A mathematical strip-saturation model for a piezoelectric plane weakened by two collinear equal cracks

A plane problem for a poled transversely isotropic piezoelectric plane cut along two equal collinear straight cracks is considered. It is assumed that the electrical yielding occurs at the continuations of the cracks due to the applied mechanical and electrical loadings. We model these crack continuations as the zones with constant cohesive saturation limit electrical displacement. The Stroh formalism and a complex variable technique are adopted to obtain the analytic solution of the problem. Closed-form expressions are derived for the developed saturation zone length, the crack opening displacement, the crack opening potential drop, the stress intensity factors, and the energy release rate. A qualitative numerical case study is presented for ceramics PZT-4, PZT-5H, and BaTiO3 to study the effects of various parameters as follows: developed saturation zone length and prescribed load, stress intensity factor, energy release rate, and crack opening displacement on crack growth resistance. The energy release rate and the stress intensity factor variations are investigated with respect to the inter-crack distance. The results obtained are presented graphically and discussed.