محمد محمد أحمد مهندس فعال جدا جدا
عدد المساهمات : 654 التقييم : 694 تاريخ التسجيل : 14/11/2012 العمر : 32 الدولة : EGYPT العمل : Student الجامعة : Menoufia
| موضوع: كتاب Mechanics and Analysis of Composite Materials الثلاثاء 16 يوليو 2013, 10:43 pm | |
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أخوانى فى الله أحضرت لكم كتاب Mechanics and Analysis of Composite Materials Valery V. Vasiliev Professor of Aerospace Composite Structures Director of School of Mechanics and Design Russian State University of Technology, Moscow Evgeny V. Morozov Professor of Manufacturing Systems School of Mechanical Engineering University of Natal, South Africa
و المحتوى كما يلي :
CONTENTS Preface v Chapter 1. Introduction 1 1 . 1 Structural Materials I 1.2. Composite Materials 9 1.2.1. Fibers for Advanced Composites 10 1.2.2. Matrix Materials 16 1.2.3. Processing 2 1 1.3. References 27 Chapter 2. Fundamentals of Mechanics of Solids 29 Stresses 29 Equilibrium Equations 30 Stress Transformation 32 Principal Stresses 34 Displacements and Strains 36 Transformation of Small Strains 39 Compatibility Equations 40 Admissible Static and Kinematic Fields 41 Constitutive Equations for an Elastic Solid 41 Formulations of the Problem 48 Variational Principles 49 Principle of Minimum Total Potential Energy 50 Principle of Minimum Strain Energy 52 Mixed Variational Principles 52 References 53 Chapter 3. Mechanics of a Unidirectional Ply 55 3.1. Ply Architecture 55 3.2. Fiber-Matrix Interaction 58 3.2.1. Theoretical and Actual Strength 58 3.2.2. Statistical Aspects of Fiber Strength 62 3.2.3. Stress Diffusion in Fibers Interacting Through the Matrix 65 3.2.4. Fracture Toughness 79 3.3. Micromechanics of a Ply 80 3.4. Mechanical Properties of a Ply under Tension, Shear, and Compression 95X Cunrenrs 3.4.1. 3.4.2. 3.4.3. 3.4.4. 3.4.5. 3.5. 3.6. 3.7. Longitudinal Tension 95 Transverse Tension 97 In-Plane Shear 100 Longitudinal Compression 103 Transverse Compression 113 Hybrid Composites 113 Phenomenological Homogeneous Model of a Ply References 119 117 Chapter 4. Mechanics of a Composite Layer 121 4.1. 4.1.1. 4.1.2. 4.2.1. 4.2.2. 4.3.1. 4.3.2. 4.4.1. 4.4.2. 4.5.1. 4.5.2. 4.5.3. 4.2. 4.3. 4.4. 4.5. 4.6. 4.7. 4.8. 4.9. Isotropic Layer 121 Linear Elastic Model 121 Nonlinear Models I24 Unidirectional Orthotropic Layer 140 Linear Elastic Model 140 Nonlinear Models 142 Unidirectional Anisotropic Layer 147 Linear Elastic Model 147 Nonlinear Models 161 Orthogonally Reinforced Orthotropic Layer 163 Linear Elastic Model 163 Nonlinear Models 166 Angle-Ply Orthotropic Layer 184 Linear Elastic Model 185 Nonlinear Models 188 Free-Edge Effects 201 Fabric Layers 205 Lattice Layer 2I2 Spatially Reinforced Layers and Bulk Materials 214 References 222 Chapter 5. Mechanics of Laminates 225 5.1. 5.2. 5.3. 5.4. 5.4.1. 5.4.2. 5.4.3. 5.5. 5.6. 5.7. 5.8. Stiffness Coefficients of a Generalized Anisotropic Layer 225 Stiffness Coefficients of a Homogeneous Layer 236 Stiffness Coefficients of a Laminate 238 Quasi-Homogeneous Laminates 240 Laminate Composed of Identical Homogeneous Layers 240 Laminate Composed of Inhomogeneous Orthotropic Layers 240 Laminate Composed of Angle-Ply Layers 242 Quasi-Isotropic Laminates 243 Symmetric Laminates 245 Antisymmetric Laminates 248 Sandwich Structures 249Contents xi 5.9. Coordinate of the Reference Plane 251 5.10. Stresses in Laminates 254 5.11. Example 256 5.12. References 269 Chapter 6. Failure Criteria and Strength of Laminates 271 6.1. Failure Criteria for an Elementary Composite Layer or Ply 271 6.1.1. Maximum Stress and Strain Criteria 274 6.1.2. Approximation Strength Criteria 281 6.1.3. Interlaminar Strength 284 6.2. Practical Recommendations and Discussion 285 6.3. Examples 294 6.4. References 300 Chapter 7. Environmental, Special Loading, and Manufacturing Effects 301 7.1. Temperature Effects 301 7.I . 1. Thermal Conductivity 302 7.1.2. Thermoelasticity 307 7.2. Hydrothermal Effects and Aging 317 7.3. Time and Time-Dependent Loading Effects 319 7.3.1. Viscoelasticity 319 7.3.2. Durability 332 7.3.3. Cyclic Loading 334 7.3.4. Impact Loading 340 7.4. Manufacturing Effects 350 7.5. References 362 Chapter 8. Optimal Composite Structures 365 8.1. Optimal Fibrous Structures 365 8.2. Composite Laminates of Uniform Strength 372 8.3. Application to Pressure Vessels 379 8.4. References 392 Author Index 393 AUTHOR INDEX [Plain numbers refer to text pages on which the author (or his/her work) is cited. Boldface numbers refer to the pages where bibliographic references are listed.] Abdel-Jawad, Y.A. 78 119 Abu-Farsakh, G.A. 78 119 Abu-Laila, Kh.M. 78 119 Adams, R.D. 335 363 Adkins, J.E. 124 222 Aleksandrov, A.Ya. 239 269 Alfutov, N.A. 200 222 Anderson, J.A. 338 362 Annin, B.D. 275 300 Aoki, T. 87 120 Apinis, R.P. 337 362 Artemchuk, V.Ya. 315 363 Ashkenazi, E.K. 284 300 Ashton, J.E. 253 269 Ami, V.D. 180 223 Baev, L.V. 275 300 Barbero, E.J. 283 300 Barnes, J.A. 310-311 362 Belyankin, F.P. 276 300 Birger, LA. 134 222 Bogdanovich, A.E. 15 27 91 119 Broutman, L.J. 271 300 329 363 Brukker, L.E. 239 269 Bulavs, F.Ya. 95, 117 120 211 223 272 300 320, 332 363 Bulmanis, V.N. 318 362 Buskel, N.C.R. 338 363 Chamis, C.C. 156 222 Chen, H.-J. 239 269 Cherevatsky, A.S. 196 222 Chiao, T.T. 77 119 181 222 Chou, T.W. 15 27 338 363 Crasto, AS. 112-1 13 119 Curtis, A.R. 112 120 Dow, N.F. 107 Doxsee, L. 341 363 Dudchenko, A.A. 169 223 Dvorak, G.J. 340 363 Elpatievskii, A.N. 174, 180 223 Ermakov, Yu.N. 334335 363 Farrow, G.J. 310-311 362 Fukuda, H. Fukui, S. 205 222 15 27 77 120 Gere, J.M. 108 120 Gilman, J.J. 59 120 Gol'denblat, 1.1. Gong, X.J. 151, 156 223 Goodey, W.J. 17 28 66 120 Grakova, T.S. 318 362 Green, A.E. 124 222 Gudmundson, P. 180 223 Gunyaev, G.M. 116 120 319 Gurdal, Z. 41 53 Gurvich, M.R. 95, 117 120 211 223 Gutans, Yu.A. 63 120 271, 277, 286, 291 300 Griffith, A.A. 61-62 120 272 300 320, 332 363 Ha, S.K. 315 362 Hahn, H.T. Hamilton, J.G. 311 362 Haresceugh, R.I. 112 120 Hashimoto, S. 205 222 Hashin, Z. Herakovich, C.T. v, 142, 146, 162 222 Hodgkinson, J.M. 338 363 145, 180 222 271 300 94 120 180 222 271 300 359 362 379, 391 392394 Author index Hondo, A. 205 222 Huber, M.T. 293 Hyer, M.W. 359 362 Ilyushin, A.A. 133, 139 223 Ishida, T. 340 363 Ivanovskii, V.S. 352 363 Jackson, D. 310-311 362 Jeong, T.H. 87 120 Jones, R.M. 91, 96, 107 120 143 223 278 300 Kanagawa, Y. 340 363 Kanovich, M.Z. 118-1 I9 120 Karmishin, A.V. 253 269 Karpinos, D.M. 20 28 Katarzhnov, Yu.1. 