A semi-permeable interface crack in dissimilar piezoelectric materials is studied in detail. Attention is focused on the influence induced from the permittivity of the medium inside the crack gap on the near-tip singularity and the crack tip energy release rate (ERR). The Stroh complex variable theory (Stroh, A. N., 1958, Philos. Mag. 3, pp. 625–646;Ting, T. C. T., Int. J. Solids Struct., 22, pp. 965–983) is used to obtain the solution, from which some useful numerical results for 21 kinds of dissimilar piezoelectric materials are calculated. They are combined from seven kinds of commercial piezoelectric ceramics. The distribution of the normal electric displacement component (NEDC) along the interface crack is assumed to be uniform and the corresponding problem is then deduced to a Hilbert problem with an unknown NEDC. Solving the Hilbert problem and determining the near-tip field for each of the 21 bimaterials, we determine the crack tip singularities and find that the crack-tip singularity for a certain combination of two dissimilar piezoelectric materials can be either oscillatory or nonoscillatory when the poling axes of both piezoelectric materials are perpendicular to the interface crack. Energy analyses for as a typical nonoscillatory class bimaterial and those for as a typical oscillatory class bimaterial are specially studied in detail under four different conditions: (i) the crack gap is filled with air or vacuum; (ii) the crack gap is filled with silicon oil to avoid discharge; (iii) the crack gap is conducting; and (iv) the electrically impermeable crack. Detailed comparisons are performed among the four cases. We conclude that the different values of the permittivity have no influence on the crack tip singularity but have significant influences on the crack tip ERR under the combined electromechanical loading. We also conclude that the previous investigations under the insulating crack model are incorrect or misleading since the model overestimates the effect of the electric field on the ERR very much and the results of the ERR for the impermeable crack show significant discrepancies from those for the semi-permeable crack. Whereas the previous investigations under the conducting crack model may be accepted in a tolerant, way, the results of the ERR show very small discrepancies from those for the semi-permeable crack model, especially when it filled with silicon oil.
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September 2007
Technical Papers
Solution for a Semi-Permeable Interface Crack Between Two Dissimilar Piezoelectric Material
Q. Li,
Q. Li
School of Aerospace,
Xian Jiao-Tong University
, Xian City 710049, P.R. China
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Y. H. Chen
Y. H. Chen
School of Aerospace,
e-mail: yhchen2@mail.xjtu.edu.cn
Xian Jiao-Tong University
, Xian City 710049, P.R. China
Search for other works by this author on:
Q. Li
School of Aerospace,
Xian Jiao-Tong University
, Xian City 710049, P.R. China
Y. H. Chen
School of Aerospace,
Xian Jiao-Tong University
, Xian City 710049, P.R. Chinae-mail: yhchen2@mail.xjtu.edu.cn
J. Appl. Mech. Sep 2007, 74(5): 833-844 (12 pages)
Published Online: September 27, 2006
Article history
Received:
April 28, 2006
Revised:
September 27, 2006
Citation
Li, Q., and Chen, Y. H. (September 27, 2006). "Solution for a Semi-Permeable Interface Crack Between Two Dissimilar Piezoelectric Material." ASME. J. Appl. Mech. September 2007; 74(5): 833–844. https://doi.org/10.1115/1.2711232
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