Near-tip stress fields and intensity factors for an interface crack in metal/piezoelectric bimaterials

Abstract

The primary goal of this research is to show the fundamental features of an interface crack in metal/piezoelectric bimaterials via Stroh's theory [Phil. Mag. 7 (1958) 625]. Based on the previous works [Phil. Mag. 7 (1958) 625; J. Mech. Phys. Solids 40 (1992) 739; Int. J. Fract. 119 (2003) L41; Singularities and near-tip field intensity factors of piezoelectric interface cracks, J. Mech. Phys. Solids (in press)] and by considering a metal as a special piezoelectric material with extremely small piezoelectricity and extremely large permittivity (conductor), we obtain the two dominant parameters ε and κ for description of interface crack-tip singularity in such bimaterials. Numerical results show that almost all of such bimaterials have the feature that the first parameter ε vanishes whereas the second parameter κ remains non-zero. An interface crack in these bimaterials always possesses the stress singularity r −1/2± κ at the crack tip. From the physical point of view, this implies that an interface crack in such bimaterials shows a feature with non-oscillating singularity, which is far apart from previous results [Prik. Mat. Mekh. 39 (1975) 145; V.Z. Parton, B.A. Kudryavtsev, Electromagnetoelasticity, Gordon and Breach Science Publishers, New York, 1988; J. Mech. Phys. Solids. 51 (2003) 921] and our classical understanding in dissimilar elastic or anisotropic materials [Bull. Seism. Soc. Am. 49 (1959) 119; ASME J. Appl. Mech. 32 (1965) 400]. On the other hand, there is one exceptional metal/piezoelectric bimaterial with non-zero ε and vanishing κ, the oscillating stress singularity r −1/2±i ε at the crack tip is reached in this bimaterial. Consequently, metal/piezoelectric bimaterials are categorized into two classes: one with non-zero κ and vanishing ε could be called as κ-class metal/piezoelectric bimaterials and the other one with non-zero ε and vanishing κ could be termed as ε-class metal/piezoelectric. Analysis of the crack-tip generalized stress field is performed. Of great significance is that: if a purely electric-induced interface crack growth occurs in metal/piezoelectric bimaterials, it is most likely due to the shear mode II fracture rather than the open mode I, and then a purely remote electrical loading enhances the interface crack extension in such bimaterials. Only when an external tensile loading is applied, could the mode I fracture play a dominant role.