Journal of Mechanical Science and Technology

The Korean Society of Mechanical Engineers (대한기계학회)
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Transient Response of a Permeable Crack Normal to a Piezoelectric-elastic Interface: Anti-plane Problem

  • Kwon, Soon-Man (Department of Mechanical Design ＆ Manufacturing, Changwon National University) ;
  • Lee, Kang-Yong (School of Mechanical Engineering, Yonsei University)
  • Published : 2004.09.01
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Abstract

In this paper, the anti-plane transient response of a central crack normal to the interface between a piezoelectric ceramics and two same elastic materials is considered. The assumed crack surfaces are permeable. By virtue of integral transform methods, the electro elastic mixed boundary problems are formulated as two set of dual integral equations, which, in turn, are reduced to a Fredholm integral equation of the second kind in the Laplace transform domain. Time domain solutions are obtained by inverting Laplace domain solutions using a numerical scheme. Numerical values on the quasi-static stress intensity factor and the dynamic energy release rate are presented to show the dependences upon the geometry, material combination, electromechanical coupling coefficient and electric field.

Keywords

References

  1. Bleustein, J. L., 1968, 'A New Surface Wave in Piezoelectric Materials,' Applied Physics Letters, Vol. 13, pp.412-413 https://doi.org/10.1063/1.1652495
  2. Chen, Z. T., 1998, 'Crack Tip Field of an Infinite Piezoelectric Strip Under Anti-plane Impact,' Mechanics Research Communications, Vol. 25, pp.313-319 https://doi.org/10.1016/S0093-6413(98)00043-3
  3. Chen, Z. T. and Karihaloo, B. L., 1999, 'Dynamic Response of a Cracked Piezoelectric Ceramic Under Arbitrary Electro-Mechanical Impact,' International Journal of Solids and Structures, Vol. 36, pp. 5125-5133 https://doi.org/10.1016/S0020-7683(98)00243-1
  4. Chen, Z. T. and Meguid, S. A., 2000, 'The Transient Response of a Piezoelectric Strip with a Vertical Crack Under Electromechanical Impact Load,' International Journal of Solids and Structures, Vol. 37, pp. 6051-6062 https://doi.org/10.1016/S0020-7683(99)00259-0
  5. Chen, Z. T. and Yu, S. W., 1997, 'Anti-plane Dynamic Fracture Mechanics in Piezoelectric Materials,' International Journal of Fracture, Vol. 85, pp. L3-Ll2
  6. Chen, Z. T. and Yu, S. W., 1998, 'Anti-plane Vibration of Cracked Piezoelectric Materials,' Mechanics Research Communications, Vol. 25, pp. 321-327 https://doi.org/10.1016/S0093-6413(98)00044-5
  7. Copson, E. T., 1961, 'On certain Dual Integral Equations,' Proceedings of the Glasgow Mathematical Association, Vol. 5, pp. 19-24
  8. Crawley, E. F., 1994, 'Intelligent Structures for Aerospace: a Technology Overview and Assessment,' AIAA Journal, Vol. 25, pp. 1373-1385
  9. Kwon, S. M. and Lee, K. Y., 2000, '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, pp. 4859-4869 https://doi.org/10.1016/S0020-7683(99)00186-9
  10. Kwon, S. M. and Lee, K. Y., 2001, 'Transient Response of a Rectangular Piezoelectric Medium with a Center Crack,' European Journal of Mechanics, Vol. 20, pp.447-468 https://doi.org/10.1016/S0997-7538(01)01137-8
  11. Kwon, S. M. and Lee, K. Y., 2004, 'Dynamic Response of an Anti-plane Shear Crack in a Functionally Graded Piezoelectric Strip,' KSME International Journal, Vol. 18, pp. 419-431
  12. Kwon, J. H. and Meguid, S. A., 2002, 'Analysis of a Central Crack Normal to a Piezoelectric-Orthotropic Interface,' International Journal of Solids and Structures, Vol. 39, pp. 841-860 https://doi.org/10.1016/S0020-7683(01)00252-9
  13. Li, X. F. and Fan, T. Y., 2002, 'Transient Analysis of a Piezoelectric Strip with a Permeable Crack Under Anti-plane Impact Loads,' International Journal of Engineering Science, Vol. 40, pp. 131-143 https://doi.org/10.1016/S0020-7225(01)00039-8
  14. Meguid S. A. and Wang X. D., 1998, 'Dynamic Antiplane Behaviour of Interacting Cracks in a Piezoelectric Medium,' International Journal of Fracture, Vol. 91, pp.391-403 https://doi.org/10.1023/A:1007521018293
  15. Miller, M. K. and Guy, W. T., 1966, 'Numerical Inversion of the Laplace Transform by Use of Jacobi Polynomials,' SIAM Journal on Numerical Analysis, Vol. 3, pp.624-635 https://doi.org/10.1137/0703055
  16. Park, S. B. and Sun, C. T., 1995a, 'Effect of Electric Field on Fracture of Piezoelectric Ceramics,' International Journal of Fracture, Vol. 70, pp.203-216 https://doi.org/10.1007/BF00012935
  17. Park, S. B. and Sun, C. T., 1995b, 'Fracture Criteria for Piezoelectric Ceramics,' Journal of the American Ceramic Society, Vol. 78, pp. 1475-1480
  18. Romeo, M., 2001, 'A Solution for Transient Surface Waves of the B-G Type in a Dissipative Piezoelectric Crystal,' ZAMP, Vol. 52, pp.730-748 https://doi.org/10.1007/PL00001571
  19. Shin, J. W., Kwon, S. M. and Lee, K. Y., 2001, 'An Eccentric Crack in a Piezoelectric Strip Under Anti-plane Shear Impact Loading,' International Journal of Solids and Structures, Vol. 38, pp. 1483-1494 https://doi.org/10.1016/S0020-7683(00)00097-4
  20. Shindo, Y., Tanaka, K. and Narita, F., 1997, 'Singular Stress and Electric Fields of a Piezoelectric Ceramic Strip with a Finite Crack Under Longitudinal Shear,' Acta Mechanica, Vol. 120, pp.1-15 https://doi.org/10.1007/BF01174314
  21. Sih, G. C. and Chen, E. P., 1981, Mechanics of Fracture 6: Cracks in Composite Materials. Edited by Sih, G., Noordhoff International Publishing, The Hague, pp. 213-218
  22. Sneddon, I. N., 1972, The Use of Integral Transforms. McGraw-Hill Book Company
  23. The Use of Integral Transforms Sneddon, I. N.