Periodic cracks in a functionally graded piezoelectric layer bonded to a piezoelectric half-plane

Studied is the problem of a periodic array of cracks in a functionally graded piezoelectric strip bonded to a homogeneous piezoelectric material. The properties of the functionally graded piezoelectric strip, such as elastic modulus, piezoelectric constant and dielectric constant, are assumed in exponential forms and vary along the crack direction. The crack surface condition is assumed to be electrically impermeable or permeable. Integral transform and dislocation density functions are employed to reduce the problem to the solution of a system of singular integral equations. The effects of the periodic crack spacing, material constants and the geometry parameters on the stress intensity factor, the energy release ratio and the energy density factor are studied.