279-280 300 Kawata, K. 205 222 Khonichev, V.I. 337 362 Kim, H.G. 87 120 Kim, R.Y. 112-113 119 Kincis, T.Ya. 96, 113 120 Kingston-Lee, D.M. 308 363 KO,F.K. 15 27 Kobayashi, R. 205 222 Koltunov, M.A. 118-1 19 120 Kondo, K. 87 120 Kopnov, V.A. 271, 277, 286, 291 300 Krock, R.H. 271 300 329 363 Kruklinsh, A.A. 95, 117 120 211 223 Kruzhkova, E.Yu. 318 363 Kurshin, L.M. 239 269 Kutinov, V.F. 336, 355 272 300 320, 332 363 Lagace, P.A. 96 120 186, 196223 Lapotkin, V.A. 315 363 Lee, D.J. 87 120 Li, L. 341 363 Limonov, V.A. 338 362 Lungren, J.-E. 180 223 Margolin, G.G. 276 300 Matthews, F.L. 338 363 Mikelsons, M.Ya. 63, 337-338 362 Mileiko, S.T. 79 120 Milyutin, G.I. 318 362 Mises, R. 293 Miyazawa, T. 77 120 Morozov, E.V. 222 223 277 300 360-362 363 Morton, J. 338 363 Murakami, S. 340 363 Nanyaro, A.P. 284 300 Natrusov, V.I. 118-1 19 120 Ni, R.G. 335 363 Obraztsov, I.F. Otani, N. 205 222 79 120 200 222 379. 391 392 Pagano, N.J. 150,221 223 Pastore, C.M. Patterson, J.M. 311 362 Perov, Yu.Yu. 318 363 Peters, S.T. 9, 15, 27 28 Phillips, L.M. 308 363 Pleshkov, L.V. 118-1 19 120 Polyakov, V.A. Popkova, L.K. 360-362 363 Popov, N.S. 318 362 Prevo, K.M. 311 363 Prokhorov, G. 275 Protasov, V.D. 336, 339 363 Prusakov, A.P. 239 269 15 27 91 119 15 28 215-216 223 Rabotnov, Yu.N. 331 363 Rach, V.A. 352 363 Reese, E. 338 363 Reifsnaider, K.L. 180 223 Rogers, E.F. 308 363 Roginskii, S.L. 118-1 19 120 Rosen, B.W. 94, 107 120 Rowlands, R.E. 271 300 Roze, A.V. 87, 354 363 Rrenjie, W. 341 363 Salov, O.V. 183223 Salov, V.A. 182-183 223 Schapery, R.A. 329 363 Schulte, K. 338 363 Scott, M.L. 15 27 Sendeckyj, G.P. 271 300 Shen, S.H. 317 363 Sibiryakov, A.V. 344 363 329 363Author index 395 Sih, G.C. Simms, 1.J. 310-311 362 Skudra, A.M. 272 300 320, 332 363 Sobol’, L.A. 315 363 Soutis, C. 316 363 Springer, G.S. 315, 317 362-363 Strife, J.R. 31 1 363 Sukhanov, A.V. 315 363 77 119 181 222 275 300 95, 117 120 211 223 Takana. N. 205 222 Tamuzh, V.P. 77 119 156 222 275 300 Taraschuch, 1.V. 338 362 Tarnopol’skii, Yu.M. 336, 338 362 339 363 15,20 28 64, 87,96, 113 120 215-216 223 354 362-363 391 392 Tatarnikov, O.V. 277 300 Tennyson, R.C. 284 300 Tikhomirov, P.V. 78 120 Timoshenko, S.P. 108 120 Toland, R.H. 271 300 Tomatsu, H. 77 120 Tsai, S.W. 271,278 300 Tsushima, E. 340 363 Turkmen, D. 316 363 145, 150, 180 222-223 239 269 Van Fo Fy (Vanin), G.A. 88,91 120 Varshavskii, V.Ya. 115 120 Vasiliev, V.V. 20 28 41 53 64 120 157, 169, 174, 180-181, 183, 215, 217 222-223 254, 261 269 285, 294 300 344 363 379-380, 391,392 Verchery, G. 253 269 Verpoest, I. 341 363 Vicario, A.A. Jr. 271 300 Volkov, N. 275 Vorobey, V.V. 277 300 150-1 51, 156 223 Wada, A. 15 27 Wharram, G.E. 284 300 Whitford, L.E. 221 223 Whitney, J.M. 253 269 Woolstencroft, D.H. I12 120 Wostenholm, G. 310-31 1 362 Wu, E.M. 271 300 Yakushiji, M. 15 27 Yates, B. 310-311 362 Yatsenko, V.F. 276 300 Yunshu, W. 341 363 Yushanov. S.P. 78 120 Zabolotskii, A.A. 115 120 Zakrzhevskii, A.M. 318 362 Zhenlong, G. 341 363 Zhigun, I.G. Zinoviev, P.A. 200 222 334-335 363 15 28 215-216 223SUBJECT INDEX absorption of moisture 180 acting pulse 343 active loading 132 actual fiber distribution 56 actual strength 58, 62 adhesion 17 adhesion failure 97, 102 adhesion strength 119 admissible kinematic field 41 admissible static field 41 admissible stress state 92 advanced composites 9, 377 aging 317, 319 aging theory 331 Al2O3-A1 composite 96, 167 alumina (A1203) fibers 7, 13 aluminum alloy 131-132, 138 aluminum matrix composite materials 20 aluminum shear web 378 amplitude of stress 334 angle of rotation 157, 226 angle of rotation of a body element 40 angle of rotation of the element 191 angle of rotation of the normal 263 angle-ply antisymmetric panel 359 angle-ply carbon-epoxy laminate 340 angle-ply composite cylinder 361 angle-ply laminate 3I 1 angle-ply layer angle-ply orthotropic layer 184 angle-ply structure 248 anisotropic layer 148, 309 antisymmetric laminates 248, 356 apparent coefficientsof thermal apparent cross-sectional area 207 apparent CTE of a unidirectional ply 308 apparent (effective) mechanical characapparent longitudinal modulus of the apparent material stiffness 142 185, 187, 195-196, 201, 260, 267 expansion 315 teristics I18 PlY 86 apparent modulus 92, 160, 207, 245, apparent modulus of an angle-ply apparent modulus of elasticity 207 apparent shear modulus 86 apparent strain 324 apparent stress 324 apparent thermal conductivity 302-303, apparent thermal expansion coeffiapproach macrophenomenological 273 approximation criterion 292-293 approximation polynomial criteria 291 approximation strength criteria 274, 281, aramid (aromatic polyamide) fibers 12 aramid composite 370 aramid epoxy angle-ply composites 311 aramid fabric skin 306 aramid fabric-epoxy composite 208, 304 aramid fibers 6, 112 aramid-epoxy composite layer 344 aramid-epoxy composite material 8, 336, aramidasbestos fibers 14 asymptotic solutions for inhomogeneous solids 91 atoms’ interaction curve 60 automobile leaf-springs 337, 339 average shear strains 231 average strains 232 average stresses 231-232, 243, 377 averaging of stress and strain fields 91 axial displacement 157, 263 352 specimen 204 306 cients 310 293 344 319 bagasse fibers 14 balanced laminates 242 ballistic limit 347 ballistic test 346-347 397398 Subject index bamboo fibers 14 basalt fibers 6, 11 bending 158, 227, 229,237, 355 bending fatigue test 338 bending moment 157 bending stiffness coefficients of the laminate 239 bending stiffness coefficients 229 bending stiffnesses 239, 241, 253 bending-stretching coupling 242 biaxial braided fabrics 210 biaxial compression of a unidirectional composite 118 bismaleimide resin 6, 19 blade of the turbojet engine compressor 346 body forces 29, 31, 42, 5I boron carbide (B4C)fibers 7, 13 boron fibers 7, 13, 21, 112 boron nitride fibers 7 boron-aluminum composite 20, 79, 96, boron-aluminum unidirectional boron-poxy