The spread of plasticity from stress concentrations

Abstract

In a recent paper dealing with a model of a relaxed crack, the plastic relaxation round an isolated crack is represented by an array of dislocations coplanar with the crack itself. Similar models are used here to discuss the behaviour of an infinite sequence of relaxed cracks with a constant distance of vertical separation. When the body deforms in an anti-plane strain mode, exact solutions are obtained for the extent of spread of plasticity from each crack and the associated dislocation distribution function. For deformation under plane strain shear conditions the form of the governing singular integral equation does not allow exact solutions to be obtained; instead iterative solutions have been found for the case of widely spaced cracks. A comparison of the results for anti-plane strain and plane strain conditions reveals wide differences; the paper thus emphasizes the need for exercising caution in using anti-plane strain models, whose behaviour it is relatively simple to analyze, as a substitute for the more frequent plane strain conditions which are met with in practice. Finally some applications of the plane strain results to fracture at stress concentrations are briefly discussed.