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Fracture Mechanics
von: Alan T. Zehnder
Springer-Verlag, 2012
ISBN: 9789400725959 , 235 Seiten
Format: PDF, OL
Kopierschutz: Wasserzeichen
Preis: 181,89 EUR
Fracture Mechanics
4
Preface
6
References
6
Contents
8
Acronyms
12
Chapter 1: Introduction
16
1.1 Notable Fractures
16
1.2 Basic Fracture Mechanics Concepts
18
1.2.1 Small Scale Yielding Model
19
1.2.2 Fracture Criteria
19
1.3 Fracture Unit Conversions
20
1.4 Exercises
20
References
21
Chapter 2: Linear Elastic Stress Analysis of 2D Cracks
22
2.1 Notation
22
2.2 Introduction
22
2.3 Modes of Fracture
23
2.4 Mode III Field
23
2.4.1 Asymptotic Mode III Field
24
2.4.2 Full Field for Finite Crack in an In?nite Body
28
2.4.2.1 Complex Variables Formulation of Anti-Plane Shear
28
2.4.2.2 Solution to the Problem
29
2.5 Mode I and Mode II Fields
31
2.5.1 Review of Plane Stress and Plane Strain Field Equations
31
2.5.1.1 Plane Strain
31
2.5.1.2 Plane Stress
32
2.5.1.3 Stress Function
32
2.5.2 Asymptotic Mode I Field
32
2.5.2.1 Stress Field
32
2.5.2.2 Displacement Field
34
2.5.3 Asymptotic Mode II Field
36
2.6 Complex Variables Method for Mode I and Mode II Cracks
36
2.6.1 Westergaard Approach for Mode-I
37
2.6.2 Westergaard Approach for Mode-II
37
2.6.3 General Solution for Internal Crack with Applied Tractions
37
2.6.4 Full Stress Field for Mode-I Crack in an In?nite Plate
38
2.6.5 Stress Intensity Factor Under Remote Shear Loading
40
2.6.6 Stress Intensity Factors for Cracks Loaded with Tractions
41
2.6.7 Asymptotic Mode I Field Derived from Full Field Solution
41
2.6.8 Asymptotic Mode II Field Derived from Full Field Solution
43
2.6.9 Stress Intensity Factors for Semi-in?nite Crack
43
2.7 Some Comments
43
2.7.1 Three-Dimensional Cracks
44
2.8 Exercises
46
References
47
Chapter 3: Energy Flows in Elastic Fracture
48
3.1 Generalized Force and Displacement
48
3.1.1 Prescribed Loads
48
3.1.2 Prescribed Displacements
49
3.2 Elastic Strain Energy
50
3.3 Energy Release Rate, G
51
3.3.1 Prescribed Displacement
51
3.3.2 Prescribed Loads
52
3.3.3 General Loading
53
3.4 Interpretation of G from Load-Displacement Records
53
3.4.1 Multiple Specimen Method for Nonlinear Materials
53
3.4.2 Compliance Method for Linearly Elastic Materials
56
3.4.3 Applications of the Compliance Method
57
3.4.3.1 Determination of G in DCB Sample
57
3.4.3.2 Use of Compliance to Determine Crack Length
58
3.5 Crack Closure Integral for G
58
3.6 G in Terms of KI, KII, KIII for 2D Cracks That Grow Straight Ahead
62
3.6.1 Mode-III Loading
62
3.6.2 Mode I Loading
63
3.6.3 Mode II Loading
63
3.6.4 General Loading (2D Crack)
63
3.7 Contour Integral for G (J-Integral)
64
3.7.1 Two Dimensional Problems
64
3.7.2 Three-Dimensional Problems
66
3.7.3 Example Application of J-Integral
66
3.8 Exercises
67
References
69
Chapter 4: Criteria for Elastic Fracture
70
4.1 Introduction
70
4.2 Initiation Under Mode-I Loading
70
4.3 Crack Growth Stability and Resistance Curve
73
4.3.1 Loading by Compliant System
75
4.3.2 Resistance Curve
76
4.4 Mixed-Mode Fracture Initiation and Growth
78
4.4.1 Maximum Hoop Stress Theory
78
4.4.2 Maximum Energy Release Rate Criterion
80
4.4.3 Crack Path Stability Under Pure Mode-I Loading
81
4.4.4 Second Order Theory for Crack Kinking and Turning
84
4.5 Criteria for Fracture in Anisotropic Materials
85
4.6 Crack Growth Under Fatigue Loading
86
4.7 Stress Corrosion Cracking
89
4.8 Exercises
89
References
91
Chapter 5: Determining K and G
92
5.1 Analytical Methods
92
5.1.1 Elasticity Theory
92
5.1.1.1 Finite Crack in an In?nite Body
92
5.1.1.2 Semi-in?nite Crack in an In?nite Body
93
5.1.1.3 Array of Cracks Under Remote Loading
93
5.1.2 Energy and Compliance Methods
94
5.1.2.1 4-Point Bending Debond Specimen: Energy Method
94
5.2 Stress Intensity Handbooks and Software
95
5.3 Boundary Collocation
95
5.4 Computational Methods: A Primer
99
5.4.1 Stress and Displacement Correlation
99
5.4.1.1 Stress Correlation
99
5.4.1.2 Displacement Correlation
100
5.4.2 Global Energy and Compliance
100
5.4.3 Crack Closure Integrals
101
5.4.3.1 Nodal Release
101
5.4.3.2 Modi?ed Crack Closure Integral
102
5.4.4 Domain Integral
104
