Two collinear unequal cracks in a poled piezoelectric plane: Mode I case solved by a new approach of real fundamental solutions

Abstract

The purpose of the present work is to study the problem of two collinear unequal cracks in a piezoelectric plane under mode I electromechanical loadings via a new approach. For the first time, real fundamental solutions are derived for in-plane piezoelectric governing equations. The cracks are simulated by continuously distributed generalized dislocations and Cauchy singular integral equations are established from the solution of a generalized point dislocation. Both the theorectical derivation and numerical computations are validated by the exact solution in a special case. Parametric studies are conducted to reveal the effects of crack space, crack length, electric loading and remanent electric displacement on energy release rate. It is found that negative electric displacement loading can decrease both the total energy release rate (TERR) and the mechanical strain energy release rate (MSERR), implying that it has a shielding effect on cracks definitely. Positive electric displacement loading can enhance MSERR, but meanwhile it can enhance or reduce TERR depending on the magnitude of the electric loading factor. The effect of a remanent electric displacement along the poling direction is equivalent to that of a positive electric field loading and should be considered in engineering design.