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An interface crack in piezoelectric bimaterial with one electrically conductive and two electrically permeable zones at its faces

Volodymyr Govorukha, Marc Kamlah and Shuo Zhao

Vol. 17 (2022), No. 5, 455–468
Abstract

A mode III partially electroded interface crack between two different piezoelectric materials under the action of antiplane mechanical and in-plane electric loadings is analyzed. From the point of view of the boundary conditions on the crack faces, one zone of the crack faces in such crack can be considered as electrically conductive while the other parts are electrically permeable. Using special representations of field variables via sectionally analytic vector-functions, a homogeneous combined Dirichlet–Riemann boundary value problem is formulated. An exact analytical solution of this problem is obtained. Analytical expressions for the shear stress, electric field and also for the crack faces sliding displacement jump are derived. The intensity factors for stress and electric fields are determined as well. The dependencies of the mentioned values on the magnitude of the external electric loading and different ratios between the electrically conductive and electrically permeable crack face zone lengths are also demonstrated.

Keywords
antiplane problem, piezoelectric material, interface crack, field intensity factors
Milestones
Received: 1 April 2022
Revised: 3 August 2022
Accepted: 22 September 2022
Published: 22 February 2023
Authors
Volodymyr Govorukha
Department of Higher Mathematics and Physics
Dnipro State Agrarian and Economic University
Dnipro
Ukraine
Marc Kamlah
Institute for Applied Materials
Karlsruhe Institute of Technology
Eggenstein-Leopoldshafen
Germany
Shuo Zhao
School of Mechanical Engineering
Hebei University of Science and Technology
Shijiazhuang
China