composite 96,167,304,344, boron-epoxy optimal laminate 378 Borsic 13 boundary and initial conditions 341 boundary and interface conditions 169 boundary conditions 69,73 boundary conditions for free longitudinal houndary-layer solution 266 braided structures 210 braiding 22-23, 215 brittle and ductile metal alloys 79 brittle materials 79 brittle matrix 277 bulk materials 214 bulk modulus 124 bundle of fibers 64 burst pressure 179-180, 299-300 162-163, 167 composite 146 376 edges of the specimen 203 capron fibers 6 carbon composites 378 carbon fabric tape 206 carbon fabric-poxy composite 208 carbon fibers 7, 11, 21, 112 carbon matrix 21, 26, 277 carbon-carbon composites 2I , 96, 167, carbon-carbon conical shell 27 carbon-carbon fabric composite 316 carbon-carbon unidirectional composite carbon-epoxy composite 25, 57, 96, 113, 167, 304, 316, 336, 378 carbon-epoxy cylindrical pressure vessel 177 carbon-epoxy external skin 306 carbon-epoxy lattice layer 306 carbon-epoxy lattice spacecraft fitcarbon+poxy layer 154, 161, 187 carbon-poxy unidirectional ply 177, 197 carbon-PEEK composite 96, I67 carbon-phenolic composite 21 carbon-epoxy ply 75 Carbonic HM-85 fibers 12 carbonization 11, 21, 301 Cartesian coordinate frame 32, 138 Cartesian coordinates 29-30 Castigliano’s formulas 125-126 ceramic composites 21, 30I ceramic fibers 13, 21 ceramic matrix 21, 277 ceramic matrix composites 21 change of the fibers orientation angles changes of curvatures of the laminate 256 chemical shrinkage of the resin 360 chemical vapor deposition circumferential crack 61 circumferential plies 296 circumferential unidirectional layer 140 circumferential winding 25, 350 circumferentially wound cylinder 96 Clapeyron’s theorem 50 coal pitch 12 coefficient of moisture expansion 3I8 coefficient of the strength variation 64 coefficient of thermal expansion coefficientsof the compliance matrix 219 cohesion failure 97, 102 coir fibers 14 combined stress state 278 301 112, 277-278 ting 213 196 13, 21, 24 (CTE) 307Subject index 399 Compatibility conditions 40 compatibility conditions at fiber-matrix compatibility equations 40, 52, 69-70 compatible deformation of the layers 255 complementary elastic potential 125-126, compliance 1 compliance coefficients 86, 152, 156, 230 compliance matrix 45-46 composite beam theory 157 composite body of a space telescope 305 composite bundles 66 composite fibers 182 composite laminate 121, 124 composite laminates of uniform composite lattice shear web structure 214 composite layer 121, 140 composite materials 9, 21-22, 163 composite panel 378 composite pins 215 composite pressure vessel 370, 391 composite profiles 23 composite section of a space telescope 306 composite shell with radial reinforcement composite structures of uniform compression across the fibers 95, 200 compression along the fibers 95 compression failure modes 104 compression molding 24 compression strength of composites 112 compressive cycle 338 compressive direct pulse 343 compressive stress 197 concept of the accumulation of material damage 332 constitutive equation 5, 324 constitutive equation of the deformation theory 139 constitutive equation of the hereditary theory 321 constitutive equations 3, 41, 45, 48, 53, interfaces I10 128, 143 strength 372 1I9 strength 365 70, 81, 85, 92, 125, 127-128, 130, 136, 140-141, 143-144, 146, 153, 164, 166, 201, 21 1, 218, 229, 237, 242-244, 262, 328, 362, 372 constitutive equations for an angle-ply layer 186 constitutive equations for an anisotropic layer 227 constitutive equations for an anisotropic unidirectional layer 147, 149 constitutive equations for the generalized layer 235 constitutive equations for the monotropic model of the ply 84, 366 constitutive equations for transverse shear 230, 232-233 constitutive equations of the deformation theory of plasticity 132, 136 constitutive equations of the flow theory 137 constitutive equations of thermoelastisity 310 constitutive equations of thermoplasticity 315 constitutive equations relating transverse shear stresses 186 constitutive law 3 convolution theorem 327 coordinate of the reference plane 251 coordinates of the layer 140 cotton fibers 14 coupling 248 coupling coefficients 162, 241, 249 coupling effects 229, 271 coupling stiffness coefficients 253 coupling stiffnesses coupling stiffness coefficients of the laminate 239 crack 61, 168, 171 crack induced by the fiber damage 67 crack length 61 crack propagation 336 cracked cross-ply composite laminate 180 cracks in the matrix cracks parallel to fibers 279 creep 5, 8, 319 creep compliance 321-322, 327, 329-330 creep compliance function 321 creep curve 320, 329 creep deformation 5, 331 creep diagram 320, 325, 331 creep kernel 321 151, 154, 239, 241 176, 197-200, 205, 297, 340, 376400 Subject index creep problem 329 creep strain 8 creep test 319, 322 CRISM vi, 23, 25-27, 122-123, 148, 185, critical stress 62 cross-ply antisymmetric panel 357 cross-ply glass-epoxy layer 183 cross-ply laminate 166, 369 cross-ply layer 163, 166, 248 cross-ply layer in a plane stress state cross-ply layer with a crack CTE 307, 313, 360 cubic constitutive law 128 cubic criterion 284 curing 301, 318, 351 curved composite pipe 196 cycle of vibration 334 cyclic loading 334-336, 338 206, 213-214, 294, 306, 350 175 168 dacron fibers 6 damping capacity 346 deflection 160, 263 deformable epoxy matrix 182 deformation theory of plasticity 128, 139 degradation of material properties 318 degraded ply 176 delamination 77, 112, 172, 205, 285, 340, 343-344 differential equilibrium equations 32 direct stress wave 344 directions of principal strains 368 directions of principal stresses 377 displacement boundary conditions 48 displacement formulation 48 displacements 36, 39, 42, 73, 226 dissipation factor 33&335 dome meridian 387 dry bundle of fibers 76 ductile materials 79 durability 332 effect of aging 319 effective (apparent) moduli 81 effective (apparent) stiffnesses 213 effective (apparent) transverse modulus effective elastic constants 84 effective modulus 114 88 effective strength 66 eight-sector test fixture 102 elastic constants 47, 21 1, 222, 304, elastic constants of a unidirectional