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Summary
Summary
How do engineering materials deform when bearing mechanical loads? To answer this crucial question, the book bridges the gap between continuum mechanics and materials science. The different kinds of material deformation (elasticity, plasticity, fracture, creep, fatigue) are explained in detail. The book also discusses the physical processes occurring during the deformation of all classes of engineering materials (metals, ceramics, polymers, and composites) and shows how these materials can be strengthened to meet the design requirements. It provides the knowledge needed in selecting the appropriate engineering material for a certain design problem. The reader will thus learn how to critically employ design rules and thus to avoid failure of mechanical components.
'Mechanical Behaviour of Engineering Materials' is both a valuable textbook and a useful reference for graduate students and practising engineers.
Table of Contents
1 The structure of materials | p. 1 |
1.1 Atomic structure and the chemical bond | p. 1 |
1.2 Metals | p. 5 |
1.2.1 Metallic bond | p. 5 |
1.2.2 Crystal structures | p. 7 |
1.2.3 Polycrystalline metals | p. 14 |
1.3 Ceramics | p. 15 |
1.3.1 Covalents bond | p. 16 |
1.3.2 Ionic bond | p. 18 |
1.3.3 Dipole bond | p. 19 |
1.3.4 Van der Waals bond | p. 19 |
1.3.5 Hydrogen bond | p. 20 |
1.3.6 The crystal structure of ceramics | p. 21 |
1.3.7 Amorphous ceramics | p. 22 |
1.4 Polymers | p. 23 |
1.4.1 The chemical structure of polymers | p. 24 |
1.4.2 The structure of polymers | p. 25 |
2 Elasticity | p. 31 |
2.1 Deformation modes | p. 31 |
2.2 Stress and strain | p. 32 |
2.2.1 Stress | p. 32 |
2.2.2 Strain | p. 34 |
2.3 Atomic interactions | p. 37 |
2.4 Hooke's law | p. 39 |
2.4.1 Elastic strain energy | p. 42 |
2.4.2 Elastic deformation under multiaxial loads | p. 43 |
2.4.3 Isotropic material | p. 46 |
2.4.4 Cubic lattice | p. 50 |
2.4.5 Orthorhombic crystals and orthotropic elasticity | p. 53 |
2.4.6 Transversally isotropic elasticity | p. 54 |
2.4.7 Other crystal lattices | p. 55 |
2.4.8 Examples | p. 55 |
2.5 Isotropy and anisotropy of macroscopic components | p. 57 |
2.6 Temperature dependence of Young's modulus | p. 60 |
3 Plasticity and failure | p. 63 |
3.1 Nominal and true strain | p. 64 |
3.2 Stress-strain diagrams | p. 68 |
3.2.1 Types of stress-strain diagrams | p. 68 |
3.2.2 Analysis of a stress-strain diagram | p. 73 |
3.2.3 Approximation of the stress-strain curve | p. 81 |
3.3 Plasticity theory | p. 83 |
3.3.1 Yield criteria | p. 84 |
3.3.2 Yield criteria of metals | p. 86 |
3.3.3 Yield criteria of polymers | p. 92 |
3.3.4 Flow rules | p. 93 |
3.3.5 Hardening | p. 97 |
3.3.6 Application of a yield criterion, flow rule, and hardening rule | p. 103 |
3.4 Hardness | p. 107 |
3.4.1 Scratch tests | p. 108 |
3.4.2 Indentation tests | p. 108 |
3.4.3 Rebound tests | p. 110 |
3.5 Material failure | p. 110 |
3.5.1 Shear fracture | p. 111 |
3.5.2 Cleavage fracture | p. 114 |
3.5.3 Fracture criteria | p. 116 |
4 Notches | p. 119 |
4.1 Stress concentration factor | p. 119 |
4.2 Neuber's rule | p. 122 |
4.3 Tensile testing of notched specimens | p. 125 |
5 Fracture mechanics | p. 129 |
5.1 Introduction to fracture mechanics | p. 129 |
5.1.1 Definitions | p. 129 |
5.2 Linear-elastic fracture mechanics | p. 131 |
5.2.1 The stress field near a crack tip | p. 131 |
5.2.2 The energy balance of crack propagation | p. 134 |
5.2.3 Dimensioning pre-cracked components under static loads | p. 142 |
5.2.4 Fracture parameters of different materials | p. 144 |
5.2.5 Material behaviour during crack propagation | p. 146 |
5.2.6 Subcritical crack propagation | p. 150 |
5.2.7 Measuring fracture parameters | p. 152 |
5.3 Elastic-plastic fracture mechanics | p. 158 |
