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Metallurgical and Materials Transactions A

, Volume 43, Issue 11, pp 4266–4280 | Cite as

A Microstructure-Based Constitutive Model for Superplastic Forming

  • Reza Jafari Nedoushan
  • Mahmoud Farzin
  • Mohammad Mashayekhi
  • Dorel BanabicEmail author
Article

Abstract

A constitutive model is proposed for simulations of hot metal forming processes. This model is constructed based on dominant mechanisms that take part in hot forming and includes intergranular deformation, grain boundary sliding, and grain boundary diffusion. A Taylor type polycrystalline model is used to predict intergranular deformation. Previous works on grain boundary sliding and grain boundary diffusion are extended to drive three-dimensional macro stress–strain rate relationships for each mechanism. In these relationships, the effect of grain size is also taken into account. The proposed model is first used to simulate step strain-rate tests and the results are compared with experimental data. It is shown that the model can be used to predict flow stresses for various grain sizes and strain rates. The yield locus is then predicted for multiaxial stress states, and it is observed that it is very close to the von Mises yield criterion. It is also shown that the proposed model can be directly used to simulate hot forming processes. Bulge forming process and gas pressure tray forming are simulated, and the results are compared with experimental data.

Keywords

Flow Stress Constitutive Model Slip System Material Point Stress Exponent 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

The DB work was supported by the Romanian National University Research Council (CNCSIS), Program PCCE, Grant No. 6/2010.

