1, 2]. They describe the problem, guidelines [3], lightning damage to composite, current protection solutions, and alternatives. The objectives of LSP are to minimize structural damage, prevent hazardous electrical shocks to occupants, and to prevent ignition at fuel tanks. For nonmetallic components, compliance may be achieved by designing LSP to minimize the effect of a strike or to divert the resulting electrical current so as not to endanger the aircraft. A partial list of LSP guidelines and standards developed by government, military, and industry is shown in Table 2.1. The US Federal Aviation Administration (FAA) guidelines are non-specific, and allow manufacturers to implement different designs and certification strategies. The Society for Automotive Engineers (SAE) provides aerospace recommended practices (ARP) that can be utilized to demonstrate compliance. SAE ARP 5414 [4], divides the surface of an aircraft into a set of six regions called lightning strike zones that represent areas likely to sustain lightning currents (Figure 2.1) [2]. Lightning zoning is a functional step in showing that the aircraft is sufficiently protected from both direct (the focus of this chapter) and indirect effects of lightning (addressed in Chapter 1). Zone 1 will have initial lightning strikes attaching themselves to the structure, these strike locations are called attachment points, and first return strokes, with Zone 1A having low expectation of hang on, Zone 1B having a high expectation of hang on, and Zone 1C having the first return stroke of reduced amplitude and a low expectation of hang on. Zone 2 will have subsequent swept strokes or re-strikes, with Zone 2A having low expectation of hang on and Zone 2B having a high expectation of hang on. Swept strokes occur as the

Lightning strike protection systems Standard ASTM D4935-10 IEEE STD 299 MIL-STD 285 MIL-STD-1757A RTCA/DO-160G SAE AC20-53A SAE AC20-155 SAE ARP1870A SAE ARP 5412B SAE ARP 5414A SAE ARP 5415A SAE ARP 5416 SAE ARP 5577

27

Title Standard test method for measuring the electromagnetic shielding effectiveness of planar materials Standard for measuring the effectiveness for electromagnetic shielding enclosures Method of attenuation measurements for enclosures, electromagnetic shielding, for electronic test purposes Lightning qualification test techniques for aerospace vehicles and hardware Environment conditions and test procedures for airborne equipment Documents to support aircraft lightning protection certification Protection of aircraft fuel systems against fuel vapor ignition caused by lightning Aerospace systems electrical bonding and grounding for electromagnetic compatibility and safety Aircraft lightning environment and related test waveform Aircraft lightning zoning User’s manual for certification of aircraft electrical/electronic systems for the indirect effects of lightning Aircraft lightning test methods Aircraft lightning direct effects certification

Table 2.1: Partial list of guidelines and standards. The user should check for latest revision of these documents. aircraft flies into the lightning channel, making the lightning strike sweep across the surface. Zone 3 would support large lightning currents between areas of direct or swept stroke attachment points. The boundaries between zones are determined by laboratory tests of lightning strikes. A hang on is defined as a lightning strike plasma channel attached to the aircraft 0.1 ms or longer. SAE ARP 5412 [5], defines four current components (A–D) representing the lightning flash current waveforms recommended for evaluating direct effects, as shown in Figure 1.2 (p. 13). Component A represents the first return stroke. Components B and C represent the lightning environment that might be caused by intermediate and long duration currents following return strokes or re-strikes. Current component D represents a subsequent stroke. It can be seen in Figure 1.2 (not to scale), that components B and C have much lower peak amplitudes than components A and D, but a very high charge transfer. Components B and C can be interpreted as currents that bridge the initial stroke A to the subsequent stroke D. Current waveform A is applied to Zone 1 regions only. Charge transfer is defined as the electrical charge [coulomb] that is transferred from the lightning strike plasma channel to the aircraft. It is higher for a hang-on because of the longer attachment time of the hang-on to the aircraft skin.

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Typical Landing Gear

19.7 in (0.5 m)

19.7 in (0.5 m)

Zone 1B 19.7 in (0.5 m)

19.7 in (0.5 m) 19.7 in (0.5 m)

19.7 in (0.5 m) 19.7 in (0.5 m)

19.7 in (0.5 m)

Zone 1A Zone 1B 19.7 in (0.5 m) Zone 1C Zone 2A Zone 2B Zone 3 (Direct Attachment) Zone 3 (Conducted) 19.7 in (0.5 m)

19.7 in (0.5 m)

19.7 in (0.5 m)

19.7 in (0.5 m)

51.2 in (1.3 m)

51.2 in (1.3 m)

51.2 in (1.3 m)

51.2 in (1.3 m)

Figure 2.1: Lightning strike zones. Copyright, Boeing (2012).

29

Lightning strike protection systems COMPONENT A (First return stroke) Peak amplitude Action integral Time duration

200kA (± 10%) 2 x 106 A2 s(± 20%) 500 µs

COMPONENT B (Intermediate current) Average amplitude Max. charge transfer Time duration

2kA (± 20%) 10 Coulombs (± 10%) 5 ms

COMPONENT C (Continuing current) Amplitude Charge transfer Time duration

200-800 A 200 Coulombs (± 20%) 0.25 to 1 s

COMPONENT D (Subsequent return stroke) Peak amplitude Action integral Time duration

100 kA (± 10%) 0.25 x 106 A2 S(± 20%) 500 µs

Table 2.2: Simulated lightning current waveforms per SAE 5412 [5]. See Figure 1.2 (p. 13). The physical consequences of a lightning strike on an aircraft can be summarized as: a. Dielectric puncture of skin covering electrically conducting elements, which produce holes that result in direct attachment of the lightning channel to the enclosed equipment. b. Thermal convection from the plasma lightning channel and the aircraft surface. c. Exploding conductors due to lack of sufficient cross section area to transfer the lightning current. d. Resistive heating at the lightning arc contact point that decomposes the FRP resin. e. Thermal sparking at interface joints between two parts with insufficient cross section area to transfer the lightning current. f. Voltage sparks due to induced voltages in the aircraft structure or wiring. g. An overpressure due to the explosion of the lightning channel, which leads to the propagation of a strong shock wave in radial direction away from the arc. The explosion is due to fast increase in the arc temperature in the conducting channel, up to 30,000 K within a time interval of a few microseconds.

30

Multifunctional Composites

h. A magnetic force due to fast conduction in any metallic component, including for example a metallic element used as part of LSP. Common approaches used to minimize lightning strike damage on composite aircraft components include a metallic mesh or conducting paints that are applied on the surface to shield and protect the underlying load bearing composite material. Copper has a melting temperature Tm = 1,083 C, a boiling temperature Tb = 2,800 C (pressure = 1 atm) and a critical temperature Tc = 8,000 C (pressure = 1 atm). Critical temperature is the highest temperature at which a substance can exist as a liquid. Since vaporization temperature of copper is a function of local pressure P and a shock wave is present, vaporization may occur below the boiling temperature. Consequently, when a copper mesh embedded at the surface of the composite is subjected to high energy electric load, complicated coupled physical processes occur. The copper surface heats up, melts, vaporizes, and once the surface temperature reaches approximately 90% of the critical temperature, explosive boiling occurs, which results in ejection of a mixture of vapor and liquid droplets. Considering the behavior of typical thermosetting plastics, when subjected to increasing temperature the material will decompose (between 300 and 500 C). Above 500 the material will be a char, and ablation will begin above 3,000 C. Carbon fiber tows char when subjected to increasing temperature, and ultimately ablate (3,316 C). For all materials, thermal and electrical properties will change with phase and temperature. Haigh [7] studied the mechanical effects of lightning strike on test panels, using mechanical and optical instruments to measure the force imparted by an electric arc on a panel over time. The extracted force measurements were then compared to equivalent tests in which only mechanical impulse loading was applied. Gineste et al. [8] used visual interferometric optical methods to measure deflections at multiple locations over time. A model was developed to extract the mechanical impulse from the measured deflection induced by the strike. Lepetit et al. [9] studied the impact of explosive boiling on LSP paint and its influence on the induced composite damage. The methodologies of [7–9] ignore the electric properties of the material and the coupling between the electromagnetic and the thermal behaviors. However, deformation and high thermal strains occur at the arc contact point due to plasma impact at extreme temperature (>30,000 K), and joule heating due to electric resistivity of the material. The preceding models also neglect the decomposition of the epoxy material due to thermal load and its effect on orthotropic electric/thermal conductivity of the material. Thus, only magnetic and overpressure forces due to electric arc strike are included in [7–9]. Major causes of damage (plasma and resistive heating) have been neglected. Leptit [9] captures the effect of explosive boiling experimentally, but his numerical modeling, based on explicit dynamic analysis, again neglects coupling between electromagnetic and thermal phenomena. Ogasawara [10], modeled lightning strikes using coupled electromagnetic/thermal FEA, including coupling between electromagnetic and thermal behavior. The simulations considered specimens without LSP. Furthermore, simulations ignored the temperature dependency of the electrical/thermal material properties and used a

