A screw dislocation near a damaged arbitrary inhomogeneity-matrix interface

In the literature, the analytical solutions concerned with the interaction between screw dislocation and surfaces/interfaces have been mainly limited to simple geometries and perfect interfaces. The focus of the current work is to provide an approach based on a rigorous semi-analytical theory suitable for treatment of such surfaces/interfaces that concurrently have complex geometry and imperfect bonding. The proposed approach captures the singularity of the elastic fields exactly. A vast variety of the pertinent interaction problems such as dislocation near a multi-inhomogeneity with arbitrary geometry bonded imperfectly to a matrix, dislocation near the free boundaries of a finite elastic medium of arbitrary geometry, and so on is considered. In the present approach the out-of-plane component of the displacement in each domain is decomposed as the displacement corresponding to a screw dislocation in a homogeneous elastic body of infinite extent and the disturbance displacement due to the interaction. Subsequently, the disturbance displacement in each medium is expressed in terms of eigenfunction expansion. Damaged interfaces are modeled by a spring layer of vanishing thickness, and the amount of damage is controlled via the stiffness of the spring. For the illustration of the robustness of the proposed methodology a variety of examples including the interaction of a screw dislocation with a circular as well as a star-shaped inhomogeneities, two interacting inhomogeneities, imperfectly bonded to an unbounded medium are given. Also, examples for highlighting the effect of free surfaces in the case of finite domains are provided. It is revealed that in the cases where matrix is stiffer than the inhomogeneity and the dislocation is inside the inhomogeneity, or the other way around, then the amount of interface damage can change the sign of the image force.