Opening and contact zones of an interface crack in a piezoelectric bimaterial under combined compressive-shear loading

Abstract

A plane problem for a tunnel electrically permeable interface crack between two semi-infinite piezoelectric spaces is studied. A remote mechanical and electrical loading is applied. Elastic displacements and potential jumps as well as stresses and electrical displacement along the interface are presented using a sectionally holomorphic vector function. It is assumed that the interface crack includes zones of crack opening and frictionless contact. The problem is reduced to a combined Dirichlet–Riemann boundary value problem which is solved analytically. From the obtained solution, simple analytical expressions are derived for all mechanical and electrical characteristics at the interface. A quite simple transcendental equation, which determines the point of separation of open and close sections of the crack, is found. For the analysis of the obtained results, the main attention is devoted to the case of compressive-shear loading. The analytical analysis and numerical results show that, even if the applied normal stress is compressive, a certain crack opening zone exists for all considered loading values provided the shear field is present. It is found that the shear stress intensity factor at the closed crack tip and the energy release rates at the both crack tips depend very slightly on the magnitude of compressive loading.