Lightning strike protection systems

31

technique for the application of the electric arc load which may produce inaccurate results [10]. Chemartin [11] presents a comprehensive survey of thermal and mechanical direct effects of lightning strike on aircraft skin panels. They performed both numerical simulation and experimental tests to study the plasma between the cathode and the panel (anode), capturing its temperature and conduction profile. They simulated lightning strike in flight conditions in order to characterize the sweeping stroke process and to evaluate dwell time, the later being an important parameter for definition of the wave form to be applied on swept zones of aircraft. Their numerical approach is very comprehensive, including not only damage and electric spark generation in aircraft panels, but also electric arc physics. Using basic mathematical expressions they model the thermal and mechanical forces applied on aircraft panels, but do not model the panel structure, its interaction with the force applied or resulting panel damage. Common LSP technology provides a conductive path using either a metal mesh [12,13] or Epoxy resin-based CNT composites [14,15]. While metal meshes are heavy, CNT composites increase the resin viscosity, making it difficult to manufacture voidfree composites. Liu, et al. [16] proposed a comprehensive simulation procedure combining electrical-thermal and blow-off impulse (BOI) analysis, to investigate lightning direct effects on damage behavior of composite. Wang, et al. [17] modeled ablation damage of carbon fiber/epoxy composite laminates from lightning strike by coupled thermal-electrical-structural analysis and element deletion. At the same time, the residual strength of the composite laminate after lightning ablation is predicted by Hashin criterion [17]. Using experimental methods to study the impact of lightning strike is expensive and limited to studying the effect of a few parameters at a time, such as decomposition and delamination in the vicinity of the lightning strike. Using a purely empirical approach to optimize the performance of a lightning protection system is inevitably time consuming and expensive. Thus, in this chapter we build on the preceding work by proposing an improved technique to model the lightning strike effects on composite panel with and without a LSP. We address the resistive heating force, its interaction with the composite structure, and the LSP thermal performance. Coupled electromagnetic/thermal FEA is proposed with temperature-dependent material properties. A user material subroutine is used to model the complex physical behavior of the protection system. Magnetic forces and overpressure participation are addressed in Section 2.4. Developing a numerical tool that models the complex physical process of lightning strike on composite panels with protection systems is essential for the efficient optimization of current LSP systems and developing new protection system concepts.

2.2

Experimental verification

This section summarizes lightning strike testing. SAE-ARP 5416 [18] describes test techniques for simulating direct and indirect lightning strike effects on aircraft structures. MIL-STD-1757A [19] presents a set of standard test waveforms and

32

Multifunctional Composites

Figure 2.2: Charge transfer of a current waveform.

techniques for lightning qualification testing of aerospace vehicles and hardware. Plumer [20] presents a description of the phenomenology related to aircraft lightning interaction, the environmental parameters (i.e., current, statistics, repetition rate, and so on.) and the associated representative waveforms. There are generally three configurations for lightning strike test setup. The simplest configuration is for the specimen to be located on top of a continuous copper plate [21]. In the second configuration, the specimen is supported on copper bars around its boundary [22]. In the third configuration, the specimen is supported at its two short ends between copper electrodes, which may be encapsulated by nonconductive phenolic resin, and whose position is adjusted to be in close contact with the specimen [11, 18, 19]. In all cases, a spark generator is designed to simulate the impulse current waveform of lightning strike as described in [18, 19]. These waveforms represent idealized environments that may be applied to aircraft components for analysis and/or testing. The waveforms are not intended to reproduce a specific lightning event. Instead, they are intended to be composite waveforms whose effects upon aircraft are similar to those expected from normal lightning. The primary parameters of each waveform are: peak current amplitude, action integral, and time duration. Since the action integral measures the energy of the strike, it is a very important quantity for a simulated strike to accurately represent an actual lightning event. The four components of the idealized current waveforms for a direct-strike lightning are depicted in Figure 1.2 and further described in Table 2.2. The current waveform characteristics (Figure 2.2) can be described in equation form as Electric power = V I = (I R)I = I 2 R

;

[J/s]

(2.1)

33

Lightning strike protection systems

Figure 2.3: Test setup of composite panel under lightning strike type I. To express this as a dissipated thermal power energy per unit resistance, we have Z tf Action integral (AI) = I 2 (t) dt ; [J/Ohm] (2.2) t0

and Electrical charge (Q) =

Z

tf

I(t)dt

;

[As]

(2.3)

t0

Waveform D represents a typical restrike, after the primary strike to the airframe, which is used to certify the majority of the fuselage. Waveform D calls for a maximum of 100 kA, released in less than 0.5 ms, and an action integral of 250 × 103 A2 s. However, strikes of 100 kA prescribed by waveforms D are typically used to strike full scale test articles or subcomponents that are representative of actual hardware, but 100 kA is too high for testing coupon-sized specimens such as those used in this work. Herein, strikes of 40 kA are used, corresponding to an action integral of 39.55 × 103 A2 s, i.e.,
I(t) = 43762.0 e−α t − e−β t (2.4) α = 22708.0, ; β = 1294530.0 The action integral is a measure of the delivered energy carried by the waveform current. The test setup type I, shown in Figure 2.3, is mainly used by researchers to investigate lightning strike damage as it is less expensive than type-II to build. The short distance between cathode and anode requires a small capacitance to generate the required current. Type II lightning strike test (Figure 2.4) uses a spherical electric isolator to minimize the effect of overpressure generated during lightning strike. Then, a thin copper wire (diameter < 0.1 mm) is used to guide the electric charge towards the composite panel. Currently, waveform-C is the only electric current that is numerically simulated using multi-physics software, as discussed in the next section.

2.3

Virtual verification

Abdelal [23] used coupled thermal-electrical FE analysis to simulate waveform D strike on a composite panel specimen located on top of a copper plate. The simulation considers an electric current applied at the composite panel center. Appropriate

34

Multifunctional Composites

Figure 2.4: Test setup of composite panel under lightning strike type II. electrical and thermal boundary conditions are applied to represent the experimental setup. Temperature dependent thermal/electrical material properties are modeled and the heat generated in the panel specimen due to heat resistivity is also modeled. A lightning strike (electric arc) can be described as a channel of negative electrons advancing at very high speed between two leaders (clouds to earth). Clouds act like a cathode with a negative electrode and are the source of electrons (electron donor). The earth acts like an anode with a positive electrode (electron acceptor). The electric arc is a response to a breakdown of the medium in the gap between two electrodes that occurs when the voltage across the gap is sufficiently high. Once the breakdown occurs, an ionized region is formed in the gas between the two electrodes and current flows through the ionized region. For lightning, the arc velocity is approximately 2 × 105 m/s, carrying a charge of about 2 to 20 ×10−4 Coulombs. Fisher [1] reported that the current channel has surge impedance of the order of 3000 Ohms for a return stroke of amplitude 100 kA. This large impedance is due to the resistance associated with the collection of charge at the upper end of the lightning channel. Once the charge has been collected and the current in the channel reaches its final value, the longitudinal resistance becomes smaller, of the order of 500 Ohms. As noted earlier, the energy released in the ionized region is enough to raise the temperature of the current path to 30,000 K (plasma). Thus arc interaction with a structure has both thermal and mechanical effects. The thermal effect is due to plasma current on the aircraft surface and joule heat effect due to electric resistivity of the aircraft structure. Kaddani et al. [24] derived an equation to describe the heat flux from plasma arc to aircraft surface   5kb QA = J Ua + Φmat + (Tpl − Tmat ) ; [W/m2 ] (2.5) 2e where J [A/m2 ] is the total current, Ua [V] is the voltage drop near the anodic surface, Φmat [V] is the material work function due to current J, kb is Boltzman’s

35

Lightning strike protection systems

constant, e is the electron electrical charge. The material work function, which is related to the cathode material, is the minimum energy required to release electrons from the ground atoms (first energy level electrons). The conductive flux is negligible in the case of high current arcs [5], such as lightning, and thus is not considered in the proposed model. The integral form of Maxwell’s equation of conservation of electric charge is given by Z Z J . n dS = rc dV (2.6) v

S

where V is the control volume with surface S, n is the outward normal to S, J is the electrical current per unit area (current density), and rc is the internal volumetric current source per unit volume. The flow of electrical current is described by Ohm’s law J = σ E . E = −σ E .

∂φ ∂x

(2.7)

where φ, E, and σ E are the electrical potential, electrical potential, and electrical conductivity, respectively. The electrical conductivity σ E can be isotropic, orthotropic, or anisotropic, and it is independent of the electrical field E. The amount of electrical energy dissipated by current flow in a conductor is described by Joule’s law Pec = JE =

∂φ E ∂φ σ = Eσ E E ∂x ∂x

(2.8)

In transient analysis, an averaged value of Pec is calculated over the time increment ∆t, as Z 1 1 Pec = Pec dt = Eσ E E − Eσ E ∆E + ∆Eσ E ∆E (2.9) ∆t 3 where E and σ E are values at time t and ∆t. The amount of energy released as internal heat within the body, is r = νv Pec , where νv is an energy conversion factor. Finally, the thermal energy balance is described by Z Z Z ρ U˙ δθ dV = q dS + r dV (2.10) V

S

V

·

where V is the volume with surface S, ρ is the density, U is the time rate of internal energy; q is the heat flux per unit area, and r is heat generated inside the body. The thermal performance of the composite laminate will be necessarily different from the performance of the LSP system. While the thermal performance of the composite material may be characterized by resistive heating, decomposition, and ablation, that of the protection system may be characterized by resistive heating, melting, evaporation, and ultimately explosive boiling. Oliveira [25] discusses the principles of phase explosion (explosive boiling).

