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Computer modeling of heat flow in welds

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Abstract

This paper summarizes progress in the development of methods, models, and software for analyzing or simulating the flow of heat in welds as realistically and accurately as possible. First the fundamental equations for heat transfer are presented and then a formulation for a nonlinear transient finite element analysis (FEA) to solve them is described. Next the magnetohydrodynamics of the arc and the fluid mechanics of the weld pool are approximated by a flux or power density distribution selected to predict the temperature field as accurately as possible. To assess the accuracy of a model, the computed and experimentally determined fusion zone boundaries are compared. For arc welds, accurate results are obtained with a power density distribution in which surfaces of constant power density are ellipsoids and on radial lines the power density obeys a Gaussian distribution. Three dimensional, in-plane and cross-sectional kinematic models for heat flow are defined. Guidelines for spatial and time discretization are discussed. The FEA computed and experimentally measured temperature field,T(x, y, z, t), for several welding situations is used to demonstrate the effect of temperature dependent thermal properties, radiation, convection, and the distribution of energy in the arc.

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References

  1. R. R. Rykalin:Welding in the World, 1974, vol. 12, No. 9/10, pp. 227–48 (Houdrement Lecture, International Institute of Welding, London, 1974, pp. 1–23).

    Google Scholar 

  2. The Physics of Welding, J. F. Lancaster, ed., Pergamon Press, 1984, pp. 1–293.

  3. A. H. Dilawari, J. Szekely, and T. W. Eagar:Metall. Trans. B, 1978, vol. 9B,pp. 371–81.

    Google Scholar 

  4. A. H. Dilawari, T. W. Eagar, and J. Szekely:Welding Journal, January 1978, pp. 24–30.

  5. S. Lawson and H. Kerr:Welding Research International, 1976, vol. 6, No. 5, 6.

  6. D. Rosenthal:Trans. ASME, 1946, vol. 68, pp. 849–65.

    Google Scholar 

  7. P. S. Myers, O. A. Uyehara, and G. L. Borman:Welding Research Council Bulletin, New York, NY, 1967, No. 123.

  8. O. Westby: Report, Department of Metallurgy and Metals Working, The Technical University, Trondheim, Norway, 1968.

    Google Scholar 

  9. Z. Paley and P.D. Hibbert:Welding Journal Research Supplement, 1975, vol. 54, pp. 385s-92s.

    Google Scholar 

  10. V. Pavelic, R. Tanbakuchi, O. A. Uyehara, and P. S. Myers:Welding Journal Research Supplement, 1969, vol. 48, pp. 295s-305s.

    Google Scholar 

  11. S. Kou:Metall. Trans. A, 1982, vol. 13A, pp. 363–71.

    CAS  Google Scholar 

  12. J. H. Argyris, J. Szimmat, and K.J. Willan:Computer Methods in Applied Mechanics and Engineering, 1982, vol. 33, pp. 635–66.

    Article  Google Scholar 

  13. J.A. Goldak, A. Chakravarti, and M.J. Bibby:Trans. AIME, June 1984, vol. 15B, pp. 299–305.

    Google Scholar 

  14. N. Christensen, L. de.V. Davies, and K. Gjermundsen:British Welding Journal, 1965, vol. 12, pp. 54–75.

    Google Scholar 

  15. M.J. Bibby, G.Y. Shing, and J.A. Goldak:CIM Metallurgical Quarterly, Jan. 1985, in press.

  16. A. P. Chakravarti, J. Goldak, and A. S. Rao:Thermal Analysis of Welds, International Conference on Numerical Methods in Thermal Problems, Swansea, U.K., Nov. 1985.

    Google Scholar 

  17. J.F. Key, H.B. Smartt, J.W. Chan, and M.E. McIlwain:Welding Technology for Energy Applications, Proceedings International Conference, Gatlinburg, TN, 16–19 May, 1982, compiled by S. A. David and G. M. Slaughter, pp. 179–99.

  18. E. Friedman:Journal Pressure Vessel Technology, Trans. ASME, 1975, vol. 97, pp. 206–13.

    Google Scholar 

  19. B.A.B. Andersson:Journal of Engineering Materials and Technology, Trans. ASME, 1978, vol. 100, pp. 356–62.

    CAS  Google Scholar 

  20. D. R. Chapman:AIAA Journal, December 1969, vol. 17, No. 12, pp. 1293–1313.

    Google Scholar 

  21. B. M. Irons and S. Ahmad:Techniques for Finite Elements, Ellis Horwood, West Sussex, U.K., 1980.

    Google Scholar 

  22. A. Kela, H. Voelcker, and J. A. Goldak: International Conference on Accuracy Estimates and Adaptive Refinements in Finite Element Computations (ARFEC), Sponsored by the International Association of Computational Mechanics, Lisbon, Portugal, June 19–20, 1984.

