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Analysis of a mode III interface crack in a piezoelectric bimaterial based on the dielectric breakdown model

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Abstract

A mode III electrically conductive crack between two different piezoelectric materials under the action of anti-plane mechanical and in-plane electric loadings is analyzed. The strip dielectric breakdown (DB) model, which is free from the electric field singularity, is developed for this crack. According to this model, the electric field along a DB-zone situated in continuation of a crack is assumed to be equal to the electric breakdown strength. The DB-zone lengths are found from the condition of a finite electric field at the end point of such a zone. Using special representations of field variables via sectionally analytic functions, an inhomogeneous combined Dirichlet–Riemann boundary value problem is formulated and solved analytically. Explicit expressions for the shear stress, the electric field and the crack faces’ sliding displacement jump are derived. The stress intensity factor is determined as well. The dependencies of the mentioned values on the magnitude of the external electromechanical loading are presented.

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Acknowledgements

Part of this work was executed during a stay of V. G. at Karlsruhe Institute of Technology (KIT). The authors gratefully acknowledge the support from KIT by funding the guest stay of V. G.

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Authors and Affiliations

  1. Department of Computational Mathematics, Oles Honchar Dnipro National University, Gagarin Av. 72, Dnipro, 49010, Ukraine

    V. Govorukha

  2. Institute of Applied Materials, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, 76344, Eggenstein-Leopoldshafen, Germany

    M. Kamlah

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  1. V. Govorukha
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  2. M. Kamlah
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Correspondence to V. Govorukha.

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Govorukha, V., Kamlah, M. Analysis of a mode III interface crack in a piezoelectric bimaterial based on the dielectric breakdown model. Arch Appl Mech 90, 1201–1213 (2020). https://doi.org/10.1007/s00419-020-01668-5

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  • DOI: https://doi.org/10.1007/s00419-020-01668-5

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