Analysis of a crack with finite electrical permeability between two piezoelectric materials

Abstract

A crack with finite electrical permeability between two piezoelectric materials is investigated. Initially, it is believed that the length of the crack is much smaller than the size of the body, so the latter is considered infinitely large. Assuming that the electric flux through the crack does not change along its length, an analytical solution to the given problem is constructed. On the base of this solution the magnitude of the electric flux, as well as other components of the electromechanical fields are found. A fairly simple formula for the energy release rate (EER) is also derived. For some values of the electrical permeability of the crack medium and external loads, the amount of electric flow through the crack and EER are calculated. Approbation of the obtained results was carried out on the example of a similar problem, but for the domain of finite dimensions. The finite element method (FEM) was used and the inverse approach was applied. According to this approach, the electric flux through the crack, which is obtained analytically, is used, and the solution is carried out using FEM. The analysis of the obtained numerical results confirmed the reliability of the methodology and the obtained analytical solution.
 Keywords: crack with finite electrical permeability; piezoelectric bimaterial; analytical solution; finite element method.