Preface ....................................................... xv
Symbols .................................................... xviii
Frequently used abbreviations ............................... xxii
1 Structure of non-polymeric glasses ........................ 1
1.1 Overview .................................................. 1
1.2 Glass formability in metallic alloys ...................... 3
1.3 Atomic packing in disordered metallic solids .............. 3
1.4 Energetic characterization of the structure of metallic
glasses ................................................... 7
1.4.1 The atomic site stress tensor ...................... 7
1.4.2 Calorimetry ........................................ 9
1.5 Free volume .............................................. 10
1.6 Viscosity of glass-forming liquids ....................... 14
1.7 Structural relaxations ................................... 16
1.7.1 A computational model ............................. 16
1.7.2 Kinetic models of structural relaxations in
metallic glasses .................................. 20
1.8 The distributed character of structural relaxations and
the glass transition ..................................... 21
1.9 The dependence of the glass-transition temperature on
cooling rate ............................................. 25
1.10 Crystallization in bulk metallic glasses ................. 26
1.11 Deformation-induced alterations of atomic structure in
sub-cooled liquids and glasses ........................... 27
1.12 The range of metallic alloys that have been obtained as
bulk metallic glasses .................................... 30
1.13 The structure of amorphous silicon ....................... 30
1.14 Characterization of the structure of amorphous silicon ... 32
Suggested further reading on structure of non-polymeric
glasses .................................................. 36
References ............................................... 37
2 Structure of solid polymers .............................. 40
2.1 Overview ................................................. 40
2.2 Structure of polymers .................................... 41
2.3 Molecular architecture ................................... 46
2.4 Molecular weight ......................................... 47
2.5 Structure of amorphous polymers .......................... 49
2.5.1 Molecular-structure models of amorphous polymers .. 49
2.5.2 Chemically specific molecular-structure models
of amorphous polymers ............................. 49
2.5.3 Chemically non-specific models of amorphous
polymer structure ................................. 53
2.5.4 Experimental means of characterization of the
structure of glassy polymers ...................... 54
2.6 Crystalline polymers ..................................... 54
2.6.1 The fringed-micelle model of semi-crystalline
polymers .......................................... 54
2.6.2 Spherulites ....................................... 55
2.6.3 Hedrites .......................................... 58
2.6.4 Polymer single crystals ........................... 58
2.6.5 Crystallization from the melt and growth of
spherulites ....................................... 61
2.7 Defects in polymer crystals .............................. 66
2.7.1 Overview .......................................... 66
2.7.2 Chain defects ..................................... 67
2.7.3 Lattice defects ................................... 71
2.8 Chain-extended polymers .................................. 71
Suggested further reading on structure of solid
polymers ................................................. 72
References ............................................... 73
3 Constitutive connections between stress and strain in
polymers ................................................. 77
3.1 Overview ................................................. 77
3.2 Stresses and strains ..................................... 77
3.2.1 Stresses .......................................... 77
3.2.2 Strains ........................................... 78
3.3 Linear elasticity of polymers ............................ 81
3.4 Plasticity of polymers ................................... 83
3.4.1 Generalized yield conditions ...................... 83
3.4.2 The associated-flow rule .......................... 85
3.5 Thermally activated deformation .......................... 87
References ............................................... 89
4 Small-strain elastic response ............................ 90
4.1 Overview ................................................. 90
4.2 Small-strain elasticity in crystals ...................... 91
4.2.1 The generalized Hooke's law ....................... 91
4.2.2 Orthorhombic crystals or orthotropic solids ....... 93
4.2.3 Hexagonal crystals ................................ 93
4.2.4 Cubic crystals .................................... 93
4.2.5 Isotropic materials ............................... 93
4.2.6 Temperature and strain dependence of elastic
response .......................................... 95
4.3 Theoretical determination of elastic constants of
polymers ................................................. 96
4.3.1 Glassy polymers ................................... 96
4.3.2 Crystalline polymers .............................. 97
4.4 Elastic response of textured anisotropic polymers ....... 102
4.5 Elastic properties of heterogeneous polymers ............ 104
4.5.1 Methods of estimating the elastic properties of
heterogeneous polymers ........................... 104