36

Multifunctional Composites

Normal boiling with heterogeneous nucleation occurs at a temperature close to the boiling temperature (Tb ), but if superheating takes place and the temperature is near the critical temperature (Ttc ), then phase explosion may occur by homogeneous nucleation. Phase explosion is characterized by surface break down within a very short time period, resulting in vapor and equilibrium liquid droplets. This means that the design of a protection system is limited by the critical temperature of its material, as increased damage will arise if explosive boiling occurs. Rather than modeling explosive boiling, it is avoided by designing the LSP system in such a way that it does not reach critical temperature. The assumed ablation mechanism is vaporization because explosive boiling only occurs when the target reaches thermodynamic critical temperature. The flow of vaporized material from the surface (ablation rate, m/sec) follows the Hertz-Knudsen equation    r 1 Lv 1 m Po − exp (2.11) v (T ) = 2πkB T ρ R Tb T where m is the atomic mass of the material, Tb is the boiling temperature at the pressure p0 , kB is Boltzmann’s constant, and Lv is the latent heat of vaporization of the material. The heat conduction equation is ρ (T ) Cp (T )

∂T (x, y, z, t) = ∇ [k (T ) ∇ (T (x, y, z, t))] + R (t) ∂t

(2.12)

where x, y, and z are the space coordinates and ρ, Cp , k, are the mass density, specific heat at constant pressure, and thermal conductivity of the target material, respectively. The source term R(t) represents the thermal energy absorbed by the material. The heat of decomposition of composite materials can be modeled using one of two techniques. The first one is to add the latent heat to Cp [26] Cp = Cpb fb + Cpa fa + Hs Mi (1 − α) Mi (1 − α) + Me α Me α = Mi (1 − α) + Me α

fb = fa

dα dT (2.13)

where CP B and Cpa are the specific heat of the composite and char material, respectively, fa and fb are the volume fraction of the composite and char material, respectively, Hs is the decomposition heat and α is the decomposition degree; Mi is the initial mass of composite material (ρ0 Volume), Me is the final mass of composite material (Mi ff 0 ), and ff 0 is the initial fiber volume fraction. The second technique is to rewrite the heat conduction equation as ρ (T ) Cp (T )

∂T (x, y, z, t) ∂α = ∇ [k (T ) ∇ (T (x, y, z, t))] + Q (t) − ρ Hs ∂t ∂t (2.14)

R ) to model the and use the heatval user material subroutine (available in Abaqus decomposition kinetics and heat during the lightning strike event. Decomposition

Lightning strike protection systems

37

heat is negative energy, which is consumed by the kinetic reaction. Damage in composite materials can be reduced by increasing the value of decomposition heat. Commonly, the epoxy decomposition can be simulated by modeling the pyrolysis behavior of the composite, which can be estimated using thermogravimetric analysis. The experimental results reported by Ogasawara [10] can be described by   dα = A exp −Q/RT (1 − α)n dt

(2.15)

where R is the universal gas constant (R = 8.31 J/mol/K). The estimated parameters are n = 3.5, A = 5.0 × 1013 min−1 , and Q = 180 kJ/mol/K. The heating rates applied during the experimental setup are of 2.5, 10, or 20 C/min. The onset of weight reduction is around 300 C, with no further change by 500 C. However, using (2.15) to model the decomposition rate is not appropriate because the heating rate under lightning strike conditions is much higher than the experimental applied heating rate. The experimental composite panel specimen is made of carbon fiber/epoxy (IM600/133), with a 32-ply quasi-isotropic layup ([45/0/−45/90]4S ). The ply thickness is 0.147 mm, resulting in a panel thickness of 4.7 mm. The specimen is 300 by 300 mm. Material thermoelectric properties, such as thermal conductivity, specific heat, and sublimation heat are defined in Tables 2.3–2.4. The composite panel is divided into two partitions. One partition represents the region under the lightning strike conducting channel. The second partition represents the remaining part of the composite specimen. The latent decomposition heat of the fiber/epoxy material is assumed to be 4.8 × 103 KJ/Kg, which is released between 300 C and 500 C. A linear rate of decomposition is assumed in the decomposition temperature range. The latent sublimation heat, which is released at sublimation temperature of 3,316 C, is assumed to be 43 × 103 KJ/Kg. The last two rows in Tables 2.3–2.4 are the assumed thermo-electrical properties of the ablated gas in regions of the experimental specimen once ablation has occurred. The electric properties of any ablated regions under the lightning conducting channel are defined to have high conductivity in the thickness direction to allow the electric charge to move to the next layer into the specimen once the preceding layer has been ablated. Ogasawara et al. [10] did not include the thermal conductivity between composite laminates. Thermal contact-conductivity has been measured experimentally [27] and found at room temperature to be of the order of 500 W/m2 K. As the epoxy thermal conductivity is reduced by 30% after it is decomposed, the thermal contactconductivity is also reduced by the same percentage. To date there is no available published data for the electric contact-conductivity between composite laminates. Thus, it is assumed to be perfect within the simulations. For illustration, a copper mesh is used for LSP. The copper mesh thickness is assumed to be 0.05 mm and to cover 24% of the specimen surface area. However, the proposed modeling technique is generic and may be applied to different protection systems, such as aluminum mesh or paint. The function of the copper mesh is to conduct the lightning strike electric charge quickly to protect the underneath composite material from damage. It is assumed that copper will heat up, according

38

Multifunctional Composites

Temperature

Density

◦C

kg/mm3 J/kg ◦ K 1.52E-06 1065 1.52E-06 2100 1.10E-06 2100 1.10E-06 1700 1.10E-06 1900 1.10E-06 2509 1.10E-06 5875 1.10E-06 5875 (#) no-load elements.

25 343 500 510 1000 3316 >3316 (*) gas >3316 (#) gas (*) load elements.

Specific heat

Longitudinal thermal conductivity 1/Ω mm 0.008 0.002608 0.001736 0.001736 0.001736 0.001736 0.001015 0.001015

Transverse thermal conductivity 1/Ω mm 0.00067 0.00018 0.0001 0.0001 0.0001 0.0001 0.001015 0.001015

Table 2.3: Carbon fiber/epoxy thermal properties vs. temperature. Data taken from [28, 29].

Temperature

◦C

25 343 500 510 1000 3316 >3316 (*) gas >3316 (#) gas (*) load elements.

Longitudinal Transverse electrical electrical conductivity conductivity 1/Ω mm 1/Ω mm 35.97 0.001145 35.97 0.001145 35.97 2 35.97 2 35.97 2 35.97 2 0.2 0.2 0.2 0.2 (#) no-load elements.

In-depth electrical conductivity 1/Ω mm 3.88E-06 3.88E-06 2 2 2 2 1.00E+06 0.2

Table 2.4: Carbon fiber/epoxy electrical properties vs. temperature. Data taken from [28, 29].

39

Lightning strike protection systems Temp.

Density

Specific heat

◦C

kg/mm3 8.95E-06 1.10E-06 1.10E-06 1.10E-06

J/kg ◦ K 385 431 431 490.952 550

25 500 510 1000 1700 2600 3227 8000

Longitudinal Thermal conductivity 1/Ω mm 0.401 0.37 0.339 0.15 0.18 0.18

Longitudinal electrical conductivity 1/Ω mm 58140 20120 4651 3704 2404 2227 1500 1400

Table 2.5: Copper thermal and electrical material properties. Melting temp. 1083 C, Boiling temp. 2800 C, Critical temp. 8000 C. Data taken from [30–32]. to its specific heat, until it reaches its melting temperature point (1,083 C) and it consumes the heat of fusion (2.05 × 105 J/Kg). Above this temperature the copper will heat up until it reaches its boiling point (2,567 C) and will start consuming its heat of evaporation (4.8×106 J/Kg) as it evaporates. Heating up and evaporation of copper is stopped by either total ablation, or explosive boiling of the copper mesh, as it reaches its critical temperature (8,000 C). Since the effect of explosive boiling is not modeled, the critical temperature is used as a simulation limit. Copper thermo-electrical properties are listed in Table 2.5. Copper thermal performance is simulated in Abaqus using a user material subroutine UMATHT [33], which defines the thermal constitutive behavior of the material as well as internal heat generation during the heat transfer processes. It also defines the internal energy per unit mass and its variation with respect to temperature and to spatial gradients of temperature, and the heat flux vector and its variation with respect to temperature and to gradients of temperature. The material subroutine calculation steps are: 1. Calculate the material specific heat due to latent heat (melting, evaporation). CP =

Cps + Cpl HL + ∆Tm 2

(2.16)

where HL is material latent heat (melting, evaporation), Cps is material specific heat at solidus temperature, Cpl is material specific heat at liquids temperature, and ∆Tm is the difference between liquids and solidus temperatures. 2. Calculate the change in internal energy due to heat conduction ∆U c = Cp ∆T

(2.17)

3. Calculate the change in internal energy due to joule heat effect ∆Ue = µ Pec (1/ρ)

(2.18)

40

Multifunctional Composites where µ is the joule heat factor (0.92), Pec is the dissipated electrical energy, and ρ is the material density. 4. Check material ablation using (2.11), and explosive boiling temperature. 5. Calculate total change in internal energy, ∆Ut = ∆Uc + ∆Ue .

