Dynamic analysis of interfacial multiple cracks in piezoelectric thin film/substrate

The dynamic fracture characteristics of mode-III cracks are investigated. This is a crucial problem in piezoelectric devices. The theoretical solution to this problem is described using the integral-transform method (Laplace and Fourier transforms) and the Chebyshev point method. A crack-propagation model is provided to obtain the stress and electrical-displacement fields near the crack tips. The results show that crack propagation is related to the electromechanical coupling coefficient and film thickness. The effect of film thickness has not been considered in previous literature. In the case of multiple cracks, according to their mutual effects, the nondimensional DSIF inside the crack tip is more significant than that outside the crack tip, regardless of the number of cracks. When the film thickness is small, the change in the DSIF is significant, indicating appropriate circumstances, and a thinner film thickness is more conducive to safe design. Negative electrical-displacement loads always prevent crack propagation, whereas positive electric-displacement loads can promote or prevent crack propagation. Numerical examples are provided to highlight the result.