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