Magnetoelectroelastic field induced by a crack terminating at the interface of a bi-magnetoelectric material

Abstract

An analysis is presented of the magnetoelectroelastic behaviour induced by a crack, terminating at and normal to the interface of two bonded dissimilar magnetoelectric materials. A singular integral equation with generalised Cauchy kernel is derived by solving a boundary value problem, and a closed-form solution is then obtained. When subjected to anti-plane mechanical loading and in-plane electric and magnetic fields, an explicit expression for the out-of-plane displacement jump across the crack surface and asymptotic generalised stress field near the crack tips are derived, respectively. The results indicate that the generalised stress field is still dominated by a traditional square-root singularity r ^− 0.5 for the crack tip in a homogeneous magnetoelectric material, whereas it is a function of for the crack tip at the interface, where r is the distance from the cracks tip and α is a parameter dependent on material properties. Based on the field intensity factors and energy release rates, such power-law singularity makes cracks propagate through the interface easily or with difficulty, depending on whether α > 0.5 or α < 0.5, respectively. When α = 0.5, two crack tips exhibit the square-root singularity. In particular, when two magnetoelectric solids are identical, the results for a crack embedded in a magnetoelectric solid are recovered.

Keywords:

• magnetoelectric material
• singularity of the crack tip
• crack terminating at the interface

Acknowledgements

This work was supported by the National Natural Science Foundation of China (through grant No. 10672189), and supported by the China-Korea Binational Joint Research (No. 10711140645).