 | Roesler J. Mechanical behaviour of engineering materials: metals, ceramics, polymers, and composites / Roesler J., Harders H., Baeker M. - Вerlin; New York: Springer, 2007. - xv, 534 p. - ISBN 978-3-540-73446-8
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1 The structure of materials .................................. 1
1.1 Atomic structure and the chemical bond .................. 1
1.2 Metals ................................................. 5
1.2.1 Metallic bond ................................... 5
1.2.2 Crystal structures .............................. 7
1.2.3 Polycrystalline metals ......................... 14
1.3 Ceramics .............................................. 15
1.3.1 Covalent bond .................................. 16
1.3.2 Ionic bond ..................................... 18
1.3.3 Dipole bond .................................... 19
1.3.4 Van der Waals bond ............................. 19
1.3.5 Hydrogen bond .................................. 20
1.3.6 The crystal structure of ceramics .............. 21
1.3.7 Amorphous ceramics ............................. 22
1.4 Polymers .............................................. 23
1.4.1 The chemical structure of polymers ............. 24
1.4.2 The structure of polymers ...................... 25
2 Elasticity ................................................. 31
2.1 Deformation modes ..................................... 31
2.2 Stress and strain ..................................... 32
2.2.1 Stress ......................................... 32
2.2.2 Strain ......................................... 34
2.3 Atomic interactions ................................... 37
2.4 Hooke's law ........................................... 39
2.4.1 Elastic strain energy .......................... 42
2.4.2 Elastic deformation under multiaxial loads1 .... 43
2.4.3 Isotropic material ............................. 46
2.4.4 Cubic lattice .................................. 50
2.4.5 Orthorhombic crystals and orthotropic
elasticity ..................................... 53
2.4.6 Transversally isotropic elasticity ............. 54
2.4.7 Other crystal lattices ......................... 55
2.4.8 Examples ....................................... 55
2.5 Isotropy and anisotropy of macroscopic components ..... 57
2.6 Temperature dependence of Young's modulus ............. 60
3 Plasticity and failure ...................................... 63
3.1 Nominal and true strain ............................... 64
3.2 Stress-strain diagrams ................................ 68
3.2.1 Types of stress-strain diagrams ................ 68
3.2.2 Analysis of a stress-strain diagram ............ 73
3.2.3 Approximation of the stress-strain curve ....... 81
3.3 Plasticity theory ..................................... 83
3.3.1 Yield criteria ................................. 84
3.3.2 Yield criteria of metals ....................... 86
3.3.3 Yield criteria of polymers ..................... 92
3.3.4 Flow rules ..................................... 93
3.3.5 Hardening ...................................... 97
3.3.6 Application of a yield criterion,
flow rule, and hardening rule ................. 103
3.4 Hardness ............................................. 107
3.4.1 Scratch tests .................................. 108
3.4.2 Indentation tests .............................. 108
3.4.3 Rebound tests .................................. 110
3.5 Material failure ..................................... 110
3.5.1 Shear fracture ................................ 1ll
3.5.2 Cleavage fracture ............................. 114
3.5.3 Fracture criteria ............................. 116
4 Notches ................................................... 119
4.1 Stress concentration factor .......................... 119
4.2 Neuber's rule ........................................ 122
4.3 Tensile testing of notched specimens ................. 125
5 Fracture mechanics ........................................ 129
5.1 Introduction to fracture mechanics ................... 129
5.1.1 Definitions .................................... 129
5.2 Linear-elastic fracture mechanics .................... 131
5.2.1 The stress field near a crack tip ............. 131
5.2.2 The energy balance of crack propagation ....... 134
5.2.3 Dimensioning pre-cracked components
under static loads ............................ 142
5.2.4 Fracture parameters of different materials .... 144
5.2.5 Material behaviour during crack
propagation ................................... 146
5.2.6 Subcritical crack propagation ................. 150
5.2.7 Measuring fracture parameters ................. 152
5.3 Elastic-plastic fracture mechanics ................... 158
5.3.1 Crack tip opening displacement (ctod) ......... 158
5.3.2 J integral .................................... 159
5.3.3 Material behaviour during crack
propagation ................................... 161
5.3.4 Measuring elastic-plastic fracture
mechanics parameters .......................... 163
6 Mechanical behaviour of metals ............................ 165
6.1 Theoretical strength ................................. 165
6.2 Dislocations ......................................... 166
6.2.1 Types of dislocations ......................... 166
6.2.2 The stress field of a dislocation ............. 168
6.2.3 Dislocation movement .......................... 170
6.2.4 Slip systems .................................. 173
6.2.5 The critical resolved shear stress ............ 178
