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Analytical Fracture Mechanics

Dover Civil and Mechanical Engineering

By: UNGER

Paperback

Published: 10th November 2011
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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 solution technique for second-order nonlinear partial differential equation governing a mode I elastoplastic crack problem, plastic zone transitions, environmental cracking, and small-scale yielding versus exact linear elastic solutions. "Recommended." — Applied Mechanics Review.

Color Plates
Prefacep. xi
Acknowledgmentsp. xiii
Introduction
Equations of Continuum Mechanicsp. 1
Equilibriump. 1
Strain-Displacementp. 4
Change of Volumep. 4
Compatibility of Strainsp. 4
Equations of Elasticityp. 5
Equations of Plasticityp. 6
Strain Hardeningp. 9
Material Stabilityp. 11
Incremental Strain-Stress Relationshipsp. 12
Flow Theory versus Deformation Theoryp. 16
Plane Problems of Elasticity Theoryp. 16
Cartesian Coordinatesp. 17
Polar Coordinatesp. 19
Kolosov Equationsp. 21
Boundary Conditionsp. 23
Linear Elastic Fracture Mechanicsp. 23
Mode Ip. 25
Mode IIp. 28
Mode IIIp. 29
Strip Models of Crack Tip Plasticityp. 34
Mode I Small-Scale Yielding Strip Modelp. 39
Mode III Small-Scale Yielding Strip Modelp. 41
Exact Elastoplastic Solutions for Mode IIIp. 45
Isotropic Hardeningp. 52
Plane Strain Problems Involving Plastic Theoryp. 63
Plane Strainp. 63
Prandtl-Hill Solutionp. 75
Failure Criteriap. 82
Power Law Hardening Materials under Plane Strainp. 90
Plane Stress Problems Involving Plastic Materialp. 94
Tresca Yield Conditionp. 95
Mises Yield Conditionp. 99
Power Law Hardening Materials under Plane Stressp. 105
Numerical Solutions of the Mode I Elastoplastic Problemp. 105
Numerical Solutionsp. 108
Miscellaneous Mathematical Topicsp. 114
Complete Solutionsp. 114
Monge-Ampere Family of Partial Differential Equationsp. 118
Order Symbolsp. 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 IIIp. 122
Mode IIIp. 122
Mode Ip. 127
Parabolic-Hyperbolic Plastic Boundaryp. 136
Uniqueness and Continuity of Stressp. 137
Stress Discontinuitiesp. 142
Developable Surfacesp. 143
Strain Rates for Plane Stress under the Tresca Yield Conditionp. 147
Mode I Displacementsp. 150
Speculations Concerning an Analytical Mode I Elastoplastic Solutionp. 163
Plastic Zone Transitions
A Finite-Width Dugdale Zone Model for Mode IIIp. 172
Elastic Solutionp. 172
Plastic Solutionp. 178
Recovery of Previous Solutionsp. 183
Crack Tip Opening Displacementp. 185
Commentsp. 186
An Energy-Dissipation Analysis for the Transition Modelp. 186
Effective Crack Length for the Transition Modelp. 193
Fracture Assessment Diagramsp. 197
Environmental Cracking
Hydrogen-Assisted Crackingp. 208
Kinetic Processesp. 210
Modelsp. 215
Growth of the Cohesive Zonep. 216
Crack Propagationp. 220
Overview of Some Previous Models of Environmental Crackingp. 231
Analysis for Impending Hydrogen-Assisted Crack Propagationp. 233
Crack Tip Opening Displacementp. 237
Function [psi](c, a, [alpha])p. 240
Asymptotic Expansionp. 242
Discussionp. 245
A Modified Stefan Problem Related to Stress Corrosion Crackingp. 246
Analysisp. 250
Small and Large Values of [upsilon]/V[superscript 0]p. 256
Discussionp. 258
Small-Scale Yielding versus Exact Linear Elastic Solutions
The Fundamental Modes of Fracturep. 261
Elastic-Plastic Loci as Predicted by Linear Elastic Fracture Mechanicsp. 274
Inverse Cassinian Oval Coordinates for Mode IIIp. 280
Appendixp. 285
Referencesp. 299
Indexp. 307
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780486417370
ISBN-10: 0486417379
Series: Dover Civil and Mechanical Engineering
Audience: General
Format: Paperback
Language: English
Number Of Pages: 314
Published: 10th November 2011
Dimensions (cm): 22.9 x 15.2  x 1.9
Weight (kg): 0.417