Closed-form solutions for modified polarization saturated models in two unequal collinear cracked piezoelectric media considering coalesced interior zones

Abstract

Abstract In this paper, we present polynomial varying modified polarization saturation models for semipermeable two unequal collinear cracks with coalesced interior zones in piezoelectric media. Under the influence of far-field electromechanical loadings, the cracks situated in an infinite arbitrary polarized piezoelectric media are opened in self-similar manner, forming a strip saturated zone in front of the cracks-tips. Here, we modify the polarization saturation (PS) model in a way by arresting these zones with linear, quadratic and cubic polynomials types variable saturated conditions in place of constant saturated condition. Such modified PS models are, by using complex variable and Stroh formalism techniques, firstly reduced into simultaneous non-homogeneous Riemann-Hilbert problems in complex variable field functions, and the corresponding solutions are then obtained. The closed-form solutions for standard fracture parameters such as saturated zone lengths, local stress intensity factors(LSIFs), crack opening displacements and crack opening potentials are derived. Numerical studies are illustrated for all the modified PS models by analyzing the effects on saturated zone lengths and LSIFs with respect to the variations in electrical loadings, poling direction and crack lengths. Moreover, the obtained results are compared with the results of PS model. The study concludes that the saturated zone lengths and LSIFs increase significantly with the increase in degree of polynomial varying saturation condition.