6.2.6 Taylor factor ................................. 182
6.2.7 Dislocation interaction ....................... 184
6.2.8 Generation, multiplication and annihilation
of dislocations ............................... 185
6.2.9 Forces acting on dislocations ................. 187
6.3 Overcoming obstacles ................................. 189
6.3.1 Athermal processes ............................ 190
6.3.2 Thermally activated processes ................. 193
6.3.3 Ductile-brittle transition .................... 196
6.3.4 Climb ......................................... 196
6.3.5 Intersection of dislocations .................. 197
6.4 Strengthening mechanisms ............................. 198
6.4.1 Work hardening ................................ 198
6.4.2 Grain boundary strengthening .................. 200
6.4.3 Solid solution hardening ...................... 203
6.4.4 Particle strengthening ........................ 209
6.4.5 Hardening of steels ........................... 218
6.5 Mechanical twinning .................................. 223
7 Mechanical behaviour of ceramics .......................... 227
7.1 Manufacturing ceramics ............................... 228
7.2 Mechanisms of crack propagation ...................... 229
7.2.1 Crack deflection .............................. 230
7.2.2 Crack bridging ................................ 230
7.2.3 Microcrack formation and crack branching ...... 231
7.2.4 Stress-induced phase transformations .......... 232
7.2.5 Stable crack growth ........................... 234
7.2.6 Subcritical crack growth in ceramics .......... 234
7.3 Statistical fracture mechanics ....................... 236
7.3.1 Weibull statistics ............................ 236
7.3.2 Weibull statistics for subcritical crack
growth ........................................ 242
7.3.3 Measuring the parameters δ0 and m ............ 243
7.4 Proof test ........................................... 246
7.5 Strengthening ceramics ............................... 248
7.5.1 Reducing defect size .......................... 249
7.5.2 Crack deflection .............................. 249
7.5.3 Microcracks ................................... 251
7.5.4 Transformation toughening ..................... 252
7.5.5 Adding ductile particles ...................... 255
8 Mechanical behaviour of polymers .......................... 257
8.1 Physical properties of polymers ...................... 257
8.1.1 Relaxation processes .......................... 257
8.1.2 Glass transition temperature ................. 260
8.1.3 Melting temperature ........................... 261
8.2 Time-dependent deformation of polymers ............... 263
8.2.1 Phenomenological description of
time-dependence ............................... 263
8.2.2 Time-dependence and thermal activation ........ 266
8.3 Elastic properties of polymers ....................... 269
8.3.1 Elastic properties of thermoplastics .......... 269
8.3.2 Elastic properties of elastomers and
duromers ...................................... 273
8.4 Plastic behaviour .................................... 274
8.4.1 Amorphous thermoplastics ...................... 275
8.4.2 Semi-crystalline thermoplastics ............... 281
8.5 Increasing the thermal stability ..................... 284
8.5.1 Increasing the glass and the melting
temperature ................................... 284
8.5.2 Increasing the crystallinity .................. 287
8.6 Increasing strength and stiffness .................... 289
8.7 Increasing the ductility ............................. 290
8.8 Environmental effects ................................. 292
9 Mechanical behaviour of fibre reinforced composites ....... 295
9.1 Strengthening methods ................................ 296
9.1.1 Classifying by particle geometry .............. 296
9.1.2 Classifying by matrix systems ................. 299
9.2 Elasticity of fibre composites ....................... 300
9.2.1 Loading in parallel to the fibres ............. 301
9.2.2 Loading perpendicular to the fibres ........... 301
9.2.3 The anisotropy in general ..................... 302
9.3 Plasticity and fracture of composites ................ 303
9.3.1 Tensile loading with continuous fibres ........ 303
9.3.2 Load transfer between matrix and fibre ........ 305
9.3.3 Crack propagation in fibre composites ......... 308
9.3.4 Statistics of composite failure ............... 312
9.3.5 Failure under compressive loads ............... 313
9.3.6 Matrix-dominated failure and arbitrary
loads ......................................... 315
9.4 Examples of composites ............................... 315
9.4.1 Polymer matrix composites ..................... 315
9.4.2 Metal matrix composites ....................... 321
9.4.3 Ceramic matrix composites ..................... 323
9.4.4 Biological composites ......................... 325
10 Fatigue ................................................... 333
10.1 Types of loads ....................................... 333
10.2 Fatigue failure of metals ............................ 337
10.2.1 Crack initiation .............................. 338
10.2.2 Crack propagation (stage II) .................. 342
10.2.3 Final fracture ................................ 344
10.3 Fatigue of ceramics .................................. 345
10.4 Fatigue of polymers .................................. 346
10.4.1 Thermal fatigue ............................... 346
10.4.2 Mechanical fatigue ............................ 347
