The use of only discrete edge image dislocations to solve the problem of an edge dislocation, moving or stationary, near a welded interface separating material of different elastic constants (or a free surface) was thwarted, as was well known, because an image edge dislocation could not deal simultaneously with the continuity at the interface of both the shear traction stress and the normal traction stress. In this paper, it was shown that the problem could be solved with only discrete edge image dislocation components if an edge dislocation was first separated into an edge dislocation component whose stress–displacement fields depended only on the shear wave velocity and an edge dislocation component whose stress–displacement fields depended only on the longitudinal wave velocity.

The Problem of a Moving Subsonic Edge Dislocation Near an Interface Solved with Only Discrete Image Dislocations. J.Weertman: Philosophical Magazine, 2011, 91[3], 373-88