Calculating Dislocation Spacings in Pile-Ups at Grain Boundaries

Dislocation pile-ups near planar grain boundaries have been analyzed employing full anisotropic elastic solutions, single-crystal anisotropic approximations, and isotropic approximations. The calculations were performed for a series of iron-silicon bicrystal configurations and results from the various methods compared. Three of the bicrystal/slip system combinations exhibited repulsive image forces, allowing elastically self-consistent position calculations. Based on these results, either linear elastic or nonlinear effects can dominate the behavior of these pile-ups, depending on specific boundary conditions.