The fracture behaviour of functionally graded piezoelectric materials containing collinear dielectric cracks

Abstract

In this paper, the problem of two collinear cracks in functionally graded piezoelectric materials (FGPMs) under in-plane electromechanical loads is examined. The elastic, piezoelectric and dielectric constants of the FGPMs are assumed to vary continuously in space. The theoretical formulations are derived by using Fourier transforms and the resulting singular integral equations are solved with Chebyshev polynomials. A dielectric crack model with deformation-dependent electric boundary condition is adopted in the fracture analysis of FGPMs. Numerical simulations are made to show the effect of the dielectric medium, the material gradient and the geometry of interacting cracks upon the fracture parameters at crack tips. A critical state for applied electromechanical loading is identified, which determines whether the traditionally impermeable (or permeable) crack model serves as the upper or lower bound of the current dielectric crack model.

Investigation of the critical states of dielectric cracks in functionally graded piezoelectric materials

“…This critical state provides a defining point, at which the nonlinear response of the dielectric crack undergoes a transition. A similar phenomenon was observed by Yan & Jiang (2009) for the cracks in the FGPMs. The introduction of material gradient in the FGPMs will make crack interaction more complicated.…”

“…The traditional crack models without considering the dielectric medium effect may not be accurate in this situation. Therefore, a dielectric crack model accounting for the effects of both crack filling and crack deformation, even though cumbersome, has been widely used to study the fracture behaviour of piezoelectric materials (Hao & Shen 1994;Xu & Rajapakse 2001;Wang & Jiang 2002;Yan & Jiang 2009). This dielectric crack model is expected to provide more accurate results than the traditional crack models under certain conditions, and a transition among different crack models will occur according to the applied loads.…”

Two collinear unequal cracks in a poled piezoelectric plane: Mode I case solved by a new approach of real fundamental solutions

“…and dealt with transient or dynamic collinear unequal cracks in piezoelectric materials by the methods of integral transform and singular integral equation. Also by these methods, Yan et al (2009) studied two collinear unequal cracks in functionally graded piezoelectric materials. In the present work, we study two collinear unequal cracks under mode I electromechanical loadings by the methods of generalized dislocation simulation and singular integral equations (SIEs).…”

Numerical estimation of stress intensity factors in cracked functionally graded piezoelectric materials – A scaled boundary finite element approach

“…The stress intensity factors (SIFs) (K I , K II , K III ) and the electric displacement intensity factor (EDIF) (K IV ) are the key parameters in quantifying the strength and the reliability of the cracked FGPMs. One approach to study the fracture parameters is to seek analytical and/or closed form solutions [5,6,[8][9][10][11][12]. However, for complex geometries and load cases, such an approach is intractable and hence numerical solutions are sought.…”