5.3.1 Crack tip opening displacement (CTOD) | p. 158 |
5.3.2 J integral | p. 159 |
5.3.3 Material behaviour during crack propagation | p. 161 |
5.3.4 Measuring elastic-plastic fracture mechanics parameters | p. 163 |
6 Mechanical behaviour of metals | p. 165 |
6.1 Theoretical strength | p. 165 |
6.2 Dislocations | p. 166 |
6.2.1 Types of dislocations | p. 166 |
6.2.2 The stress field of a dislocation | p. 168 |
6.2.3 Dislocation movement | p. 170 |
6.2.4 Slip systems | p. 173 |
6.2.5 The critical resolved shear stress | p. 178 |
6.2.6 Taylor factor | p. 182 |
6.2.7 Dislocation interaction | p. 184 |
6.2.8 Generation, multiplication and annihilation of dislocations | p. 185 |
6.2.9 Forces acting on dislocations | p. 187 |
6.3 Overcoming obstacles | p. 189 |
6.3.1 Athermal processes | p. 190 |
6.3.2 Thermally activated processes | p. 193 |
6.3.3 Ductile-brittle transition | p. 196 |
6.3.4 Climb | p. 196 |
6.3.5 Intersection of dislocations | p. 197 |
6.4 Strengthening mechanisms | p. 198 |
6.4.1 Work hardening | p. 198 |
6.4.2 Grain boundary strengthening | p. 200 |
6.4.3 Solid solution hardening | p. 203 |
6.4.4 Particle strengthening | p. 209 |
6.4.5 Hardening of steels | p. 218 |
6.5 Mechanical twinning | p. 223 |
7 Mechanical behaviour of ceramics | p. 227 |
7.1 Manufacturing ceramics | p. 228 |
7.2 Mechanisms of crack propagation | p. 229 |
7.2.1 Crack deflection | p. 230 |
7.2.2 Crack bridging | p. 230 |
7.2.3 Microcrack formation and crack branching | p. 231 |
7.2.4 Stress-induced phase transformations | p. 232 |
7.2.5 Stable crack growth | p. 234 |
7.2.6 Subcritical crack growth in ceramics | p. 234 |
7.3 Statistical fracture mechanics | p. 236 |
7.3.1 Weibull statistics | p. 236 |
7.3.2 Weibull statistics for subcritical crack growth | p. 242 |
7.3.3 Measuring the parameters [sigma subscript 0] and m | p. 243 |
7.4 Proof test | p. 246 |
7.5 Strengthening ceramics | p. 248 |
7.5.1 Reducing defect size | p. 249 |
7.5.2 Crack deflection | p. 249 |
7.5.3 Microcracks | p. 251 |
7.5.4 Transformation toughening | p. 252 |
7.5.5 Adding ductile particles | p. 255 |
8 Mechanical behaviour of polymers | p. 257 |
8.1 Physical properties of polymers | p. 257 |
8.1.1 Relaxation processes | p. 257 |
8.1.2 Glass transition temperature | p. 260 |
8.1.3 Melting temperature | p. 261 |
8.2 Time-dependent deformation of polymers | p. 263 |
8.2.1 Phenomenological description of time-dependence | p. 263 |
8.2.2 Time-dependence and thermal activation | p. 266 |
8.3 Elastic properties of polymers | p. 269 |
8.3.1 Elastic properties of thermoplastics | p. 269 |
8.3.2 Elastic properties of elastomers and duromers | p. 273 |
8.4 Plastic behaviour | p. 274 |
8.4.1 Amorphous thermoplastics | p. 275 |
8.4.2 Semi-crystalline thermoplastics | p. 281 |
8.5 Increasing the thermal stability | p. 284 |
8.5.1 Increasing the glass and the melting temperature | p. 284 |
8.5.2 Increasing the crystallinity | p. 287 |
8.6 Increasing strength and stiffness | p. 289 |
8.7 Increasing the ductility | p. 290 |
8.8 Environmental effects | p. 292 |
9 Mechanical behaviour of fibre reinforced composites | p. 295 |
9.1 Strengthening methods | p. 296 |
9.1.1 Classifying by particle geometry | p. 296 |
9.1.2 Classifying by matrix systems | p. 299 |
9.2 Elasticity of fibre composites | p. 300 |
9.2.1 Loading in parallel to the fibres | p. 301 |
9.2.2 Loading perpendicular to the fibres | p. 301 |
9.2.3 The anisotropy in general | p. 302 |
9.3 Plasticity and fracture of composites | p. 303 |
9.3.1 Tensile loading with continuous fibres | p. 303 |
9.3.2 Load transfer between matrix and fibre | p. 305 |
9.3.3 Crack propagation in fibre composites | p. 308 |
9.3.4 Statistics of composite failure | p. 312 |
9.3.5 Failure under compressive loads | p. 313 |
9.3.6 Matrix-dominated failure and arbitrary loads | p. 315 |
