A permeable crack model is proposed to analyze crack growth in a piezoelectric ceramic. In this model, a permeable crack is modeled as a vanishing thin, finite dimension, rectangular slit with dielectric medium inside. A first-order approximation solution is derived in terms of the slit height, The main contribution of this paper is that the newly proposed permeable crack model reveals that there exists a realistic leaky mode for electrical field, which allows applied electric field passing through the dielectric medium inside a crack. By taking into account the leaky mode effect, a correct estimation of electrical and mechanical fields in front of a crack tip in a piezoelectric ceramic is obtained. To demonstrate this new finding, a closed-form solution is obtained for a mode III permeable crack under both mechanical as well electrical loads. Both local and global energy release rates are calculated based on the permeable crack solution obtained. It is found that the global energy release rate derived for a permeable crack is in a broad agreement with some known experimental observations. It may be served as a fracture criterion for piezoelectric materials. This contribution reconciles the outstanding discrepancy between experimental observation and theoretical analysis on crack growth problem in piezoelectric materials.
On Global Energy Release Rate of a Permeable Crack in a Piezoelectric Ceramic
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 ASME Applied Mechanics Division, Mar. 28, 2002; final revision, Aug. 26, 2002. Associate Editor: H. Gao. Discussion on the paper should be addressed to the Editor, Prof. Robert M. McMeeking, 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.
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Li, S. (March 27, 2003). "On Global Energy Release Rate of a Permeable Crack in a Piezoelectric Ceramic ." ASME. J. Appl. Mech. March 2003; 70(2): 246–252. https://doi.org/10.1115/1.1544539
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