Transient response of cracked nonhomogeneous substrate with piezoelectric coating by dislocation method

Abstract

The transient response of a functionally graded material (FGM) orthotropic strip with a piezoelectric coating weakened by multiple cracks is investigated. The system is subjected to out-of-plane mechanical and in-plane electrical loading. The properties of the nonhomogeneous substrate are assumed to vary exponentially along the thickness and the energy dissipation is modeled by viscous damping. In this study, the rate of the gradual change of the shear moduli, mass density, and damping constant are assumed to be same. At first, the transient response of a Volterra-type dislocation in an FGM orthotropic strip is obtained analytically. Imposing a distributed dislocation density on the crack surface and using the Fourier and Laplace integral transforms, the problem is reduced to a system of singular integral equations for a substrate weakened by multiple cracks in the form of Cauchy singularity; which are solved numerically to obtain the dynamic stress intensity factors at the crack tips. Finally, the effects of the geometrical parameters, material properties, viscous damping and cracks arrangement on the dynamic fracture behavior of the interacting cracks are studied.

Dynamic response of cracked non‐homogeneous magneto‐electro‐elastic layer sandwiched by two dissimilar orthotropic layers

“…Q are given in Appendix A. Substituting Equation 19 into (18) and taking the inverse Fourier transform of resultant equations yields the stress, electric displacement, and magnetic induction in the Laplace transform domain…”

“…Furthermore, the distributed dislocation technique has been proved to be a useful method in the transient analysis of medium with multiple cracks under impact loads. [15][16][17][18][19][20] The transient fracture problem of piezoelectric-piezomagnetic sandwich structures under the combined anti-plane mechanical and in-plane electrical impacts was investigated by Zhao et al 21 Transient analysis of two bonded functionally graded magneto-electro-elastic layers with multiple interfacial cracks was analyzed by Milan and Ayatollahi. 22 The transient response of multiple impermeable cracks in a piezoelectric layer bonded to an orthotropic layer under anti-plane mechanical and in-plane electrical impact loads was obtained by Ayatollahi et al 23 According to our knowledge, although crack problems in MEEM or FGMEE layer have been investigated by many researchers, the transient analysis of multiple embedded cracks in the FGMEE layer bonded between two orthotropic layers under impact loads has not been investigated.…”

Dynamic performance for piezoelectric bi-materials with an interfacial crack near an eccentric elliptical hole under anti-plane shearing

“…Based on the complex function method, Choi and Shin [8] examined three collinear impermeable interfacial cracks in bonded dissimilar piezoelectric materials and obtained a closed form solution. Ershad et al [9] and Bagheri [10] studied the transient response of a cracked non-homogeneous substrate with piezoelectric coating and multiple interface cracks in two nonhomogeneous half-layers by the dislocation method. Reda et al [11] proposed a methodology for the computation of the homogenized response of stratified piezoelectric materials and proved the applicability of this method for the quasi-electrostatic wave propagation analysis of stratified composites.…”

Fundamental solutions of two 3D rectangular semi-permeable cracks in transversely isotropic piezoelectric media based on the non-local theory

“…Piezoelectric media (PM) have been applied as electric devices because of the excellent electric-mechanical coupling effects. Owing to the brittleness of PM, the static or dynamic fracture behavior of PM has been studied (Chen, 2006;Ershad et al, 2018;Bagheri and Noroozi, 2018;Zhu et al, 2017;Yu et al, 2018;Bagheri, 2017;Afshar and Bagheri, 2018;Li et al, 2009;Bagheri and Mirzaei, 2019;Zhou et al, 2007). For example, Chen (2006) studied the interfacial coplanar cracks in piezoelectric bi-material under pure mechanical impact loading.…”