Interaction between a cycloid wavy surface and a screw dislocation in a piezoelectric material

We consider two important problems concerning the interaction between a cycloid surface and a screw dislocation. First, we examine the interaction between a traction-free and charge-free periodic cycloid wavy surface and a screw dislocation under anti-plane mechanical and in-plane electrical loading in a hexagonal piezoelectric solid. With the aid of conformal mapping and analytic continuation, we derive an elementary closed-form solution of the two-dimensional analytic vector function in the image plane characterizing the electroelastic field in the piezoelectric solid. The stresses, electric displacements, strains and electric fields in both the corresponding Cartesian and the curvilinear coordinate systems are determined. The image force acting on the piezoelectric screw dislocation is then obtained using the generalized Peach–Koehler formula. For a cusped cycloid surface, the resultant stress and electric displacement intensity factors at the cusp tips and crack extension force on the cusp tips are presented. Secondly, we use essentially the same approach to investigate the problem of the interaction of a screw dislocation with a traction-free and conducting cycloid surface in a hexagonal piezoelectric half-plane. A simple dislocation emission criterion is proposed.