Electrostatic tractions at crack faces and their influence on the fracture mechanics of piezoelectrics

Abstract

The influence of electrostatic tractions acting upon crack faces on the fracture mechanical quantities in piezoelectric materials under electromechanical loading is investigated. The physical background are the mechanical and dielectric equilibria at an interface between two dielectric domains and related mechanical stresses. The model is applied to a crack problem, where a dielectric interface exists between the solid material and the insulating crack medium. The analytical solution for a crack in an infinite piezoelectric body accounting for intrinsic charges and electrostatic stresses on the crack faces gives insight into the influence of crack boundary conditions on the field intensity factors. Varying loading conditions and the dielectric permittivity of the flaw yields a parameter range in which induced crack surface tractions are relevant. Then, the calculation of the J -integral for thermodynamically consistent crack boundary conditions is discussed. The line integral along the crack faces is replaced by a simple jump term. This approach comes out to be exact only for a simplified model of the electrostatic tractions.

Some new aspects of boundary conditions at cracks in piezoelectrics

“…First, the tractions σ C 22 can be neglected, which will be referred to as the "Hao and Shen" model. Second, piezoelectric field coupling can be neglected in the calculation of Coulomb stresses, i.e., e jq = 0, which was studied in [2]. This limiting case will be denoted by "dielectrical model".…”

“…These fields might be either of external origin or in a piezoelectric material induced by mechanical loads. To incorporate the latter, the existing models for Coulomb traction [1,2] will be extended from a theory of rigid dielectric bodies toward a theory of elastic piezoelectric materials.…”

“…Recently, a more general equation has been derived by Ricoeur and Kuna [1] starting from thermodynamical considerations and the theory of configurational forces. A simplification of this approach has then been applied to crack problems by the same authors [2]. In the same paper, methods for the efficient calculation of the J -integral for intrinsic electrical and mechanical crack surface loads have been pointed out.…”

“…In the same paper, methods for the efficient calculation of the J -integral for intrinsic electrical and mechanical crack surface loads have been pointed out. However, the investigation in [2] still neglects the influence of piezoelectric field coupling on the electrostatic crack surface tractions. The new model reveals effects, which have not been predicted by others, i.e., a coupling of Mode-I and Mode-II loading and a relation between collinear stresses parallel to the crack faces and the Mode-I SIF.…”

“…Like in our previous approach [1,2], the crack faces are modeled as interfaces between two dissimilar dielectric media. The mechanical stresses providing equilibrium are assumed to be those acting at crack faces in a dielectric solid.…”