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 neartip field intensity factors of piezoelectric interface cracks, J. Mech. Phys. Solids (in press)] and by considering a metal as a special piezoelectric material withextremely small piezoelectricity and extremely large permittivity (conductor), we obtain the two dominant parameters e and j for description of interface cracktip singularity in such bimaterials. Numerical results show that almost all of such bimaterials have the feature that the first parameter e vanishes whereas the second parameter j remains non-zero. An interface crack in these bimaterials always possesses the stress singularity r-1/±k 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 ingularity, which is far apart from previous results [Prik. Mat. Mekh. 39 (1975) 145; V.Z. Parton, B.A. Kudryavtsev, Electromagnetoelasticity, Gordon and BreachSc ience 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 withnon-z ero e and vanishing j, the oscillating stress singularity r-1/2ie at the crack tip is reached in this bimaterial. Consequently, metal/piezoelectric bimaterials are categorized into two classes: one withnon-zero j and vanishing e could be called as j-class metal/piezoelectric bimaterials and the other one with non-zero e and vanishing j could be termed as e-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 growthoc curs 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.

The J-integral analysis is performed for the plane problems of multiple subinterface microcracks near the tip of an interface macrocrack in bimaterial solids. The analysis starts from a general solution based on the "pseudo-traction" method which has been addressed thoroughly in homogeneous cases. The contribution to the J-integral induced from the subinterface microcracks is shown in a consistent relation with those induced from an interface macrocrack tip and the remote stress field. A new technique is developed to evaluate the second component (being expressed by J*2 in this paper) of the well-known Jk-vector of a subinterface crack for considering a contour enclosing the whole crack, which is necessary to evaluate the contribution to the J-integral arising from the subinterface microcracks. The consistency of the J-integral for numerical examples is proved, where two kinds of material combinations presented by Hutchinson et at. [ASME J. Appl. Mech., 1987, 54, 828-832] are considered. Some discussion and conclusions are then given which seem very useful in the investigation of microcrack shielding problems in bimaterial cases.

The path-independence of the J-integral considering discontinuities (e.g. microcracks) in a near-tip stress field is studied in detail. The well-known integral defined by Rice and the related Jk-vector discussed by Bergez, Cherepanov, and Herrmann and Herrmann are evaluated, respectively, along three different closed contours. The first of them is surrounding the tip of a semi-infinite crack only, the second encloses the discontinuities completely, while the third encloses both the tip and the discontinuities. It is found that there is a simple, but universal relation among three values of the J-integral corresponding to the contributions induced from the semi-infinite crack tip, the discon-tinuities and the remote stress field, respectively. This means that the interaction effect between a macrocrack and discontinuities can be considered as the redistribution of the J-integral arising from the existence of the discontinuities.

This paper has two goals. First, we propose the 'pseudotraction electric displacement' method for solving the interaction problem of multiple parallel cracks in transversely isotropic piezoelectric ceramics. Second, we present a fundamental understanding for the role that the electric displacement loading plays in the interaction problem. Detailed comparisons between the results under the compound mechanical electric loading conditions and those derived under purely mechanical loading conditions are performed. It is shown that the mechanical fracture parameters such as the stress intensity factors are no longer independent of the electric loading as they wofiuld be in single crack problems. Quite contrary, the electric displacement loading has a signicant in uence on the stress intensity factors, the total potential energy release rate and the mechanical strain energy release rate. This important conclusion is mainly due to the interaction effect, i.e., one of the multiple cracks releases the stresses and disturbs the electric fields near the other crack. It is also found that there are some special relative locations for the multiple parallel cracks at which the electric displacement loading has no effect on the Mode I stress intensity factor. However, the mechanical strain energy release rate has no such a property.