Dynamic Antiplane Behaviour of Radial Collinear Cracks Emanating from Multiple Noncircular Cavities in Piezoelectric Material

Abstract

To further clarify the fracture mechanics characteristics of piezoelectric materials with defects, this paper studies the dynamic antiplane problems of radial collinear cracks emanating from multiple noncircular cavities in piezoelectric material. First, the expressions of Green function satisfying the boundary conditions in the semi-infinite piezoelectric medium with multiple depressions of arbitrary shape, the total displacement and the electric potential in the piezoelectric medium containing noncircular cavities and without cracks are derived by using complex variable function method and conformal mapping technology. Then, based on the crack-division technique and conjunction method, the problem is transformed into a set of Fredholm definite integral equations of the first kind. And the direct numerical integration method is used to solve it. As an example, the influences of defect size, SH wave frequency and material parameters on the dynamic stress concentration at the crack tip are given, which provides some theoretical guidance for the engineering design, production and safe use of piezoelectric devices.