The Interaction between a Piezoelectric Screw Dislocation and a Semi-Elliptical Surface Crack in Piezoelectric Bi-Material

Abstract

By using the complex variable method, the electro-elastic interaction between a piezoelectric screw dislocation in the infinite half-plane and a semi-elliptical interface crack under remote anti-plane shear stresses and in-plane electric loads in piezoelectric bi-material is investigated, and the general solutions to the problem are obtained. The complex potentials, the generalized stress fields, the generalized stress intensity factors and energy release rate of crack tip, and the image force acting on the dislocation are also calculated. The influences of the electro-elastic constants and the location of the screw dislocation upon the stress intensity factor and the image force are discussed, while the influence of remote loading upon the energy release rate is also analyzed. The results indicate that the crack and the lower half plane may attract or repel dislocation with parameters changes when dislocation lies on the upper half plane and the shape of the crack is fixed. The shielding effect is stronger when the piezoelectric coefficient of the upper half plane is larger than that of the lower half plane, and the influence of relative shear modulus upon the shielding effect is relatively smaller when the relative piezoelectric coefficients take fixed values. The energy release rate may be positive or negative under a combined electric load and mechanical load. Both increasing electric field and decreasing mechanical load can decrease the energy release rate thereby enhancing the restraint of the crack expansion.