A new extended pre-fracture zone model for a limited permeable crack in an interlayer between magnetoelectroelastic materials

Abstract

This paper considers the plane problem for two identical semi-infinite magnetoelectroelastic (MEE) materials, which are adhered together by a thin interlayer. A limited permeable crack is assumed to form in the interlayer parallel to its faces, and the interlayer is softer than the adherent MEE materials. To avoid singularities in the vicinity of a crack, which do not exist in reality, the extended pre-fracture zones including three distinct zones, i.e., the mechanical yield zone, the electrical saturation zone and the magnetic saturation zone, of finite lengths are introduced as crack continuations. The problem is formulated mathematically as a system of three linear equations, which can be solved exactly. The unknown lengths of the extended pre-fracture zones are determined by requiring that the stress, the electrical displacement and the magnetic induction are all finite at the ends of these zones. The fracture parameters, such as the crack opening displacement, and the jumps in the electrical and/or magnetic potentials through the crack region as well as the energy release rate are obtained. All these parameters are presented in a simple explicit form which can be determined efficiently without complicated computation that makes the present results rather convenient for any theoretical analysis and engineering applications. Additionally, numerical results are presented to study the influence of various factors on fracture parameters.