Vol. 3, No. 8, 2008

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

Vladimir B. Govorukha and Marc Kamlah

Vol. 3 (2008), No. 8, 1447–1463

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.

piezoelectric material, nonlinear fracture mechanics, interface crack, prefracture zone
Received: 7 April 2008
Revised: 21 May 2008
Accepted: 29 June 2008
Published: 1 October 2008
Vladimir B. Govorukha
Department of Computational Mathematics
Dniepropetrovsk National University
Nauchny str. 13
Dniepropetrovsk 49050
Marc Kamlah
Forschungszentrum Karlsruhe
Institute for Materials Research II
Postfach 3640
76021 Karlsruhe