Vol. 15, No. 1, 2020

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A dielectric breakdown model for an interface crack in a piezoelectric bimaterial

Yuri Lapusta, Alla Sheveleva, Frédéric Chapelle and Volodymyr Loboda

Vol. 15 (2020), No. 1, 87–105
Abstract

A mode III electrically conductive crack between two piezoelectric semi-infinite spaces under the action of anti-plane mechanical loading and in-plane electrical field parallel to the crack faces is considered. All electromechanical quantities are presented as piecewise analytic vector functions. The problem is solved analytically, revealing an oscillating singularity at the crack tips in the stress and electric fields. To eliminate the electric field singularity the dielectric breakdown (DB) model is applied. According to this model, the electric field along some zone of the crack continuation is initially assumed to be equal to the electric breakdown strength and the length of this zone remains still unknown. A nonhomogeneous combined Dirichlet–Riemann boundary value problem for the crack with DB zone is formulated. An exact analytical solution of this problem is presented and the DB zone length is found from the electric field finiteness at the end point of this zone. The simple transcendental equation with respect to DB zone length is solved numerically and all required electromechanical quantities are found in closed analytical form. The DB model for a crack in a homogeneous material is also considered and compared with known results.

Keywords
dielectric breakdown model, electrically conductive interface crack, piezoelectric material
Milestones
Received: 15 June 2019
Revised: 11 November 2019
Accepted: 15 November 2019
Published: 26 February 2020
Authors
Yuri Lapusta
Université Clermont Auvergne, CNRS
SIGMA Clermont, Institut Pascal
F-63000 Clermont-Ferrand
France
Alla Sheveleva
Department of Theoretical and Computational Mechanics
Oles Honchar Dnipro National University
Dnipro
49010
Ukraine
Frédéric Chapelle
Université Clermont Auvergne, CNRS
SIGMA Clermont, Institut Pascal
F-63000 Clermont-Ferrand
France
Volodymyr Loboda
Department of Theoretical and Computational Mechanics
Oles Honchar Dnipro National University
Dnipro
49010
Ukraine