균열을 가진 압전재료에서의 가중함수이론

Weight Function Theory for Piezoelectric Materials with a Crack

  • 손인호 (부산대학교 기계설계공학과) ;
  • 안득만 (부산대학교 기계공학부, 기계기술연구소)
  • 발행 : 2003.07.01

초록

In this paper, a two-dimensional electroelastic analysis is performed on a piezoelectric material with an open crack. The approach of Lekhnitskii's complex potential functions is used in the derivation and Bueckner's weight function theory is extended to piezoelectric materials. The stress intensity factors and the electric displacement intensity factor are calculated by the weight function theory.

키워드

참고문헌

  1. Ting, T. C. T., Anisotropic Elasticity Theory and Applications, Oxford University Press, 1996
  2. Pak, Y., 'Linear electro-elastic fracture mechanics of piezoelectric materials,' Int. J. of Fracture, Vol. 54, pp. 79-100, 1992 https://doi.org/10.1007/BF00040857
  3. Suo, Z., Kuo, C.-M., Barnett, D. M. and Willis, J. R., 'Fracture mechanics for piezoelectric ceramics,' J. of the Mechanics and Physics of Solids, Vol. 40, pp. 739-765, 1992 https://doi.org/10.1016/0022-5096(92)90002-J
  4. Beom, H. G. and Atluri, S. N., 'Near-tip fields and intensity factors for interfacial cracks in dissimilar anisotropic piezoelectric media,' Int. J. of Fracture, Vol. 75, pp. 163-183, 1996 https://doi.org/10.1007/BF00034075
  5. Deng, W. and Meguid, S., 'Analysis of conducting rigid inclusion at the interface of two dissimilar piezoelectric materials,' J. of Applied Mechanics, Vol. 65, pp. 76-84, 1998 https://doi.org/10.1115/1.2789049
  6. Wang, T. C. and Han, X. L., 'Fracture mechanics of Piezoelectric materials,' Int. J. of Fracture, Vol. 98, pp. 15-35, 1999
  7. Ma, L. and Chen, Y., 'Weight functions for interface cracks in dissimilar anisotropic piezoelectric materials,' Int. J. of Fracture, Vol. 110, pp. 263-279, 2001 https://doi.org/10.1023/A:1010805704212
  8. Lekhitskii, S., Theory of Elasticity of an Anisotropic Elastic Body, Holden-Day Inc., San Francisco, 1963
  9. Sosa, H., 'Plane problems in piezoelectric media with defects,' Int. J. of Solids and Structures, Vol. 28, pp. 491-505, 1991 https://doi.org/10.1016/0020-7683(91)90061-J
  10. Sosa, H., 'On the fracture mechanics of piezoelectric solids,' Int. J. of Solids and Structures, Vol. 29, pp. 2613-2622, 1992 https://doi.org/10.1016/0020-7683(92)90225-I
  11. Gao, C. and Fan, W., 'Exact solutions for the plane problem in piezoelectric materials with an elliptic or a crack,' Int. J. of Solids and Structures, Vol. 36, pp. 2527-2540, 1999 https://doi.org/10.1016/S0020-7683(98)00120-6
  12. Xu, X. and Rajapakse, R., 'A theoretical study of branched cracks in piezoelectrics,' Acta. Materialia, Vol. 48, pp. 1865-1882, 2000 https://doi.org/10.1016/S1359-6454(99)00469-3
  13. Xu, X. and Rajapakse, R., 'On a plane crack in piezoelectric solids,' Int. J. of Solids and Structures, Vol. 38, pp. 7643-7658, 2001 https://doi.org/10.1016/S0020-7683(01)00029-4
  14. Nye, J., Physical Properties of Crystals, Oxford University Press, 1957
  15. Qin, Q., Fracture Mechanics of Piezoelectric Materials, WIT Press, 2001
  16. Pak, Y., 'Crack Extension Force in a Piezoelectric Material,' J. of Applied Mechanics, Vol. 57, pp. 647-653, 1990 https://doi.org/10.1115/1.2897071
  17. Muskhelishvili, N., Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff International Publishing, 1977
  18. Liu, Y. and Fan, H., 'On the conventional boundary integral equation formulation for piezoelectric solids with defects or of thin shapes,' Eng. Analysis with boundary Elements, Vol. 25, pp. 77 -91, 2001 https://doi.org/10.1016/S0955-7997(01)00004-2
  19. Parton and Kudryavtsev, Electromagnetoelasticity Piezoelectrics and Electrically Conductive Solids, Gordon and Breach Science Publishers, 1988
  20. An, D., 'Weight function theory for a rectilinear anisotropic body,' Int. J. of Fracture, Vol. 34, pp. 85-109, 1987 https://doi.org/10.1007/BF00019766
  21. Elastic, piezoelectric, pyroelectric, piezooptic, electrooptic constants, and nonlinear dielectric susceptibilities of crystals, Berlin:Springer-Verlag, 1979