Scattering of anti-plane shear waves by an interface crack between two bonded dissimilar functionally graded piezoelectric materials

Abstract

In the present paper, the dynamic behaviour of a Griffith crack situated at the interface of two bonded dissimilar functionally graded piezoelectric materials (FGPMs) is considered. It is assumed that the elastic stiffness, piezoelectric constant, dielectric permittivity and mass density of the FGPMs vary continuously as an exponential function of the x and y coordinates, and that the FGPMs are under anti-plane mechanical loading and in-plane electrical loading. By using an integral transform technique the problem is reduced to four pairs of dual integral equations, which are transformed into four simultaneous Fredholm integral equations with four unknown functions. By solving the four simultaneous Fredholm integral equations numerically the effects of the material properties on the stress and electric displacement intensity factors are calculated and displayed graphically.

Analysis of a Griffith crack at the interface of two piezoelectric materials under anti-plane loading

“…28,29) into (32), and electric potential (Eqs. 30, 31) into (34), we obtain at the end the equations system…”

“…Häusler et al [13] studied the fracture behavior of metal-piezoceramic interfaces under mechanical and electro-mechanical loading using commercial multilayer actuators. The dynamic behavior of a Griffith crack situated at the interface of two bonded dissimilar FGPM is displayed in [34]. Chen et al [3] studied the transient response of a semi-infinite mode III interfacial crack propagating between piezoelectric-piezomagnetic materials.…”

“…(30),(31),(32),(33),(34) and (35) form a system of six linear algebraic equations which can be rewritten in a compact form(A) (1) e |λ|h −C44 (1) e −|λ|h 0 e15 (1) e |λ|h −e15 (1) e −|λ|h 0 e15 (1) e |λ|h −e15 (1) e −|λ|h 0 −ε11 (1) e |λ|h ε11…”

BIEM analysis of dynamically loaded anti-plane cracks in graded piezoelectric finite solids

“…A strip with a crack parallel to the edge and exponentially varying material properties according to the space coordinates was treated by Wang et al (2003). Anti-plane crack analysis of graded piezoelectric materials under dynamic loading is investigated in Singh et al (2007Singh et al ( , 2009, Kwon et al (2002), Kwon and Lee (2004), Kwon (2003), Liang (2006), Jin and Zhong (2002), Ma et al (2004Ma et al ( , 2005. Recently also a variety of meshless methods has been proposed and applied for in-plane dynamic analysis in cracked graded piezoelectrics, see .…”

A fracture mechanics model for a crack problem of functionally graded materials with stochastic mechanical properties

“…The problem of two collinear cracks in functionally graded piezoelectric materials under in-plane electromechanical loads was examined by Yan et al (2009). The dynamic behaviour of a Griffith crack situated at the interface of two bonded, dissimilar, functionally graded piezoelectric materials was considered by Rokne et al (2009). Besides the above work, an analysis of a coupled plane elasticity problem of crack/contact mechanics for a coating/substrate system with functionally graded properties was performed by Choi & Paulino (2010).…”