A set of electrically conducting collinear cracks between two dissimilar piezoelectric materials

Abstract

The plane problem of multiple collinear cracks between two piezoelectric semi-infinite spaces is considered. The cracks can have arbitrary lengths and distances between each other and they are assumed to be electrically conductive. The materials are polarized in the orthogonal to the interface direction. In-plane combined tension-shear loading and the electric field parallel to the crack faces are prescribed at infinity. The Riemann-Hilbert problems of linear relationship are formulated and solved analytically by using the presentations of electro-mechanical quantities via sectionally-analytic functions. The arbitrary constants are found from the conditions at infinity and the system of linear algebraic equations which dimension is equal to the number of cracks. Stresses, electric field outside cracks as well as mechanical and electrical displacement jumps along the crack regions are found in the relatively simple analytical forms. Special attention was devoted to the energy release rate (ERR) determination. Due to analysis of asymptotic fields at the tips of single and multipleinterface cracks, the analytical presentations of the ERR for any crack tips are obtained. Numerical illustrations for several interface cracks are presented. The variations of stresses, electric field and the crack opening along the interface are demonstrated. The ERR are given for different crack tips, loading, crack locations and different physical aspects of the interaction effect are discussed. The particular cases of purely elastic and purely electrically conductive states are considered and good agreement with known results is demonstrated.