The simulation boundary conditions are defined to match as closely as possible the experimental setup of Ogasawara [10]. Thus, the electrical potential at the bottom of the specimen is assumed to be zero, as the conducting copper plate is electrically grounded in the experimental setup (Figure 2.3 ). The electrical potential at the side surfaces is also assumed as zero, because electrical discharge from the side surfaces to the bottom copper plate is observed during impulse tests [23]. Thermal radiation is allowed for the upper and side surfaces of the specimen, whereas the bottom surface is assumed to be adiabatic. Although it is clear that heat transfer to the copper plate at the bottom surface should be included in the analysis, initial analysis indicates that the temperature increment at the bottom of the specimen is negligible. It is therefore ignored. The emissivity and environment temperature are assumed to be 0.9 and 25 C, respectively. Researchers usually apply electrical charge at the center node of the composite plate using a concentrated electric charge time profile in FEA. This type of load application is appropriate only for electromagnetic analysis, but not for thermal/structural analysis [23]. Applying electric load at a single one node makes the temperature profile at this node and the surrounding area dependent on mesh density. Increasing the number of elements around this point leads to increases in temperature profile. Thus, ignoring the size of lightning bolt, which range from 1 to 10 mm in diameter [7], significantly influences the predicted results. Thus, a 10 mm diameter conducting electrical channel is assumed in this example. Modeling a realistic electric channel eliminates local modeling issues. A quarter model of the specimen is used due to symmetry (Figure 2.5). Each lamina of the composite laminate [45/0/ − 45/90]4S is meshed using eightnode isoparametric solid elements. Symmetry of the laminate is used to discretize only in the top half of the specimen. Orthotropic material properties are calculated for the elements in the bottom half of the composite panel. The copper mesh geometry is modeled in detail at the specimen center (50 x 50 mm) but idealised elsewhere using averaged properties (Figure 2.5). The copper mesh is meshed with R R12). Each of the 16 laminas above the mid 8,503 DC3D8E elements (Abaqus surface is meshed with 437 DC3D8E elements, while the 16 laminas below the mid surface are modeled using DC3D8E elements and average orthotropic properties. The total number of elements is 13,972. Two simulations are presented: Case I and Case II. Case I is for the specimen without copper mesh, allowing comparison with published literature. Case II is with copper mesh, allowing comparison of thermal damage between Case I and II. The experimental results (Figure 2.6) show recession up to 0.6 mm. The simulation predicts thermal damage up to 0.73 mm (5th ply) layer (Figure 2.7 ), which agrees well with the simulation results.

Lightning strike protection systems

41

Figure 2.5: Discretization of the meshed panel. Darker area represents the mesh for the LSP. The remaining surface has averaged LSP properties.

Figure 2.6: Cross-section of the CFRP laminate. Reprinted from [10], copyright (2010), with permission from Elsevier.

Figure 2.7: Decomposed laminate layout showing the depth of thermal damage.

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Multifunctional Composites

Figure 2.8: Temperature distribution on the top lamina at the end of step-1. Experimentally, recession is primarily due to epoxy decomposition, which leaves a mix of fibers and carbon. The applied load (peak of 40 kA) and the conducting electric channel (diameter of 10 mm) does not result in fiber ablation as peak fiber temperature is below 3,316 C. In [10], use of a single node load application causes unrealistic simulation temperatures (> 104 C). In such case, inclusion of an artificial electric conductivity is necessary to simulate the ablation mechanism of each lamina and the application of the electric current load to the next lamina, but this is not necessary with the modeling method proposed herein. The temperature profile of the top lamina at the end of step-1 is shown in Figure 2.8 . As shown in Figure 2.9 , the temperature is cooler at the lamina center, as the electric potential gradient is higher along the in-plane direction than the through the thickness. Thus the dissipated electric energy (2.8) is higher further from the strike center. This is due to the lower electric conductivity in the through thickness direction and electric contact-conductivity between laminas. Thus the electric current follows the easier path along the lamina fiber directions (the top lamina is a 45 degree lamina). The maximum temperature achieved is 2,588 C, and the average temperature in the area in contact with the lightning strike conducting channel is 550 C, thus the epoxy is fully decomposed but the lamina is not ablated. The temperature profile of the top lamina at the end of Step-2 is shown in Figure 2.10.a, while the decomposition degree is shown in Figure 2.10.b. The decomposition is defined in the range 0 to 1, where 0 represents pristine composite material and 1 represents fully decomposed resin material, with properties that are a mix of resin char and carbon fibers. The heat energy coming from dissipated electric energy is transferred along the top lamina fibers, which are oriented in the 45 degree direction. Assuming the damage threshold is defined by a decomposition value of 0.3, the predicted damage area is approximately 16 by 16 mm. Thus, for the top lamina, the damaged area is similar to the loaded area. The predicted decomposition for the 2nd lamina has a maximum width of 40 mm. The prediction agrees well with the experimental results [10] shown in Figure 2.11. The lightning current strikes the top lamina, which decomposes with time while the local elec-

Lightning strike protection systems

43

Figure 2.9: Electric potential gradient on the top lamina.

Figure 2.10: (a) temperature profile and (b) decomposition of the top lamina at the end of Step-2. trical/thermal material properties change from pristine properties to a mix of char and carbon fiber properties. Char has a higher electric conductivity, which results in increased conductivity in the thickness direction. The electric current thus reaches the 2nd lamina with longitudinal fibers (at 0 degree). This lamina conducts the electric charge along the fiber direction and conducts thermal heat from the top lamina. This accelerates the decomposition along the 0-direction and produces the results shown in Figures 2.7 and 2.11. Top views of the decomposition profile in the 2nd, 3rd, 4th, and 5th laminas are shown in Figure 2.12. Damage size is approximately 40 X 12 mm in the 2nd lamina, 22 X 22 mm in the 3rd lamina, 6 X 30 mm in the 4th lamina, and 6 X 6 mm in the 5th lamina. The damage area is clearly a function of the thermal conductivity of each lamina and thermal contact-conductivity between adjacent laminates. The temperature profile at five locations along the panel centerline is shown in Figure 2.13. The resin is locally decomposed resulting in variable thermal/electrical properties. Char, which has higher specific heat and higher convection to air, does not cool as quickly as pristine composite. In this case, modeling char material properties after decomposition enables realistic prediction of damage. Also, by using an increased electric conductivity for the char material in the thickness direction, the model is able to capture the shift of the conducting electric channel. The function of the protecting copper mesh is to conduct the electric charge

44

Multifunctional Composites

Figure 2.11: Side view of decomposition profile.

Figure 2.12: Decomposition profile for 2nd, 3rd, 4th, and 5th layer, respectively.

Figure 2.13: Temperature profile for up to 5 nodes on the centerline, along the thickness direction, for (a) time step 1 and (b) time step 2.

Lightning strike protection systems

45

Figure 2.14: Temperature and ablation of the copper mesh near the loading area. rapidly away from the lightning strike zone, thus reducing the damage to the composite panel. Copper conducts electric charge, heats it up to the melting point (1,083 C), then up to the evaporation temperature (2,567 C), and finally it starts to ablate. The damage mechanism for the composite material is controlled by the heat conduction from the copper mesh, which is defined by the thermal contactconductivity between the copper mesh and the composite material. Two figures are now discussed to elucidate the behavior of the copper mesh under lightning strike at two different locations. Temperature and ablation profiles at a point 7 mm from the center of the lightning strike are shown in Figure 2.14. The ablation is not fast enough to stop copper from heating to its critical temperature (8,000 C). This means copper in the area of the lightning strike heats up to explosive boiling and may cause more damage to the composite panel. The effect of explosive boiling damage is not modeled, assuming it has to be avoided by design. Temperature and ablation profiles at a point on the copper mesh at a distance 14 mm from the center of the lightning strike are shown in Figure 2.15. Here ablation is controlled by heat conduction in the copper mesh and ablation occurs faster than in the previous case. The thickness of the copper mesh is fully ablated at a temperature of 2,616 C. Fast ablation of the copper mesh at lower temperature means less composite damage due to heat conduction. Slower ablation in the area of the strike leads to greater local damage but could be reduced by reducing the thermal contact-conductivity between the copper mesh and the adjacent composite lamina. Thus, using and adhesive with reduced thermal conductivity, between the copper mesh and the composite panel, reduces both heat conduction and the damaged area in the composite panel. Excluding the effect of explosive boiling, damage to the composite material in the protected specimen is down to the 3rd lamina (Figure 2.16). The damage area

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Figure 2.15: Temperature and ablation of the copper mesh away from the loading area. is 24 X 24 mm in the top lamina, 30 X 20 mm in the 2nd lamina, and 12 X 12 mm in the 3rd lamina. These results are based on the assumption that the thermal contact-conductivity between copper and composite has the same values as between laminas. Thus, the use of a copper mesh only reduces the maximum damage area by 25% for the case of a 40 kA lightning strike on a composite panel. Two techniques can be used to further reduce the damaged area of composite. One technique is to reduce the thermal contact-conductivity, and the second is to use a thinner copper mesh that ablates at a reduced temperature, for example 5,500 C. It is a general practice of the aerospace companies to include a Glass/Epoxy lamina in between the copper mesh and the composite panel. Two advantages can be achieved by the inclusion of Glass/Epoxy lamina. One advantage is to act as a thermal insulation layer between the copper mesh and the composite panel. The second advantage is that Glass/Epoxy has two reaction heats at high temperature. One reaction heat consumes 239 KJ/kg during decomposition of the Epoxy, and the reaction between carbon and silica consumes 2,093 KJ/kg.

