Elastic interaction between a screw dislocation and surface crack

Abstract

An analytical solution for the two-dimensional elastic problem of a screw dislocation near a mode III surface crack, a shear crack subject to antiplane stress, has been derived. The dislocation-crack interaction has a negative singularity at the tip of the crack irrespective to the applied stresses. In the case that the applied stress is in the direction of driving a dislocation into the medium, a metastable position exists beyond which the dislocation will be repelled by the crack. Thus a dislocation free zone is expected in the immediate vicinity of the tip of the crack. The size of the dislocation free zone decreases with increasing applied stresses. Provided that the metastable position is larger than a Burgers vector away from the crack tip, dislocations cannot be generated at the tip of the crack; instead, they have to be nucleated or generated from pre-existing sources at some distance from the tip of the crack, a conclusion in agreement with Li’s result using dislocation modelling of the crack tip stress field. The critical applied stress for the direct generation of dislocation from the crack tip is calculated. The conditions for the generation of a single or two dislocations and dislocation dipole in front of the surface crack are examined. The effect of the dislocations on the stress intensity factor and the crack driving force is presented. The study is further generalized to the consideration of a two-screw dislocation system.