Interaction between multiple piezoelectric inclusions and a crack in a non-piezoelectric elastic matrix

Abstract

In this paper, a general method is presented for evaluating the interaction between multiple piezoelectric inclusions and a nearby crack in a non-piezoelectric elastic matrix. The elastic matrix is subjected to a uniform far field in-plane tension and all inclusions are subjected to an out-of-plane uniform electric field. The crack in the elastic matrix is treated as a continuous distribution of edge dislocations, and then the solution of a unit edge dislocation interacting with multiple piezoelectric inclusions in an elastic medium is derived as the Green function. The problem is formulated into a set of singular integral equations which are solved by a numerical method, and the stress intensity factors (SIFs) at the crack are obtained in terms of the dislocation density functions evaluated from the singular integral equations. Numerical examples are given for a few typical arrays of piezoelectric inclusions with various material properties and geometric parameters. The results indicate that the applied uniform electric-field plays an important role in the interaction between multiple piezoelectric inclusions and the matrix crack., Moreover, it is found that the influences of ‘softer’ piezoelectric inclusions on the SIFs are quite different from that of ‘harder’ piezoelectric inclusions, and the SIFs at the crack tip are greatly affected by the geometry and array of piezoelectric inclusions.