ply 81, 170 elastic deformation 5 elastic energy 3 elastic material 3, 43 elastic model 3-4 elastic potential 4, 44, 46, 61, 125, 128, elastic potential energy 334 elastic solid 41, 126 elastic strains 128, 145, 307 elastic volume deformation 129 elastic waves 344 elastic-plastic behavior of metal layer elastic-plastic material model 5, 162 elastic-plastic material 133 elastic-plastic Poisson’s ratio 129 elastic-viscoelastic analogy 327, 329 elasticity theory 145 elastomers 124 elementary cross-ply couples 240 elementary layer 55 elliptic integrals 387 elongation 2 energy criteria 49 energy dissipation 334-335 energy of buckled fibers 109 engineering elastic constants 237 environmental effects 301 epoxy matrix 17 epoxy resin 6, 17, 23, 100, 180 equilibrium equations 30, 48, 51-53, 69, Euclidean space 41,49 Euler integral 383 experimental ballistic limit 348 experimental creep diagram 322 experimental isochrone stress-strain experimental material characteristics 272 experimental stressstrain curve 138 experimental stress-strain diagram 142, experimental thermal expansion 307-308 145 128 169, 202,262, 365 diagram 331 146 coefficients 308Subject index 401 exponential approximation 322 extension-shear coupling coefficient 46 extension-twisting coupling effect 249 fabric carbonfabric composites 208, 209, 276-277, 304, 338, 375 fabric count 209 fabric layers 205 fabric weave 209 fabric-epoxy composites 376 facings 249-250 failure criteria 293 failure criteria for an elementary composite failure criteria of approximation type 273 failure criterion 271, 282, 378 failure envelope 27I , 275-276, 278, failure mechanism 95 failure mode failure mode under longitudinal compression 106 failure modes of the unidirectional composite under in-plane pure shear failure modes of unidirectional rings failure of longitudinal plies 174 failure of the fibers failure of the laminate 376 failure of the matrix 179, 197, 297 failure surface 271-275 failure under compression along the fibers 103 failure under transverse compression fatigue curve 337 fatigue diagram 337, 339 fatigue failure 339 fatigue fracture 336, 340 fatigue strength 80, 180, 336, 338 fiber bending stiffness 112 fiber buckling 107 fiber defects 76 fiber elasticity modulus 68 fiber failure 97, 102 fiber fraction 91 fiber fragmentation test 77 fiber ineffective length 77 fiber modulus 82, 86 layer/ply 271 282-283 113, 272-273, 278, 280, 299-300 100 102 115, 176, 179 113 fiber orientation angle after the deformation I94 fiber placement technology 24 fiber processability 15 fiber properties 82 fiber sensitivity to damage 66 fiber strength 62, 82 fiber strength deviation 64 fiber strength in compression I12 fiber volume fraction 55, 66, 79, 84, 91, 96, 106,208, 304 fiber with a crack 61 fiber-matrix adhesion strength I19 fiber-matrix interaction 58, 77 fiber-matrix interface 80 fiberglass composites I80 fiberglass fabric 23 fiberglass fabric composite 209 fibcrs 9, 55 fibers bending 107 fibers for advanced composites 6, 10 fibers microbuckling 107 fibers orientation angles 365, 378 fibrous technology 22 filament winding 24, 26, 184, 256, 301, filament wound composite pressure filament wound fiberglass pressure filament wound glass-epoxy pressure filament wound membrane shells of filament wound pressure vessel 371 fill direction 375 fill yarns 207-208 filled materials 9 finite element method 135 first-order micromechanical model 118, 307 first-order microstructural model of a hybrid unidirectional ply 114 first order microstructural model 308 first order model of a unidirectional first-order model of a ply fixture for transverse tension and com- 352 vessel 121, 123, 140 vessel 299-300 vessel 331 revolution 379 PlY 85 84, 90, 92, 304 pression of unidirectional strips 104402 Subject index flexural strength 319 flow theory of plasticity 136, 139 flying projectile 346 foam core 239, 249-250, 344, 346 force boundary conditions 32, 48, 52 force-deflection curve 347 formation of cracks 174 four-layered structure of the space telescope 313 fourth-order criterion 284 Fracture Mechanics 61-62 fracture toughness 79 fracture work 347 free shear deformation 161 free temperature strains 360 free tension 158 free-edgeeffect in an angle-ply specimen free-edge effects 201, 205 furfural resin 21 201 generalized anisotropic layer 225 generalized strains 227, 229 geodesic line 385 geodesic winding 26 geometrically nonlinear problem of the ply glass fabric 208 glass fabric-epoxy composite 208, 304 glass fabric-epoxy-phenolic composite glass fibers 6, 10 glass transition temperature 18-19 glass-epoxy composite 77, 96, 167, 182, glass-epoxy composite material 118 glass-epoxy fabric composite 275-276 glass-epoxy fabric tape 294 glass-epoxy sandwich layer 170 glass-epoxy unidirectional composite glass-phenolic fabric composite 276 global coordinate frame 121, 147 global coordinates of the laminate 271 graphite fibers 1 1 graphitization 11, 21 Green’s formulas 44 Green’s integral transformation 32, 50 deformation 189 339 256, 304, 360, 370, 376 183,278 hand lay-up 24-25, 301 heat transfer 303 heat transfer in an orthotropic ply 304 helical plies 296 helicopter rotor blades 337 hereditary theory 320, 326-327 hereditary theory constitutive equations 326 hexagonal array 58 hexagonal fiber distribution 56 high-cycle fatigue 338 high-modulus carbon fibers 7, 11 high-strength carbon fibers 7, 11 higher-order microstructural models 90, highly deformable composite material high-modulus (HM) and high-strength high-modulus carbon-poxy composite history of loading 4-5, 136, 138 homogeneous layer 225 homogeneous model of the laminate 242 homogeneous orthotropic layer 163 honeycomb core 249 Hooke’s law 4, 121, 128, 136, 149, 205, 307, 380 hoop layer 260,267 Huber-Mises plasticity criterion 292 hybrid composites 113-1 14 hybrid composite elements I2 hybrid thermoset-thermoplastic unidirectional composite 183 hybrid unidirectional composites 116 hygrothermal effects 317 hyperbolic shell 387 304 195 (HS) carbon fibers 12 308 impact energy 340 impact loading 340 impact resistance 349 impact tensile stress 346 impregnation 22 incompressible material 124, 129 inflection