Preface ...................................................... xiii
Nomenclature ................................................. xvii
1 Introduction ................................................. 1
1.1 Stress-Strain Curves .................................... 2
1.2 Failure Mechanisms ...................................... 3
1.2.1 Failure at the atomic level ...................... 3
1.2.2 Failure modes in engineering components .......... 3
1.3 Stress Concentrations ................................... 6
1.4 Elastic Stress Fields for Notches and Cracks ............ 8
1.4.1 Stress fields at the microstructural level ...... 10
1.5 Fracture Mechanics ..................................... 11
1.5.1 The effect of constraint on fracture
toughness ....................................... 13
1.5.2 Non-linear behaviour: Plasticity and damage
zones ........................................... 14
1.5.3 Elastic-plastic fracture mechanics .............. 16
1.6 The Failure of Notched Specimens ....................... 16
1.7 Finite Element Analysis ................................ 17
1.8 Concluding Remarks: Limitations and Challenges in
Failure Prediction ..................................... 18
2 The Theory of Critical Distances: Basics .................... 21
2.1 Introduction ........................................... 21
2.2 Example 1: Brittle Fracture in a Notched Specimen ...... 21
2.2.1 Necessary information: The stress-distance
curve and material parameters ................... 23
2.2.2 The point method ................................ 24
2.3 Example 2: Fatigue Failure in an Engineering
Component .............................................. 25
2.4 Relating the TCD to LEFM ............................... 26
2.5 Finding Values for the Material Constants .............. 27
2.6 Some Other TCD Methods: The LM, AM and VM .............. 28
2.6.1 The line method ................................. 28
2.6.2 The area and volume methods ..................... 29
2.7 Example 3: Predicting Size Effects ..................... 30
2.8 Concluding Remarks ..................................... 31
3 The Theory of Critical Distances in Detail .................. 33
3.1 Introduction ........................................... 34
3.2 History ................................................ 34
3.2.1 Early work ...................................... 34
3.2.2 Parallel developments ........................... 36
3.3 Related Theories ....................................... 38
3.3.1 The imaginary radius ............................ 38
3.3.2 Introduced crack and imaginary crack models ..... 39
3.3.3 Linking the imaginary crack method to the PM
and LM .......................................... 41
3.3.4 The finite crack extension method: 'Finite
fracture mechanics' ............................. 43
3.3.5 Linking FFM to the other methods ................ 45
3.3.6 Combined stress and energy methods .............. 45
3.4 What is the TCD? Towards a General Definition .......... 47
4 Other Theories of Fracture .................................. 51
4.1 Introduction ........................................... 52
4.2 Some Classifications ................................... 52
4.3 Mechanistic Models ..................................... 54
4.4 Statistical Models ..................................... 55
4.5 Mrxlified Fracture Mechanics ........................... 55
4.6 Plastic-Zone and Process-Zone Theories ................. 57
4.7 Damage Mechanics ....................................... 59
4.8 Concluding Remarks ..................................... 60
5 Ceramics .................................................... 63
5.1 Introduction ........................................... 63
5.2 Engineering Ceramics ................................... 64
5.2.1 The effect of small defects ..................... 66
5.2.2 Notches ......................................... 74
5.2.3 Large blunt notches ............................. 80
5.2.4 Discussion: other theories and observations ..... 81
5.3 Building materials ..................................... 84
5.4 Geological Materials ................................... 86
5.5 Nanomaterials .......................................... 87
5.6 Concluding Remarks ..................................... 89
6 Polymers .................................................... 93
6.1 Introduction ........................................... 93
6.2 Notches ................................................ 95
6.2.1 Sharp notches ................................... 95
6.2.2 A wider range of notches ........................ 99
6.2.3 V-Shaped notches ............................... 106
6.3 Size Effects .......................................... 107
6.4 Constraint and the Ductile-Brittle Transition ......... 109
6.5 Strain Rate and Temperature Effects ................... 113
6.6 Discussion ............................................ 114
7 Metals ..................................................... 119
7.1 Introduction .......................................... 119
7.2 Predicting Brittle Fracture Using the TCD ............. 121
7.2.1 The effect of notch root radius ................ 121
7.2.2 The effect of constraint ....................... 124
7.2.3 The role of microstructure ..................... 129
7.2.4 Blunt notches and non-damaging notches ......... 131
7.3 Discussion ............................................ 133
7.3.1 Applicability of the TCD ....................... 133
7.3.2 Other theoretical models ....................... 135
8 Composites ................................................. 141
