Three Dimensional Crack Problems

Three-Dimensional Crack Problems

A Special Crack Tip Element for Three-dimensional Crack Problems

This paper develops a finite element method for determining the stress intensity factors along the edge of a crack in an arbitrary three-dimensional body. A special element is placed around the crack front and in each special element the stresses and displacements are derived using the asymptotic nature of the stress and displacement fields near a crack tip. The method is based on the authors' previous technique for evaluating the stress intensity factors in cracked sheets, and coincides with this method in the case of a through crack in a thin sheet. As illustrative examples the problems of a semicircular surface flaw and an internal penny shaped crack are considered. In each case the computed values of the stress intensity factors are in excellent agreement with known analytical results.

Solution of Crack Problems

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.