2.4

Free electric arc model

The lightning channel is thermal plasma (temperature > 10,000 C) that consists of electrons, atoms, and molecules at ground state or excited state, positive ions, negative ions and photons. Simulating the lightning channel is essential to estimate the electric current density profile, pressure wave profile, and heat flux profile applied to the aircraft structure. Accurate simulation of thermal plasma requires calculating composition, thermodynamic, and transport properties of the plasma [34, 35]. R [36] has a module that models thermal plasma, but reCOMSOL Multiphysics

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Lightning strike protection systems

Figure 2.16: Decomposed area for the top 3 layers. quires background experience in atomic, molecular, and gaseous electronics theory. However, plasma can be modeled using a simpler technique that is often sufficiently accurate. A macroscopic description of plasma can be used instead of describing plasma in terms of its components. Magnetohydrodynamics (MHD) [34–46] studies the motion of an electrically conducting fluid in presence of an applied magnetic field. Once the fluid starts conducting electricity, a magnetic field is induced that applies an electromagnetic force (Lorentz force) on the flow. The Lorentz force modifies the fluid velocity and pressure profiles. The governing equations of MHD describe the motion of a conducting fluid in a magnetic field. These set of equations include Navier Stokes equations for fluid flow, Maxwell’s equations of electromagnetism, and thermal conduction equations for heat transfer. These partial differential equations can solved numerically using FEA (e.g., COMSOL) or a finite R ). volume method (e.g., Fluent The lightning strike electric arc model is based on gas tungsten arc (GTA) models [47–52]. Some researchers simulate the arc-plasma region with imposed temperature values at the cathode and anode boundaries [47–51]. Other researchers model the anode and cathode behavior separately; thus taking into account the discontinuities between the arc-plasma interface and the anode. Lago et al. models [51, 52] do not include the cathode region, but simulate the effect of metal vapor in the plasma column and a moving torch. The models of Tanaka and Lowke [53, 54] are the most complete. They are based on the Sansonnens et al. model [55]. As such, they include both anode and cathode regions with weld pool formation. The boundary conditions are applied directly at the external borders. No assumption about cathode surface temperature is made. Traidia coupled the welding arc and the weld pool dynamic in pulsed GTA welding [34]. However, all these models are extremely expensive in terms of computer time because the heat transfer stability criteria requires that the following equation be satisfied ∆t >

ρc ∆ℓ2 6k

(2.19)

where ∆T is the time increment, ρ is the density, c is the specific heat, k is the thermal conductivity, and ∆ℓ is the characteristic (typical) mesh size. The smaller the time-step required for convergence, the smaller the characteristic length required for the mesh. Thus simulating thermal plasma due to waveforms A, D, which are

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of microseconds scale, or waveform B, which is of milliseconds scale, requires very fine mesh. For example, simulating waveform-B requires time-steps in the range of 10−10 s or less, which requires small elements. Even using large HPC computers, such simulations may take weeks or months to complete. This section proposes a novel solution to the problem by applying similitude theory [56] to create virtual prototype models with equivalent physics, yet of smaller size, to efficiently simulate lightning strike behavior. Novel simulation of the lightning strike waveform-B (milliseconds time scale), which can be extended to simulate waveforms-A or D, is presented next.

2.4.1

Formulation

The following assumptions are made before using MHD equations to model thermal plasma induced by an electric arc channel: • The plasma is at local thermodynamic equilibrium (LTE), which means the electrons and heavy species are at equal temperature. • The fluid flow is Newtonian and laminar.

2.4.2

Electric module (ec) and Magnetic module (mf )

The electromagnetic behavior is modeled using standard Maxwell equations under variable waveform electric current ∇×H =σ E+ε

∂E ∂t

∂H ∂t B = µH, D = εE ∂A E = −∇V − ∂t

∇ × E = −µ

∂D J = σ (E + u × B) +   ∂t ∂A 1 σ +∇× ∇ × A + σ ∇V = 0 ∂t µ

(2.20) (2.21) (2.22) (2.23) (2.24) (2.25)

where H is the magnetic field intensity vector, D is the electric displacement vector, σ is the electrical conductivity of the corresponding domain (cathode, plasma, anode), J is the current density, ǫ is the dielectric constant (permittivity), µ is the domain permeability, E is the electrical field intensity, V is the electrical potential, B is the magnetic flux density, and A is the magnetic potential.

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Fluid flow equations (spf ) The fluid flow is modeled applying the Navier-Stokes equation ∂ρ + ∇ · (ρυ) = 0 (2.26) ∂t      2 − ∂→ υ ρ + υ · ∇υ = ∇ · −pI + µ ∇υ + (∇υ)T − µ (∇ · υ) I + J × B (2.27) ∂t 3 where υ is the velocity vector field, t is time, ρ is density, µ is viscosity, p is the pressure field, J is the electric current density, and B is the magnetic flux density. The choice of fluid flow boundary conditions is very important for both convergence and accuracy. Heat transfer module (ht) The energy conservation equation is used to model heat transfer in the fluid and solid domains   5 kB ∂T + υ · ∇T = ∇ · (k∇T ) + J · E + J · ∇T − 4πεN (2.28) ρ Cp ∂t 2e The last three terms in (2.28) are Joule heating, electronic enthalpic flux, and plasma radiation loss, respectively. Also T is the temperature, k is the thermal conductivity, KB is the Boltzmann constant, e is the electron charge, and ǫN is the net emission coefficient of plasma [34]. Traidia [34] recommends modeling a sheath of thickness 0.1 mm next to the anode surface to simulate the non-local thermodynamic equilibrium (NLTE) condition for the heavy species, as temperature in this layer differs from the electron temperature. This transition sheath zone is modeled as an ohmic conductor, which ensures transition between plasma and cathode. Within this layer the electric conductivity corresponds to the cathode, while the remaining material properties correspond to the plasma. The heat flux at the boundary between the anode and plasma has to satisfy the following equation [34] qanode · n − q · n = |J · n| φa − ε kB T 4

(2.29)

where n is the normal vector to the top surface, φa is the work function of the anode, e is the anode emissivity, and kB is Boltzmann’s constant. The first term |J · n| φa represents heating by electron condensation (energy received by the anode from the incoming electrons). The second term ε kB T 4 represents radiation cooling losses. The heat flux at the boundary between the cathode and plasma has to satisfy the following equation [34] qcathode · n − q · n = ji Vi − je φc − ε kB T 4

(2.30)

where ji and je are the ion current and the electron current, respectively, φc is the cathode work function, and Vi is the argon ionization potential. The first term ji Vi

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represents the heating energy received by the cathode from the impacted ions. The second term je φc represents the energy consumed at the cathode to emit electrons. Electron and ion currents are calculated from the following equations [34] 2



jr = Ar T exp   jr je =  J~ · ~n ji = J~ · ~n − je

 −e φe σB T   if J~ · ~n − jr > 0   if J~ · ~n − jr ≤ 0

(2.31)

where Ar is Richardson’s constant, φe is the effective work function for thermionic emission, and e is the elementary electron charge.

2.5

Similitude modeling

Similitude is a mathematical discipline that includes similarity and dimensional analysis. Similarity means that two physical systems are similar if certain dimensionless ratios are equal in both systems [56]. The requirements of similitude are derived from the main partial differential equations and the initial boundary conditions that describe the system. The first step is to derive the dimensionless form of the main equations that model the system. This derivation will produce dimensionless terms, which are called similarity conditions. The first constraint of similitude is the equality of these similarity conditions in both the prototype and the full scale model. The second similarity constraint is the equality of the dimensionless independent variables that constitute the dimensionless initial and boundary conditions [56]. The input to thermal plasma simulations is the waveform electric current profile. The electromagnetic field is the main volume force that drives the flow in the fluid domain. Thus, the electromagnetic model is the driving force for the simulation. Initially, an absolute model of the electromagnetic system is derived that relates the independent variables in both the full scale and the prototype model, before deriving the similarity conditions of the Magnetohydrodynamic (MHD) system. George [57] discusses two types of electromagnetic models: the geometrical model and the absolute model. The geometrical model simulates the geometrical configuration, while ignoring the power level of the full scale system. The absolute model simulates both the geometrical configuration and the power level of the full scale system. George [57], in his earlier attempt to derive both models based on Maxwell’s equations, stressed that the derivation is only valid if Maxwell’s equations are linear. Nonlinearity of Maxwell’s equations comes from nonlinear media, where the permittivity ǫ is a function of the electric field intensity E. Maxwell’s equations used in modeling thermal plasma are assumed linear and permittivity ǫ equals that of air. For an absolute electromagnetic model, the following conditions

51

Lightning strike protection systems are applied (x, y, z) = d (x′ , y ′ , z ′ ) t = γ t′ E (x, y, z) = α E ′ x′ , y ′ , z ′ , t′




