Skip to main content
SpringerLink
Log in

Modeling of laser keyhole welding: Part I. mathematical modeling, numerical methodology, role of recoil pressure, multiple reflections, and free surface evolution

  • Published:
Metallurgical and Materials Transactions A Aims and scope Submit manuscript

Abstract

A three-dimensional laser-keyhole welding model is developed, featuring the self-consistent evolution of the liquid/vapor (L/V) interface together with full simulation of fluid flow and heat transfer. Important interfacial phenomena, such as free surface evolution, evaporation, kinetic Knudsen layer, homogeneous boiling, and multiple reflections, are considered and applied to the model. The level set approach is adopted to incorporate the L/V interface boundary conditions in the Navier-Stokes equation and energy equation. Both thermocapillary force and recoil pressure, which are the major driving forces for the melt flow, are incorporated in the formulation. For melting and solidification processes at the solid/liquid (S/L) interface, the mixture continuum model has been employed. The article consists of two parts. This article (Part I) presents the model formulation and discusses the effects of evaporation, free surface evolution, and multiple reflections on a steady molten pool to demonstrate the relevance of these interfacial phenomena. The results of the full keyhole simulation and the experimental verification will be provided in the companion article (Part II).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. D. Adalsteinsson and J.A. Sethian: J. Comput. Phys., 1995, vol. 118, pp. 269–77.

