Anisotropic-Asymmetric Yield Criterion and Anisotropic Hardening Law for Composite Materials: Theory and Formulations

  • Kim Ji-Hoon (School of Materials Science and Engineering, Seoul National University) ;
  • Lee Myoung-Gyu (Department of Materials Science and Engineering, Ohio State University) ;
  • Chung Kwan-Soo (School of Materials Science and Engineering, Seoul National University) ;
  • Youn Jae-Ryoun (School of Materials Science and Engineering, Seoul National University) ;
  • Kang Tae-Jin (School of Materials Science and Engineering, Seoul National University)
  • Published : 2006.03.01

Abstract

In this paper, elasto-plastic constitutive equations for highly anisotropic and asymmetric materials are developed and their numerical implementation is presented. Some engineering materials such as fiber reinforced composites show different material behavior in the different material directions (anisotropy) as well as in tension and compression (asymmetry). Although these materials have mostly been analyzed using the anisotropic elastic constitutive equations, the necessity of consideration of plastic properties has been frequently reported in the previous works. In order to include both the anisotropic and asymmetric properties of composite materials, the Drucker-Prager yield criterion is modified by adding anisotropic parameters and initial components of translation. The implementation procedure for the developed theory and algorithms is presented based on the implicit finite element scheme. The measured data from the previous work are used to validate the present constitutive equations.

Keywords

References

  1. W. Lee, J. H. Kim, H.-J. Shin, K. Chung, T. J. Kang, and J. R. Youn, Fibers and Polymers, 4, 77 (2003) https://doi.org/10.1007/BF02875441
  2. M. R. Piggot and B. Harris, J. Mater. Sci., 15, 2523 (1980) https://doi.org/10.1007/BF00550757
  3. N. L. Hancox, J. Mater Sci., 10, 234 (1975) https://doi.org/10.1007/BF00540347
  4. M. G. Lee, K. Chung, C. J. Lee, J. H. Park, J. Kim, T. J. Kang, and J. R. Youn, Composites Science and Technology, 61, 2491 (2001) https://doi.org/10.1016/S0266-3538(01)00172-5
  5. A. F. Saleeb, T. E. Wilt, N. R. Al-Zoubi, and A. S. Gendy, Composites Part B, 34, 21 (2003) https://doi.org/10.1016/S1359-8368(02)00078-1
  6. B. D. Agarwal and L. J. Broutman, 'Analysis and Performance of Fiber Composites', John Wiley & Sons, NY, 1980
  7. A. S. Khan and S. Huang, 'Continuum Theory of Plasticity', John Wiley & Sons, NY, 1995
  8. R. Hill, 'The Mathematical Theory of Plasticity', Oxford University Press, NY, 1956
  9. F. Barlat, D. J. Lege, and J. C. Brem, International Journal of Plasticity, 7, 693 (1991) https://doi.org/10.1016/0749-6419(91)90052-Z
  10. F. Barlat, J. C. Brem, J. W. Yoon, K. Chung, R. E. Dick, S.-H. Choi, F. Pourboghrat, E. Chu, and D. J. Lege, International Journal of Plasticity, 19, 1297 (2003) https://doi.org/10.1016/S0749-6419(02)00019-0
  11. A. R. Leewood, J. F. Doyle, and C. T. Sun, Comput. Struct., 25, 749 (1987) https://doi.org/10.1016/0045-7949(87)90166-0
  12. L. P. Isupov and Yu. N. Rabotnov, Izv. AN SSSR MTT, 1, 121 (1985)
  13. B. S. Sarbayev, Computational Materials Science, 6, 211 (1991) https://doi.org/10.1016/0927-0256(96)00009-2
  14. M. G. Lee, D. Kim, K. Chung, J. R. Youn, and T. J. Kang, Polymer and Polymer Composites, 12, 225 (2004)
  15. J. L. Chaboche, International Journal of Plasticity, 2, 149 (1986) https://doi.org/10.1016/0749-6419(86)90010-0
  16. R. M. Jones, 'Mechanics of Composite Materials', McGraw-Hill, NY, 1975
  17. K. Chung, M.-G. Lee, D. Kim, C. Kim, M. L. Wenner, and F. Barlat, International Journal of Plasticity, 21, 861 (2005)
  18. S. W. Tsai and E. M. Wu, J. Comp. Mater., 5, 58 (1971) https://doi.org/10.1177/002199837100500106
  19. J. W. Yoon, D. Y. Yang, and K. Chung, Computer Methods in Applied Mechanics and Engineering, 174, 23 (1999) https://doi.org/10.1016/S0045-7825(98)00275-8
  20. J. C. Simo and T. J. R. Hughes, 'Computational Inelasticity', Springer-Verlag, N.Y., U.S.A., 1997
  21. Hibbitt, Karlsson and Sorensen, 'ABAQUS User's Manual', Version 6.2.6., 2001
  22. D. Lee and W. A. Backofen, Trans. Metall. Soc. AIME, 236 (1966)