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Abstract: The strip dielectric breakdown (DB) model introduced by Zhang and Gao [T.Y. Zhang, C.F. Gao, Fracture behavior of piezoelectric materials, Thero. Appl. Fract. Mech. 41 (2004) 339–379] is used to study the generalized 2D problem of a conductive crack and an electrode in an infinite piezoelectric material. The energy release rate and stress intensity factors are derived based on the Stroh formalism, and then they are applied as failure criteria to predict the critical fracture loads. It is found that the DB strip may take the shielding effect on a conductive crack or electrode. For the case of an electrode, the local energy release rate and stress intensity factor become zero when DB happens ahead of the electrode tip. For the case of a mode-I conductive crack in a transversely isotropic piezoelectric solid, the results based on the DB model show that the critical stress intensity factor linearly increases as the applied electric field parallel to the poling direction increases, while it linearly decreases as the applied electric field anti-parallel to the poling direction increases. Finally, the upper and lower bounds of the actual critical fracture loads are proposed for a conductive crack in a piezoelectric material under combined mechanical–electrical loads. [Copyright &y& Elsevier]

In this paper, we present an explicitly analytic solution for an electrically permeable interface crack between two dissimilar magneto-electroelastic solids. Using the Stroh formalism, we first derive the general solution under arbitrary loads by reducing the generalized 2D problem to an equivalent interface crack problem in two-elastic anisotropic media, which can be solved with well-established methods. With the analytic solution, we then study the interface crack loaded by remote uniform loads, by a generalized line force or/and by a generalized line dislocation. The results show the singular and oscillatory fields ahead of the crack tips. The electric–magnetic field within the crack has a similar singularity at the crack tip as the electric–magnetic field within the solids. In particular, when uniform mechanical–electric–magnetic loads are applied at infinity, the singular intensity depends on the material properties and the mechanical loads, but not on the electric–magnetic loads. [Copyright &y& Elsevier]

Abstract: In this work, we examine the energy release rate and the J-integral of an electrically insulated crack in a piezoelectric solid under remotely uniform electrical/mechanical loads. To count the electric field inside the crack, we model the crack as a slender elliptical flaw and have explicitly analytic solutions. The analytic results show that the energy release rate, in general, does not equal to the J-integral and that the J-integral is path-dependent due to the electric traction on the crack faces. However, the energy release rate is equal to the sum of the J-integral along an infinitesimal circle around the crack tip and the average driving force produced by the electric field on the entire crack surface. Under combined mechanical and electrical loading, the energy release rate may be positive or negative, depending on the level of the mechanical load and the strength of the electric field as well. The effect of electric field on the fracture behavior is mechanical load-dependent, which has been observed in experiments. [Copyright &y& Elsevier]