Electroelastic behavior of a rectangular piezoelectric ceramic with an antiplane shear crack at arbitrary position

Electroelastic analysis of a rectangular piezoelectric ceramic containing an antiplane shear crack at arbitrary position is made in this paper. Results are presented for the cases when two opposite boundaries of the rectangular piezoelectric ceramic parallel to and normal to the crack are exerted by uniform antiplane shear mechanical and inplane electric loadings. The finite Fourier transform method is employed to reduce the mixed boundary-value problem to triple trigonometric series equations, then to a singular integral equations of the first kind. By solving numerically the resulting singular integral equation, field intensity factors and energy release rate are determined numerically for both electrically permeable and impermeable cases. In particular, if letting the height of the rectangle approach infinity, a closed-form solution is obtained analytically. The effects of the geometric parameters including crack position and crack length and applied electric field on energy release rate are shown graphically.