Electro-elastic stress analysis on piezoelectric inhomogeneity-crack interaction

The current study investigates the interaction problem of a fiber-shaped piezoelectric inhomogeneity embedded in a non-piezoelectric elastic matrix, which contains a crack. The matrix is assumed to be infinite in all directions and the crack is near the piezoelectric fiber. Different geometrical crack-inhomogeneity configurations are considered. The body is subjected to a far-field in-plane tension and a far-field anti-plane electric field. With the solution of stress field for a piezoelectric inhomogeneity embedded in an elastic matrix, the solution of current problem is obtained through a decomposition process. A set of singular integral equations in the crack domain is derived through the dislocation theory. The expressions for the stress intensity factors are then obtained in terms of the asymptotic values of dislocation density functions solved from these integral equations. Numerical examples indicate that interaction between the piezoelectric inhomogeneity and the crack is influenced by many factors, such as the configuration, the material properties of the piezoelectric inhomogeneity and matrix, as well as the far-field electrical and mechanical loadings. The stress intensity factors on crack tips obtained have been checked and confirmed by finite element analysis.