Interfacial cracks between piezoelectric and elastic materials under in-plane electric loading

Abstract

A new experimental technique for accelerated fatigue crack growth tests was recently developed (Du et al., 2001). The technique, which uses piezoelectric actuators, enables application of cyclic loading at frequencies several orders higher than that by mechanical loading. However, the validity of this technique relies on the equivalence between piezoelectric and mechanical loading. In this paper, the behavior of an interfacial crack between a piezoelectric material and an elastic material under in-plane electric loading is studied. The displacement mismatch along a bonded interface due to electric potential loading on the piezoelectric material is modeled by inserting an array of uniformly distributed dislocations along the interface. By means of Fourier transformation methods, the governing equations are converted to an integral equation, which is then converted to a standard Hilbert problem. A closed form solution for stresses, electric field, and electric displacements along the bonded interface is obtained. The results agree very well with those obtained from numerical simulations. The results show that the closed form solution is accurate not only for far field distributions of stresses and electric variables, but also for the asymptotic distributions near the crack tip. The solution also suggests the likelihood of domain switching in the piezoelectric material near the crack tip, a process that may influence the interfacial fracture resistance.