Interfacial cracks between piezoelectric and elastic materials under in-plane electric loading

Abstract

Evaluation of crack tip driving force for interfacial cracks between piezoelectric actuators and elastic substrates is crucial to successful applications of smart materials and smart structures.Here the behavior of an interfacial crack between a piezoelectric material and an elastic material under in-plane electric loading is studied. The displacement mismatch along a bonded interface due to electric potential loading on the piezoelectric material is modeled by an array of uniformly distributed dislocations along the interface. Using Fourier transformation method, the governing equations are converted to an integral equation, which is then converted to a standard Hilbert problem. A closed form solution for stresses, electric field, and electric displacements along the bonded interface is obtained. The results agree very well with that from numerical simulations using the finite element method. The results show that the closed form solution is not only accurate for far field distributions of stresses and electric variables, but also accurate for the asymptotic distributions near the crack tip. The solution also suggests the likelihood of domain switch in the piezoelectric material near the crack tip.

A hybrid complex-variable solution for piezoelectric/isotropic elastic interfacial cracks

“…In particular, the component of remote electric displacement perpendicular to the interface (D ∞ 2 ) in the piezoelectric half-plane must be zero, because it must be compatible with the vanishing electric displacement of the elastic dielectric lower half-plane along the bonded interface. For similar reason, if the isotropic elastic lower half-plane is a conducting material (such as metal), the component of remote uniform electric field parallel to the interface (E ∞ 1 ) in the piezoelectric upper half-plane must be zero, because it must be compatible with the vanishing tangential electric field of the conducting elastic lower half-plane along the bonded interface (see Liu and Hsia 2003).…”

“…Hence, interfacial cracks between a piezoelectric medium and an isotropic elastic medium request to be treated separately. To our knowledge, only few efforts (see Liu and Hsia 2003;Ou and Chen 2004a,b;Li and Chen 2008) have been made to analyse interfacial cracks between a piezoelectric material and an essentially non-piezoelectric (insulating or conducting) isotropic elastic material. In particular, majority of these above-mentioned works have employed the Stroh's formulation and assumed that the elastic material has extremely low but non-zero piezoelectric and dielectric constants.…”

Interface crack between two interface deformable piezoelectric layers

“…As for the interface crack problem of the layered piezoelectric composite structures, many studies (Du et al 2001;Hao et al 1996;Liu and Hsia 2003;Liu et al 2005;Ou and Chen 2004;Ou and Wu 2003;Ru et al 1998;Shen et al 2000;Suo et al 1992) have been conducted. Through the experimental observation and finite element simulation, Shindo et al (2004) studied the electro-elastic field concentrations ahead of the electrodes in multilayer piezoelectric actuators.…”

On the dynamic behaviour of interfacial cracks between a piezoelectric layer and an elastic substrate

“…For the impermeable crack model, a charge-free condition along the crack faces is assumed. Based on these models, the behaviour of interacting cracks in piezoelectric media (Pak and Goloubeva 1995;Chen and Han 1999a, b;Han and Wang 1999) and interfacial cracks between a piezoelectric actuator and an elastic substrate have been analysed (Liu and Hsia 2003).…”