5.4.5 Crack Tip Singular Elements
105
5.4.6 Example Calculations
109
5.4.6.1 Displacement Correlation and Domain Integral with 1/4 Point Elements
110
5.4.6.2 Global Energy
110
5.4.6.3 Modi?ed Crack Closure Integral
111
5.5 Experimental Methods
112
5.5.1 Strain Gauge Method
113
5.5.2 Photoelasticity
115
5.5.3 Digital Image Correlation
116
5.5.4 Thermoelastic Method
118
5.6 Exercises
120
References
121
Chapter 6: Fracture Toughness Tests
123
6.1 Introduction
123
6.2 ASTM Standard Fracture Test
124
6.2.1 Test Samples
124
6.2.2 Equipment
126
6.2.3 Test Procedure and Data Reduction
126
6.3 Interlaminar Fracture Toughness Tests
127
6.3.1 The Double Cantilever Beam Test
127
6.3.1.1 Geometry and Test Procedure
127
6.3.1.2 Data Reduction Methods
128
6.3.1.3 Example Results
130
6.3.2 The End Notch Flexure Test
131
6.3.3 Single Leg Bending Test
132
6.4 Indentation Method
134
6.5 Chevron-Notch Method
136
6.5.1 KIVM Measurement
137
6.5.2 KIV Measurement
138
6.5.3 Work of Fracture Approach
139
6.6 Wedge Splitting Method
141
6.7 K-R Curve Determination
144
6.7.1 Specimens
144
6.7.2 Equipment
145
6.7.2.1 Optical Measurement of Crack Length
145
6.7.2.2 Compliance Method for Crack Length
145
6.7.2.3 Other Methods for Crack Length
145
6.7.3 Test Procedure and Data Reduction
147
6.7.3.1 By Measurement of Load and Crack Length
147
6.7.3.2 By Measurement of Load and Compliance
147
6.7.3.3 Indirect Approach Using Monotonic Load-Displacement Data
148
6.7.4 Sample K-R curve
148
6.8 Exercises
148
References
149
Chapter 7: Elastic Plastic Fracture: Crack Tip Fields
151
7.1 Introduction
151
7.2 Strip Yield (Dugdale) Model
151
7.2.1 Effective Crack Length Model
157
7.3 A Model for Small Scale Yielding
158
7.4 Introduction to Plasticity Theory
160
7.5 Anti-plane Shear Cracks in Elastic-Plastic Materials in SSY
164
7.5.1 Stationary Crack in Elastic-Perfectly Plastic Material
164
7.5.2 Stationary Crack in Power-Law Hardening Material
168
7.5.3 Steady State Growth in Elastic-Perfectly Plastic Material
170
7.5.4 Transient Crack Growth in Elastic-Perfectly Plastic Material
174
7.6 Mode-I Crack in Elastic-Plastic Materials
176
7.6.1 Stationary Crack in a Power Law Hardening Material
176
7.6.1.1 Deformation Theory (HRR Field)
176
7.6.1.2 Incremental Theory
179
7.6.2 Slip Line Solutions for Rigid Plastic Material
179
7.6.2.1 Introduction to Plane Strain Slip Line Theory
179
7.6.2.2 Plane-Strain, Semi-in?nite Crack
181
7.6.2.3 Plane-Stress, Semi-in?nite Crack
183
7.6.3 Large Scale Yielding (LSY) Example
183
7.6.4 SSY Plastic Zone Size and Shape
184
7.6.5 CTOD-J Relationship
186
7.6.6 Growing Mode-I Crack
187
7.6.7 Three Dimensional Aspects
191
7.6.8 Effect of Finite Crack Tip Deformation on Stress Field
193
7.7 Exercises
195
References
196
Chapter 8: Elastic Plastic Fracture: Energy and Applications
198
8.1 Energy Flows
198
8.1.1 When Does G=J?
198
8.1.2 General Treatment of Crack Tip Contour Integrals
199
8.1.3 Crack Tip Energy Flux Integral
201
8.1.3.1 Global Path Independence for Steady State Crack Growth
201
8.1.3.2 Energy Flux as Gamma->0
202
8.1.3.3 Energy Flux for Gamma Outside Plastic Zone
202
8.1.3.4 Thermal Field Visualization of Energy Flow
204
8.2 Fracture Toughness Testing for Elastic-Plastic Materials
206
8.2.1 Samples and Equipment
206
8.2.2 Procedure and Data Reduction
207
8.2.2.1 Test Procedure
207
8.2.2.2 Data Reduction
208
8.2.2.3 Validation of Results
209
8.2.3 Examples of J-R Data
210
8.3 Calculating J and Other Ductile Fracture Parameters
210
8.3.1 Computational Methods
211
8.3.2 J Result Used in ASTM Standard JIC Test
213
8.3.2.1 Rigid Plastic Material
215
8.3.2.2 Elastic Material
215
8.3.2.3 Elastic-Plastic Material
215
8.3.3 Engineering Approach to Elastic-Plastic Fracture Analysis
215
8.3.3.1 Sample Calculation
217
8.4 Fracture Criteria and Prediction
218
8.4.1 J Controlled Crack Growth and Stability
218
8.4.2 J-Q Theory
220
8.4.3 Crack Tip Opening Displacement, Crack Tip Opening Angle
223
8.4.4 Cohesive Zone Model
226
8.4.4.1 Cohesive Zone Embedded in Elastic Material
228
8.4.4.2 Cohesive Zone Embedded in Elastic-Plastic Material
229
References
231
Index
233
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