H (x, y, z) = β H ′ x′ , y ′ , z ′ , t′




(2.32)

where d is the scale factor for space, γ is the scale factor for time, α is the scale factor for electric field intensity, and β is the scale factor for magnetic field intensity. Primed variables refer to the absolute model, while unprimed variables refer to the full scale model. Once the four scale parameters are estimated, Maxwell’s equations can be used to derive the relationship between other electromagnetic quantities (I, V, B, ǫ, µ, etc.) in both systems. Rewriting (2.20) for the absolute model and substituting in (2.21) and (2.22) yields
E (x, y, z, t) γ ′ ′ ′ ′ ′
∂E (x, y, z, t) d ∇ × H (x, y, z, t) = σ ′ x′ , y ′ , z ′ , t′ + ε x ,y ,z ,t β α α ∂t d γ ′ ′ ′ ′ ′
∂H (x, y, z, t) ∇ × E (x, y, z, t) = − µ x , y , z , t (2.33) α β ∂t

Similarity between equations (2.33) and (2.20)–(2.21) requires that the following constraints be satisfied σ′ =

dα σ β

;

ε′ =

dα ε βγ

;

µ′ =

dβ µ αγ

(2.34)

as well as the current density vector J ′ and magnetic flux density of the absolute model dασ E d = J β α β dβ 1 B d B ′ = µ′ H ′ = µ = B αγ µ β αγ J ′ = σ′E ′ =

(2.35)

and the total current in I ′ and voltage V ′ of the absolute model Z Z da I J I ′ = J ′ · n′ da′ = d · n 2 = β d dβ a

a′

P 2′ ′

V =

Z

P 1′

′

′

E · dl =

ZP 2

E dl V · = α d αd

(2.36)

P1

where n, n′ are perpendicular vectors on areas a, a′ , respectively, dl is a vector element of length along a curve between two points P 1, P 2. So up to this stage, an absolute model of the electromagnetic system is derived as a function of four scale parameters: d for space, γ for time, α for electric field, and β for magnetic field. The electromagnetic system was chosen as the main scale

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point for the rest of the MHD equations because electric current and magnetic field are the input and the driving force, respectively, for lightning strike simulation. Next, similitude theory is applied on the MHD equations to derive the similarity constraints that are required to develop a virtual prototype model that is simpler and computationally efficient. Based on the work of Kalikhman [58] and Skoglund [56], the dimensionless MHD equations are derived as   L ∂u ˜ ∂u ˜ ∂u ˜ ∂ p˜ p0 + ρ˜ u ˜ · + v˜ · ρ˜ =− + ... ∂x ˜ ∂ y˜ ∂x ˜ ρ0 u20 ∂ t˜ u0 t0       ˜ 2 ∂˜ v ∂ v 4 ∂u η0 ∂u ˜ ∂˜ η0 ∂ η˜ − + η˜ + + ... ∂x ˜ 3 ∂x ˜ 3 ∂ y˜ u0 Lρ0 ∂ y˜ ∂ y˜ ∂ x ˜ u0 Lρ0   ˜z − J˜z B ˜ y J0 B0 L J˜y B ρ0 u20 ∂ T˜ k 0 t0 ∂ ρ˜c˜p = ˜ ρ ˜i ∂t 0 cp0 L ∂ x

∂ T˜ k˜ij ∂x ˜j

!

qg0 t0 q˜ + . . . ρ0 cp0 T0   5 kB˜ J 0 k B T0 ˜ ˜ ˜ ~J · ∇T + ρ˜cp~u · ∇T eρ0 u0 cp0 T0 2e

(2.37)

+

(2.38)

where qg is rate of heat generated per unit volume, and variables with zero subscript are reference parameters. Based on the dimensional analysis of the MHD equations, the similitude constraints are then derived. Each of the similitude constraint is then used with (2.33)–(2.35) to derive the relationship of fluid flow and heat variables between the prototype and the full scale models, as follows L γ σB 2 L d4 uLρ d2 ⇒ um = uF , ⇒ ρm = ρ , ⇒ η = η F τu d ρu βαγ 3 η βαγ 2 ηcp cpm uη γ2 βαγ 2 cpF ⇒ cpm Tm = 2 cpF TF , ⇒ = Lρcp T d k km d2 k F 1 εN τ d2 kT ⇒ k T = k T , ⇒ ε = εN F m m F F Nm Lρu3 βα ρcp T βα

(2.39)

where m refers to the virtual prototype model, F refers to the full-scale model, and the characteristic values for u, ρ, µ, σ, η, Cp , k, TF , ǫN are chosen at randomly selected coordinates (x0 , y0 , z0 ). Thus a prototype model can be developed based on two steps; calculation of the electromagnetic absolute model material properties (ǫ, µ, σ) based on the scaled input electric current I and the four scaling parameters (α, β, γ, d), followed by using the similitude constraints [59] to calculate the fluid flow and the heat flow modules scaled material properties (ρ, η, Cp , k). The objective of scaling is to slow down the applied waveform lightning strike electric current, thus allowing the numerical simulations to use a larger time increment without affecting the heat transfer constraint (2.19).

53

Lightning strike protection systems Temp. K 300 5000 10000 15000 20000 30000

s S/m 200 2300 7200 10100 10500

ρ Kg/m3 1.7 0.1 0.04 0.03 0.02 0.008

η Kg/m/s 0.00025 0.00009 0.00026 0.000058 0.000025 0.000012

CP J/Kg/K 800 1000 2000 7000 5000 8000

k W/m/K 0.2 0.2 0.6 2.3 2.6 5

ǫN W/m3 0 0 1.00E+08 1.70E+09 2.20E+09 4.50E+09

Table 2.6: Material properties vs. temperature for full-scale model. Most data taken from [28]. Argon ionization potential = 15.7 V. Cathode: Tungsten, solid, Ho et al. [36]. Cathode work function = 4.52 V, effective work function = 2.63 V [28]. Anode: Steel AISI 4340 [36]. Anode work function = 4.65 V [28].

2.6

Numerical simulation

COMSOL multiphysics is used to model MHD to simulate thermal plasma due to lightning strike waveform-B, by implementing (2.20)–(2.31). The calculation domain and boundary conditions are shown in Figure 2.17. Zero initial conditions are assumed for all domains. The domain consists of three sub domains: cathode, anode, and fluid (plasma). Material properties for each domain are defined as a function of temperature and they are part of the COMSOL Material Library. The material properties for all domains are given in Table 2.6. Using scaling factors γ = 0.1, d = 1, β = 100, α = 0.01, the relationship between the input scaled and original electric current waveform-B is
I (t) = 11300 e−700t − e−2000t    11300  −700t′ γ ′ ′ ′ I ′ (t) = e − e−2000t γ = 113 e−70t − e−200t (2.40) dβ Thus, the amplitude of the input current is scaled by a factor of 100 and the time is slowed down by a factor of 0.1. Next the electromagnetic, fluid flow, and heat transfer scaled material properties are calculated. They are based on the absolute model and similitude constraints (2.34),(2.35),(2.39). A steady state solution is calculated first assuming a very small current density of 100 A/m2 . The simulation is a multiphysics solution of a highly nonlinear problem. Thus, a steady-state solution is used as initial condition for the transient solver. The mesh is controlled by COMSOL settings (physics-controlled-mesh: extra fine). The resulting number of elements is 14,882. The discretization of the individual domains leads to a model with 199,100 degrees of freedom (dof). Each physics is approximated as follows: • Electric currents (EC): Quadratic elements. • Magnetic field (mf): Quadratic elements. • Heat transfer in fluids (ht): Linear elements.

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Figure 2.17: Geometrical domain and boundary conditions. • Laminar flow (spf): Linear and quadratic elements. Numerical results for temperature, velocity, and pressure at time=0.01 seconds (prototype time scale) are shown in Figures 2.18–2.20, respectively. The factors to convert results to full-scale model are: time = 0.1, temperature = 100, velocity = 10, pressure = 0.1. An HPC2008 windows cluster was used to simulate the problem on a single node (16 cores, 64 GB RAM). Simulation time was 9 hours and 25 minutes.

2.7

Conclusions

Lightning strike is made of plasma at 30,000 K degrees temperature, and electrons that progress at speed higher than 5000 m/sec, to conduct 39.55E3 Joule/Ohm of energy (40 kA strike) within micro-seconds. The lightning strike has direct effects on structures: resistive heating, magnetic forces, and overpressure. A simulation methodology is developed in this chapter using a coupled electrical/thermal FEA, including temperature dependent material properties, char material properties to simulate material status after decomposition, gas material properties to simulate material ablation status, and modeling the complex physics of LSP systems using

Lightning strike protection systems

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Figure 2.18: Temperature contour plot, prototype time scale, waveform-B (factor = 100), range 28.9–81.8 K.

Figure 2.19: Contour plot of velocity magnitude, prototype time scale, waveform-B (factor = 10), range 6.53–255 m/s.

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Figure 2.20: Pressure contour plot, prototype time scale, waveform-B (factor = 0.1), range -7.27 104 –4.45 105 Pa.

