Exact solution for finite electrode layers embedded at the interface of two piezoelectric half-planes

Abstract

The exact solution is obtained for two bonded dissimilar piezoelectric half-planes with discontinuous thin electrode layers embedded at the interface. In contrast with existing models on interfacial insulating cracks or rigid electrode layers, the present model is based on the assumption that tractions and displacements are continuous across the thin electrode layers. As a result, the present model leads to a mixed boundary value problem, rather than a conventional generalized traction or displacement boundary value problem to which the existing models have led. Detailed discussion is given for the case of practical significance in which two piezoelectric half-planes are poled in opposite directions perpendicular to the interface. In this case, the electroelastic field exhibits the inverse square-root singularity and an oscillatory singularity does not appear. It is found that the interfacial tractions and the normal electrical displacement vanish along all electrode-free parts of the interface. On the other hand, along the interfaces between piezoelectric half-planes and the embedded electrode layer, the normal traction and the normal electrical displacement exhibit electrode-tip singularity and the sign of the normal traction is determined by the sign of the electric charge of the electrode layer. The implications of these results to reliability of layered piezoelectric devices are discussed.