Modeling of electrical boundary condition and domain switching in piezoelectric materials

Abstract

The electrical boundary condition along the crack surfaces forms an important aspect in the study of fracture in piezoelectric materials. A finite element is developed to model the dielectric property of the medium that fills the crack cavity in a piezoelectric material and interfaced with the commercial code ABAQUS. The crack cavity permeability effects on the near tip electric fields in a compact tension specimen are investigated. Domain switching near the crack tip causes changes in the stresses and electric fields near the crack tip which in turn affects the fracture behavior. Domain switching in the material causes change in properties owing to the change in the polarization direction of the domains. The constitutive relations reflecting this change in the material property and the finite element solution procedure incorporating the change in material properties and also the strains due to crystal shape change are discussed. An internal energy density criterion is used to model the domain switching. The incremental domain switching solution procedure is also discussed and is used to model an existing compact tension experiment. The near tip stress field and the stress intensity factor are investigated.