9.4 Examples of composites | p. 315 |
9.4.1 Polymer matrix composites | p. 315 |
9.4.2 Metal matrix composites | p. 321 |
9.4.3 Ceramic matrix composites | p. 323 |
9.4.4 Biological composites | p. 325 |
10 Fatigue | p. 333 |
10.1 Types of loads | p. 333 |
10.2 Fatigue failure of metals | p. 337 |
10.2.1 Crack initiation | p. 338 |
10.2.2 Crack propagation (stage II) | p. 342 |
10.2.3 Final fracture | p. 344 |
10.3 Fatigue of ceramics | p. 345 |
10.4 Fatigue of polymers | p. 346 |
10.4.1 Thermal fatigue | p. 346 |
10.4.2 Mechanical fatigue | p. 347 |
10.5 Fatigue of fibre composites | p. 347 |
10.6 Phenomenological description of the fatigue strength | p. 349 |
10.6.1 Fatigue crack growth | p. 349 |
10.6.2 Stress-cycle diagrams (S-N diagrams) | p. 357 |
10.6.3 The role of mean stress | p. 366 |
10.6.4 Fatigue assessment with variable amplitude loading | p. 368 |
10.6.5 Cyclic stress-strain behaviour | p. 369 |
10.6.6 Kitagawa diagram | p. 373 |
10.7 Fatigue of notched specimens | p. 375 |
11 Creep | p. 383 |
11.1 Phenomenology of creep | p. 383 |
11.2 Creep mechanisms | p. 388 |
11.2.1 Stages of creep | p. 388 |
11.2.2 Dislocation creep | p. 389 |
11.2.3 Diffusion creep | p. 393 |
11.2.4 Grain boundary sliding | p. 396 |
11.2.5 Deformation mechanism maps | p. 396 |
11.3 Creep fracture | p. 400 |
11.4 Increasing the creep resistance | p. 401 |
12 Exercises | p. 407 |
1 Packing density of crystals | p. 407 |
2 Macromolecules | p. 407 |
3 Interaction between two atoms | p. 407 |
4 Bulk modulus | p. 408 |
5 Relation between the elastic constants | p. 408 |
6 Candy catapult | p. 409 |
7 True strain | p. 410 |
8 Interest calculation | p. 410 |
9 Large deformations | p. 410 |
10 Yield criteria | p. 410 |
11 Yield criteria of polymers | p. 411 |
12 Design of a notched shaft | p. 411 |
13 Estimating the fracture toughness K[subscript Ic] | p. 412 |
14 Determination of the fracture toughness K[subscript Ic] | p. 412 |
15 Static design of a tube | p. 413 |
16 Theoretical strength | p. 414 |
17 Estimating the dislocation density | p. 414 |
18 Thermally activated dislocation generation | p. 414 |
19 Work hardening | p. 415 |
20 Grain boundary strengthening | p. 415 |
21 Precipitation hardening | p. 415 |
22 Weibull statistics | p. 415 |
23 Design of a fluid tank | p. 416 |
24 Subcritical crack growth of a ceramic component | p. 417 |
25 Mechanical models of viscoelastic polymers | p. 417 |
26 Elastic damping | p. 418 |
27 Eyring plot | p. 418 |
28 Elasticity of fibre composites | p. 419 |
29 Properties of a polymer matrix composite | p. 419 |
30 Estimating the number of cycles to failure | p. 419 |
31 Miner's rule | p. 420 |
32 Larson-Miller parameter | p. 421 |
33 Creep deformation | p. 421 |
34 Relaxation of thermal stresses by creep | p. 421 |
13 Solution | p. 423 |
A Using tensors | p. 451 |
A.1 Introduction | p. 451 |
A.2 The order of a tensor | p. 451 |
A.3 Tensor notations | p. 452 |
A.4 Tensor operations and Einstein summation convention | p. 453 |
A.5 Coordinate transformations | p. 456 |
A.6 Important constants and tensor operations | p. 457 |
A.7 Invariants | p. 458 |
A.8 Derivations of tensor fields | p. 459 |
B Miller and Miller-Bravais indices | p. 461 |
B.1 Miller indices | p. 461 |
B.2 Miller-Bravais indices | p. 462 |
C A crash course in thermodynamics | p. 465 |
C.1 Thermal activation | p. 465 |
C.2 Free energy and free enthalpy | p. 466 |
C.3 Phase transformations and phase diagrams | p. 468 |
D The J integral | p. 473 |
D.1 Discontinuities, singularities, and Gauss' theorem | p. 473 |
D.2 Energy-momentum tensor | p. 475 |
D.3 J integral | p. 476 |
D.4 J integral at a crack tip | p. 479 |
D.5 Plasticity at the crack tip | p. 481 |
D.6 Energy interpretation of the J integral | p. 482 |
References | p. 485 |
List of symbols | p. 493 |
Index | p. 499 |