Exact solution for mixed boundary value problems at anisotropic piezoelectric bimaterial interface and unification of various interface defects

Abstract

The special mixed boundary value problem in which a debonded conducting rigid line inclusion is embedded at the interface of two piezoelectric half planes is solved analytically by employing the 8-D Stroh formalism. Different from existing interface insulating crack model and interface conducting rigid line inclusion model, the presently analyzed model is based on the assumption that all of the physical quantities, i.e., tractions, displacements, normal component of electric displacements and electric potential, are discontinuous across the interface defect. Explicit solutions for stress singularities at the tips of debonded conducting rigid line inclusion are obtained. Closed form solutions for the distribution of tractions on the interface, surface opening displacements and jump in electric potential on the debonded inclusion are also obtained, in addition real form solutions for these physical quantities are derived. Various forms of interface defect problems encountered in practice are solved within a unified framework and the stress singularities induced by those interface defects are discussed in detail. Particularly, we find that the analysis of interface cracks between the embedded electrode layer and piezoelectric ceramics can also be carried out within the unified framework.