Anti – plane crack emanating from the interface in a bounded smart PEMO- elastic structure

Abstract

The magnetoelectroelastic analysis of two bonded dissimilar piezo-electro-magneto-elastic ceramics with a crack perpendicular to and terminating at the interface is made. By using the Fourier integral transform (in perpendicular directions in each materials), the mixed boundary conditions and continuity conditions are transformed to a singular integral equation with generalized Cauchy kernel, the solution of which has been well studied, and classical methods are directly applicable here to obtain the closed form solution. The results are presented for a permeable crack under anti-plane shear loading and in-plane electric and magnetic loadings, as prescribed electric displacement and magnetic inductions or electric and magnetic fields. The results indicate that the magnetoelectroelastic field near the crack tip in the homogeneous PEMO- elastic ceramic is dominated by a traditional inverse square-root singularity, while the coupled field near the crack tip at the interface exhibits the singularity of the power law r<sup>--α</sup> , r being the distance from the interface crack tip and α depending on the material constants of a bimaterial. In particular, electric and magnetic fields have no singularity at the crack tip in a homogeneous solid, whereas they are singular around the interface crack tip. Numerical results are given graphically to show the effects of the material properties on the singularity order, field intensity factors and energy release rates. The results presented in this paper should have potential applications to the design of multilayered magnetoelectroelastic structures.