Analysis of crack-tip singularities for an interfacial permeable crack in metal/piezoelectric bimaterials

By modeling metal as a special piezoelectric material with extremely small piezoelectricity and extremely large permittivity, we have obtained the analytical solutions for an interfacial permeable crack in metal/piezoelectric bimaterials by means of the generalized Stroh formalism. The analysis shows that the stress fields near a permeable interfacial crack tip are usually with three types of singularities: r (-1/2 +/- i epsilon) and r(-1/2). Further numerical calculation on the oscillatory index E are given for 28 types of metal/piezoelectric bimaterials combined by seven commercial piezoelectric materials: PZT-4, BaTiO3, PZT-5H, PZT-6B, PZT-7A, P-7 and PZT-PIC 151 and four metals: copper, silver, lead and aluminum, respectively. The explicit expressions of the crack tip energy release rate (ERR) and the crack tip generalized stress intensity factors (CSIF) are obtained. It is found that both the ERR and GSIF are independent of the electric displacement loading, although they seriously depends on the mechanical loadings.