Analytical Fracture Mechanics

by David J. Unger

Overview

"Analytical Fracture Mechanics should prove to be a valuable resource to both the new student and the experienced researcher in fracture mechanics. It is recommended." — Applied Mechanics Review
One of the central concerns of engineering is the failure of materials. Addressing this concern, fracture mechanics — an interdisciplinary subject spanning mechanical, civil, and materials engineering, applied mathematics, and physics — predicts the conditions under which such failure will occur due to crack growth. This valuable self-contained text by an expert in the field supplements standard fracture mechanics texts by focusing on analytical methods for determining crack-tip stress and strain fields.
Following a comprehensive 120-page introduction — which provides all the background necessary for understanding the remaining chapters — the book is organized around a series of elastoplastic and hydrogen-assisted crack-tip problems and their solutions. The first chapter presents the only proven solution technique for the second order nonlinear partial differential equation governing a mode I elastoplastic crack problem. Other chapters deal with plastic zone transitions, environmental cracking, and small-scale yielding versus exact linear elastic solutions.
One of the excellent features of this book is the clarity with which groups of problems are presented and related to each other. Another is the careful attention it gives to the various modes of fracture (I, II, and III) and to showing the circumstances under which information from a solution for one mode may be used to infer information in another mode. For this edition, the author has added a new appendix, "Stress Across an Elastoplastic Boundary of a Mode I Crack: Parabolic to Hyperbolic Plasticity Transition."

Product Details

ISBN-13:	9780486417370
Publisher:	Dover Publications
Publication date:	11/10/2011
Series:	Dover Civil and Mechanical Engineering Series
Pages:	336
Product dimensions:	6.00(w) x 9.10(h) x 0.70(d)

Table of Contents

Preface
Acknowledgments
Introduction
I.  Equations of Continuum Mechanics
1.2  Equations of Elasticity 
1.3  Equations of Plasticity
1.4  Plane Problems of Elasticity Theory
1.5  Linear Elastic Fracture Mechanics
1.6  Strip Models of Crack Tip Plasticity
1.7 Exact Elastoplastic Solutions for Mode III
1.8  Plane Strain Problems Involving Plastic Theory
1.9  Plane Stress Problems Involving Plastic Material
1.10  Numerical Solutions of the Mode I Elastoplastic Problem
1.11  Miscellaneous Mathematical Topics

2 Plastic Zone Transitions
2.1  A Finite-Width Dugdale Zone Model for Mode III
2.2  An Energy-Dissipation Analysis for the Transition Model 1
2.3  Effective Crack Length for the Transition Model 
2.4  Fracture Assessment Diagrams
 
3 Environmental Cracking
3.1  Hydrogen-Assisted Cracking
3.2  Analysis for Impending Hydrogen-Assisted Crack Propagation
3.3  A Modified Stefan Problem Related to Stress Corrosion Cracking
 
4 Small-Scale Yielding versus Exact Linear Elastic Solutions
4.1  The Fundamental Modes of Fracture
4.2  Elastic-Plastic Loci as Predicted by Linear Elastic Fracture Mechanics 
4.3  Inverse Cassinian Oval Coordinates for Mode III
 Appendix 
 References 
 Index

 

Editorial Reviews

Should prove to be a valuable resource to both the new student and the experienced researcher in fracture mechanics. It is recommended.

Applied Mechanics Review