Solution of Crack Problems

The Distributed Dislocation Technique

verfasst von: D. A. Hills, P. A. Kelly, D. N. Dai, A. M. Korsunsky

Verlag: Springer Netherlands

Buchreihe : Solid Mechanics and Its Applications

Enthalten in: Professional Book Archive

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Über dieses Buch

This book is concerned with the numerical solution of crack problems. The techniques to be developed are particularly appropriate when cracks are relatively short, and are growing in the neighbourhood of some stress raising feature, causing a relatively steep stress gradient. It is therefore practicable to represent the geometry in an idealised way, so that a precise solution may be obtained. This contrasts with, say, the finite element method in which the geometry is modelled exactly, but the subsequent solution is approximate, and computationally more taxing. The family of techniques presented in this book, based loosely on the pioneering work of Eshelby in the late 1950's, and developed by Erdogan, Keer, Mura and many others cited in the text, present an attractive alternative. The basic idea is to use the superposition of the stress field present in the unfiawed body, together with an unknown distribution of 'strain nuclei' (in this book, the strain nucleus employed is the dislocation), chosen so that the crack faces become traction-free. The solution used for the stress field for the nucleus is chosen so that other boundary conditions are satisfied. The technique is therefore efficient, and may be used to model the evolution of a developing crack in two or three dimensions. Solution techniques are described in some detail, and the book should be readily accessible to most engineers, whilst preserving the rigour demanded by the researcher who wishes to develop the method itself.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction to Fracture Mechanics

Abstract

When an engineer designs a structure or piece of equipment, there are two basic forms of mechanical failure which must be considered. These are brittle fracture and, if the material employed is metallic, yielding. The second is by far the easier to take into account: it is necessary to know only the state of stress at every point in order to assemble the appropriate yield parameter. The maximum value of this quantity is found within the structure and set equal to the yield stress, which is taken as a true material property, i.e. it is independent of geometry. Usually the loading or stresses are reduced by a so-called factor of safety, which allows for unexpected overloads during the life of the structure. The load level corresponding to the onset of first yield is known as the elastic limit. There are considerable reserves of strength in any real structure if the elastic limit is moderately exceeded, partly because most real structures exhibit a high degree of redundancy, partly because cyclic loading will induce beneficial residual stresses, promoting shakedown, and partly because most common metals and alloys exhibit work hardening to a greater or lesser degree. By far the most important characteristics of yield from the point of view of design are:

(a) that the yield stress is a highly repeatable true material property, being very insensitive to the geometry of the component under consideration.
(b) that given the yield stress under uniaxial loading, the combination of stresses which will cause local failure under multiaxial conditions is well defined — assumptions of isotropy, independence of yield from hydrostatic stress and convexity of the yield surface (Paul, 1968) being necessary to obtain excellent bounding values for physically acceptable yield criteria.