Electroelastic analysis of an anti-plane shear crack in a piezoelectric ceramic strip

The electroelastic analysis of a piezoelectric strip with an anti-plane shear crack whose surfaces are parallel to the strip boundaries is made. Four cases of combined electromechanical loadings applied at the strip boundaries are considered. For the case of a crack lying at the center of a strip, the electroelastic field, field intensity factors, and energy release rate can be determined in explicit form via solving a resulting singular integral equation. For other cases, they can be given in terms of an auxiliary function, which is obtained as a power series of d via solving a resulting Fredholm integral equation using the iterative method, 2d being the ratio of the crack length over the strip width. Some numerical results are presented graphically to show the influence of crack length and crack position on the normalized energy release rate.