4.5.2 The self-consistent method ....................... 105
4.5.3 The Eshelby inclusion method ..................... 106
References .............................................. 109
5 Linear viscoelasticity of polymers ...................... 112
5.1 Introduction ............................................ 112
5.2 Phenomenological formalisms of viscoelasticity .......... 112
5.2.1 Uniaxial creep or stress-relaxation response ..... 112
5.2.2 Dynamic relaxation response ...................... 116
5.2.3 Temperature dependence of viscoelastic
relaxations ...................................... 118
5.3 Viscoelastic relaxations in amorphous polymers .......... 120
5.3.1 The α-relaxation ................................. 120
5.3.2 The free-volume model of the α-relaxation ........ 122
5.3.3 Dependence of the α-relaxation on the chemical
structure of molecules ........................... 126
5.3.4 Secondary relaxations in the glassy regime ....... 127
5.3.5 Effect of physical aging on the relaxation
spectra of polymers .............................. 130
5.3.6 Secondary relaxations in polycarbonate of
bisphenol-A ...................................... 132
5.4 Shear relaxations in partially crystalline polymers ..... 139
5.5 Some problems of viscoelastic-stress analysis ........... 143
5.6 Non-linear viscoelasticity .............................. 145
6 Suggested further reading on linear viscoelasticity of
polymers ................................................ 146
References .............................................. 146
Rubber elasticity ....................................... 148
6.1 Overview ................................................ 148
6.2 Molecular characteristics of rubbers .................... 149
6.2.1 Distinctive features of rubbers .................. 149
6.2.2 The chemical constitution of rubbers ............. 151
6.3 Thermodynamics of rubbery behavior ...................... 151
6.4 The Gaussian statistical model of rubber elasticity ..... 155
6.5 The non-Gaussian statistical model of rubber
elasticity .............................................. 159
6.5.1 The freely jointed single chain .................. 159
6.5.2 Langevin networks ................................ 161
6.5.3 Comparison of the Langevin-network model with
experiments ...................................... 164
6.6 Modes of deformation in rubber elasticity ............... 167
6.6.1 Conditions for general response .................. 167
6.6.2 Uniaxial tension or compression .................. 167
6.6.3 Equi-biaxial stretch ............................. 168
6.6.4 Plane-strain tension and pure shear .............. 168
6.6.5 Simple shear ..................................... 169
6.6.6 Plane-strain compression flow in a channel die ... 171
6.7 Gaussian rubbery-type response in glassy polymers ....... 172
References .............................................. 172
7 Inelastic behavior of non-polymeric glasses ............. 174
7.1 Overview ................................................ 174
7.2 The mechanism of plasticity in non-polymeric glasses .... 175
7.3 The kinematics of plasticity in glassy solids by shear
transformations ......................................... 176
7.4 Nucleation of shear transformations under stress ........ 179
7.4.1 The elastic strain energy of a shear
transformation in the unstressed solid ........... 179
7.4.2 The Gibbs free energy of nucleation of the
shear transformation under stress ................ 180
7.4.3 Stages in the nucleation of the shear
transformation ................................... 181
7.5 Yielding in metallic glasses ............................ 185
7.5.1 Behavior at low temperatures (T << Tg) ........... 185
7.5.2 Temperature dependence of the yield stress
(T << Tg) ........................................ 187
7.5.3 Analysis of the experimental results on yield
behavior of metallic glasses at low
temperatures ..................................... 188
7.5.4 Yielding in metallic glasses at temperatures
close to Tg ...................................... 189
7.5.5 Changing kinetics of plasticity near Tg .......... 193
7.6 Post-yield large-strain plastic response of glassy
solids: strain softening and strain hardening ........... 199
7.6.1 Features of large-strain plastic flow of glassy
solids ........................................... 199
7.6.2 Plastic-flow-induced increase in the liquid-
like material fraction, φ ........................ 200
7.6.3 Plastic-strain-induced changes in structure and
the kinetics of associated evolutions of φ ....... 203
7.6.4 Kinetics of large-strain plastic flow of
glasses at T << Tg .............................. 205
7.6.5 Kinetics of large-strain plastic flow of
glasses at T close to Tg ......................... 207
7.6.6 Multi-axial deformation: correspondences of
shear, tension, and compression at low
temperatures ..................................... 210
7.7 The strength-differential effect in disordered solids ... 213
7.8 Shear localization ...................................... 216
7.8.1 The phenomenology of shear localization in
metallic glasses ................................. 216
7.8.2 The mechanics of shear localization .............. 217
7.8.3 Temperature rises associated with shear
localization ..................................... 220
7.8.4 The flow state ................................... 221
Appendix. Plastic-floor-induced structural
alterations: the relation between flow
dilatations of free volume and liquid-like
