On contact zone models for an electrically limited permeable interface crack in a piezoelectric bimaterial

Abstract

An electrically limited permeable crack with a frictionless contact zone at the right crack tip between two semi-infinite piezoelectric spaces under the action of a remote electromechanical loading is considered. Attention is focused on the influence induced from the permittivity of the medium inside the crack gap on the contact zone length and the fracture mechanical parameters. Assuming the electric displacement constant inside the open region of the crack, the problem is reduced to a combined Dirichlet-Riemann and Hilbert boundary value problems which have been solved exactly. Stress and electric displacement intensity factors as well as the crack tip energy release rate are found in a clear analytical form. Furthermore, transcendental equations for the determination of the real contact zone length have been obtained for a general case and for a small contact zone length in an especially simple form. The dependencies of the mentioned values on the intensities of the electromechanical loading are presented in tables and associated diagrams.

Influence of concentrated loading on opening of an interface crack between piezoelectric materials in a compressive field

“…To eliminate this phenomenon, a contact zone model for a crack between isotropic materials was suggested by Comninou [19] and further developed by Atkinson [20], Simonov [21], Gautesen and Dundurs [22], Loboda [23] and others. The contact zone approach was applied to interface cracks in linear thermopiezoelectric media by Qin and Mai [24], in magnetoelectroelastic materials by Herrmann et al [25], Feng et al [26], and for an electrically permeable, impermeable and limited permeable crack in piezoelectric materials by Herrmann and Loboda [27], Herrmann et al [28] and Govorukha and Kamlah [29], respectively.…”

“…The influence of a concentrated load at the crack faces in a homogeneous piezoelectric material has been studied by Chen and Han [31] for a finite crack and by Hou et al [32] for a circular crack. The interface cracks with contact zone between two different piezoelectric materials under distributed far-field loading have been studied in [27][28][29]. However, to the best of the authors' knowledge, the combined effect of a concentrated crack face load and remote mixed-mode loading upon an interface crack in a piezoelectric bimaterial has not been considered yet.…”