Multiple cracks analysis in a FG orthotropic layer with FGPM coating under anti-plane loading

Abstract

An analytical solution to the fracture analysis of a functionally graded (FG) orthotropic substrate with FG piezoelectric coating weakened by a screw dislocation is carried out. The material properties are assumed to vary exponentially through the thickness of the layers. The problem is solved under various types of anti-plane shear and in-plane electric loadings. At first, by considering a single-screw dislocation at crack location, an analytical solution is developed. Next, by using the Fourier transform, the problem is reduced to a system of singular integral equations with Cauchy-type singularities. Then, by computing the dislocation densities, both the stress intensity factors and the stress fields at the crack tips under different electromechanical loadings are determined. In this investigation, various examples are solved to show the applicability of the proposed solution by studying the effects of the cracks configurations, material properties, and non-homogeneity parameter on the stress intensity factors. Keywords FG orthotropic substrate Á Non-homogeneous piezoelectric coating Á Distributed dislocation technique Á Stress intensity factors Á Elliptical cracks Á Mode III fracture analysis

Mixed-mode computation of the transient dynamic stress intensity factor for multiple interface cracks

“…1+ for plane stress and = 3 − 4 for plane strain situations, where is the Poisson's ratio of material. Due to the complexity of mathematics involved, the distribution of mechanical properties of FGMs may be approximated by an exponential function (Konda and Erdogan [3], Kadioğlu et al [6], Chen and Liu [12] and Sourki et al [23]) as follows:…”