ANALYSIS OF AN ISOTROPIC HOMOGENEOUS ELASTIC MATERIAL CONTAINING A FINITE INHOMOGENEITY AT THE END OF A CRACK UNDER ANTIPLANE SHEAR.

Abstract

In this paper, we consider the determination of the mode III stress intensity factor (SIF) at the tips of a finite line inhomogeneity (anti-crack) of length  units lying on the right-hand side of the -axis in an infinite elastic material with loads  and applied on the surface of the crack at lengths  and  respectively from the origin. The inhomogeneity is rigidly bonded and so is displacement free. The loading gives rise to two-dimensional boundary value problem for a Laplace equation that models the antiplane strain displacement . The problem is solved by Mellin integral transform and Wiener-Hopf technique. The displacement and stress fields were obtained leading to the stress intensity factors  and  for the deformation at the outer inhomogeneity tip and at its inner tip respectively. The existence of the stress intensity factors implies that crack initiation can start either at the outer or inner tip depending on the loading. A linear relationship is found between  and  where  is the normal stress intensity factor formed by the ratio of  to the known mode III stress intensity factor  at the tip of a crack in a material of the same geometry as the one being investigated. A similar relationship is found also for  as shown in the graph.