An interface crack with contact zones in a piezoelectric/piezomagnetic bimaterial

Abstract

An interface crack with a frictionless contact zone at the right crack tip between two semi-infinite piezoelectric/piezomagnetic spaces under the action of a remote mechanical loading, magnetic and electric fluxes as well as concentrated forces at the crack faces is considered. Assuming that all fields are independent on the coordinate x 2 co-directed with the crack front, the stresses, the electrical and the magnetic fluxes as well as the derivatives of the jumps of the displacements, the electrical and magnetic potentials are presented via a set of analytic functions in the (x 1 , x 3 )-plane with a cut along the crack region. Two cases of magneto-electric conditions at the crack faces are considered. The first case assumes that the crack is electrically and magnetically permeable, and in the second case the crack is assumed electrically permeable while the open part of the crack is magnetically impermeable. For both these cases due to the above-mentioned representation the combined Dirichlet-Riemann boundary value problems have been formulated and solved exactly. Stress, electric and magnetic induction intensity factors are found in a simple analytical form. Transcendental equations and a closed form analytical formula for the determination of the real contact zone length have been derived for both cases of magnetic conditions in the crack region. For a numerical illustration of the obtained results a bimaterial BaTiO 3 -CoFe 2 O 4 with different volume fractions of BaTiO 3 has been used, and the influence of the mechanical loading and the intensity of the magnetic flux upon the contact zone length and the associated intensity factors as well as the energy release rate has been shown.

A magnetically impermeable and electrically permeable interface crack with a contact zone in a magnetoelectroelastic bimaterial under concentrated magnetoelectromechanical loads on the crack faces

“…We point out that for the electrically impermeable and magnetically permeable case and the electromagnetically permeable case, similar behaviors (but with slightly different amplitudes) can be obtained with Figures 2 and 3 being further close to those in ref. [50] for the electromagnetically permeable case. with increasing  B , the contact zone length generally decreases whilst the Mode-II SIFs increase.…”

“…In addition, we assume that the influence of one contact zone upon the other is negligibly small [46,51], and thus, in the present study only the contact zone at the right crack tip is considered. Certainly, a contact zone at the left crack-tip can be treated similarly [50]. For the present interface crack problem, the continuity and boundary conditions at the interface can be written in the following form:…”

“…Qin and Mai [47], Herrmann and Loboda [48] and Herrmann et al [49] developed the contact zone model for solving the interface crack problems of piezoelectric bimaterials. However, to the best of our knowledge, up to now, there is only one paper on the contact zone model for an interface crack between two dissimilar magnetoelectroelastic materials [50], where two kinds of magnetoelectrical boundary conditions, i.e., magnetoelectrically permeable, magnetically impermeable and electrically permeable, were considered. For the crack problems under concentrated loads, only the magnetoelectrically permeable interface crack model was analytically investigated [50].…”

Fracture analysis of an electrically conductive interface crack with a contact zone in a magnetoelectroelastic bimaterial system

“…This is the main reason behind structural failure. In the past couple of decades, many researchers have studied the interface crack problems of MEE materials (Gao and Noda, 2004;Li and Kardomateas, 2007;Herrmann et al, 2010;Zhu et al, 2010;Feng et al, 2011;Ma et al, 2012).…”

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.…”