Periodic Dislocation Distributions in a Half-Space

Abstract

A solution is given to the stress field produced by an arbitrary periodic distribution of dislocations (or plastic distortion) in a half‐space. It is shown how the known results for discrete dislocations are obtained quite simply from this. The solution to the problem of a Frank dislocation network near a free surface is given and its stability examined. The whole‐space stress field decreases exponentially with the distance from the plane of the network, as do the stress terms due to the free surface which decrease exponentially with the distance from this surface. It is shown that the network always experiences a force attracting it to the free surface.