A transient three-dimensional analysis of non-uniform dislocation distribution growth by climb and glide over non-planar surfaces
As a basis for obtaining insight into both plastic flow described in terms of dislocation motion and dynamic crack extension, a transient 3D analysis of the non-uniform growth of dislocation distributions by climb and glide over largely arbitrary non-planar surfaces is considered. An exact solution for the case of an unbounded, isotropic, homogeneous, linearly elastic solid is obtained in vector form. It is found that information about essential distribution and surface properties are contained in the solution in a symmetric tensor. This tensor arises as a generalized consequence of the body-force equivalent representation of dislocations in elastic continua. The solution is also found to have two components: one component depends on the velocity discontinuity induced across the surface, the other depends on the displacement discontinuity at the moving boundary of the distribution and the speed of the boundary. Two examples are then considered to illustrate the utility of the solution.