Limited permeable crack moving along the interface of a piezoelectric bi-material |
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| Authors: | Y Lapusta A Komarov F Labesse-Jied R Moutou Pitti V Loboda |
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| Institution: | 1. French Institute of Advanced Mechanics, LAMI/IFMA /Clermont Université, Campus de Clermont-Ferrand/les Cézeaux, BP 265, 63175 Aubière Cedex, France;2. Department of Theoretical and Applied Mechanics, Dniepropetrovsk National University, Gagarin Av., 72, Dniepropetrovsk 49010, Ukraine;3. Clermont Université, Université Blaise Pascal - IUT d''Allier, Laboratoire de Mécanique et Ingénieries (LaMI), BP 2235, 03100 Montluçon, France;4. Clermont Université, Université Blaise Pascal, Laboratoire de Mécanique et Ingénieries (LaMI), EA 3867, BP 10448, 63000 Clermont Ferrand, France;1. Department of Engineering Mechanics, Beijing University of Technology, Beijing 100124, PR China;2. Department of Civil Engineering, University of Siegen, D-57068 Siegen, Germany;3. Department of Mechanical and Environmental Informatics, Tokyo Institute of Technology, 2-12-1-W8-22, Ookayama, Meguro-ku, Tokyo 152-8552, Japan;1. Faculty of Mechanical Engineering and Mechanics, Ningbo University, Ningbo 315211, PR China;2. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, PR China;1. Henan Key Engineering Laboratory for Anti-fatigue Manufacturing Technology and School of Mechanical Engineering, Zhengzhou University, Zhengzhou 450001, China;2. School of Mechanics and Engineering Science, Zhengzhou University, Zhengzhou 450001, China;1. Department of Engineering Mechanics, Beijing University of Technology, Beijing 100124, PR China;2. Department of Civil Engineering, University of Siegen, D-57068 Siegen, Germany |
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| Abstract: | A plane problem for a crack moving with a subsonic speed along the interface of two piezoelectric semi-infinite spaces is considered. The crack is assumed to be free from mechanical loading. The limited permeable electric condition with an account of electric traction is adopted at its faces. A uniformly distributed mixed mode mechanical loading and an electric flux are prescribed at infinity. The problem is reduced to the Riemann–Hilbert problem by means of introducing a moving coordinate system and assuming that the electric flux is uniformly distributed along the crack region. An exact solution of this problem is proposed. It permits to find in closed form all necessary electromechanical characteristics at the interface and to formulate the equation for the determination of the electric flux. Analysis of this equation confirms the correctness of the assumption concerning the uniform distribution of the electric flux in the crack region. The values of the electric flux are determined by solving the obtained equation. Thereafter, the stress and electric intensity factors as well as their asymptotic fields at the crack tip are also found. The particular case of a crack moving in a homogeneous piezoelectric material is considered. The values of the electric flux and the fracture parameters are found exactly in a simple form for this case. Also, a numerical analysis is performed for a crack propagating with a subsonic speed between PZT4 and PZT5 materials and for a crack moving in PZT4 material. The electric flux in the crack region, stress and electric intensity factors, crack opening and the energy release rate (ERR) are found as functions of the crack speed, loading and electric permeability of the crack medium. The influence of the electric traction on the crack faces upon the mentioned parameters is demonstrated. |
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