8.1 Introduction .......................................... 142
8.2 Early Work on the TCD: Whitney and Nuismer ............ 143
8.3 Does L Vary with Notch Size? .......................... 146
8.4 Non-damaging Notches .................................. 151
8.5 Practical Applications ................................ 154
8.6 Other Theoretical Models .............................. 155
8.7 Fracture of Bone ...................................... 156
8.8 Values of L for Composite Materials ................... 158
8.9 Concluding Remarks .................................... 158
9 Fatigue .................................................... 163
9.1 Introduction .......................................... 163
9.1.1 Current methods for the fatigue design of
components ..................................... 164
9.1.2 Crack closure .................................. 165
9.2 Fatigue Limit Predictions ............................. 167
9.2.1 Notches ........................................ 168
9.2.2 Size effects in notches ........................ 172
9.2.3 Short cracks ................................... 175
9.2.4 The effect of R ratio .......................... 180
9.2.5 Discussion on fatigue limit prediction ......... 182
9.3 Finite Life Predictions ............................... 185
9.4 Multiaxial and Variable Amplitude Loading ............. 187
9.5 Fatigue in Non-Metallic Materials ..................... 189
9.6 Other Recent Theories ................................. 191
9.7 Concluding Remarks .................................... 192
10 Contact Problems ........................................... 197
10.1 Introduction .......................................... 197
10.2 Contact Situations .................................... 198
10.3 Contact Stress Fields ................................. 198
10.4 Fretting Fatigue ...................................... 201
10.4.1 The use of the TCD in fretting fatigue ......... 205
10.5 Other Contact-Related Failure Modes: Opportunities
for the TCD ........................................... 206
10.5.1 Static indentation fracture .................... 206
10.5.2 Contact fatigue ................................ 208
10.5.3 Mechanical joints .............................. 209
10.5.4 Wear ........................................... 209
10.5.5 Machining ...................................... 209
11 Multiaxial Loading ......................................... 213
11.1 Introduction .......................................... 213
11.2 A Simplified View ..................................... 214
11.3 Material Response: The Factor ƒp ...................... 215
11.3.1 Multiaxial fatigue criteria .................... 217
11.3.2 Scalar invariants .............................. 217
11.3.3 Critical plane theories ........................ 218
11.4 Cracked Bodies: The Factor ƒc ......................... 219
11.5 Applying the TCD to Multiaxial Failure ................ 220
11.6 Multiaxial Brittle Fracture ........................... 220
11.7 Multiaxial Fatigue .................................... 222
11.8 Size Effects in Multiaxial Failure .................... 224
11.8.1 Fatigue ........................................ 224
11.8.2 Fracture of bone ............................... 229
11.9 Out-of-Plane Shear .................................... 230
11.10 Contact Problems ..................................... 232
11.11 Concluding Remarks ................................... 232
12 Case Studies and Practical Aspects ......................... 235
12.1 Introduction .......................................... 235
12.2 An Automotive Crankshaft .............................. 236
12.3 A Vehicle Suspension Arm .............................. 238
12.4 Failure Analysis of a Marine Component ................ 240
12.5 A Component Feature: Angled Holes ..................... 243
12.6 Welded Joints ......................................... 244
12.6.1 Application of the TCD to fatigue in welded
joints ......................................... 245
12.7 Other Joints .......................................... 247
12.8 Three-Dimensional Stress Concentrations ............... 250
12.9 Size Effects and Microscopic Components ............... 253
12.10 Simplified Models .................................... 256
12.10.1 Mesh density ................................. 256
12.10.2 Defeaturing .................................. 256
12.11 Concluding Remarks ................................... 257
13 Theoretical Aspects ........................................ 261
13.1 Introduction .......................................... 261
13.2 What Is the TCD? ...................................... 262
13.3 Why Does the TCD Work? ................................ 263
13.4 The TCD and Other Fracture Theories ................... 265
13.4.1 Continuum mechanics theories ................... 265
13.4.2 Process zone models ............................ 266
13.4.3 Mechanistic models ............................. 267
13.4.4 Weibull models of cleavage fracture ............ 268
13.4.5 Models of fatigue crack initiation and
growth ......................................... 269
13.5 Values of L ........................................... 270
13.6 The Value of σ0/σu ..................................... 271
13.7 The Range and Limitations of the TCD .................. 272
13.8 Concluding Remarks .................................... 274
Author Index .................................................. 277
Subject Index ................................................. 281
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