Mixed mode transient analysis of functionally graded piezoelectric plane weakened by multiple cracks

Abstract

In this paper, a functionally graded piezoelectric (FGP) plane weakened by multiple parallel cracks is investigated under mixed mode mechanical and electrical impacts. The system contains Volterra type glide and climb edge dislocations. The material properties of the system are assumed to vary exponentially along the x-axis. At first, the stress field and electric displacement in FGP plane are derived by using a single dislocation. Then, a system of singular integral equations with a simple Cauchy kernel of the transient dynamic problem is obtained by determining a distributed dislocation density on the crack surface and using the Fourier and Laplace integral transforms, which are solved numerically using the Lobatto-Chebyshev integration formula. The dynamic field intensity factors are determined through numerical Laplace inversion and the distributed dislocation technique (DDT). Finally, various examples are provided to investigate the influence of the material properties, electromechanical coupling factor, loading conditions and cracks arrangement on the dynamic fracture behavior of the interacting cracks.