point 388 inhomogeneous microstructure 80 initial static strength 333 initial strains 134 initial stresses 134Subject index 403 initial tension of the tape 352 in-plane contraction 229 in-plane deformation 359 in-plane displacements 357 in-plane extension 229 in-plane loading 243 in-plane normal stress 80 in-plane shear 95, 100,227, 229, 273, 278, in-plane shear of the laminate 372 in-plane shear strength 96, 208 in-plane shear stress 80 in-plane stressed state of the layer 237 in-plane stresses 143 in-plane tension or compression 227 in-plane thermal conductivities of the instant elastic strain 322 instantaneous modulus of the material integral equilibrium equations 32 interaction of fracture modes 112 interaction of normal stresses 276 interaction of stresses 276, 283 interaction of the fabric layers 349 interaction of the layers 262 interlaminar delamination 341 interlaminar fracture 284 interlaminar normal stress 341 interlaminar shear stiffness 204 interlaminar shear strength 284-285 interlaminar shear stress 201, 205 interlaminar strength 284 interlaminar stresses 255, 260 interstage composite lattice structure 214 invariant characteristics (invariants) of the invariant combination of stiffness invariant constitutive equations 126 invariant of the strength tensor 290-291 invariant stiffness characteristics 151 inverse Laplace transformation 329-330 isochrone stress-strain diagram 320 isotensoid 386 isotensoid shape 390 isotropic layer 121, 377 isotropic material 47 isotropic polymeric material 128 323, 356 laminate 305 324 stressed state 35 coefficients 151 iteration methods I36 iterative linearization 133 jute fibers 14 kinematic boundary conditions 48 kinematically admissible field 4142, knitted fabrics 210 knitting patterns 210 K-number 15 49-50 Lagrange’s multipliers 52-53 lamina 55 laminate 238, 240, 271, 302-303, 318, 365 laminate characteristics 225 laminate composed of angle-ply laminate composed of identical homogelaminate composed of inhomogeneous laminate curvatures 3I3 laminate failure I67 laminate in-plane deformation 313 laminate out-of-plane deformation 313 laminate load-carrying capacity 271 laminate middle plane 245 laminate reference surface 263 laminate stiffness coefficient 374 laminate strength 284, 293 laminate structure 368 laminate thickness 366 laminate twist 313 laminate under impact load 342 laminated composite material 24 laminated polymeric composite panel 355 laminates of uniform strength 375 Laplace transforms 326-327, 329 Laplace transformation 326, 329 large strains 194 lattice layer 212 lattice structure 212-213, 215 layer 121, 255, 303 layer failure 172 layer fracture 271 layer of aluminum foil 306 layer shrinkage 360 layers 242 neous layers 240 orthotropic layers 240404 Subject index layer stiffnesses 175, 229 layer strength 272 layer-wise array 58 layer-wise fiber distribution 57, 87 layer with cracks 172 lay-up manufacturing 206 lay-up method 206 lay-up technology 24 least-squares method 144 limited creep 325-326 linear elastic material model 44,127 linear elastic model 4, 44,121, 140, 147, 163, 185 linear elastic solid 126, 128 linear elasticity problem 327 linear material structure 22 linear strain-displacement equations 38 linear viscoelasticity problem 327 linear-viscoelastic material behavior 320 linear-viscoelastic material 320 linen fibers 14 local buckling of fibers 107 local buckling of plies 341 local waviness 354 longitudinal compression 103, 112-1 13, longitudinal compression of a unidireclongitudinal compressive strength 96, longitudinal conductivity 304 longitudinal CTE 304 longitudinal modulus 96-97, 208, 316 longitudinal modulus of a ply 81 longitudinal modulus of a unidirectional longitudinal stress 85 longitudinal tensile strength 95-97, 208 longitudinal tension 95, 273, 323 long-term loading 332, 334 long-term strength of composite materials long-time modulus 324, 326 low-cycle fatigue 338 low-cycle loading 339 lower bound for the actual transverse shear stiffness 233, 235 lower bound on the apparent transverse modulus 93 273, 280 tional ply 279 208, 316 composite 208 332 machine lay-up 24 macroheterogeneity 22 magnesium matrix 20 mandrel 359-361 manufacturing effects 301, 350 mass fraction 55 master curve 130 material aging 318 material anisotropy 46 material coordinates 140 material damage accumulation 332, 336 material degradation 332 material durability 333 material failure 79, 118, 278 material failure under transverse tension material fracture 60 material hardening 200 material long-term strength 338 material macrostructure 22 material microstructure 22 material penetration 340 material porosity 57 material relaxation time 335 material shrinkage 352, 359 material stiffness material strength material strength characteristics 287 material strength in compression 341 material strength in shear 156 material strength under compression 283, 355 material strength under tension and in shear 291 matrix 9, 16, 55 matrix cracking 196 matrix degradation 180, 319 matrix fraction 55, 91 matrix material 9, 16 matrix modulus 81, 86 matrix of compliance coefficients 45 matrix shear modulus 68, 77, 82 matrix shear stiffness 77 matrix stiffness 16, 67, 76 matrix strength 8142 matrix viscosity 17 matrix volume fraction 55, 84, 304 maximum bending stiffness 247 97 1-2, 16, 180, 318 1 , 16, 273, 277, 283, 291, 308, 318, 340Subject index 405 maximum shear stress 77 maximum shear stress criterion 293 maximum strain criterion 274, 279 maximum strain failure criterion 278 maximum stress criterion 274-278, 283, maximum stress strength criterion 197 mean strength 65 mean stress 123, 338 mean value of the fiber strength 63 mechanical characteristics of the fibers 81 mechanical characteristics of the mechanical properties of a ply 95 mechanics of laminates 225 Mechanics of Materials 9 Mechanics of Solids 8, 29, 48-49, 272 mechanism of the crack stopping 80 melts 22 membrane stiffness coefficients 229, 239 membrane stiffnesses 239, 241, 297-298 membrane-bending coupling 242 membrane-bending coupling coefficients 229, 236, 252 memory function 321 meridian of the optimal shell 381 metal alloys 6 metal fibers 13 metal layer 124 