Analytical Fracture Mechanics

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ISBN: 9780127091204 | 0127091203
Cover: Hardcover
Copyright: 9/1/1995

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Self-contained treatment supplements standard texts by focusing on analytical methods for determining crack-tip stress and strain fields. Topics include plastic zone transitions, environmental cracking, more. "Recommended." "Applied Mechanics Review."

Color Plates
Preface	p. xi
Acknowledgments	p. xiii
Introduction
Equations of Continuum Mechanics	p. 1
Equilibrium	p. 1
Strain-Displacement	p. 4
Change of Volume	p. 4
Compatibility of Strains	p. 4
Equations of Elasticity	p. 5
Equations of Plasticity	p. 6
Strain Hardening	p. 9
Material Stability	p. 11
Incremental Strain-Stress Relationships	p. 12
Flow Theory versus Deformation Theory	p. 16
Plane Problems of Elasticity Theory	p. 16
Cartesian Coordinates	p. 17
Polar Coordinates	p. 19
Kolosov Equations	p. 21
Boundary Conditions	p. 23
Linear Elastic Fracture Mechanics	p. 23
Mode I	p. 25
Mode II	p. 28
Mode III	p. 29
Strip Models of Crack Tip Plasticity	p. 34
Mode I Small-Scale Yielding Strip Model	p. 39
Mode III Small-Scale Yielding Strip Model	p. 41
Exact Elastoplastic Solutions for Mode III	p. 45
Isotropic Hardening	p. 52
Plane Strain Problems Involving Plastic Theory	p. 63
Plane Strain	p. 63
Prandtl-Hill Solution	p. 75
Failure Criteria	p. 82
Power Law Hardening Materials under Plane Strain	p. 90
Plane Stress Problems Involving Plastic Material	p. 94
Tresca Yield Condition	p. 95
Mises Yield Condition	p. 99
Power Law Hardening Materials under Plane Stress	p. 105
Numerical Solutions of the Mode I Elastoplastic Problem	p. 105
Numerical Solutions	p. 108
Miscellaneous Mathematical Topics	p. 114
Complete Solutions	p. 114
Monge-Ampere Family of Partial Differential Equations	p. 118
Order Symbols	p. 120
On the Continuance of an Analytical Solution across the Elastic-Plastic Boundary of a Mode I Fracture Mechanics Problem
Elastoplastic Stress Analyses for Modes I and III	p. 122
Mode III	p. 122
Mode I	p. 127
Parabolic-Hyperbolic Plastic Boundary	p. 136
Uniqueness and Continuity of Stress	p. 137
Stress Discontinuities	p. 142
Developable Surfaces	p. 143
Strain Rates for Plane Stress under the Tresca Yield Condition	p. 147
Mode I Displacements	p. 150
Speculations Concerning an Analytical Mode I Elastoplastic Solution	p. 163
Plastic Zone Transitions
A Finite-Width Dugdale Zone Model for Mode III	p. 172
Elastic Solution	p. 172
Plastic Solution	p. 178
Recovery of Previous Solutions	p. 183
Crack Tip Opening Displacement	p. 185
Comments	p. 186
An Energy-Dissipation Analysis for the Transition Model	p. 186
Effective Crack Length for the Transition Model	p. 193
Fracture Assessment Diagrams	p. 197
Environmental Cracking
Hydrogen-Assisted Cracking	p. 208
Kinetic Processes	p. 210
Models	p. 215
Growth of the Cohesive Zone	p. 216
Crack Propagation	p. 220
Overview of Some Previous Models of Environmental Cracking	p. 231
Analysis for Impending Hydrogen-Assisted Crack Propagation	p. 233
Crack Tip Opening Displacement	p. 237
Function [psi](c, a, [alpha])	p. 240
Asymptotic Expansion	p. 242
Discussion	p. 245
A Modified Stefan Problem Related to Stress Corrosion Cracking	p. 246
Analysis	p. 250
Small and Large Values of [upsilon]/V[superscript 0]	p. 256
Discussion	p. 258
Small-Scale Yielding versus Exact Linear Elastic Solutions
The Fundamental Modes of Fracture	p. 261
Elastic-Plastic Loci as Predicted by Linear Elastic Fracture Mechanics	p. 274
Inverse Cassinian Oval Coordinates for Mode III	p. 280
Appendix	p. 285
References	p. 299
Index	p. 307
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Analytical Fracture Mechanics

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