A screw dislocation interacting with a semi-infinite crack partially penetrating a parabolic elastic inhomogeneity

We consider the interaction of a screw dislocation with a semi-infinite crack partially penetrating a parabolic elastic inhomogeneity embedded in an infinite elastic matrix subjected to anti-plane mechanical loading. Analytical solutions are derived in the case when the screw dislocation is located either in the matrix or inside the parabolic inhomogeneity. In addition, the local mode III stress intensity factor at the crack tip and the image force acting on the screw dislocation are obtained and illustrated accordingly. Moreover, we establish a dislocation emission criterion from the crack.