Preface ...................................................... xiii
Acknowledgments ................................................ xv
1 Stress and Strain ............................................ 1
1.1 Introduction ............................................ 1
1.2 Tensor Notation for Stress .............................. 5
1.3 Stress in Rotated Coordinate System ..................... 8
1.4 Principal Stress ....................................... 11
1.5 Stress Invariants ...................................... 16
1.6 Stress Deviator ........................................ 16
1.7 Strain ................................................. 17
1.8 True Stress and True Strain ............................ 20
Problems .................................................... 23
2 Types of Mechanical Behavior ................................ 27
2.1 Introduction ........................................... 27
2.2 Elasticity and Brittle Fracture ........................ 28
2.3 Permanent Deformation .................................. 31
3 Elasticity .................................................. 35
3.1 Introduction ........................................... 35
3.2 Elasticity of Isotropic Bodies ......................... 36
3.3 Reduced Notation for Stresses, Strains, and Elastic
Constants .............................................. 38
3.4 Effect of Symmetry on Elastic Constants ................ 41
3.5 Orientation Dependence of Elastic Moduli in Single
Crystals and Composites ................................ 43
3.6 Values of Polycrystalline Moduli in Terms of
Single-Crystal Constants ............................... 44
3.7 Variation of Elastic Constants with Lattice
Parameter .............................................. 45
3.8 Variation of Elastic Constants with Temperature ........ 47
3.9 Elastic Properties of Porous Ceramics .................. 49
3.10 Stored Elastic Energy .................................. 52
Problems .................................................... 53
4 Strength of Defect-Free Solids .............................. 55
4.1 Introduction ........................................... 55
4.2 Theoretical Strength in Tension ........................ 55
4.3 Theoretical Strength in Shear .......................... 59
Problems .................................................... 60
5 Linear Elastic Fracture Mechanics ........................... 63
5.1 Introduction ........................................... 63
5.2 Stress Concentrations .................................. 64
5.3 Griffith Theory of Fracture of a Brittle Solid ......... 65
5.4 Stress at Crack Tip: An Estimate ....................... 69
5.5 Crack Shape in Brittle Solids .......................... 70
5.6 Irwin Formulation of Fracture Mechanics: Stress
Intensity Factor ....................................... 71
5.7 Irwin Formulation of Fracture Mechanics: Energy
Release Rate ........................................... 75
5.8 Some Useful Stress Intensity Factors ................... 79
5.9 The J Integral ......................................... 81
5.10 Cracks with Internal Loading ........................... 83
5.11 Failure under Multiaxial Stress ........................ 85
Problems .................................................... 87
6 Measurements of Elasticity, Strength, and Fracture
Toughness ................................................... 89
6.1 Introduction ........................................... 89
6.2 Tensile Tests .......................................... 91
6.3 Flexure Tests .......................................... 95
6.4 Double-Cantilever-Beam Test ........................... 104
6.5 Double-Torsion Test ................................... 106
6.6 Indentation Test ...................................... 106
6.7 Biaxial Flexure Testing ............................... 113
6.8 Elastic Constant Determination Using Vibrational
and Ultrasonic Methods ................................ 113
Problems ................................................... 115
7 Statistical Treatment of Strength .......................... 119
7.1 Introduction .......................................... 119
7.2 Statistical Distributions ............................. 120
7.3 Strength Distribution Functions ....................... 121
7.4 Weakest Link Theory ................................... 125
7.5 Determining Weibull Parameters ........................ 128
7.6 Effect of Specimen Size ............................... 129
7.7 Adaptation to Bend Testing ............................ 130
7.8 Safety Factors ........................................ 136
7.9 Example of Safe Stress Calculation .................... 136
7.10 Proof Testing ......................................... 138
7.11 Use of Pooled Fracture Data in Linear Regression
Determination of Weibull Parameters ................... 140
7.12 Method of Maximum Likelihood in Weibull Parameter
Estimation ............................................ 141
7.13 Statistics of Failure under Multiaxial Stress ......... 144
7.14 Effects of Slow Crack Propagation and R-Curve
Behavior on Statistical Distributions of Strength ..... 146
7.15 Surface Flaw Distributions and Multiple Flaw
Distributions ......................................... 147
Problems ................................................... 149
8 Subcritical Crack Propagation .............................. 151
8.1 Introduction .......................................... 151
8.2 Observed Subcritical Crack Propagation ................ 152