material ......................................... 222
References .............................................. 224
8 Plasticity of glassy polymers ........................... 228
8.1 Overview ................................................ 228
8.2 The rheology of glassy polymers ......................... 229
8.2.1 Important provisos ............................... 229
8.2.2 The phenomenology of plastic flow in glassy
polymers ......................................... 230
8.3 The mechanism of plastic flow in glassy polymers ........ 234
8.3.1 Computer simulation of plastic flow .............. 234
8.3.2 Simulation results in polypropylene .............. 236
8.3.3 Simulation results in polycarbonate .............. 238
8.4 Temperature dependence of yield stresses of glassy
polymers ................................................ 243
8.5 The kinetic model of plastic yield in glassy polymers ... 243
8.5.1 Temperature dependence of the plastic
resistance ....................................... 243
8.5.2 The thermal activation parameters ................ 247
8.5.3 A kinetic model of flow of linear-chain glassy
polymers ......................................... 248
8.6 Large-strain plastic flow in glassy polymers ............ 249
8.6.1 Development of post-yield large-strain plastic
flow ............................................. 249
8.6.2 A model for post-yield plastic flow of glassy
polymers ......................................... 254
8.6.3 Stored energy and Bauschinger back strains ....... 258
8.6.4 The strength-differential effect and the multi-
axial yield condition ............................ 259
8.7 Strain hardening in glassy polymers ..................... 262
8.8 Comparison of experiments and simulations on the
yielding and large-strain plastic flow of glassy
polymers ................................................ 264
References .............................................. 270
9 Plasticity of semi-crystalline polymers ................. 273
9.1 Overview ................................................ 273
9.2 Mechanisms of plastic deformation ....................... 274
9.3 Plasticity of two semi-crystalline polymers: high-
density polyethylene (HDPE) and polyamide-6 (Nylon-6) ... 276
9.3.1 Methodology of deformation ....................... 276
9.3.2 Plastic strain-induced alterations of
spherulite morphology in Nylon-6 in uniaxial
tension .......................................... 277
9.3.3 Large-strain plastic flow in HDPE in
plane-strain compression ......................... 280
9.3.4 Large-strain plastic flow in monoclinic Nylon-6
by plane-strain compression ...................... 291
9.3.5 Measurement of critical resolved shear stresses
in textured HDPE and Nylon-6 and their
normal-stress dependence ......................... 292
9.4 The kinetics of plastic flow in semi-crystalline
polymers ................................................ 295
9.4.1 Modes of dislocation nucleation in lamellae ...... 298
9.4.2 The strain-rate expression ....................... 301
9.4.3 The dominant nucleation mode ..................... 303
9.4.4 Activation volumes ............................... 304
9.4.5 Temperature dependence of the plastic
resistance ....................................... 307
9.5 Simulation of plastic-strain-induced texture
development in HDPE ..................................... 309
9.5.1 Characteristics of the simulation ................ 309
9.5.2 Basic assumptions of the model ................... 309
9.5.3 Constitutive relations ........................... 311
9.5.4 Composite inclusion .............................. 315
9.5.5 Interaction law and solution procedure ........... 315
9.5.6 Parameter selection in the model ................. 316
9.5.7 Predicted results of the composite model and
comparison with experiments ...................... 317
Suggested further reading on plasticity of semi-
crystalline polymers .................................... 321
References .............................................. 321
10 Deformation instabilities in extensional plastic flow
of polymers ............................................. 325
10.1 Overview ................................................ 325
10.2 Deformation instabilities in extensional plastic flow
of polymers ............................................. 325
10.3 Conditions for impending localization in extensional
deformation ............................................. 326
10.3.1 Basic shear response ............................ 326
10.3.2 Basic extensional response ...................... 328
10.4 Stability of extensional plastic flow ................... 331
10.5 The effect of strain-rate sensitivity on stability in
extensional plastic flow ................................ 333
10.5.1 In the onset of necking .......................... 333
10.5.2 In the post-necking behavior ..................... 335
10.6 Plastic drawing of polymers ............................. 336
References .............................................. 341
11 Crazing in glassy homo- and hetero-polymers ............. 342
11.1 Overview ................................................ 342
11.2 The phenomenology of crazing in glassy homo-polymers .... 343
11.3 Simulation of cavitation in a glassy polymer at the
atomic level ............................................ 345
11.4 Craze initiation ........................................ 347
11.4.1 Experimental observations ........................ 347
11.4.2 Intrinsic crazing ................................ 349
