Metallurgical and Materials Transactions A

, Volume 37, Issue 4, pp 1247–1259 | Cite as

Numerical simulation of three-dimensional heat transfer and plastic flow during friction stir welding

  • R. Nandan
  • G. G. Roy
  • T. Debroy


Three-dimensional visco-plastic flow of metals and the temperature fields in friction stir welding have been modeled based on the previous work on thermomechanical processing of metals. The equations of conservation of mass, momentum, and energy were solved in three dimensions using spatially variable thermophysical properties and non-Newtonian viscosity. The framework for the numerical solution of fluid flow and heat transfer was adapted from decades of previous work in fusion welding. Non-Newtonian viscosity for the metal flow was calculated considering strain rate, temperature, and temperature-dependent material properties. The computed profiles of strain rate and viscosity were examined in light of the existing literature on thermomechanical processing. The heat and mass flow during welding was found to be strongly three-dimensional. Significant asymmetry of heat and mass flow, which increased with welding speed and rotational speed, was observed. Convective transport of heat was an important mechanism of heat transfer near the tool surface. The numerically simulated temperature fields, cooling rates, and the geometry of the thermomechanically affected zone agreed well with independently determined experimental values.


Heat Transfer Welding Material Transaction Friction Stir Weld Friction Stir Welding 
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  1. 1.
    W.M. Thomas, E.D. Nicholas, J.C. Needham, M.G. Murch, P. Templesmith, and C.J. Dawes: International patent application no. PCT/GB92/02203 and GB patent application no. 9125978.9, 1991.Google Scholar
  2. 2.
    M.J. Russel and H.R. Shercliff: Proceedings of the 7th International Conference on “Joints in Aluminum” (INALCO ’98), The Welding Institute, Cambridge, U.K., 1998. vol. 2, pp. 185–95.Google Scholar
  3. 3.
    J.E. Gould and Z. Feng: J. Mater. Process. Manuf. Sci., 1998, vol. 7, pp. 185–94.CrossRefGoogle Scholar
  4. 4.
    H. Schmidt, J. Hattel, and J. Wert: Modeling Simulations Mater. Sci. Eng., 2004, vol. 12, pp. 143–57.CrossRefGoogle Scholar
  5. 5.
    Ø. Frigaard, Ø. Grong, and O.T. Midling: Metall. Mater. Trans. A, 2001, vol. 32, pp. 1189–200.CrossRefGoogle Scholar
  6. 6.
    Y.J. Chao, X. Qi, and W. Tang: Trans. ASME, 2003, vol. 125, pp. 138–45.Google Scholar
  7. 7.
    M. Song and R. Kovacevic: Proc. Instn. Mech. Engrs. Part B: J. Eng Manuf., 2003, vol. 217 (B1), pp. 73–85.Google Scholar
  8. 8.
    M. Song and R. Kovacevic: Int. J. Machine Tool Manuf., 2003, vol. 43 (6), pp. 605–15.CrossRefGoogle Scholar
  9. 9.
    M. Song and R. Kovacecic: Proc. Instn. Mech. Engrs. Part B: J. Eng Manuf., 2004, vol. 218, pp. 17–33.Google Scholar
  10. 10.
    M.Z.H. Khandkar, J.A. Khan, and A.P. Reynolds: Sci. Technol. Weld. Joining, 2003, vol. 8 (3), pp. 165–74.CrossRefGoogle Scholar
  11. 11.
    P.A. Colegrove and H.R. Shercliff: Sci. Technol. Weld. Joining, 2004, vol. 9 (4), pp. 345–51.CrossRefGoogle Scholar
  12. 12.
    T.U. Seidel and A.P. Reynolds: Sci. Technol. Weld. Joining, 2003, vol. 8, pp. 175–83.CrossRefGoogle Scholar
  13. 13.
    C.B. Smith, G.B. Bendzsak, T.H. North, J.F. Hinrichs, J.S. Noruk, and R.J. Heideman: Proceedings of the 9th International Conference on Computer Technology in Welding, Detroit, 2000, pp. 475–86.Google Scholar
  14. 14.
    P. Ulysse: Int. J. Machine Tools Manuf., 2002, vol. 42, pp. 1549–57.CrossRefGoogle Scholar
  15. 15.
    P.A. Colegrove and H.R. Shercliff: J. Mater. Process. Technol., 2005, in press.Google Scholar
  16. 16.
    W. Zhang, G.G. Roy, J.W. Elmer, and T. DebRoy: J. Appl. Phys., 2003, vol. 93, pp. 3022–33.CrossRefGoogle Scholar
  17. 17.
    T. Sheppard and D.S. Wright: Metal. Technol, 1979, vol. 6, pp. 215–23.Google Scholar
  18. 18.
    O.C. Zienkiewicz and I.C. Cormeau: Int. J. Numer. Methods Eng., 1974, vol. 8, pp. 821–45.CrossRefGoogle Scholar
  19. 19.
    T. Sheppard and A. Jackson: Mater. Sci. Technol., 1997, vol. 13, pp. 203–09.Google Scholar
  20. 20.
    ASM Handbook, vol. 2, ASM International, Columbus, OH, 1990, pp. 102–03.Google Scholar
  21. 21.
    D.R. Lesuer, G.J. Kay, and M.M. LeBlanc: “Modeling Large-Strain, High-Rate Deformation in Metals,” Third Biennial Tri-Laboratory Engineering Conference on Modeling and Simulation, Pleasanton. CA, November 3–5, 1999. Also available on the web at as a report of the Lawrence Livermore National Laboratory Report #UCRL-JC-134118 dated July 20, 2001.Google Scholar
  22. 22.
    S.V. Patankar: Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Corporation, New York, NY, 1980.Google Scholar
  23. 23.
    X. He, J. Elmer, and T. DebRoy: J. Appl. Phys., 2005, vol. 97, p. 84909.CrossRefGoogle Scholar
  24. 24.
    A. De and T. DebRoy: Welding J., 2005, vol. 84 (7), pp. 101–12.Google Scholar
  25. 25.
    S. Mishra and T. DebRoy: J. Phys. D. 2005, vol. 38, pp. 2977–85.CrossRefGoogle Scholar
  26. 26.
    W. Zhang, T. DebRoy, and J.W. Elmer: Sci. Technol. Weld. Joining, 2005, vol. 10 (5), pp. 574–82.CrossRefGoogle Scholar
  27. 27.
    W. Zhang, T. DebRoy, T.A. Palmer, and J.W. Elmer: Acta Mater., 2005, vol. 53 (16), pp. 4441–53.CrossRefGoogle Scholar
  28. 28.
    S. Mishra and T. DebRoy: J. Appl. Phys., 2005, vol. 98, p. 044902.Google Scholar
  29. 29.
    P.J. Halley and M.E. Mackay: J. Rheol., 1994, vol. 38 (1), pp. 41–51.CrossRefGoogle Scholar

Copyright information

© ASM International & TMS-The Minerals, Metals and Materials Society 2006

Authors and Affiliations

  • R. Nandan
    • 1
  • G. G. Roy
    • 1
  • T. Debroy
    • 1
  1. 1.Department of Materials Science and EngineeringThe Pennsylvania State UniversityUniversity ParkU.S.A.

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