The Stress Fields Around Some Dislocation Arrays

Abstract

The stress fields around some edge dislocation arrays have been calculated using the approximation of Leibfried (1951) that the discrete dislocations are replaced by a continuous dislocation density. Haasen and Leibfried (1954) have calculated one such stress distribution (corresponding to (ti) below) via the stress function which they evaluated as a superposition integral over the dislocation distribution of the stress function of an infinitesimal dislocation. The results given here were evaluated directly as the superposition of the stress fields of the infinitesimal dislocations making up the distribution. Like most of the integrals which occur in this approximation, they can be evaluated most readily by contour integration (Haasen and Leibfried 1954). A multiple coordinate system is used and is such that the results can be written compactly and approximations and limiting cases can be easily obtained.