A mode III crack in a functionally graded piezoelectric strip bonded to two dissimilar piezoelectric half-planes

In the present paper, the anti-plane shear problem for a cracked functionally graded piezoelectric material (FGPM) layer bonded to two piezoelectric half-planes is studied. The properties of the functionally graded piezoelectric strip, such as elastic modulus, piezoelectric constant and dielectric constant, vary continuously as an exponential function. The crack surface condition is assumed to be electrically impermeable or permeable. Integral transforms are employed to reduce the problem to Cauchy singular equations that can be solved numerically. 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. It is found that for the permeable case, the electric displacement loadings has no contribution to the stress intensity factor and electric displacement intensity factor.