Mechanical and electrical yielding for an electrically insulated crack in an interlayer between piezoelectric materials

A plane problem for a crack in a thin ductile layer between two piezoelectric materials under remote electromechanical loading is considered. The piezoelectric substrates are of the same material. They are modeled by half-spaces. For the interlayer thickness tending to zero, electrical and mechanical yielding zones of different unknown lengths are introduced at the crack continuations. These zones are modeled by jumps of electric potential and mechanical displacement jumps, respectively. A vector Hilbert problem is formulated and solved exactly. The lengths of the yield zones are found from the conditions of finiteness of the normal stress and of the electrical displacement. The crack opening and the electric potential jumps at the initial crack tip are found in closed form for the cases of electrical yield zone longer and shorter than the mechanical one. Simple formulae for energy release rate are presented for Griffith crack and the developed electromechanical yield models. Also, an approximate model for eliminating the mechanical and electrical singularities is suggested. Numerical results are presented for different values of yield parameters and of remote electromechanical loading. A good agreement between the energy release rate values obtained for a Griffith crack, exact and approximate yield zone models are established.