Interaction of a screw dislocation with a parabolic cavity and a semi-infinite crack

We derive an analytic solution to the problem of a screw dislocation interacting with a parabolic cavity and a semi-infinite sharp crack using conformal mapping techniques and the method of images. Closed-form expressions for the image force acting on the screw dislocation, the mode III stress intensity factor at the crack tip and the generalized mode III stress intensity factor for the parabolic cavity are obtained. The correctness of the solution is validated by comparison with existing solutions in the literature.