UMATH material subroutine. The technique used in this paper captures many aspects of the multiphysics that interact to simulate lightning strike on composite panel. Simulation of the LSP system include melting, evaporation, and ablation, while interacting with the composite panel through temperature dependent thermal contact-conductivity property. Material properties used in simulating lightning strike on composite panels can be classified in two categories. One category includes those that can be experimentally measured, such as electric/thermal conductivity, specific heat, phase transformation temperature and heat, density, as well as char and gas material properties. A second category includes those that are very difficult to measure. These include the size of conducting lightning strike channel, thermal contact-conductivity between composite laminas, thermal contact-conductivity between the protection system and the composite panel, and ablation model. Thus, the simulation code can be used to calibrate the material properties in the second category, fitting model results to experimental data of lightning strike on composite panel coupons. Then, the calibrated model can be used to design a new protection system or for optimization of existing technology. Perhaps thermal contact-conductivity can be measured experimentally and shifted to the first category, but measuring any material property at elevated temperatures up to 3000 K is not easy. Simulation results of the unprotected composite panel agree with the experimental ones. The simulation is capable of capturing the damage size (decomposition area), and the temperature profile in the composite panel. Including a copper mesh to protect composite panel is not efficient due to slow ablation rate of copper near the lightning strike zone, which causes damage due to heat conduction towards the composite panel. Including a low thermal conductivity adhesive between the copper mesh and the composite panel can reduce damage caused by heat conduction from the copper mesh. Areas farther from the lightning strike zone have faster ablation rate, which reduces the damaged area.

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The work in this chapter is the first phase of a research project to investigate the lightning strike problem on composite structures. The protection system, once evaporated, produces different plasma that is ionized and interacts with the plasma of the lightning arc. Its interaction between the plasma arc and the plasma that is produced during evaporation of protection systems is not yet investigated. Also, the contribution of overpressure and magnetic forces has yet to be investigated. Magnetic forces are a major part of damage for metallic structures, yet they may be less important for composite panels. The thickness of the protection system is small compared to the total thickness of the full composite panel, thus magnetic forces effect may be ignored. Estimating the overpressure contribution requires thermal plasma modeling. Many researchers were able to numerically simulate lightning strike waveformC, with a time scale in the range of seconds. Yet simulating waveform-B or D is not trivial due to the constraints on element size and solution step time. One of the earlier trials to simulate a full-scale model required approximately 70 days on a HPC2008 windows cluster. Thus, a numerical solution is required to simulate waveform-B or D efficiently. One way is to invest in developing a new heat transfer element to improve its stability constraints with respect to time increment and mesh element size. The other option, which is proposed in this chapter, is to use similitude on the MHD equations to build prototype models that are efficient. A prototype model was developed based on the electromagnetic absolute model and similarity constraints. The prototype model for waveform-B is capable of estimating current flux, temperature, velocity, and pressure profiles efficiently in less than 10 hrs of computer time. Future work will focus on simulating waveform-D and A using similitude theory.

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[8] P N Gineste, R Clerc, C Castanie, H Andreu, and E Buzaud. Assessment of lightning direct effects damages by modeling techniques. In International Aerospace and Ground Conference on Lightning and Static Electricity, Pittsfield, 2009. [9] B Lepetit, C Escure, S Guinard, I Revel, and G Peres. Thermo-mechanical effects induced by lightning on carbon fiber composite materials. In International Aerospace and Ground Conference on Lightning and Static Electricity, Paris, 2011. [10] T Ogasawara, Y Hirano, and A Yoshimura. Coupled thermal-electrical analysis for carbon fiber/epoxy composites exposed to simulated lightning current. Composites Part A, 41:973–981, 2010. [11] L Chemartin, P Lalande, B Peyrou, A Chazottes, and P Q Elias. Direct effects of lightning on aircraft structure: Analysis of the thermal electrical and mechanical constraints. Journal of Aerospace Lab, 5:1–15, 2012. [12] H Kawakami and P Feraboli. Lightning strike damage resistance and tolerance of scarfrepaired mesh-protected carbon fiber composites. Composites Part A, 42(2011):1247– 1262, 2011. [13] J M Welch. Repair design and test process considerations for lightning strikes. In 3rd FAA/EASA/Boeing/Airbus joint workshop on safety and certification, Amsterdam, NL, 2007. [14] R D Farahani and D Therriault. Electrical conductivity of hybrid/patterned nanocomposites films. In 19th International Conference on Composite Materials (ICCM19), 2013. [15] F Xin and L Li. Decoration of carbon nanotubes with silver nanoparticles for advanced cnt/polymer nanocomposites. Composites Part A, 42(2011):961–967, 2011. [16] Z. Q. Liu, Z. F. Yue, and Y. Y. Wang, F. S.and Ji. Combining analysis of coupled electrical-thermal and blow-off impulse effects on composite laminate induced by lightning strike. Applied Composite Materials, June:1–19, 2014. [17] F S Wang, N Ding, Z Q Liu, Y Y Ji, and Z F Yue. Ablation damage characteristic and residual strength prediction of carbon fiber/epoxy composite suffered from lightning strike. Composite Structures, 117(2014):222–233, 2014. [18] SAE. Aerospace recommended practice ARP 5416. Aircraft lightning test methods. Technical report, SAE, 1999. [19] US DOD. Lightning qualification test techniques for aerospace vehicles and hardware. Technical Report MIL-STD-1757A, US DOD, 1983. [20] J.A. Plumer, J.-P. Moreau, and R.F. Hess. The new aircraft lightning environment and related test waveforms standard from SAE AE4L and EUROCAE WG31. SAE Technical Papers, 1999. [21] Y Hirano, S Katsumata, Iwahori Y, and A Todoroki. Artificial lightning testing on graphite/epoxy composite laminate. Composites Part A, 2015. [22] Dexmet. https://www.youtube.com/watch?v=de5LwdPD0X4, 2005. [23] G Abdelal and A Murphy. Nonlinear numerical modeling of lightning strike effect on composite panels with temperature dependent material properties. Composite Structures, 109(01):268–278, 2014. [24] A Kaddani, C Delalondre, O Simonin, and H Minoo. Thermal and electrical coupling of arc electrodes. High Temp Chem Processes, 3:441–448, 1994.

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Index Carbon nanotube, 221, 275, 276, 322, 362 Carbon/carbon composite, 355 Carbon/phenolic composite, 363 Carboxyl-terminated butadience-acrylonitrile, 74 Carreau-Yasuda model, 150 Cellulose acetate, 290 Charge-coupled device, 254 Chemical vapor deposition, 282 Chlorobenzene, 216 Classical laminated plate theory, 181 Classical lamination theory, 81 Clay nanocomposite, 76 Coefficient of thermal expansion, 344 Comparative vacuum monitoring, 260 Complex modulus approach, 184 Compression after impact, 77, 253, 254 Compression molding, 219 Computational fluid dynamics, 25 Computer numeric control, 249 COMSOL, 46, 47, 53 Constrained layer damping, 146, 171 Constructal theory, 246 Continuum damage healing mechanics, 226 Corona effect, 124 Coulomb friction, 152

5-ethylidiene-2-norbornene, 216 Abaqus, 36, 39, 40 ABS copolymer, 311 Action integral, 33 Aerospace recommended practices, 26 Aging, 262, 296 Aliphatic polyamide, 273 Aliphatic polyurethane, 123 Ammonium perchlorate composite propellant, 344 Ammonium polyphosphate, 326 Analog resistance ablator detector, 352 Anelastic displacement fields, 184 Angiogenesis, 238 Antenna performance, 2 Aramid, 118, 122, 358 Arrhenius eq., 311 Atmospheric radiation, 2 Atmospheric re-entry demonstrator, 356 Augmenting thermodynamic fields, 184 Automated tape placement, 87, 262 Barely visible impact damage, 63, 257 Barium Lead Zirconate Titanate, 387 Bending cracks, 69 Biocomposite, 239 Biomimetic, 215 Bismaleimide, 113 Bisphenol-A, 113 Blade passage frequency, 137 Blow-off impulse, 31 Boltzman, 35, 36, 49 Bulk molding compound, 344 Carbon Carbon Carbon Carbon Carbon Carbon

Damage threshold velocity, 107 Degrees of freedom, 53, 183 Design areas, 1 Dicyclopentadiene, 79, 209, 215, 255 Diels-Alder reaction, 214 Differential scanning calorimetry, 153, 348 Digital image correlation, 245 Dipentaerythritol, 320 Direct current, 377 Direct effects of lightning, 2, 4, 12 Direct frequency analysis, 184

black, 346, 367 dioxide, 306 fiber, 295 lightweight ceramic ablator, 359 monoxide, 306 nanofiber, 362, 366

425

426 Double cantilever beam, 222 Double cleavage drilled compression, 223, 255 Double-cleavage drilled compression, 253 Dynamic mechanical analysis, 173 Dynamic mechanical analyzer, 153 Einstein-Smoluchowski, 241 Elastomeric heat shielding material, 356 Electric currents, 53 Electrical bonding and grounding, 2 Electrical charge, 33 Electrical discharge machining, 249, 355 Electromagnetic compatibility, 1 Electromagnetic effects, 1 Electromagnetic interference, 2 Electrospinning, 252 Electrostatic discharge, 2 EMA3D, 17 EPIKURE, 216 EPON, 216 Erosion efficiency, 117 Ethylene propylene diene monomer, 358 Exfoliation, 283 Failure threshold energy, 63 Federal Aviation Administration, 26 Felt reusable surface insulation, 340 Fiber Bragg grating, 148 Fiber reinforced polymer, 305 Fiber reinforced polymeric ablator, 344 Fiber-metal laminates, 80 Fibrous refractory composite insulation, 342 Finite difference time domain, 10, 17 Finite element analysis, 10, 25, 30, 31, 40, 47, 54 Finite volume method, 47 Fire reaction, 306 Fire resistance, 306 Fire retardant, 306 Flame resistance, 306 Flame retardant, 316, 357 Fluent, 47 Fractional derivative model, 185 Fracture toughness, 254 Free layer damping, 171 Furan-maleimide reaction, 214 Gas tungsten arc, 47 Generalized Maxwell model, 150 Geologically fresh abrasive, 119, 124

