Crack branching in thermopiezoelectric materials

Solutions are presented for an electrically impermeable crack branching out of the crack plane in a thermopiezoelectric medium under thermo-electro-mechanical loads based on Stroh formalism. Explicit Green’s functions for the interaction of a crack and a thermopiezoelectric dislocation (i.e., a thermal dislocation, a mechanical dislocation and an electric dipole located at the same point) are developed. The problem then can be expressed in terms of coupled singular integral equations for the thermopiezoelectric dislocation density functions associated with a branched crack. Some essential fracture mechanics parameters, such as stress and electric displacement intensity factors, and energy release rate at the branched crack tip are obtained. Numerical results are presented for the effect of applied thermal flux loads and electric field on the crack propagation path.