8.3 Crack Velocity Theory and Molecular Mechanism ......... 155
8.4 Time to Failure under Constant Stress ................. 158
8.5 Failure under Constant Stress Rate .................... 162
8.6 Comparison of Times to Failure under Constant Stress
and Constant Stress Rate .............................. 164
8.7 Relation of Weibull Statistical Parameters with
and without Subcritical Crack Growth .................. 164
8.8 Construction of Strength-Probability-Time Diagrams .... 166
8.9 Proof Testing to Guarantee Minimum Life ............... 171
8.10 Subcritical Crack Growth and Failure from Flaws
Originating from Residual Stress Concentrations ....... 172
8.11 Slow Crack Propagation at High Temperature ............ 173
Problems ................................................... 175
9 Stable Crack Propagation and R-Curve Behavior .............. 177
9.1 Introduction .......................................... 177
9.2 R-Curve (T-Curve) Concept ............................. 179
9.3 R-Curve Effects of Strength Distributions ............. 185
9.4 Effect of R-Curve on Subcritical Crack Growth ......... 186
Problems ................................................... 186
10 Overview of Toughening Mechanisms in Ceramics .............. 189
10.1 Introduction .......................................... 189
10.2 Toughening by Crack Deflection ........................ 191
10.3 Toughening by Crack Bowing ............................ 193
10.4 General Remarks on Crack Tip Shielding ................ 194
11 Effect of Microstructure on Toughness and Strength ......... 199
11.1 Introduction .......................................... 199
11.2 Fracture Modes in Polycrystalline Ceramics ............ 200
11.3 Crystalline Anisotropy in Polycrystalline Ceramics .... 204
11.4 Effect of Grain Size on Toughness ..................... 207
11.5 Natural Flaws in Polycrystalline Ceramics ............. 210
11.6 Effect of Grain Size on Fracture Strength ............. 212
11.7 Effect of Second-Phase Particles on Fracture
Strength .............................................. 217
11.8 Relationship between Strength and Toughness ........... 219
11.9 Effect of Porosity on Toughness and Strength .......... 220
11.10 Fracture of Traditional Ceramics ..................... 222
Problems ................................................... 224
12 Toughening by Transformation ............................... 227
12.1 Introduction .......................................... 227
12.2 Basic Facts of Transformation Toughening .............. 228
12.3 Theory of Transformation Toughening ................... 230
12.4 Shear-Dilatant Transformation Theory .................. 233
12.5 Grain-Size-Dependent Transformation Behavior .......... 233
12.6 Application of Theory to Ca-Stabilized Zirconia ....... 242
Problems ................................................... 245
13 Mechanical Properties of Continuous-Fiber-Reinforced
Ceramic Matrix Composites .................................. 249
13.1 Introduction .......................................... 249
13.2 Elastic Behavior of Composites ........................ 250
13.3 Fracture Behavior of Composites with Continuous,
Aligned Fibers ........................................ 253
13.4 Complete Matrix Cracking of Composites with
Continuous, Aligned Fibers ............................ 255
13.5 Propagation of Short, Fully Bridged Cracks ............ 260
13.6 Propagation of Partially Bridged Cracks ............... 264
13.7 Additional Treatment of Crack-Bridging Effects ........ 267
13.8 Additional Statistical Treatments ..................... 269
13.9 Summary of Fiber-Toughening Mechanisms ................ 270
13.10 Other Failure Mechanisms in Continuous, Aligned-
Fiber Composites ..................................... 270
13.11 Tensile Stress-Strain Curve of Continuous, Aligned-
Fiber Composites ..................................... 271
13.12 Laminated Composites ................................. 273
Problems ................................................... 274
14 Mechanical Properties of Whisker-, Ligament-, and
Platelet-Reinforced Ceramic Matrix Composites .............. 277
14.1 Introduction .......................................... 277
14.2 Model for Whisker Toughening .......................... 278
14.3 Combined Toughening Mechanisms in Whisker-Reinforced
Composites ............................................ 288
14.4 Ligament-Reinforced Ceramic Matrix Composites ......... 288
14.5 Platelet-Reinforced Ceramic Matrix Composites ......... 289
Problems ................................................... 289
15 Cyclic Fatigue of Ceramics ................................. 291
15.1 Introduction .......................................... 291
15.2 Cyclic Fatigue of Metals .............................. 292
15.3 Cyclic Fatigue of Ceramics ............................ 295
15.4 Mechanisms of Cyclic Fatigue of Ceramics .............. 298
15.5 Cyclic Fatigue by Degradation of Crack Bridges ........ 298
15.6 Short-Crack Fatigue of Ceramics ....................... 298
15.7 Implications of Cyclic Fatigue in Design of
Ceramics .............................................. 301
Problems ................................................... 301
16 Thermal Stress and Thermal Shock in Ceramics ............... 303
16.1 Introduction .......................................... 303
16.2 Magnitude of Thermal Stresses ......................... 304
16.3 Figure of Merit for Various Thermal Stress
Conditions ............................................ 304
