Numerical Studies of Some Modified Polarization Saturation Models in 2-D Semipermeable Piezoelectric Media Using Distributed Dislocation Method

Abstract

In this paper, some modified polarization saturation models are proposed and studied numerically in 2-D semipermeable piezoelectric media using distributed dislocation technique (DDT). The polarization saturation (PS) model is modified here by varying the saturated condition imposed on the electrically saturated strip, i.e. a constant saturated condition to linear, quadratic and cubic varying electric displacement saturated condition. Numerical studies for these proposed models are simulated by considering their equivalent forms based on the principle of superposition. A centre-cracked problem in 2-D semipermeable piezoelectric media under arbitrary poling direction and in-plane electromechanical loadings is considered for these analyzes. To validate the developed numerical codes and iterative numerical approach for finding the unknown saturated zone length, the obtained results for PS model are compared with the analytical results available in literature. Thereafter, the results are presented for modified PS models, they show the effect of variation in saturation condition on saturated zone length, critical applied electric displacement loading and crack opening potential (COP), whereas no significant effect has been observed on local intensity factor (LIF) and crack opening displacement (COD). Further, saturated zone length increases with respect to increase in degree of variation of saturation condition, i.e. from constant to cubic. Moreover, the variation shows the effect on implication of applied electric loading and defines the critical applied electric loading corresponding to each model. It is observed that the critical value of applied electric loading significantly decreases with the increase in degree of variation of saturation condition. Here, a significant effect of poling direction is also found in all the parameters such as saturated zone length, LIF, COD and COP.