Analytical Fracture Mechanics
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Table of contents
- Cover
- Contentsvii
- Prefacexi
- Acknowledgmentsxiii
- Introduction1
- I.1 Equations of Continuum Mechanics1
- I.2 Equations of Elasticity5
- I.3 Equations of Plasticity6
- I.4 Plane Problems of Elasticity Theory16
- I.5 Linear Elastic Fracture Mechanics23
- I.6 Strip Models of Crack Tip Plasticity34
- I.7 Exact Elastoplastic Solutions for Mode III45
- I.8 Plane Strain Problems Involving Plastic Theory63
- I.9 Plane Stress Problems Involving Plastic Material94
- I.10 Numerical Solutions of the Mode I Elastoplastic Problem105
- I.11 Miscellaneous Mathematical Topics114
- Chapter 1. On the Continuance of an Analytical Solution across the Elastic–Plastic Boundary of a M121
- 1.1 Elastoplastic Stress Analyses for Modes I and III122
- 1.2 Developable Surfaces143
- 1.3 Strain Rates for Plane Stress under the Tresca Yield Condition147
- 1.4 Mode I Displacements150
- 1.5 Speculations Concerning an Analytical Mode I Elastoplastic Solution163
- Color Plates168
- Chapter 2. Plastic Zone Transitions171
- 2.1 A Finite-Width Dugdale Zone Model for Mode III172
- 2.2 An Energy-Dissipation Analysis for the Transition Model186
- 2.3 Effective Crack Length for the Transition Model193
- 2.4 Fracture Assessment Diagrams197
- Chapter 3. Environmental Cracking207
- 3.1 Hydrogen-Assisted Cracking208
- 3.2 Analysis for Impending Hydrogen-Assisted Crack Propagation233
- 3.3 A Modified Stefan Problem Related to Stress Corrosion Cracking246
- Chapter 4. Small-Scale Yielding versus Exact Linear Elastic Solutions261
- 4.1 The Fundamental Modes of Fracture261
- 4.2 Elastic–Plastic Loci as Predicted by Linear Elastic Fracture Mechanics274
- 4.3 Inverse Cassinian Oval Coordinates for Mode III280
- References285
- Index293
- Color Plate Section301
Fracture mechanics is an interdisciplinary subject that predicts the conditions under which materials fail due to crack growth. It spans several fields of interest including: mechanical, civil, and materials engineering, applied mathematics and physics. This book provides detailed coverage of the subject not commonly found in other texts.
Analytical Fracture Mechanics contains the first analytical continuation of both stress and displacement across a finite-dimensional, elastic-plastic boundary of a mode I crack problem. The book provides a transition model of crack tip plasticitythat has important implications regarding failure bounds for the mode III fracture assessment diagram. It also presents an analytical solution to a true moving boundary value problem for environmentally assisted crack growth and a decohesion model of hydrogen embrittlement that exhibits all three stages of steady-state crack propagation.
The text will be of great interest to professors, graduate students, and other researchers of theoretical and applied mechanics, and engineering mechanics and science.
Key Features
* Presents the only analytical proven solution technique amenable to the second-order nonlinear partial differential equation governing a mode I elastoplastic crack problem
* Places emphasis on the near crack tip partial differential equations governing plasticity and process zone theory in environmental cracking phenomena
* Provides fundamental solutions of linear elastic fracture mechanics
* Explains how transport-controlled stage II environmental crack growth can be mapped onto the classic Stefan problem
* Predicts failure curves on fracture assessment diagram for mode III crack problem as transition occurs from plastic strip to finite-dimensional plastic zone
* Gives a summary of pertinent equations of linear elasticity and plasticity
Analytical Fracture Mechanics contains the first analytical continuation of both stress and displacement across a finite-dimensional, elastic-plastic boundary of a mode I crack problem. The book provides a transition model of crack tip plasticitythat has important implications regarding failure bounds for the mode III fracture assessment diagram. It also presents an analytical solution to a true moving boundary value problem for environmentally assisted crack growth and a decohesion model of hydrogen embrittlement that exhibits all three stages of steady-state crack propagation.
The text will be of great interest to professors, graduate students, and other researchers of theoretical and applied mechanics, and engineering mechanics and science.
Key Features
* Presents the only analytical proven solution technique amenable to the second-order nonlinear partial differential equation governing a mode I elastoplastic crack problem
* Places emphasis on the near crack tip partial differential equations governing plasticity and process zone theory in environmental cracking phenomena
* Provides fundamental solutions of linear elastic fracture mechanics
* Explains how transport-controlled stage II environmental crack growth can be mapped onto the classic Stefan problem
* Predicts failure curves on fracture assessment diagram for mode III crack problem as transition occurs from plastic strip to finite-dimensional plastic zone
* Gives a summary of pertinent equations of linear elasticity and plasticity