Closed-form solution for piezoelectric layer with two collinear cracks parallel to the boundaries

Singh, B. M.; Rokne, J.; Dhaliwal, R. S.

doi:https://doi.org/10.1155/MPE/2006/91846

Mathematical Problems in Engineering

On this page

Abstract References Copyright Related Articles

Open Access

Volume 2006 | Article ID 091846 | https://doi.org/10.1155/MPE/2006/91846

Closed-form solution for piezoelectric layer with two collinear cracks parallel to the boundaries

B. M. Singh,¹J. Rokne,¹and R. S. Dhaliwal^1,2

Received06 Feb 2005

Revised16 Nov 2005

Accepted26 Mar 2006

Published11 May 2006

Abstract

We consider the problem of determining the stress distribution in an infinitely long piezoelectric layer of finite width, with two collinear cracks of equal length and parallel to the layer boundaries. Within the framework of reigning piezoelectric theory under mode III, the cracked piezoelectric layer subjected to combined electromechanical loading is analyzed. The faces of the layers are subjected to electromechanical loading. The collinear cracks are located at the middle plane of the layer parallel to its face. By the use of Fourier transforms we reduce the problem to solving a set of triple integral equations with cosine kernel and a weight function. The triple integral equations are solved exactly. Closed form analytical expressions for stress intensity factors, electric displacement intensity factors, and shape of crack and energy release rate are derived. As the limiting case, the solution of the problem with one crack in the layer is derived. Some numerical results for the physical quantities are obtained and displayed graphically.

References

R. S. Dhaliwal, B. M. Singh, and D. S. Chehil, “Two coplanar Griffith cracks under shear loading in an infinitely long elastic layer,” Engineering Fracture Mechanics, vol. 23, no. 4, pp. 695–704, 1986.
View at: Publisher Site | Google Scholar
I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, Academic Press, New York, 1980.
View at: Google Scholar | Zentralblatt MATH | MathSciNet
S. M. Kwon and K. Y. Lee, “Analysis of stress and electric fields in a rectangular piezoelectric body with a center crack under anti-plane shear loading,” International Journal of Solids and Structures, vol. 37, no. 35, pp. 4859–4869, 2000.
View at: Publisher Site | Google Scholar | Zentralblatt MATH
X.-F. Li and X.-Y. Duan, “Closed-form solution for a mode-III crack at the mid-plane of a piezoelectric layer,” Mechanics Research Communications, vol. 28, no. 6, pp. 703–710, 2001.
View at: Publisher Site | Google Scholar | Zentralblatt MATH
Y. E. Pak, “Crack extension force in a piezoelectric materials,” Journal of Applied Mechanics, vol. 57, no. 3, pp. 647–653, 1990.
View at: Google Scholar | Zentralblatt MATH
Y. E. Pak, “Linear electro-elastic fracture mechanics of piezoelectric materials,” International Journal of Fracture, vol. 54, pp. 79–100, 1992.
View at: Google Scholar
S. B. Park and C. T. Sun, “Effect of electric field on fracture of piezoelectric ceramics,” International Journal of Fracture, vol. 70, no. 3, pp. 203–216, 1995.
View at: Publisher Site | Google Scholar
J. W. Shin, S. M. Kwon, and K. Y. Lee, “Eccentric crack in a piezoelectric strip under electromechanical loading,” Journal of Applied Mechanics, vol. 67, no. 4, pp. 846–847, 2000.
View at: Publisher Site | Google Scholar
Y. Shindo, F. Narita, and K. Tanaka, “Electroelastic intensification near anti-plane shear crack in orthotropic piezoelectric ceramic strip,” Theoretical and Applied Fracture Mechanics, vol. 25, no. 1, pp. 65–71, 1996.
View at: Publisher Site | Google Scholar
Y. Shindo, K. Tanaka, and F. Narita, “Singular stress and electric fields of a piezoelectric ceramic strip with a finite crack under longitudinal shear,” Acta Mechanica, vol. 120, no. 1–4, pp. 31–45, 1997.
View at: Publisher Site | Google Scholar | Zentralblatt MATH
P.-Y. Zhang and P. Tong, “Fracture mechanics for a mode III crack in a piezoelectric material,” International Journal of Solids and Structures, vol. 33, no. 3, pp. 343–359, 1996.
View at: Publisher Site | Google Scholar | Zentralblatt MATH

Copyright

Copyright © 2006 B. M. Singh et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

PDF Download Citation Order printed copies

Views

225

Downloads

742

Citations