metal mandrel 23 metal matrices 19 metal matrix composites metal pins 215 metal wires 6 method of elastic solutions 133-135, method of elastic variables 134, 136 method of Lagrange multipliers 366 method of reduced bending stiffnesses method of reduced or minimum bending method of successive loading 134, 136, method of variable elasticity parameters microbuckling of fibers 341 microcomposite material 82 microcomposite strand 82 285, 295, 375 matrix 81 13, 20, 316 I89 254 stiffnesses 253 197, 317 134 microcracking of the matrix 166 microcracks 62 microheterogeneity 22 micromechanical analysis 95 micromechanical models 83, 87, 91 micromechanics 81 , 91 micromechanics of a ply 80 microphenomenological approach 271 microstructural approach 332 microstructural model of the secondmicrostructural model 272 microstructural thermal stresses 308 microstructure of the material 90 middle plane of the layer 236 mineral fibers 11 mineral-fiber composites 301 mixed variational principles 52 mode of failure 281, 297 model bundles 64 model isotensoid 390 model of a unidirectional ply with a broken modes of fiber local buckling 107 modulus of an angle-ply layer 204 modulus of elasticity 4, 46, 59, 123, 245 modulus of the =t4angle-ply layer moisture 301 moisture absorption 317 moisture concentration 317 moisture content 317 moisture diffusion coefficient 317 moisture diffusion process 317 monotropic layer 369 monotropic model 83, 385 monotropic model of unidirectional ply multiaxial woven fabrics 209 multi-dimensionally reinforced materials order 89 fiber 67 187 298, 365, 375-376, 378 216 natural fibers 14 natural silk fibers 14 near net-shape manufacturing of tubes and profiles 210 needle punching 215 Newton’s method 134-1 35 nickel matrix 20 nitron fibers 6406 Subject index nonlinear behavior of isotropic polymeric nonlinear behavior of a cross-ply nonlinear behavior of an angle-ply nonlinear behavior of composite material nonlinear behavior of elastomers 124 nonlinear constitutive equations 161, 188 nonlinear constitutive theory 124, 142 nonlinear deformation of an anisotropic nonlinear elastic behavior of a unidirecnonlinear elastic material 133 nonlinear elastic material model 5, 124, nonlinear elastic models 126 nonlinear elastic-plastic behavior of metal nonlinear hereditary theory 331 nonlinear material behavior 5 nonlinear models 124, 142, 161, 166, 188 nonlinear phenomenological model of the nonlinear stress-strain diagram 17, 127, nonlinear viscoelastic behavior 331 nonsymmetric laminate 257 normal deflection 226 normal element 226 normal stress 29, 33, 72 normalized strength 15-16 number of layers 225 nylon 6 material 128 layer 166 layer 188 145 unidirectional layer 161 tional layer 143 I62 layers 128 cross-ply layer 174 211 oblique plane 33 off-axis compression 278 off-axis tension 278 off-axis test 155-157 off-axis test of a unidirectional one-term exponential approximation 323 one-term exponential approximation of the optimal angles 368 optimal composite structures 365 optimal composite vessel 370 composite 153 creep compliance 326 optimal filament wound shell 381-383, optimal laminate 368-370, 372, 374-377 optimal orientation angles 377-378 optimal structural parameters of the optimal structure of the end closure of optimal structures 369 optimality conditions 367, 376 optimality criterion 365, 373 organic fibers 12 organic resin 21 organosilicone resin 6, 19 orthogonally reinforced orthotropic orthotropic angle-ply *4 layer 187 orthotropic core 250 orthotropic homogeneous material 118 orthotropic laminate 239 orthotropic layer 140, 233, 271-272, 309, orthotropic material 4W7, 146,287,290, orthotropic ply 80, 271 385 laminate 374 pressure vessel 387 layer 163 373 327 PA1 6, 19 PAN-based carbon fibers 11 parametric equation for the shell PEEK 6, 19 periodical system of fibers 91 permanent failure 174 petroleum pitch 12 phenol-formaldehyde resin 6 phenolic resin 21 phenomenological homogeneous model of a ply 117 phenomenological model 217 phenomenological model of a composite material 118 phenomenological theory 29 Physics of Solids 59 pitch 21 pitch-based carbon fibers 11 plain weave 209 plane laminated material structure 22, 24 plane stress state 130, 143, 146, 163, 271, meridian 383 372Subject index 407 plastic behavior 130 plastic deformation 5 plastic Poisson’s ratio 132 plastic potential 145-146 plastic strain 5, 8, 128-130, 137, 145 plasticity criterion of maximum shear stress 293 plasticity theory 130 ply degradation 177, 197 ply interaction 201 ply longitudinal modulus 115 ply microstructure 81, 83 ply orientation 121 ply stiffness across the fibers 91 ply stiffness in shear 91 ply strength 365 ply thermal conductivity 305 ply transverse stiffness 91 ply waviness 353-355 ply dissipation factor 335 Poisson’s effect 279 Poisson’s ratio 46, 86, 96-97, 123, 208, polar opening 388 polyacrylonitrile (PAN) filaments I1 polyamide-imide (PAI) 6 polyester 6 polyester resin 6. 17 polyetheretherketone (PEEK) 6 polyethylene 6 polyethylene fibers 7, 12 polyimidc resin 6, 17, 19 polymeric and metal matrices 99 polymeric composites 18, 301, 318 polymeric layer 124 polymeric matrices 17-1 8, 318-3 19 polynomial approximation 125 polynomial criterion 281, 284 polyphenylenesulfide (PPS) 6 polypropylene fibers 6 polystyrene 6 polysulfone (PSU) 6, 19 potential energy 3, 43 potential energy of the body power approximation 130-133, 138 power hardening law 132 power law for the plastic potential 128, 130, 137-1 38, ply 55, 121 245, 252 46 146 preimpregnated fiberglass fabric 25 preliminary tension 24, 352 prepreg 22-23 pressure vessel 26, 140, 179,369-370,379, principal axes 34, 36 principal coordinates 34, 36 principal material axes 140,217,255,271, principal material coordinates 147, 388 291, 309, 335 153-154, 161, 163, 166, 211, 218, 260, 285-287, 295, 304, 368, 374, 380 principal planes 35-36 principal strains 373 principal stresses 34-36, 293, 373, 376, principle of minimum strain energy 52, principle of minimum total potential process of the failure 349 processing 21 processing temperature 18-1 9 projectile residual velocity 347 projectile striking velocity 347 properties