    Google Scholar 

  23. M. S. Sheperd and K. H. Law: International Conference on Accuracy Estimates and Adaptive Refinements in Finite Element Computations (ARFEC), Sponsored by the International Association of Computational Mechanics, Lisbon, Portugal, June 19–20, 1984.

    Google Scholar 

  24. O. C. Zienkiewicz:The Finite Element Method, McGraw-Hill Book Company, New York, NY, 3rd ed., 1977.

    Google Scholar 

  25. T.J. R. Hughes:Computer Methods in Applied Mechanics and Engineering, 1977, vol. 10, pp. 135–39.

    Article  Google Scholar 

  26. J. Donea:International Journal for Numerical Methods in Engineering, 1974, vol. 8, pp. 103–10.

    Article  Google Scholar 

  27. Z. Pammer:International Journal for Numerical Methods in Engineering, 1983, vol. 15, pp. 495–505.

    Article  Google Scholar 

  28. W. M. Rohsenow and J. P. Hartnet:Handbook of Heat Transfer, McGraw-Hill, New York, NY, 1973.

    Google Scholar 

  29. Y. S. Touloukian, Powell, Ho, and Klemens:Thermal Conductivity: Metallic Elements of Alloys, Plenum Publishing Co., New York, NY, 1970.

    Google Scholar 

  30. Physical Constants of Some Commercial Steels at Elevated Temperatures, The British Iron and Steel Research Association, London, Butterworths Scientific Publications, 1953.

  31. N. Yurioka, S. Ohsita, and H. Tamehiro: The Specialist Symposium on Pipeline Welding in the 80’s, Melbourne, Australia, March 18/81.

  32. K. Farnia and J. V. Beck:Journal of Heat Transfer, Trans. ASME, vol. 99, pp. 471–78.

  33. G. Comini, S. del Guidice, R.L. Lewis, and O.C. Zienkiewicz:IJNME, 1974, vol. 8, pp. 613–24.

    Article  Google Scholar 

  34. W. D. Relphe, III and K. J. Bathe:IJNME, 1982, vol. 18, pp. 119–34.

    Article  Google Scholar 

  35. D. Blanchard and M. Fremont:IJNME, 1984, vol. 20, pp. 757–71.

    Article  Google Scholar 

  36. S. Al-Araji and J. V. Beck:Journal of Heat Transfer, Trans. ASME, 1975, pp. 148–49.

  37. M.F. Ashby and K. E. Easterling:Acta Metall., 1982, vol. 30, pp. 1969–78.

    Article  CAS  Google Scholar 

  38. J. C. Ion and K. E. Easterling: The Third Scandinavian Symposium in Materials Science, 20–21 June, 1983, The University of Oulu, Finland, Metal Abstracts 8407-72-0526.

  39. V. A. Vinokurov:Welding Stresses and Distortions, The British Library, Lending Division, Translated from Russian into English by J.E. Baker, 1977, pp. 118–19.

  40. B. Patel: Ph.D. Thesis, Carleton University, Ottawa, ON, Canada, Jan., 1985.

    Google Scholar 

  41. T.K. Hellen:IJNME, 1983, vol. 19, pp. 1713–37.

    Article  Google Scholar 

  42. T.K. Hellen:IJNME, 1975, vol. 9, pp. 187–97.

    Article  Google Scholar 

  43. I. Kalev:Computers and Structures, 1981, vol. 13, pp. 709–16.

    Article  Google Scholar 

  44. B. Patel, J. A. Goldak, and M. J. Bibby: Carleton University, Ottawa, ON, Canada, unpublished research, 1985.

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Authors and Affiliations

  1. Department of Mechanical and Aeronautical Engineering, Carleton University, K1S 5B6, Ottawa, ON, Canada

    J. Goldak (Professor), M. Bibby (Professor), J. Moore (Graduate Student), R. House (Graduate Student) & B. Patel (Graduate Student)

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  1. J. Goldak
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  2. M. Bibby
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  3. J. Moore
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  4. R. House
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  5. B. Patel
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Goldak, J., Bibby, M., Moore, J. et al. Computer modeling of heat flow in welds. Metall Trans B 17, 587–600 (1986). https://doi.org/10.1007/BF02670226

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  • DOI: https://doi.org/10.1007/BF02670226

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