16.4 Crack Propagation under Thermal Stress ................ 306
Problems ................................................... 313
17 Fractography ............................................... 317
17.1 Introduction .......................................... 317
17.2 Qualitative Features of Fracture Surfaces ............. 318
17.3 Quantitative Fractography ............................. 325
17.4 Fractal Concepts in Fractography ...................... 328
17.5 Fractography of Single Crystals and Polycrystals ...... 328
Problems ................................................... 330
18 Dislocations and Plastic Deformation in Ductile Crystals ... 333
18.1 Introduction .......................................... 333
18.2 Definition of Dislocations ............................ 334
18.3 Glide and Climb of Dislocations ....................... 337
18.4 Force on a Dislocation ................................ 337
18.5 Stress Field and Energy of a Dislocation .............. 339
18.6 Force Required to Move a Dislocation .................. 340
18.7 Line Tension of a Dislocation ......................... 341
18.8 Dislocation Multiplication ............................ 342
18.9 Forces between Dislocations ........................... 343
18.10 Dislocation Pileups .................................. 345
18.11 Orowan's Equation for Strain Rate .................... 346
18.12 Dislocation Velocity ................................. 347
18.13 Hardening by Solid Solution and Precipitation ........ 348
18.14 Slip Systems ......................................... 349
18.15 Partial Dislocations ................................. 351
18.16 Deformation Twinning ................................. 353
Problems ................................................... 356
19 Dislocations and Plastic Deformation in Ceramics ........... 357
19.1 Introduction .......................................... 357
19.2 Slip Systems in Ceramics .............................. 358
19.3 Independent Slip Systems .............................. 359
19.4 Plastic Deformation in Single-Crystal Alumina ......... 360
19.5 Twinning in Aluminum Oxide ............................ 366
19.6 Plastic Deformation of Single-Crystal Magnesium
Oxide ................................................. 368
19.7 Plastic Deformation of Single-Crystal Cubic
Zirconia .............................................. 369
Problems ................................................... 369
20 Creep in Ceramics .......................................... 371
20.1 Introduction .......................................... 371
20.2 Nabarro-Herring Creep ................................. 373
20.3 Combined Diffusional Creep Mechanisms ................. 374
20.4 Power Law Creep ....................................... 376
20.5 Combined Diffusional and Power Law Creep .............. 378
20.6 Role of Grain Boundaries in High-Temperature
Deformation and Failure ............................... 379
20.7 Damage-Enhanced Creep ................................. 380
20.8 Superplasticity ....................................... 382
20.9 Deformation Mechanism Maps ............................ 388
Problems ................................................... 388
21 Creep Rupture at High Temperatures and Safe Life Design .... 391
21.1 Introduction .......................................... 391
21.2 General Process of Creep Damage and Failure in
Ceramics .............................................. 391
21.3 Monkman-Grant Technique of Life Prediction ............ 395
21.4 Two-Stage Strain Projection Technique ................. 397
21.5 Fracture Mechanism Maps ............................... 399
Problems ................................................... 403
22 Hardness and Wear .......................................... 405
22.1 Introduction .......................................... 405
22.2 Spherical Indenters versus Sharp Indenters ............ 406
22.3 Methods of Hardness Measurement ....................... 408
22.4 Deformation around Indentation ........................ 410
22.5 Cracking around Indentation ........................... 412
22.6 Indentation Size Effect ............................... 413
22.7 Wear Resistance ....................................... 416
Problems ................................................... 421
23 Mechanical Properties of Glass and Glass Ceramics .......... 423
23.1 Introduction .......................................... 423
23.2 Typical Inorganic Glasses ............................. 423
23.3 Viscosity of Glass .................................... 424
23.4 Elasticity of Inorganic Glasses ....................... 425
23.5 Strength and Fracture Surface Energy of Inorganic
Glasses ............................................... 426
23.6 Achieving High Strength in Bulk Glasses ............... 427
23.7 Glass Ceramics ........................................ 429
Problems ................................................... 429
24 Mechanical Properties of Polycrystalline Ceramics
in General and Design Considerations ....................... 431
24.1 Introduction .......................................... 431
24.2 Mechanical Properties of Polycrystalline Ceramics in
General ............................................... 432
24.3 Design Involving Mechanical Properties ................ 436
References ................................................. 439
Index ......................................................... 473
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