Prefracture zone modeling for an electrically impermeable interface crack in a piezoelectric bimaterial compound

Abstract

This work is concerned with the analytical characterization of the electromechanical nonlinear effects in the fields surrounding the tip of an interface crack located between two piezoelectric materials. It is assumed that a prefracture zone arises along a line segment in front of the crack tip. The prefracture zone is modeled by electrical displacement reaching a saturation limit and constant stress distribution. This reduces the problem to a linear interface crack analysis leading to a Hilbert problem, which is solved exactly. The prefracture zone length and the stress magnitude in this zone are found from algebraic and transcendental equations. The latter are derived from the requirement of stresses and electrical displacement to be finite at the end of prefracture zone towards the undamaged ligament. Numerical results for certain material combinations and remote loadings are presented and analyzed. In addition, energy release rate and crack opening displacements are introduced, which offers the possibility of formulating a fracture criterion based on the crack opening displacements.