A theoretical model of conductive cracks in piezoelectric materials under electromechanical cycling

This article develops an analytical model for the conductive cracks in piezoelectric ceramics under electromechanical cycling. An electrical yielding strip and a mechanical yielding strip are assumed to develop at the crack tips when the medium is subjected to external electromechanical loads. The yielding strip is assumed to have constant stress and constant electric field. Based on these assumptions and extending the accumulated plastic displacement criterion for crack propagation in traditional structural materials to piezoelectric ceramics, a fatigue crack growth law is derived. The law, similar to the well known Paris law, is a fourth-power function of the effective stress intensity factor. Graphical results for the effect of electric load on the effective crack tip stress intensity factor and crack growth rate are provided. The law is given in closed-form so that it might be used in the future for the fatigue and reliability analysis and design of piezoelectric materials.