11.4.3 Tension-torsion experiments ...................... 349
11.5 A craze-initiation model ................................ 353
11.6 Comparison of the predictions of the craze-initiation
model with experiments .................................. 356
11.7 Craze growth ............................................ 359
11.7.1 Craze stresses ................................... 359
11.7.2 Craze microstructure ............................. 364
11.7.3 Craze-growth experiments ......................... 366
11.8 A craze-growth model .................................... 368
11.9 Comparison of the craze-growth model with experiments ... 374
11.10 Crazing in block copolymers ............................ 376
11.10.1 Morphology of diblock copolymers ................ 376
11.10.2 Crazing experiments in PS/PB diblock
copolymers ...................................... 378
11.10.3 A model of craze growth in a PS/PB diblock
copolymer with spherical PB domains ............. 381
11.10.4 Comparison of the predictions of the craze-
growth model in PS/PB diblock copolymers with
experiments ..................................... 385
References .............................................. 387
12 Fracture of polymers .................................... 391
12.1 Overview ................................................ 391
12.2 Cracks and fracture ..................................... 391
12.2.1 Two complementary perspectives in crack
mechanics ........................................ 391
12.2.2 Cracks in LEFM ................................... 392
12.2.3 The energy-release rate G\ in LEFM with crack
extension ........................................ 396
12.3 Cracks with plastic zones ............................... 398
12.3.1 Pervasiveness of plasticity at the crack tip ..... 398
12.3.2 Cracks with small-scale yielding (SSY) ........... 399
12.3.3 Crack-tip fields with contained plasticity ....... 404
12.3.4 Crack fields in fully developed plasticity ....... 407
12.4 Stability of crack advance .............................. 414
12.5 Intrinsic brittleness of polymers ....................... 416
12.6 Brittle-to-ductile transitions in fracture .............. 418
12.7 Mechanisms and forms of fracture in polymers ............ 419
12.7.1 The crack-tip process zone ....................... 419
12.7.2 The role of chain scission in polymer fracture ... 419
12.7.3 Fracture of unoriented polymers .................. 420
12.7.4 Cohesive separation .............................. 420
12.7.5 Fracture in glassy polymers involving crazing .... 422
12.7.6 Molecular-scission-controlled fracture of
oriented semi-crystalline polymers ............... 425
12.7.7 Fracture toughnesses of a selection of polymers .. 428
12.8 Impact fracture of polymers ............................. 429
12.8.1 Application of fracture mechanics to impact
fracture ......................................... 429
12.8.2 Fracture of polymers at high strain rate ......... 431
12.8.1 Suggested further reading on fracture of
polymers ......................................... 432
References .............................................. 433
13 Toughening of polymers .................................. 435
13.1 Overview ................................................ 435
13.2 Strategies of toughening of polymers .................... 436
13.3 Different manifestations of toughness in polymers ....... 437
13.4 The generic fracture response of polymers in uniaxial
tension ................................................. 438
13.5 Toughening of crazable glassy polymers by compliant
particles ............................................... 440
13.5.1 Types of compliant composite particles ........... 440
13.5.2 Brittleness of glassy homo-polymers and
alleviating it through craze plasticity .......... 443
13.5.3 The mechanism of toughening in particle-
modified crazable glassy polymers ................ 445
13.5.4 Elasticity of compliant particles ................ 447
13.5.5 Craze initiation from compliant particles and
the craze-flow stress ............................ 449
13.5.6 The role of compliant-particle size in
toughening glassy polymers ....................... 449
13.5.7 A model for the craze-flow stress of particle-
toughened polystyrene ............................ 452
13.5.8 Special HIPS blends prepared to evaluate the
toughening model ................................. 454
13.5.9 Comparison of the behavior of special HIPS
blends with model predictions .................... 457
13.6 Diluent-induced toughening of glassy polymers ........... 459
13.6.1 Different manifestations of toughening with
diluents ......................................... 459
13.6.2 Factors affecting diluent toughening of PS ....... 462
13.6.3 A model of diluent-induced toughening of glassy
polymers ......................................... 465
13.6.4 Comparison of the diluent-induced-toughening
model with experiments ........................... 472
13.7 Toughening of semi-crystalline polymers ................. 475
13.7.1 Toughness of unmodified HDPE and polyamides of
Nylon-6 and -66 .................................. 475
13.7.2 Toughening semi-crystalline polymers by
particle modification ............................ 477
13.8 Toughening of brittle thermosetting polymers ............ 492
References .............................................. 497
Author index ................................................. 501
Subject index ................................................ 507
|
