Interface crack problem in elastic dielectric/piezoelectric bimaterials

Abstract

By considering an isotropic elastic dielectric material as a transversely isotropic piezoelectric material with little piezoelectricity, the interface crack problem in elastic/piezoelectric bimaterials is treated in this paper based on Stroh's complex potential theory (1958) with the impermeable crack model. In order to obtain universal results, Numerical results of the near tip stress field and the electric field for 35 kinds of dissimilar bimaterials constructed by five kinds of elastic dielectric materials, namely Epoxy, Polymer, Al₂O₃, SiC and Si₃N₄, and seven kinds of piezoelectric ceramics, namely PZT-4, BaTiO₃, PZT-5H, PZT-6B, PZT-7A, P-7, and PZT-PIC151, are presented. It is concluded that all the combinations lead to the same results: in which the first crack tip singularity parameter ε does not vanish whereas the second parameter κ always vanishes. From the physical point of view, an interface crack in such a dissimilar material shows a similar oscillating singularity as that in dissimilar elastic bimaterials. Moreover, by using a maximization value technique, the regular inverse square root singularity r ^−1/2 of the stress and the electric field at the crack tip can be realized, although, theoretically, an interface crack in such bimaterials possesses the well-known oscillating singularity r ^{−1/2± iε}. Of great significance is that, in the absence of mechanical loadings, a purely electric loading can induce relative large model I or II stress intensity factor for a interface crack in some elastic/piezoelectric bimaterials, which implies that the electric-induced failure may be realized in such bimaterials.