Analytical Fracture MechanicsFracture 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.
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Contents
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Chapter 1 On the Continuance of an Analytical Solution across the ElasticPlastic Boundary of a Mode I Fracture Mechanics Problem | 121 |
Chapter 2 Plastic Zone Transitions | 171 |
Chapter 3 Environmental Cracking | 207 |
Chapter 4 SmallScale Yielding versus Exact Linear Elastic Solutions | 261 |
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293 | |
Color Plate Section | 301 |
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Common terms and phrases
analytical Approximate boundary condition Cartesian coordinates Cherepanov cohesive force constant coordinate system crack growth crack length crack problem crack propagation crack tip opening crack velocity curve deformation theory Dugdale model elastic stress elastic-plastic boundary elastoplastic elastoplastic problem elastoplastic solution elliptic equilibrium FIGURE Fract fracture mechanics hardening Headington Hill Hall Hult-McClintock hydrogen increment infinite plate integral J. W. Hutchinson linear elastic linear elastic solution Mech Mises yield condition mode III problem modes of fracture Monge-Ampere equation obtain Oxford OX3 OBW parameter partial derivatives partial differential equation perfectly plastic material Pergamon Press Ltd permission from Pergamon plane strain plane stress plastic region plastic strip model plastic zone polar coordinates Prandtl principal stresses relationship satisfied shear stress shown in Fig slip line small-scale yielding solution stress field stress intensity factor substituting tensile tip opening displacement traction Tresca yield condition yield stress yield surface