Theoretical model of crack branching in magnetoelectric thermoelastic materials

Thermomagnetoelectroelastic crack branching of magnetoelectro thermoelastic materials is theoretically investigated based on Stroh formalism and continuous distribution of dislocation approach. The crack face boundary condition is assumed to be fully thermally, electrically and magnetically impermeable. Explicit Green's functions for the interaction of a crack and a thermomagnetoelectroelastic dislocation (i.e., a thermal dislocation, a mechanical dislocation, an electric dipole and a magnetic dipole located at a same point) are presented. The problem is reduced to two sets of coupled singular integral equations with the thermal dislocation and magnetoelectroelastic dislocation densities along the branched crack line as the unknown variables. As a result, the formulations for the stress, electric displacement and magnetic induction intensity factors and energy release rate at the branched crack tip are expressed in terms of the dislocation density functions and the branch angle. Numerical results are presented to study the effect of applied thermal flux, electric field and magnetic field on the crack propagation path by using the maximum energy release rate criterion.