Behavior of Simple Screw Dislocation Arrays under an Applied Stress

Abstract

A detailed numerical analysis has been made of the behavior of passing screw dislocation arrays on parallel slip planes as a first step in the development of a computer model of workhardening. It is found that in the absence of frictional forces, dislocations cannot pass one another since they form dipoles and become unstable. The introduction of frictional forces shows that for each dislocation there is a range of positions within which it is stable, and the actual position of the dislocation depends on its initial position as well as its direction of motion. The frictional‐force concept is extended to determine the equilibrium separation of superlattice dislocations and to determine the relaxation of a pile‐up in the absence of an applied stress. In order to determine unique positions for passing dislocations under an applied stress and a frictional stress, a model has been postulated in which the dislocations are generated from distant sources. Equilibrium configurations are determined as a function of the applied stress for a single source, as well as for two opposite sources on parallel slip planes. The stress‐strain curves are developed for both cases, and the results are discussed in detail.