Previous studies assumed that a crack is either impermeable or permeable, which are actually two limiting cases of a dielectric crack. This paper considers the electroelastic problem of a three-dimensional transversely isotropic piezoelectric material with a penny-shaped dielectric crack perpendicular to the poling axis. Using electric boundary conditions controlled by the boundaries of an opening crack, the electric displacements at the crack surfaces are determined. The Hankel transform technique is employed to reduce the considered problem to dual integral equations. By solving resulting equations, the results are presented for the case of remote uniform loading, and explicit expressions for the electroelastic field at any point in the entire piezoelectric body are given in terms of elementary functions. Moreover, the distribution of asymptotic field around the crack front and field intensity factors are determined. Numerical results for a cracked PZT-5H ceramic are evaluated to examine the influence of the dielectric permittivity of the crack interior on the field intensity factors, indicating that the electric boundary conditions at the crack surfaces play an important role in determining electroelastic field induced by a crack, and that the results are overestimated for an impermeable crack, and underestimated for a permeable crack.
Three-Dimensional Electroelastic Analysis of a Piezoelectric Material With a Penny-Shaped Dielectric Crack
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the Applied Mechanics Division, September 3, 2003; final revision, March 17, 2004. Associate Editor: H. Gao. Discussion on the paper should be addressed to the Editor, Prof. Robert M. McMeeking, Journal of Applied Mechanics, Department of Mechanical and Environmental Engineering, University of California—Santa Barbara, Santa Barbara, CA 93106-5070, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
Li, X., and Lee, K. Y. (January 27, 2005). "Three-Dimensional Electroelastic Analysis of a Piezoelectric Material With a Penny-Shaped Dielectric Crack ." ASME. J. Appl. Mech. November 2004; 71(6): 866–878. https://doi.org/10.1115/1.1795219
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