DOI QR코드

DOI QR Code

Green's Function of Edge Crack in Transversely Isotropic Piezoelectric Material Under Anti-Plane Loads

횡등방 압전재료의 면외하중 모서리 균열에 대한 그린함수

  • 최성렬 (영남대학교 기계공학부)
  • Published : 2008.01.01

Abstract

Surface edge crack in transversely isotropic piezoelectric material is analyzed. The concentrated antiplane mechanical and inplane electrical loadings are applied to an arbitrary point of the surface, where the impermeable crack boundary condition is imposed. Using Mellin transform the problem is formulated, from which Wiener-Hopf equations are derived. By solving the equations the solution is obtained in a closed form. Mechanical and electric intensity factors and energy release rate are obtained and discussed. This problem could be used as a Green's function to generate the solutions of other problems with the same geometry but of different loading conditions.

Keywords

Piezoelectric Material;Anti-Plane Shear;Electric Displacement;Intensity Factor

References

  1. Parton, V. Z., 1976, 'Fracture Mechanics of Piezoelectric Materials,' Acta Astronautica, Vol. 3, pp. 671-683 https://doi.org/10.1016/0094-5765(76)90105-3
  2. Pak, Y. E., 1990, 'Crack Extension Force in a Piezoelectric Materials,' Journal of Applied Mechanics, Vol. 57, pp. 647-653 https://doi.org/10.1115/1.2897071
  3. Suo, Z., Kuo, C.M., Barnet, D.M., Willis, J.R., 1992, 'Fracture Mechanics for Piezoelectric Ceramics,' Journal of Mechanics and Physics of Solids, Vol. 57, pp. 647-653
  4. Wang, B.L., Mai, Y.-W., 2002, 'A Piezoelectric Material Strip with a Crack Perpendicular to its Boyundary Surfaces,' International Journal of Solids and Structures, Vol. 39, pp. 4501-4524 https://doi.org/10.1016/S0020-7683(02)00378-5
  5. Pak, Y. E., 1992, 'Linear Electro-elastic Fracture Mechanics of Piezoelectric Materials,' Int. J. Frac., Vol. 54, pp. 79-100 https://doi.org/10.1007/BF00040857
  6. Sosa, H. A. and Pak, Y. E., 1990, 'Three -Dimensional Eigenfunction Analysis of a Crack in a Piezoelectric Material,' Int. J. Solids Structures, Vol. 26, No.1, pp. 1-15 https://doi.org/10.1016/0020-7683(90)90090-I
  7. Park, S.B. and Sun, C.T., 1995, 'Effect of Electric Field on Fracture of Piezoelectric Ceramics,' International Journal of Fracture, Vol. 70, pp. 203-216 https://doi.org/10.1007/BF00012935
  8. Zhang, T. -Y and Tong, P., 1996, 'Fracture Mechanics for a Mode III Crack in a Piezoelectric Material,' Int. J. Solids Structures, Vol. 33, No.3, pp. 343-359 https://doi.org/10.1016/0020-7683(95)00046-D
  9. Zhang, T.Y and Hack, J.E., 1992, 'Mode-III Cracks in Piezoelectric Materiasl,' J. Appl. Phys., Vol. 71, No.12, pp. 5865-5870 https://doi.org/10.1063/1.350483
  10. Gao, C.-F.and Fan, W.-X., 1999, 'A General Solution for the Plane Problem in Piezoelectric Media with Collinear Cracks,' International Journal of Engineering Science, Vol. 37, pp. 347-363 https://doi.org/10.1016/S0020-7225(98)00067-6
  11. Kwon, J. H., Kwon, S. M., Shin, J. W. and Lee, K. Y., 2000, 'Determination of Intensity Factors in Piezoelectric Ceramic Strip with Impermeable Crack,' Trans. of the KSME(A), Vol. 24, No. 6, pp. 1601-1607
  12. 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,' Int. J. Solids Structures, Vol. 37, pp. 4859-4869 https://doi.org/10.1016/S0020-7683(99)00186-9
  13. Shin, J. W., Kwon, S. M. and Lee, K. Y., 2001, 'Eccentric Crack in a Piezoelectric Strip Under Electro-Mechanical Loading,' KSME International Journal, Vol. 15, No. 1, pp. 21-25 https://doi.org/10.1007/BF03184794
  14. Shindo, Y., Narita, F. and Tanaka, K., 1996, 'Electroelastic Intensification Near Anti-Plane Shear Crack in Orthotropic Piezoelectric Ceramic Strip,' Theoretical and Applied Fracture Mechanics, Vol. 25, pp. 65-71 https://doi.org/10.1016/0167-8442(96)00008-0
  15. Kwon, J. H., 2004, 'Central Crack in a Piezoelectric Disc,' KSME International Journal, Vol. 18, No. 9, pp. 1549-1558
  16. Liu, W.-J. and Chu, C.-H., 2007, 'Electroelastic Analysis of a Piezoelectric Finite Wedge with Mixed Type Boundary Conditions Under a Pair of Concentrated Shear Forces and free Charges,' Theoretical and Applied Fracture Mechanics, Vol. 48, pp. 203-224 https://doi.org/10.1016/j.tafmec.2007.08.006
  17. Choi, S. T. and Earmme, Y. Y., 1998, 'Antiplane Problem of Interfacial Circular-Arc Cracks in Transversely Isotropic Piezoelectric Media,' Trans. of the KSME(A), Vol. 22, No. 5, pp. 868-876
  18. Choi, S. R., 2007, 'Green's Function of Cracks in Piezoelectric Materials,' Trans. of the KSME, Vol. 31, No. 9, pp. 967-974 https://doi.org/10.3795/KSME-A.2007.31.9.967
  19. Noble, B., 1958, Methods Based on the Wiener-Hopf Technique, Pergamon Press, London
  20. Choi, S.R. and Earmme, Y.Y., 1990, 'Analysis of a Kinked Crack in Anti-Plane Shear,' Mechanics of Materials, Vol. 9, pp. 195-294 https://doi.org/10.1016/0167-6636(90)90002-W
  21. Choi, S. R., 1993, 'Analysis of Interfacial Surface Crack Perpendicular to the Surface,' Trans. of the KSME, Vol. 17, No. 2, pp. 277-284
  22. Tada, H., Paris, P. and Irwin, G., 1973, Methods The Stress Analysis of Crack Handbook, Del Research Corp., Hellertown

Cited by

  1. Inclined Edge Crack in a Piezoelectric Material Under Antiplane Loads vol.39, pp.6, 2015, https://doi.org/10.3795/KSME-A.2015.39.6.589
  2. A Permeable Wedge Crack in a Piezoelectric Material Under Antiplane Deformation vol.39, pp.9, 2015, https://doi.org/10.3795/KSME-A.2015.39.9.859
  3. Asymmetric impermeable wedge crack in a piezoelectric material under anti-plane deformation vol.32, pp.10, 2018, https://doi.org/10.1007/s12206-018-0924-z