A piezoelectric screw dislocation interacting with an imperfect piezoelectric bimaterial interface

A general method is presented for the analytical solution of a piezoelectric screw dislocation located within one of two joined piezoelectric half-planes. The bonding along the half-plane is considered to be imperfect with the assumption that the imperfect interface is mechanically compliant and dielectrically weakly (or highly) conducting. For a mechanically compliant interface tractions are continuous but displacements are discontinuous across the imperfect interface. In this context, jumps in the displacement components are assumed to be proportional to their respective interface traction components. Similarly, for a dielectrically weakly conducting interface the normal electric displacement is continuous but the electric potential is discontinuous across the interface. The jump in electric potential is proportional to the normal electric displacement. In contrast, for a dielectrically highly conducting interface the electric potential is continuous across the interface whereas the normal electric displacement has a discontinuity across the interface which is proportional to a certain differential expression of the electric potential. Explicit expressions are derived for the complex field potentials. The results show that there are two dimensionless parameters measuring the interface “rigidity” as compared to one for the purely elastic case. When the imperfect interface is compliant and weakly conducting, the two dimensionless parameters can be positive real values or complex conjugates with positive real parts. When the imperfect interface is compliant and highly conducting the two dimensionless parameters can only be positive real values. An expression for the image force acting on the screw dislocation due to its interaction with a compliant and weakly conducting interface is also given. It is found that the image force is only dependent on two dimensionless generalized Dundurs constants as well as two dimensionless parameters measuring the interface “rigidity”.