An anti-plane shear crack in bonded functionally graded piezoelectric materials under electromechanical loading

This paper is concerned with the problem of a Griffith crack in bonded functionally graded piezoelectric materials under the anti-plane shear loading. To make the analysis tractable, the properties of the functionally graded piezoelectric materials, 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 loading parameter λ, material constants and the geometry parameters on the stress intensity factor, the energy release ratio and the energy density factor are studied.