References

  1. 1.
    A.J. Barnes: J. Mater. Eng. Perform., 2007, vol. 16, pp. 440–54.CrossRefGoogle Scholar
  2. 2.
    H.L. Xing, C.W. Wang, K.F. Zhang, and Z.R. Wang: J. Mater. Process. Tech., 2004, vol. 151, pp. 196–202.CrossRefGoogle Scholar
  3. 3.
    J. Bonet, A. Gil, R.D. Wood, R. Said, and R.V. Curtis: Comput. Meth. Appl. Mech. Eng., 2006, vol. 195, pp. 6580–6603.CrossRefGoogle Scholar
  4. 4.
    M.T. Eric, L. Hector, R. Verma, P. Krajewski, and J.-K. Chang: J. Mater. Eng. Perform., 2010, vol. 19, pp. 488–94.CrossRefGoogle Scholar
  5. 5.
    O.D. Sherby and J. Wadsworth: Progr. Mater. Sci., 1989, vol. 33, pp. 169–221.CrossRefGoogle Scholar
  6. 6.
    M.A. Khaleel, K.I. Johnson, C.H. Hamilton, and M.T. Smith: Int. J. Plast., 1998, vol. 14, pp. 1133–54.CrossRefGoogle Scholar
  7. 7.
    M.K. Khraisheh, F.K. Abu-Farha, M.A. Nazzal, and K.J. Weinmann: CIRP Annals—Manufact. Technol., 2006, vol. 55, pp. 233–36.CrossRefGoogle Scholar
  8. 8.
    S.G. Luckey Jr., P.A. Friedman, and K.J. Weinmann: J. Mater. Process. Tech., 2007, vol. 194, pp. 30–37.CrossRefGoogle Scholar
  9. 9.
    M.A. Nazzal, M.K. Khraisheh, and F.K. Abu-Farha: J. Mater. Process. Tech., 2007, vol. 191, pp. 189–92.CrossRefGoogle Scholar
  10. 10.
    H. Raman, G. Luckey, G. Kridli, and P. Friedman: J. Mater. Eng. Perform., 2007, vol. 16, pp. 284–92.CrossRefGoogle Scholar
  11. 11.
    R. Verma, L. Hector, P. Krajewski, and E. Taleff: JOM, 2009, vol. 61, pp. 29–37.CrossRefGoogle Scholar
  12. 12.
    G.Y. Li, M.J. Tan, and K.M. Liew: J. Mater. Process. Tech., 2004, vol. 150, pp. 76–83.CrossRefGoogle Scholar
  13. 13.
    G. Giuliano: Mater. Des., 2008, vol. 29, pp. 1330–33.CrossRefGoogle Scholar
  14. 14.
    N. Chandra: Int. J. Non-Lin. Mech., 2002, vol. 37, pp. 461–84.CrossRefGoogle Scholar
  15. 15.
    S. Agarwal, C. Briant, P. Krajewski, A. Bower, and E. Taleff: J. Mater. Eng. Perform., 2007, vol. 16, pp. 170–78.CrossRefGoogle Scholar
  16. 16.
    A.F. Bower and E. Wininger: J. Mech. Phys. Solids, 2004, vol. 52, pp. 1289–1317.CrossRefGoogle Scholar
  17. 17.
    D.E. Cipoletti, A.F. Bower, Y. Qi, and P.E. Krajewski: Mater. Sci. Eng. A, 2009, vol. 504, pp. 175–82.CrossRefGoogle Scholar
  18. 18.
    N. Du, A.F. Bower, P.E. Krajewski, and E.M. Taleff: Mater. Sci. Eng. A, 2008, vol. 494, pp. 86–91.CrossRefGoogle Scholar
  19. 19.
    P.E. Krajewski, L.G. Hector Jr., N. Du, and A.F. Bower: Acta Mater., 2010, vol. 58, pp. 1074–86.CrossRefGoogle Scholar
  20. 20.
    J.H. Kim, S.L. Semiatin, and C.S. Lee: Acta Mater., 2003, vol. 51, pp. 5613–26.CrossRefGoogle Scholar
  21. 21.
    T.G. Langdon: Acta Metall. Mater., 1994, vol. 42, pp. 2437–43.CrossRefGoogle Scholar
  22. 22.
    F.C. Liu and Z.Y. Ma: Scripta Mater., 2010, vol. 62, pp. 125–28.CrossRefGoogle Scholar
  23. 23.
    S.S. Park, H. Garmestani, G.T. Bae, N.J. Kim, P.E. Krajewski, S. Kim, and E.W. Lee: Mater. Sci. Eng. A, 2006, vols. 435–436, pp. 687–92.Google Scholar
  24. 24.
    M.-A. Kulas, W.P. Green, E.M. Taleff, P.E. Krajewski, and T.R. Mcnelley: Metall. Mater. Trans. A, 2005, vol. 36A, pp. 1249–61.CrossRefGoogle Scholar
  25. 25.
    W. Green, M.-A. Kulas, A. Niazi, E. Taleff, K. Oishi, P. Krajewski, and T. McNelley: Metall. Mater. Trans. A, 2006, vol. 37A, pp. 2727–38.CrossRefGoogle Scholar
  26. 26.
    T.R. McNelley, K. Oh-Ishi, A.P. Zhilyaev, S. Swaminathan, P.E. Krajewski, and E.M. Taleff: Metall. Mater. Trans. A, 2008, vol. 39A, pp. 50–64.CrossRefGoogle Scholar
  27. 27.
    K. Inal, K.W. Neale, and A. Aboutajeddine: Int. J. Plast., 2005, vol. 21, pp. 1255–66.CrossRefGoogle Scholar
  28. 28.
    K. Inal, P.D. Wu, and K.W. Neale: Int. J. Plast., 2000, vol. 16, pp. 635–48.CrossRefGoogle Scholar
  29. 29.
    K. Inal, P.D. Wu, and K.W. Neale: Int. J. Solid. Struct., 2002, vol. 39, pp. 3469–86.CrossRefGoogle Scholar
  30. 30.
    K. Inal, P.D. Wu, and K.W. Neale: Int. J. Solid. Struct., 2002, vol. 39, pp. 983–1002.CrossRefGoogle Scholar
  31. 31.
    K. Inal, P.D. Wu, and K.W. Neale: Modell. Simul. Mater. Sci. Eng., 2002, vol. 10, pp. 237–52.CrossRefGoogle Scholar
  32. 32.
    P. Tugcu, K.W. Neale, P.D. Wu, and K. Inal: Int. J. Plast., 2004, vol. 20, pp. 1603–53.CrossRefGoogle Scholar
  33. 33.
    A.C.F. Cocks: Mech. Mater., 1992, vol. 13, pp. 165–74.CrossRefGoogle Scholar
  34. 34.
    J. Pan and A.C.F. Cocks: Comput. Mater. Sci., 1993, vol. 1, pp. 95–109.CrossRefGoogle Scholar
  35. 35.
    F. Dunne and N. Petrinic: Introduction to Computational Plasticity, Oxford University Press Inc., Oxford, U.K., 2006.Google Scholar
  36. 36.
    D. Peirce, R.J. Asaro, and A. Needleman: Acta Metall., 1982, vol. 30, pp. 1087–1119.CrossRefGoogle Scholar
  37. 37.
    D. Peirce, R.J. Asaro, and A. Needleman: Acta Metall., 1983, vol. 31, pp. 1951–76.CrossRefGoogle Scholar
  38. 38.
    R.J. Asaro: J. Appl. Mech., 1983, vol. 50, pp. 921–34.CrossRefGoogle Scholar
  39. 39.
    R.J. Asaro, W.H. John, and Y.W. Theodore: Advances in Applied Mechanics, vol. 23, Elsevier, Atlanta, GA, 1983, pp. 1–115.Google Scholar
  40. 40.
    Y. Huang: A User Material Subroutine Incorporating Single Crystal Plasticity in the ABAQUS Finite Element Program, Harvard University, Cambridge, MA, 1992.Google Scholar
  41. 41.
    T. Iwakuma and S. Nemat-Nasser: Proc. Royal Soc. London, 1984, vol. 394, no. 1806, pp. 87–119.Google Scholar
  42. 42.
    A. Molinari, G.R. Canova, and S. Ahzi: Acta Metall., 1987, vol. 35, pp. 2983–94.CrossRefGoogle Scholar
  43. 43.
    G.Z. Sachs and D. Verein: Der Verein dutsher Ingenieur, 1928, vol. 72, p. 734.Google Scholar
  44. 44.
    G.I. Taylor: JIM, 1938, vol. 62, pp. 307–24.Google Scholar
  45. 45.
    Z.R. Wang, Y.W. Xu, and D.J. Guo: Proceedings of the First National Meeting on Plastic Mechanics in Chinese, 1986.Google Scholar
  46. 46.
    M.T. Eric, G.H. Louis, R.B. John, V. Ravi, and E.K. Paul: Acta Mater., 2009, vol. 57, pp. 2812–22.CrossRefGoogle Scholar
  47. 47.
    Y. Luo, S.G. Luckey, P.A. Friedman, and Y. Peng: Int. J. Mach Tools Manufact., 2008, vol. 48, pp. 1509–18.CrossRefGoogle Scholar

Copyright information

© The Minerals, Metals & Materials Society and ASM International 2012

Authors and Affiliations

  • Reza Jafari Nedoushan
    • 1
  • Mahmoud Farzin
    • 1
  • Mohammad Mashayekhi
    • 1
  • Dorel Banabic
    • 2
    Email author
  1. 1.Department of Mechanical EngineeringIsfahan University of TechnologyIsfahanIran
  2. 2.Mechanical Technology DepartmentTechnical University of Cluj-NapocaCluj-NapocaRomania

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