Abstract
A finite crack under transient anti-plane shear loads in a functionally graded piezoelectric material (FGPM) bonded to a homogeneous piezoelectric strip is considered. It is assumed that the electroelastic material properties of the FGPM vary continuously according to exponential functions along the thickness of the strip, and that the two layered strips is under combined anti-plane shear mechanical and in-plane electrical impact loads. The analysis is conducted on the electrically unified crack boundary condition. Laplace and Fourier transforms are used to reduce the mixed boundary value problems to Fredholm integral equations of the second kind in the Laplace transform domain. Then, a numerical Laplace inversion is performed and the dynamic intensities are obtained as functions of time and geometric parameters, which are displayed graphically.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bleustein, J.L. (1968). A new surface wave in piezoelectric materials. Applied Physics Letters 13, 412-413.
Copson, E.T. (1961). On certain dual integral equations. Proceedings of the Glasgow Mathematical Association 5, 19-24.
Erdogan, F. (1985). The crack problem for bonded nonhomogeneous materials under antiplane shear loading. Journal of Applied Mechanics, Transactions of ASME 52, 823-828.
Jin, Z.-H. and Batra, R.C. 1996. Some basic fracture mechanics concepts in functionally graded materials. Journal of the Mechanics and Physics of Solids 44, 1221-1235.
Jin, B. and Zhong, Z. (2002). A moving mode-III crack in functionally graded piezoelectric material: permeable problem. Mechanics Research Communications 29, 217-224.
Kwon, S.M., Son, M.S. and Lee, K.Y. (2002). Transient behavior in a cracked piezoelectric layered composite: anti-plane problem. Mechanics of Materials 34, 593-603.
Li, C. and Weng, G.J. (2002). Antiplane crack problem in functionally graded piezoelectric materials. Journal of Applied Mechanics, Transactions of ASME 69, 481-488.
Lim, C.W. and He, L.H. (2001). Exact solution of a compositionally graded piezoelectric layer under uniform stretch, bending and twisting. International Journal of Mechanical Science 43, 2479-2492.
Meguid, S.A., Wang, X.D. and Jiang, L.Y. (2002). On the dynamic propagation of a finite crack in functionally graded materials. Engineering Fracture Mechanics 69, 1753-1768.
Miller, M.K. and Guy, W.T. (1966). Numerical inversion of the Laplace transform by use of Jacobi polynomials. SIAM Journal on Numerical Analysis 3, 624-635.
Shelley, W.F., Wan, S. and Bowman, K.J. (1999). Functionally graded piezoelectric ceramics. Materials Science Forum 308-311, 515-520.
Sneddon, I.N. (1972). The Use of Integral Transforms, McGraw-Hill Book Company, New York.
Wu, C.M., Kahn, M. and Moy, W. (1996). Piezoelectric ceramics with functional gradients: a new application in material design. Journal of the American Ceramic Society 79, 809-812.
Xu, X.L. and Rajapakse, R.K.N.O. (2001). On a plane crack in piezoelectric solids. International Journal of Solids and Structures 38, 7643-7658.
Yamada, K., Sakamura, J. and Nakamura, K. (2000). Equivalent network representation for thickness vibration modes in piezoelectric plates with an exponentially graded parameter. Japanese Journal of Applied Physics 39, L34-L37.
Zhu, X., Wang, Q. and Meng, Z. (1995). A functionally gradient piezoelectric actuator prepared by power metallurgical process in PNN-PZ-PT system. Journal of Materials Science Letters 14, 516-518.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kwon, S.M. Impact response of an anti-plane crack in a FGPM bonded to a homogeneous piezoelectric strip. International Journal of Fracture 123, 187–208 (2003). https://doi.org/10.1023/B:FRAC.0000007377.73716.34
Issue Date:
DOI: https://doi.org/10.1023/B:FRAC.0000007377.73716.34