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  HomeContents of Chinese Journal of Mechanical Engineering,2012 No.4 Exact Solutions for Piezoelectric Materials with an Elliptic Hole or a Crack under Uniform Internal Pressure

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Exact Solutions for Piezoelectric Materials with an Elliptic Hole or a Crack under Uniform Internal Pressure


LIU Shuhong1, *, SHEN Yingming2, and LIU Jinxi1
1 Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China
2 Department of Science and Technology, Shijiazhuang Tiedao University, Shijiazhuang 050043, China

Received June 2, 2011; revised January 18, 2012; accepted February 1, 2012


Abstract: The existing investigations on piezoelectric materials containing an elliptic hole or a crack mainly focus on remote uniform tensile loads. In order to have a better understanding for the fracture behavior of piezoelectric materials under different loading conditions, theoretical and numerical solutions are presented for an elliptic hole or a crack in transversely isotropic piezoelectric materials subjected to uniform internal pressure and remote electro-mechanical loads. On the basis of the complex variable approach, analytical solutions of the elastic and electric fields inside and outside the defect are derived by satisfying permeable electric boundary condition at the surface of the elliptical hole. As an example of PZT-4 ceramics, numerical results of electro-elastic fields inside and outside the crack under various electric boundary conditions and electro-mechanical loads are given, and graphs of the electro-elastic fields in the vicinity of the crack tip are presented. The non-singular term is compared to the asymptotic one in the figures. It is shown that the dielectric constant of the air in the crack has no effect on the electric displacement component perpendicular to the crack, and the stresses in the piezoelectric material depend on the material properties and the mechanical loads on the crack surface and at infinity, but not on the electric loads at infinity. The figures obtained are strikingly similar to the available results. Unlike the existing work, the existence of electric fields inside an elliptic hole or a crack is considered, and the piezoelectric solid is subjected to complicated electro-mechanical loads.

Key words: piezoelectric material, elliptic hole, crack, boundary condition, electro-elastic fields

 


* Corresponding author. E-mail: liush@stdu.edu.cn
This project is supported by Hebei Provincial Natural Science Foundation of China (Grant No. A2011210033), Foundation of Hebei Education Department of China (Grant No. ZH2011116), and Hebei Provincial Research Program for Higher Education and Teaching Reform of China (Grant No. 103024)
© Chinese Mechanical Engineering Society and Springer-Verlag Berlin Heidelberg 2012
 

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Biographical notes
LIU Shuhong, born in 1968, is currently a professor at Shijiazhuang Tiedao University, China. She received her PHD degree from Beijing Jiaotong University, China, in 2004. Her main research interests include solid mechanics, structural safety evaluation and mechanical bearing capacity of intelligent materials.
Tel: +86-311-87936546; E-mail: liush@stdu.edu.cn

SHEN Yingming, born in 1973, is currently an associate professor at Shijiazhuang Tiedao University, China. He received his master degree from Southwest Jiaotong University, China, in 2001. His main research interests include mechanical bearing capacity and application of intelligent materials.
Tel: +86-311-87936049; E-mail: shxt7@sohu.com

LIU Jinxi, born in 1961, is currently a professor at Shijiazhuang Tiedao University, China. He received his PHD degree from Harbin Institute of Technology, China, in 1997. His main research interests include mechanics of piezoelectric solids with defects and wave propagation in piezoelectric-piezomagnetic composites.
Tel: +86-311-87936682; E-mail: liujx02@hotmail.com
 

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