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 |  موضوع: كتاب Mechanical Properties of Ceramics الأحد 29 ديسمبر 2013, 9:40 am | |
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Mechanical Properties of Ceramics
JOHN B. WACHTMAN
W. ROGER CANNON
M. JOHN MATTHEWSON
Rutgers University
ويتناول الموضوعات الأتية :
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
1.4.1 Principal Stresses in Three Dimensions 15
1.5 Stress Invariants 16
1.6 Stress Deviator 16
1.7 Strain 17
1.8 True Stress and True Strain 20
1.8.1 True Strain 21
1.8.2 True Stress 22
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
v
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
5.7.1 Relationship betweenGandKI 76
5.8 Some Useful Stress Intensity Factors 79
5.9 TheJIntegral 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
6.3.1 Three-Point Bending 98
6.3.2 Four-Point Bending 100
6.3.3 Fracture Toughness Measurement by Bending 101
6.4 Double-Cantilever-Beam Test 104
vi CONTENTS
6.5 Double-Torsion Test 106
6.6 Indentation Test 106
6.6.1 Direct Method 108
6.6.2 Indirect Method 109
6.6.3 Modified Method 111
6.6.4 Summary of the Three Methods 112
6.6.5 ASTM Standard C 1421 Method 112
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
7.3.1 Gaussian, or Normal, Distribution 122
7.3.2 Weibull Distribution 122
7.3.3 Comparison of the Normal and Weibull Distributions 124
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 andR-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
CONTENTS vii
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 andR-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 ofRCurve 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
viii CONTENTS
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
CONTENTS ix
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
x CONTENTS
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
CONTENTS xi
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
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