Analysis of a Screw Dislocation Inside a Circular Inclusion With Interfacial Cracks in Piezoelectric Composites

The electroelastic interaction of a screw dislocation inside a circular inclusion with interfacial cracks in piezoelectric composite materials under anti-plane shear and in-plane electric loads at infinity is investigated. The general solution to this problem was obtained by means of Riemann- Schwarz's symmetry principle integrated with analysis of singularities of corresponding complex potentials. As a typical example, closed form expressions of the complex potentials and electroelastic field components in the matrix and inhomogeneity regions were derived explicitly when the interface contains a single crack. The image force acting on the screw dislocation was calculated by using the generalized Peach-Koehler formula. The influence of interfacial crack geometry and piezoelectric material property combinations upon the image force was discussed in detail. The results show that interfacial crack has significant perturbation effect on the image force and the equilibrium position of the screw dislocation. The presence of the interfacial crack can change the direction of the image force when the length of the crack goes up to a critical value. The obtained explicit solutions can be used as Green's functions to study the problem on the interaction between interfacial cracks and arbitrary shape crack inside the inclusion. The present solutions can lead to previously known results as the special case.