ABSTRACT
Dislocation elastic interactions are affected by the presence of surfaces, cracks, etc., which introduce a variety of image-like effects. In deriving analytic expressions for the forces on dislocations in two dimensions, it is convenient to introduce the Goursat potentials. In terms of these potentials, forces on the dislocations can be expressed relatively simply in terms of the residues of the complex potential functions. The potentials must then be found by any of the standard techniques of analysis. For cracks, the Greens functions for the potential functions for dislocations can be derived in a relatively simple way, giving rise to analytic results for the forces without finding the stress directly. For wedges, it is necessary to use mapping theory to map known solutions for simple boundaries to more complex shapes such as wedges. Some analytic tricks will be explained for carrying out this procedure.