10.5 Fatigue of fibre composites .......................... 347
10.6 Phenomenological description of the fatigue
strength ............................................. 349
10.6.1 Fatigue crack growth .......................... 349
10.6.2 Stress-cycle diagrams (S-N diagrams) .......... 357
10.6.3 The role of mean stress ....................... 366
10.6.4 Fatigue assessment with variable amplitude
loading ....................................... 368
10.6.5 Cyclic stress-strain behaviour ................ 369
10.6.6 Kitagawa diagram .............................. 373
10.7 Fatigue of notched specimens ........................ 375
11 Creep ..................................................... 383
11.1 Phenomenology of creep ............................... 383
11.2 Creep mechanisms ..................................... 388
11.2.1 Stages of creep ............................... 388
11.2.2 Dislocation creep ............................. 389
11.2.3 Diffusion creep ............................... 393
11.2.4 Grain boundary sliding ........................ 396
11.2.5 Deformation mechanism maps .................... 396
11.3 Creep fracture ....................................... 400
11.4 Increasing the creep resistance ...................... 401
12 Exercises ................................................. 407
1 Packing density of crystals ............................ 407
2 Macromolecules ......................................... 407
3 Interaction between two atoms .......................... 407
4 Bulk modulus ........................................... 408
5 Relation between the elastic constants ................. 408
6 Candy catapult ......................................... 409
7 True strain ............................................ 410
8 Interest calculation ................................... 410
9 Large deformations ..................................... 410
10 Yield criteria ......................................... 410
11 Yield criteria of polymers ............................. 411
12 Design of a notched shaft .............................. 411
13 Estimating the fracture toughness KIс .................. 412
14 Determination of the fracture toughness KIс ............ 412
15 Static design of a tube ................................ 413
16 Theoretical strength ................................... 414
17 Estimating the dislocation density ..................... 414
18 Thermally activated dislocation generation ............. 414
19 Work hardening ......................................... 415
20 Grain boundary strengthening ........................... 415
21 Precipitation hardening ................................ 415
22 Weibull statistics ..................................... 415
23 Design of a fluid tank ................................. 416
24 Subcritical crack growth of a ceramic
component .............................................. 417
25 Mechanical models of viscoelastic polymers ............. 417
26 Elastic damping ........................................ 418
27 Eyring plot ............................................ 418
28 Elasticity of fibre composites ......................... 419
29 Properties of a polymer matrix composite ............... 419
30 Estimating the number of cycles to failure ............. 419
31 Miner's rule ........................................... 420
32 Larson-Miller parameter ................................ 421
33 Creep deformation ...................................... 421
34 Relaxation of thermal stresses by creep ................ 421
13 Solutions ................................................. 423
A Using tensors ............................................. 451
A.l Introduction .......................................... 451
A.2 The order of a tensor ................................. 451
A.3 Tensor notations ...................................... 452
A.4 Tensor operations and Einstein summation
convention ............................................ 453
A.5 Coordinate transformations ............................ 456
A.6 Important constants and tensor operations ............. 457
A.7 Invariants ............................................ 458
A.8 Derivations of tensor fields .......................... 459
B Miller and Miller-Bravais indices ......................... 461
B.l Miller indices ........................................ 461
B.2 Miller-Bravais indices ................................ 462
C A crash course in thermodynamics .......................... 465
C.l Thermal activation .................................... 465
C.2 Free energy and free enthalpy ......................... 466
C.3 Phase transformations and phase diagrams .............. 468
D The J integral ........................................... 473
D.l Discontinuities, singularities, and
Gauss' theorem ............................................ 473
D.2 Energy-momentum tensor ................................ 475
D.3 J integral ............................................ 476
D.4 J integral at a crack tip ............................. 479
D.5 Plasticity at the crack tip ........................... 481
D.6 Energy interpretation of the J integral ............... 482
References ................................................... 485
List of symbols .............................................. 493
Index ........................................................ 499
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