Multifunctional Composites Giant magneto-resistance, 396 Golla-Hughes-McTavish model, 184 Graphene, 271, 274 Graphene nanoplatelet, 294, 295 Graphene nanoribbons, 276 Graphene oxide, 274, 282, 284 Grubbs’ catalyst, 215, 219, 224, 227, 255 Hagen-Poiseuille, 241 Halogen-based fire retardant, 307, 317 Healing efficiency, 254 Heat release rate, 313 Heat shielding material, 356 Heat transfer, 53 Hertz-Knudsen eq., 36 Hertzian impact, 152 Hexadecyl functionalization, 276 Hexane, 216 High density carbon/carbon, 355 High intensity radiated field, 2 High-temp reusable surface insulation, 340 Hollow glass fiber, 210 Hydroxyl end-functionalized polydimethylsiloxane, 217 Imidazole, 217 Indirect effects of lightning, 2–4, 12, 13 Integrated layer damping, 171 Interfacial shear strength, 224 Interlaminar shear strength, 244, 363 Intermediate-scale calorimeter, 311 Intumescent fire retardant, 307 Intumescent flame retardants, 319 Kelvin-Voigt, 184 Kevlar, 76, 118, 139, 358 Knots calibrated airspeed, 104 Kundt’s tube, 143 Laminar flow, 54 Laminar flow control, 258 Layer-by-layer deposition, 282 Layered double hydroxide, 290, 322 Layered silicate, 362 Lead zirconate titanate, 152, 386 Lichtenberg figures, 249 Lightning strike protection, 25, 26 Lightweight ceramic ablator, 359 Limiting oxygen index, 311 Liquid droplet erosion, 99 Liquid oxygen kerosene engine, 346

427

Index Local thermodynamic equilibrium, 48 Lorentz force, 47 Low density carbon/carbon, 355 Low-temp reusable surface insulation, 340 Lower flammability limit, 310 Magnesium hydroxide, 326 Magnetic field, 53 Magnetic graphite nanoplatelet, 286 Magnetoelectric, 380, 398, 401, 403, 417 Magnetohydrodynamics, 47, 50 Mars science laboratory entry descent and landing instrumentation, 353 Mass loss rate, 311 Material subroutine, 56 Maxwell, 184 Maxwell eq., 47 Maxwell model, 149 Melamine phosphate, 320, 326 Melamine urea-formaldehyde, 209 Mercaptan, 216 Method of moments, 10 Micro electro mechanical systems, 148 Microfibrillated cellulose, 277 Mineral filler fire retardant, 307 Mineral filler flame retardant, 321 MMT/poly(butylenessuccinate), 284 Modal strain energy method, 187 Moisture vapor transmission rate, 287 Molybdenum disulphide, 115 Montmorillonite, 76, 274, 289, 290, 293, 322, 323, 362 Moving sled, 109 Multi-wall carbon nanotube, 76, 77 Multiple impact jet apparatus, 107, 109 Multiwall carbon nanotube, 221, 277, 367 Murray’s law, 245 Nanocomposite rocket ablative material, 362 Nanostructured polymeric ablative, 360 National Fire Protection Association, 308 Natural rubber, 114 Navier Stokes eq., 47 Newtonian model, 150 Non ablative TPS material, 339 Non-crimped fabric composites, 88 Non-local thermodynamic equilibrium, 49

Normal sound transmission loss, 144 Nuclear electromagnetic pulse, 2 Nylon-6, 311 Oberst beam, 174 Open-circuit voltage, 13 Organically modified layered silicate, 362 Out-of-autoclave process, 262 Outlet guide vane, 138, 141 Oxy-acetylene torch testbed, 349, 366 Oxygen transmission rate, 280 Partial constrained layer damping, 146, 195 PEEK, 76 Pentaerythritol, 320, 326 Percolation, 386 Phenolic, 139 Phenolic impregnated carbon ablator, 359 Phenolics, 343 Phosphorus-based fire retardant, 307 Phosphorus-based flame retardant, 318 Piezoceramic, 152 Piezoelectric, 152, 398, 418 Piezomagnetic, 384, 398, 418 Piezopolymer, 152 Plasticized starch, 277 Poly(acrylic acid), 290 Poly(caprolactam), 362 Poly(ethylene terephthalate), 273, 297 Poly(ethylene-co-methacrylic acid), 213 Poly(methacrylic acid), 286 Poly(methl methacrylate), 249 Poly(methyl methacrylate), 213, 311 Poly(methyl vinyl ether-co-maleic acid), 273 Poly(N-iso-propylacrylamid), 286 Poly(p-phenylene-2,6-benzobisoxazole), 118, 358 Poly(propylene carbonate), 252 Poly(vinyl alcohol), 209, 273, 311 Poly(vinyl chloride), 311 Poly(vinylidene fluoride), 311 Polyacetal, 311 Polyamide, 139 Polyamide-6, 326 Polyamide-6 clay, 326 Polyaryletherketone, 114 Polybutadiene, 311 Polycaprolactone, 252, 276

428 Polycarbonate, 213 Polydiethoxysiloxane, 217 Polydimethylsiloxane, 123, 356 Polyester, 113 Polyether ether ketone, 113, 213 Polyetherimide, 74, 114, 115, 295 polyetherimide, 114 Polyethersulphone, 74 Polyethylene, 311 Polyethylene terephthalate, 213 Polyethylenimine, 113, 282, 284, 290 Polyhedral silsesquioxane, 322 Polyimide, 113, 139 Polyisoprene, 311 Polylactide, 252 Polymer ablative, 338 Polymer layered silicate nanocomposite, 362 Polymer matrix composite, 305 Polymer nanocomposite, 76 Polymer/clay nanocomposite, 284 Polymer/graphene nanocomposite, 284 Polymer/layered silicate nanocomposite, 322 Polyolefins, 273 Polyphenylenesulphide, 115 Polypropylene, 113, 311, 320 Polypropylene/butyl, 151 Polysaccharide, 252 Polysiloxane, 356 Polystyrene, 213, 311 Polystyrene nanocomposite, 284 Polysulfonamide, 358 Polytetrafluoroethylene, 151, 311, 342 Polyurethane, 114, 151 Polyurethane acrylate, 114 Polyvinylidene fluoride, 152 Polyvinylidenedifluoride, 391 Polyvinylpyrrolidone, 285 Power distribution, 2 power law model, 150 Precipitation static, 2 Printed circuit board, 258 Product composite, 383, 418 Product property, 383, 418 Prony series, 184 Pullulan, 252 Pulsating jet erosion test, 107, 109 Reaction to fire, 306 Reinforced carbon carbon, 340

Multifunctional Composites Rigid polyurethane foam, 326 Ring opening metathesis polymerization, 215 Ross-Kerwin-Ungar model, 175 Scanning electron microscopy, 355 Seebeck junction, 355 Sepiolite, 322 Shape memory alloy, 152 Short-circuit current, 13 Silicone, 311, 356 Siloxane, 217 Simulated hail ice, 63 Simulated solid rocket motor, 349 Single degree of freedom model, 134 Single impact jet apparatus, 109 Skin effect, 14 Smoke density, 321 Smoke production, 321 Society for Automotive Engineers, 26 Solid particle erosion, 99, 113 Solid rocket motor, 338 Source/victim testing, 2 Space Shuttle Orbiter, 339 Specific extinction area, 314 Standard linear solid, 184 Stationary sample erosion test, 107, 109 Stiffness recovery, 254 Stiffness reduction, 254 Styrene-butadiene rubber, 114 Super light ablator, 357 Superconducting quantum interference, 396 Taber abraser, 119 Tailored fiber placement, 89 Tapered double cantilever beam, 222, 253 Thermal gravimetric analysis, 153, 311, 348 Thermal mechanical analysis, 348 Thermal protection system, 337 Thermally reduced graphene oxide, 294 Thermocouple, 355 Thermoplastic polyurethane, 114, 276 Time domain analysis, 184 Time-to-ignition, 312 Tortuosity, 271 Total heat release, 323 Transmission loss, 137, 161 Transverse shear crack, 68 Tripentaerythritol, 320 Twaron, 358

429

Index Ultra-high-molecular-weightpolyethylene, 118 UMATH, 39, 56 Unconstrained layer damping, 146, 171 Urea-formaldehyde, 209 Urethane/acrylate, 151 Vacuum assisted resin transfer molding, 219 Van Oort beam, 174 Vaporization of sacrificial component, 212 Vasculature, 212, 237, 238, 240, 242, 248 Vasculogenesis, 238 Vasoconstriction, 238 Vasodilation, 238 Vermiculite, 297

Viscoelastic material, 146, 151, 169 Void volume fraction, 247 Water vapor permeability, 276 Water vapor transmission rate, 280 Wheel and jet, 105 Whirling arm, 109 Whirling arm rain erosion rig, 104 Wicket plot, 178 Width-tapered double cantilever beam, 253 X-ray diffraction, 283 Xyloglucan, 293 Yee cell, 18 Yttrium Iron garnet, 381 Zylon, 76, 358