Critical Conditions for Dislocation Nucleation from Surface Steps

Abstract

AbstractThe critical conditions for dislocation nucleation from the surface steps of various geometries are analyzed based on the Peierls-Nabarro dislocation model. By modeling a surface step as part of a three- dimensional crack surface, the half space problem is transferred into an equivalent three dimensional crack problem in an infinite medium. The profiles of embryonic dislocations, corresponding to the relative displacements between the two adjacent atomic layers along slip planes, are then rigorously solved through the variational boundary integral method. The critical conditions for dislocation nucleation are determined by solving the stress dependent activation energies required to activate embryonic dislocations from their stable to unstable saddle point configurations. For a given slip plane, the effects of step geometry such as the step height and inclined angle on dislocation nucleation are analyzed in detail. The results show that the atomic scale steps may reduce the critical stress required for dislocation nucleation from the surface by several factors. Compared to previous analyses of this type of problem based on continuum elastic dislocation theory, the presented analysis eliminates the uncertain core cutoff parameter by allowing for the existence of an extended dislocation core as the embryonic dislocation evolves. Because of the serious limitation of direct atomic simulation for this type of problem, the presented methodology of incorporating atomic information into continuum approach appears to be particularly noteworthy for providing insights of energetics of the atomic processes involved in dislocation nucleation.