A generalized antiplane singularity within a semi-infinite wedgeof arbitrary angle

Abstract

The state of stress arising within an elastic wedge generated by an antiplane singularity present within it is studied. An analytical solution is derived with a unified generic approach. The singularity may represent either an anti-plane concentrated force or a screw dislocation. To validate the general solution, two degenerate cases are presented. Further, the image force present on the screw dislocation due to the wedge free boundary is obtained. It is found that when the screw dislocations are placed in the vicinity of the wedge surface, the image force will drive dislocations to the free boundary where they will be annihilated. This implies that a dislocation-free zone may exist along the free surface of the wedge. To demonstrate the application of the fundamental solutions, a formulation for a slip band under anti-plane loading with Green’s function method is provided. The solutions developed in this study may be used as building blocks to model the damage of material near a V-notch under versatile anti-plane load conditions or torsional loading.