of unidirectional composites proportional loading 138-1 39, 156 protective coatings 21 pultrusion 22-23, 301 pure shear 35, 286, 372 pure shear in a twisted tubular specimen 103 pure transverse shear of a cross-ply layer 165 pyrolysis 11, 13, 21, 26 pyrolytic carbon 21 pyrolytic carbon matrix 24 381 91, 169, 234 energy 51,93, 233 96 quadratic approximation strength quartz fibers 6, IO quasi-homogeneous laminates 240 quasi-isotropic laminates 243, 245, 369, quasi-isotropic materials 377 quasi-isotropic properties of the quasi-static test 347 criterion 293 377 laminates 244408 Subject index radial compression 262 radial displacement 263 radius of polar opening 390 rate of loading 5, 319 rayon organic filaments 11 rectangular pulse 343 reference plane 225, 236, 252 reference surface 267 reference surface of the laminate 314 reflected pulse 343 regular inclusions 90 regular system of cracks reinforced materials 9 relaxation diagram 325 relaxation kernel 322 relaxation modulus 322, 327 residual strain 5,8, 361 resin transfer molding 26 resultants of the shear stresses 230 rheologic characteristics of structural rheological mechanical model 323 rice fibers 14 Riemannian (curved) space 41 rotation 33, 226 rotation angle 40-41, 194 rule of mixtures 86 Russian Composite Center - Central 171 materials 319 Institute of Special Machinery (CRISM) vi safety factor 180 sandwich laminate 230, 250 sandwich structure 239, 249, 252, 344 satin weave 209 secant modulus 5, 7, 131-133, 143 second-order model of a ply 87, 90, 98 second-order polynomial approximation second-order polynomial criterion 285 second-order tensor criterion 286 sewing 215 shear deformation 142, 156 shear failure under compression 105 shear mode of buckling 108 shear mode of fracture 113 shear modulus 46, 96, 123, 208 shear modulus of a ply 81 shear modulus of an angle-ply layer 281 188 shear stiITness 142 shear strain 38-39, 69, 85, 294 shear strain in the matrix layer 69 shear strength 365 shear stress 29, 34, 72, 85, 197, 198 shear stress concentration 77 shear-shear coupling coefficient 46, 153 shear-extension coupling 242 shear-extension coupling coefficient 46, shear-twisting coupling 242 short fibers 215 shrinkage characteristics of a unidirectional ply 362 shrinkage strains 360 silicon carbide 13, 21 silicon carbide (Sic) fibers 7, 13 simplest approximation criterion 283 simulation of pure shear in a square single fiber fragmentation test 77 singular approximations 326 sisal fibers 14 sixth-order approximation 143 small strains 39 small variation of displacements 51 small variation of strains 51 space of stresses 271 spatial (3D, 4D) structures 24 spatial material structure 22, 215 spatially reinforced composites 215, 217 spatially reinforced layers 214 spatially reinforced structure 217 special loading effects 301 specific elastic energy 4 specific energy 60 specific heat 302 specific modulus 4, 6-7 specific stiffness 365 specific strain energy 44, 47 specific strength 2, 6-7, 365, 369, 391 specific surface energy 60 specimen buckling I13 specimens of matrix material 82 spider silk fibers 14 square array 58 square fiber distribution 56 stacking sequence 225, 252-253, 344, 365 stacking-sequencenotations 240, 247 153 frame 105Subject index 409 standard types of specimens 95 static boundary conditions 48 static strength 79 statically admissible stress field 49 statically and kinematically admissible stress and strain fields 94 Statics of Solids 230 stiffness 1 stiffness coefficients 45, 150-1 51, 164, 217, 219, 225, 230, 232, 235, 237, 247, 251, 313 layer 236 stiffnesscoefficients of a homogeneous stiffness coefficientsof a laminate 238 stiffness coefficientsof an orthotropic stiffness degradation 339 stiffness matrix 46, 218 stiffnessof composite materials 339 stiffnessesof the degraded layer 176 stitching 215 strain 2, 37 strain concentration factor 106 strain energy 3, 129, 143, 234 strain energy of fibers 109 strain energy of the matrix strain intensity 129 strain interaction 279 strain transformation 39 strain-displacement equations 38, 48, 53, strength analysis 271, 293 strength criterion 271, 284, 287, strength deviation 63 strength dispersion 64 strength matrix 289 strength of a composite bundle of strength of a dry bundle of fibers 66, 96 strength of a unidirectional ply 64 strength of laminates 271 strength of the optimal laminate 378 strength scatter 63 strength tensor 285-286, 291 strength variation 65 stress 2, 29, 33 stress analysis of the matrix in the vicinity layer 237 109 202, 230 289-290 fibers 66, 96 of fibers 91 stress concentration 77, 171, 201, 205, stress concentration in the matrix 96 stress diffusion 16, 171 stress diffusion in fibers 65 stress diffusion in the vicinity of damaged or broken fibers 181 stress formulation 48, 69 stress function 69 stress intensity stress invariants 126-1 27 stress ratio 338 stress relaxation 319, 325 stress resultants and couples 227-229 stress space 139, 272 stress tensor 285 stress transformation 32 stress wave 343 stress-strain curve 3, 5, 100, 124-125, 144, 162, 200 stress-strain diagram of the cross-ply layer 174 stress-strain diagram 3-4, 7, 10, 12, 17, 64, 79, 97, 99, 133, 182, 209. 319 336-337 128, 130, 137, 292 stresses in laminates 254 stresses in the principal material coordistretching ability 209 structural failure criteria 273 structural materials I structural nonlinearity 189 structural strength criteria 274, 281 structure of uniform stress 382 structure of uniform stress and strain 368 sun radiation 318 surface cracks 62 surface tractions 29, 31, 42, 51 symmetric f45" angle-ply laminate 369 symmetric kq5 angle-ply laminate 370 symmetric &4 angle-ply layer 310 symmetric angle-ply layer 186 symmetric laminates 245, 247 symmetric system of helical ribs symmetry conditions 143 symmetry conditions for shear synthetic fibers 6 nates 164 212 stresses 32410 Subject index system of circumferential ribs 212 system of cracks parallel to fibers 168 table rolling 22-23 tangent modulus tape orientation angle 384 tape overlap 352 teflon 6 teflon fibers 6 temperature coefficients 312 temperature effects 301 temperature gradient 305 temperature