Generalized mathematical electro-mechanical-yielding zone model for a non-centric semi-permeable anti-plane crack in arbitrary polarized piezoelectric strip

Abstract

In the paper, we propose a generalized mathematical electro-mechanical-yielding-zone model to address the presence of a mode-III, non-centric semi-permeable crack in an arbitrary polarized long and narrow piezoelectric (PE) strip. The electro-mechanical-yielding zone model is generalized by exploring three different scenarios on the rims of mechanical-yielding zone: Linear, quadratic and cubic interpolating polynomial times the distributed anti-plane yield point shear stress. It is assumed that the mechanical-yielding zones are smaller than the electrical-yielding zones. The solution to the problem has been achieved by utilizing the Fourier cosine transform and the integral equation techniques. The analytical expressions are derived for electrical-yielding zone, mechanical-yielding zone, electric crack condition parameter and various fracture parameters, such as crack-sliding displacement (CSD), crack-opening potential drop (COPD) and energy release rate (ERR) under all considered scenarios. Furthermore, numerical case study is conducted for investigating the effects of material properties, strip width, prescribed electro-mechanical loadings, crack-face boundary conditions and poling angle on numerous fracture parameters. The results obtained from the present study undergo rigorous analysis and a graphical comparison is employed to offer a clear and insightful representation of the findings.