Mechanics Analysis Composite Materials Episode 13 pot

406 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 behavi

406 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

unidirec-nonlinear 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

21 1

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 1 18

orthotropic laminate 239 orthotropic layer 140, 233, 271-272, 309, orthotropic material 4 W 7 , 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

372

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 1 15

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 28 1, 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

38 1

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 244

408 Subject index

radial compression 262

radial displacement 263

radius of polar opening 390

rate of loading 5, 319

rayon organic filaments 1 1

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-sequence notations 240, 247

153

frame 105

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

stiffness coefficients of a homogeneous

stiffness coefficientsof a laminate 238

stiffness coefficientsof an orthotropic

stiffness degradation 339

stiffness matrix 46, 218

stiffness of composite materials 339

stiffnessesof the degraded layer 176

stitching 21 5

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 coordi-stretching 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 f 4 5 " 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 32

410 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 f 4 5 " 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 31 1

thermoplastic matrices 17-19, 183 thermoplastic polymers 6, 121, 184 thermoset matrices 17

thermoset polymeric resins 6 thermostable structures 1 14 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

12

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 2 15

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 struc-uniformly 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 52

412 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, 31 1

zero-order model of a ply 83