Mathematical model of electrical and mechanical yielding for piezoelectric strip weakened by a non-centric semi-permeable crack

A mathematical strip-electro-elastic yielding model solution is obtained for a long and narrow piezoelectric strip weakened by a non-centric, semi-permeable, mode-III crack. The crack is oriented parallel and situated asymmetrically with respect to the edges of the strip. Fourier cosine integral transform technique is adopted to solve the problem. Three different cases are considered: when developed saturation zone is bigger, smaller or equal to the developed slide-yield zone. Closed-form analytic expressions are derived for developed zones lengths, crack sliding displacement, crack opening potential drop, field intensity factors and energy release rate. A numerical case study is presented for poled BaTiO3 piezoelectric ceramic which affirms that proposed model is capable of crack arrest under small-scale mechanical and electrical yielding.