resistance 18 tensile interface stress 344 tensile load cycle 338 tensile stiffnesses 151 tensile strength 96-97, 100, 316 tensile strength of unidirectional tensile test 153 tension across the fibers 95 tension along the fibers 95 tension in two orthogonal directions 368 tension of f45" angle-ply specimen tension of a cross-ply laminate 166 tension of angle-ply specimens 204 tensor criterion 290, 293 tensor strength criterion 290 tensor-polynomial criterion 292 tensor-polynomial strength criteria 29I , test fixtures for composite rings 101 testing of a microcomposite specimen 83 tex-number 15 textile denier-numbers (den) 15 theorem of proportional loading 139 theoretical density 57 theoretical prediction of material stiffness 197 theoretical strength 58, 60, 62 theoretical strength of glass 62 theory of composite beams 217 theory of elasticity 134 theory of plasticity thermal coefficients of the layer 314 thermal conductivity 301-302, 304 thermal conductivity of the fiber 304 thermal expansion coefficients 308-309 thermal resistance 306, 316 5, 7, 132, 138, 339 composites 78 188 293 128, 145, 292 thermal strains thermal stresses 301, 307 thermoelastic behavior of a unidirectional thermoelastic deformation 317 thermoelasticity 301, 307 thennoelasticity constitutive equations thermo-mechanical diagram 18 thermoplastic carbon composite 311 thermoplastic matrices 17-19, 183 thermoplastic polymers 6, 121, 184 thermoset matrices 17 thermoset polymeric resins 6 thermostable structures 114 thick fiberglass rings 205 thin-walled cylindrical drive shaft 294 thin-walled tubular specimens 273 three-dimensional constitutive three-dimensional stressed state of a three-dimensionally woven or braided three-dimensional weaving 215 three-point beam bending test 217 time of relaxation 325 time-dependent behavior of polymeric composites 3I9 Timoshenko energy method 108 titanium carbide fibers 7 titanium matrix 20 Toray T-1000 carbon fibers total potential energy of the body 51 total shear strain 165 toughness 21 tow 15-16, 55 tow processability 15 tow tex-number 57 translational displacement 226 transverse compression 113, 273 transverse compressive strength 96, 208 transverse conductivity 304 transverse CTE 304 transverse deformability 181 transverse extension failure mode I05 transverse force 157 transverse impact loads 340 301, 307, 309-310, 317, 356 composite ply 307 311 equations 217 layer 124 fabrics 215 12Subject index 41 1 transverse modulus 96, 100, 141, 208 transverse modulus of a ply 81 transverse normal stress transverse shear compliance 249 transverse shear deformation 202, 260, transverse shear forces 230 transverse shear modulus 142, 165 transverse shear modulus of the ply 202 transverse shear stiffness coefficients 247 transverse shear stiffnesses 236, 239, transverse shear 237 transverse shear stress 202, 262, 284 transverse strains 85 transverse strength 365 transverse strength of a unidirectional transverse tensile strain 279 transverse tensile strength 96, 100, 208 transverse tension 84, 92, 97, 102, 168, 273, 323 transverse tension of a ply 91 triaxial braid 210 triaxial reinforcement 215 tubular specimen for shear test tubular specimens 274 twill weave 209 twist 361 twisting 227, 229, 237, 356, 359 two-dimensional (2D) braiding 24 two-layered angle-ply laminate 358 two-layered orthotropic cross-ply two-matrix fiberglass composite 162, 182 two-matrix fiberglass unidirectional two-matrix glass-epoxy composite 183, two-stage impregnation 181 124, 198, 266, 278, 284 263 249-250 material 99 105 laminate 356 composite 144 189 ultimate elongation 79, 95, 124, 168, 180 ultimate elongation across the fibers 180 ultimate elongation along the fibers 180 ultimate elongations 1I5 ultimate fiber volume fraction 58 ultimate pressure 296, 391 ultimate strain 16-17 ultimate stress 2, 95, 274, 278 ultimate tensile stress 6-7, 14 ultimate theoretical stress 59 uniaxial longitudinal loading 143 uniaxial tension unidirectional anisotropic layer 147 unidirectional aramid-epoxy composite unidirectional boron-aluminum unidirectional boron-epoxy composite unidirectional carbon-epoxy composite unidirectional carbon-epoxy layer 154 unidirectional carbon-glass epoxy unidirectional composite 76, 142, 144, unidirectional composite ply 80, 303, unidirectional-epoxy composites 376 unidirectional glass4poxy composite unidirectional layer 147, 297, 359 unidirectional orthotropic layer 140 unidirectional ply 5 - 5 6 , 121, 255, unidirectional tape 55 unidirectional tow (roving) 15 unidirectional two-matrix composite 183 unidirectional weave 209 unidirectionally reinforced plates 96 uniformly stressed composite strucuniformly stressed fibers 365, 371 universal form of the polynomial criterion universal stress-strain curve 131 universal stress-strain diagram 130 upper bound for the actual transverse shear upper bound on the apparent transverse 129, 131, 138, 175, 197 material 99, 338 composite 79 material 100 material 98, 335 composite 117 217, 287, 304, 329, 351 327-328, 335, 365 material 97, 322 277-278, 304, 308 tures 391 282 stiffness 233-234 modulus 94 variation of the strain energy 51 variational equations 5 1 variational principle of minimum strain energy 52412 Subject index variational principle of minimum total potential energy 51 variational principles 49, 91 viscoelastic deformation 319 viscoelastic material 334 viscoelastisity 319 viscose fibers 6 viscous strain 321 volume deformation 123 volume fraction 55, 57, 86, 95 volume modulus 124 warp direction 207, 221, 276, 375 warp yarns 207 warping 355 warping of laminates 359 water absorption 318 wave interaction 344 wave propagation 341 weave patterns 209 weight-saving factor 378 wet process 22 whiskers 60, 215 winding 351-352, 380 winding of a lattice layer 213 winding of unidirectional composite wood compressed along the fibers 105 wood fibers 14 wool fibers 14 work of external forces 43 work of fracture 80 work of internal forces 43 woven composites 206 woven fabric composites 210 woven structure 206-207 tapes 384 yarn 15 zero thermal expansion 114, 311 zero-order model of a ply 83
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