    Article  Google Scholar 

  2. D. Adalsteinsson and J.A. Sethian: J. Comput. Phys., 1995, vol. 120, pp. 128–44.

    Article  Google Scholar 

  3. D. Adalsteinsson and J.A. Sethian: J. Comput. Phys., 1995, vol. 122, pp. 348–66.

    Article  Google Scholar 

  4. S. Asai and I. Muchi: Trans. Iron Steel Inst. Jpn., 1978, vol. 18, pp. 90–98.

    CAS  Google Scholar 

  5. V. Batanov, F. Bunkin, A. Prokhorov, and V. Fedorov: Sov. Phys. JETP, 1973, vol. 36 (2) pp. 311–22.

    Google Scholar 

  6. W. Bennon and F. Incropera: Int. J. Heat Mass Transfer, 1987, vol. 30 (10), pp. 2161–70.

    Article  CAS  Google Scholar 

  7. W. Bennon and F. Incropera: Int. J. Heat Mass Transfer, 1987, vol. 30 (10), pp. 2171–87.

    Article  CAS  Google Scholar 

  8. W. Bennon and F. Incropera: Num. Heat Transfer, 1988, vol. 13, pp. 277–96.

    Google Scholar 

  9. R.L. Burden and J.D. Faires: Num. Analysis. PWS Publishing Company, Boston, MA, 1993.

    Google Scholar 

  10. V.P. Carey: Liquid-Vapor Phase Change Phenomena, Hemisphere Publishing Corporation, Bristol, PA, 1992.

    Google Scholar 

  11. C. Chan, J. Mazumder, and M. Chen: Metall. Trans. A, 1984, vol. 15A, pp. 2175–84.

    CAS  Google Scholar 

  12. C. Chan, J. Mazumder, and M. Chen: J. Appl. Phys., 1988, vol. 64 (11), pp. 6166–74.

    Article  Google Scholar 

  13. S. Chen, B. Merriman, S. Osher, and P. Smereka: J. Comput. Phys., 1997, vol. 135, pp. 8–29.

    Article  CAS  Google Scholar 

  14. V. Cracium, D. Cracium, C. Boulmer-Leborgne, and J. Hermann: Phys. Rev. B, 1998, vol. 58, p. 6787.

    Article  Google Scholar 

  15. P.G. Debenedetti: Metastable Liquids Concepts and Principles, Princeton University Press, Princeton, NJ, 1996.

    Google Scholar 

  16. C. Domb: The Critical Point, Taylor & Francis, London, 1996.

    Google Scholar 

  17. J. Dowden, M. Davis, and P. Kapadia: J. Fluid Mech., 1983, vol. 126, pp. 123–46.

    Article  Google Scholar 

  18. J. Dowden and P. Kapadia: J. Phys. D: Appl. Phys., 1995, vol. 28, pp. 2252–61.

    Article  CAS  Google Scholar 

  19. R. Fabbro and K. Chouf: J. Appl. Phys., 2000, vol. 87 (9), pp. 4075–83.

    Article  CAS  Google Scholar 

  20. F. Gagiliano and U. Paek: Appl. Opt., 1974, vol. 13 (2), pp. 274–79.

    Google Scholar 

  21. F. Hensel: J. Phys.: Condens. Matter, 1990, vol. 2, pp. SA33-SA45.

    Article  CAS  Google Scholar 

  22. F. Hensel and P. Edwards: Phys. Worlds, 1996, Apr., pp. 43–46.

  23. F. Incropera, A. Engel, and W. Bennon: Num. Heat Transfer, Part A, 1989, vol. 16, pp. 407–27.

    Google Scholar 

  24. A. Kaplan: J. Phys. D: Appl. Phys., 1994, vol. 27, pp. 1805–14.

    Article  CAS  Google Scholar 

  25. A. Kar, T. Rockstroh, and J. Mazumder: J. Appl. Phys., 1992, vol. 71 (6), pp. 2560–69.

    Article  CAS  Google Scholar 

  26. R. Kelly and A. Miotello: Appl. Surf. Sci., 1996, vol. 96–98, pp. 205–15.

    Article  Google Scholar 

  27. R. Kelly and A. Miotello: Phys. Rev. E, 1999, vol. 60, p. 2616.

    Article  CAS  Google Scholar 

  28. H. Ki: Ph.D. Thesis, University of Michigan, Ann Arbor, MI, 2001.

    Google Scholar 

  29. H. Ki, P. Mohanty, and J. Mazumder: J. Phys. D: Appl. Phys., 2001, vol. 34, pp. 364–72.

    Article  CAS  Google Scholar 

  30. H. Ki, P.S. Mohanty, and J. Mazumder: Metall. Mater. Trans. A, 2002, vol. 33A, pp. 1831–42.

    CAS  Google Scholar 

  31. C.J. Knight: AIAA J., 1979, vol. 17 (5), pp. 519–23.

    Article  CAS  Google Scholar 

  32. J. Kroos, U. Gratzke, and G. Simon: J. Phys. D: Appl. Phys., 1993, vol. 26, pp. 474–80.

    Article  CAS  Google Scholar 

  33. K.N. Lankalapalli, J.F. Tu, and M. Gartner: J. Phys. D: Appl. Phys., 1996, vol. 29, pp. 1831–41.

    Article  CAS  Google Scholar 

  34. M. Martynyuk: Russ. J. Phys. Chem., 1975, vol. 49 (10), pp. 1545–47.

    Google Scholar 

  35. M. Martynyuk: Russ. J. Phys. Chem., 1983, vol. 57 (4), pp. 494–501.

    Google Scholar 

  36. A. Matsunswa and V. Semak: J. Phys. D: Appl. Phys., 1997, vol. 30, pp. 798–809.

    Article  Google Scholar 

