Pre-fracture zones modelling for a limited permeable crack in an interlayer between magneto-electro-elastic materials

Abstract

A plane-strain problem for a limited permeable crack in an adhesive thin interlayer between two semi-infinite electro-magneto-elastic spaces is considered. The tensile mechanical stress, the electrical displacement and magnetic induction are applied at infinity. Zones of mechanical yielding and strip electric and magnetic polarization saturation zones arise in this interlayer on the continuations of the crack. It is assumed that the zone of mechanical yielding is the shortest one while both cases of the longest electric and magnetic zone are considered. The mechanical yielding zones are modelled by the crack continuations with normal compressive stresses applied at its faces. The electric and magnetic polarization saturation zones are modelled by segments at the crack continuations with prescribed saturated electric displacements and magnetic induction. These electric displacements and magnetic induction can linearly vary along the mechanical yielding zones.The problem is reduced to the Hilbert–Riemann problem of linear relationship, which is solved exactly. The equations for determination of the pre-fracture zone lengths, the expressions for the crack opening displacement jump, electrical potential and magnetic induction jumps and J-integral are obtained in an analytical form. Some numerical results which illustrate the influence of various characteristics on fracture parameters are presented in graphical and tabular form.