  37. J. Mazumder: Opt. Eng., 1991, vol. 30 (8), pp. 1208–19.

    Article  CAS  Google Scholar 

  38. J. Milewski and E. Sklar: Modeling Simul. Mater. Sci., 1996, vol. 4, pp. 305–22.

    Article  CAS  Google Scholar 

  39. W. Mulder, S. Osher, and J.A. Sethian: J. Comput. Phys., 1992, vol. 100, pp. 209–28.

    Article  Google Scholar 

  40. S. Osher and J.A. Sethian: J. Comput. Phys., 1988, vol. 79, pp. 12–49.

    Article  Google Scholar 

  41. S.V. Patankar: Numerical Heat Transfer and Fluid Flow, Taylor & Francis, 1980.

  42. C. Prakash and V. Voller: Num. Heat Transfer, Part B, 1989, vol. 15, pp. 171–89.

    Google Scholar 

  43. P. Prescott, F. Incropera, and W. Bennon: Int. J. Heat Mass Transfer, 1991, vol. 34 (9), pp. 2351–59.

    Article  CAS  Google Scholar 

  44. R. Ross and D. Greenwood: Progr. Mater. Sci., 1969, vol. 14, pp. 175–242.

    Article  CAS  Google Scholar 

  45. P. Sathyamurthy: Ph.D. Thesis, University of Minnesota, Twin Cities, MN, 1991.

    Google Scholar 

  46. V.V. Semak, W.D. Bragg, B. Damkroger, and S. Kempka: J. Phys. D: Appl. Phys., 1999, vol. 32, pp. L61-L64.

    Article  CAS  Google Scholar 

  47. J.A. Sethian: Level Set Methods and Fast Marching Methods, 2nd ed., Cambridge University Press, Cambridge, United Kingdom, 1999.

    Google Scholar 

  48. J.A. Sethian and J. Strain: J. Comput. Phys., 1992, vol. 98, pp. 231–53.

    Article  CAS  Google Scholar 

  49. V. Skripov: Metastable Liquids, John Wiley & Sons. New York, NY, 1974.

    Google Scholar 

  50. V. Smiljanovski, V. Moser, and R. Klein: Combust. Theory Modelling, 1997, vol. 1, pp. 183–215.

    Article  Google Scholar 

  51. P. Solana and G. Negro: J. Phys. D: Appl. Phys., 1997, vol. 30, pp. 3216–22.

    Article  CAS  Google Scholar 

  52. P. Solana and J. Ocana: J. Phys. D: Appl. Phys., 1997, vol. 30, pp. 1300–13.

    Article  CAS  Google Scholar 

  53. K.H. Song and X. Xu: Appl. Surf. Sci., 1998, vol. 127–129, pp. 111–16.

    Article  Google Scholar 

  54. W. Sudnik, D. Radaj. S. Breitschwerdt, and W. Erofeew: J. Phys. D: Appl. Phys., 2000, vol. 33, pp. 662–71.

    Article  CAS  Google Scholar 

  55. W. Sudnik, D. Radaj, and W. Erofeew: J. Phys. D: Appl. Phys., 1996, vol. 29, pp. 2811–17.

    Article  CAS  Google Scholar 

  56. M. Sussman, P. Smereka, and S. Osher: J. Comput. Phys., 1994, vol. 114, pp. 146–59.

    Article  Google Scholar 

  57. S. Vanka: J. Comput. Phys., 1986, vol. 65, pp. 138–58.

    Article  Google Scholar 

  58. H. Versteeg and W. Malalasekera: An Introduction to Computational Fluid Dynamics, Longman, England, 1999.

    Google Scholar 

  59. P. Wei and C. Ho: Int. J. Heat Mass Transfer, 1998, vol. 41, pp. 3299–3308.

    Article  Google Scholar 

  60. B.S. Yilbas and M. Sami: J. Phys. D: Appl. Phys., 1997, vol. 30, pp. 1996–2005.

    Article  Google Scholar 

  61. T. Ytrehus and S. Østmo: Int. J. Multiphase Flow, 1996, vol. 22 (1), pp. 133–55.

    Article  CAS  Google Scholar 

  62. R.L. Zehr: Ph.D. Thesis, University of Illinois at Urbana-Champaign, Urbana, IL, 1991.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. the Center for Laser Aided Intelligent Manufacturing, Mechanical Engineering Department, University of Michigan, 48109-2125, Ann Arbor, MI

    Hyungson Ki (Research Fellow) & Jyoti Mazumder (Professor)

  2. the Mechanical Engineering Department, University of Michigan—Dearborn, 48126-1409, Dearborn, MI

    Pravansu S. Mohanty (Assistant Professor)

Authors
  1. Hyungson Ki
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jyoti Mazumder
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Pravansu S. Mohanty
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ki, H., Mazumder, J. & Mohanty, P.S. Modeling of laser keyhole welding: Part I. mathematical modeling, numerical methodology, role of recoil pressure, multiple reflections, and free surface evolution. Metall Mater Trans A 33, 1817–1830 (2002). https://doi.org/10.1007/s11661-002-0190-6

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11661-002-0190-6

Keywords

Search

Navigation