Abstract
In recent years, numerical heat transfer and fluid flow models have provided significant insight about fusion welding processes and welded materials. A major problem in their practical use is that several input parameters cannot be easily prescribed from fundamental principles. Available inverse models of fusion welding for the determination of these unknown parameters have ignored important physical processes such as convection in the weld pool to make computational tasks tractable. As a result, these models are not very different from the neural network type models that are not required to obey any physical law. A smart, bi-directional, numerical model has been developed to determine three-dimensional temperature and velocity profiles, weld geometry and the shape of the solidified weld reinforcement surface during gas metal arc (GMA) welding of fillet joints. Apart from the transport of heat from the welding arc, additional heat from the metal droplets was also considered in the model. The model is capable of estimating unknown parameters such as the arc efficiency, effective thermal conductivity and effective viscosity from a limited number of data on weld geometry based on multivariable optimisation. Alternative strategies for the optimisation are examined. The calculated shape and size of the fusion zone, finger penetration characteristic of the GMA welds and the solidified free surface profile were in fair agreement with the experimental results for various welding conditions. In particular, the computed values of the leg length, the penetration depth and the actual throat agreed well with those measured experimentally for various heat inputs. The weld thermal cycles and the cooling rates were also in good agreement with the independent experimental data. The research presented here shows that advances in computational hardware and software have now made construction of smart, bi-directional, large transport phenomena based phenomenological models a useful undertaking.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Kim C.H., Zhang W., DebRoy T.: Modelling of temperature field and solidified surface profile during gas metal arc fillet welding, J. Appl. Phys., 2003, 94, pp. 2667–2679.
Zhao H., DebRoy T.: Macro-porosity free aluminium alloy weldments through numerical simulation of keyhole mode laser welding, J. Appl. Phys., 2003, 93, pp. 10089–10096.
Zhang W., Roy G., Elmer J.W., DebRoy T.: Modelling of heat transfer and fluid flow during gas tungsten arc spot welding of low carbon steel, J. Appl. Phys., 2003, 93, pp. 3022–3033.
He X., Fuerschbach P.W., DebRoy T.: Heat transfer and fluid flow during laser spot welding of 304 stainless steel, J. Phys. D: Appl. Phys., 2003, 36, pp. 1388–1398.
Kumar A., DebRoy T.: Calculation of three-dimensional electromagnetic force field during arc welding, J. Appl. Phys., 2003, 94, pp. 1267–1277.
Elmer J.W., Palmer T.A., Zhang W., Wood B., DebRoy T.: Kinetic modelling of phase transformations occurring in the HAZ of C-Mn steel welds based on direct observations, Acta Mat., 2003, 51, pp. 3333–3349.
Zhang W., Elmer J.W., DebRoy T.: Modelling and real time mapping of phases during GTA welding of 1005 steel, Mat. Sci. Eng. A, 2002, 333, pp. 321–335.
Hong T., DebRoy T.: Effects of time, temperature and steel composition on the growth and dissolution of inclusions in liquid steels, Ironmaking and Steelmaking, 2001, 28, pp. 450–454.
Yang Z., Sista S., Elmer J.W., DebRoy T.: Three Dimensional Monte Carlo Simulation of Grain Growth during GTA Welding of Titanium, Acta Mat., 2000, 48, pp. 4813–4825.
Yang Z., Elmer J.W., Wang J., DebRoy T.: Evolution of titanium arc weldment macro- and microstructures — Modelling and real time mapping of phases, Weld. J., 2000, 79, pp. 97–112.
Hong K., Weckmann D.C., Strong A.B., Zheng W.: Modelling turbulent thermofluid flow in stationary gas tungsten arc weld pools, Sci. Technol. Weld. Joining, 2002, 7, pp. 125–136.
Jonsson P.G., Szekely J., Choo R.T.C., Quinn T.P.: Mathematical models of transport phenomena associated with arc welding process: a survey, Model. Simul. Mater. Sci. Eng., 1994, 2, pp. 995–1016.
Hong K., Weckman D.C., Strong A.B., Pardo E.: Proceedings of the First Int. Conference on Transport Phenomena in Processing, Hawaii, ed. by Secuk I. Guceri, Technomic Pub., 1992, pp. 626- 635.
Choo R.T.C., Szekely J.: The possible role of turbulence in GTA weld pool behaviour, Weld. J., 1994, 73, pp. 25–31.
De A., DebRoy T.: Probing unknown welding parameters from convective heat transfer calculation and multivariable optimisation, J. Phys. D: Appl. Phys., 2004, 37, pp. 140–150.
Zhang W., Kim C.H., DebRoy T.: Heat transfer, fluid flow and solidified surface profile during gas metal arc fillet welding, unpublished document, Department of Materials Science and Engineering, The Pennsylvania State University, August 2003.
S. Kou Y.H. Wang: Weld pool convection and its effect, Metallurgical Transactions B, 1986, 17, pp. 2271–2278.
Voller V.R., Prakash C.: A fixed grid numerical modelling methodology for convection-diffusion mushy region phase-change problems, Int. J. Heat Mass Transfer, 1987, 30, pp. 1709–1719.
Hoffmann K.A., Chiang S.T.: Computational fluid dynamics for engineering — Volume II, Engineering Education System, Wichita, KS, USA, 1993.
Thompson J.F., Warsi Z.U.A., Wayne Mastin C.: Numerical grid generation: fundamentals and applications, Elsevier Science, New York, 1985.
Patankar S.V., Numerical heat transfer and fluid flow, McGraw-Hill, New York, 1982.
Lin M.L., Eagar T.W.: Pressures produced by gas tungsten arcs, Metall. Trans. B, 1986, 17B, pp. 601–607.
Beck J.V.: Modelling of casting, welding and advanced solidification process V, ed. by M. Rappaz, M.R. Orzu, and K.W. Mahin, The Minerals, Metals & Materials Society, Warrendale, PA, 1991, pp. 503–518.
Beck J.V., Blackwell B. C.R. St. Clair: Inverse heat conduction: III-Posed Problems Wiley International, NY, 1985.
Beck J.V., Arnold K.J.: Parameter estimation in engineering and science, John Wiley and Sons, NY, 1977.
Ozisik M.N., Orlande H.R B.: Inverse heat transfer: Fundamentals and applications, Taylor and Francis, NY, 2000.
Bard Y.: Nonlinear parameter estimation, Academic Press, NY, 1974.
Dennis J., Schnabel R.: Numerical methods for unconstrained optimisations and non-linear equations, Prentice Hall, 1983.
Tikhonov N.: Solution of incorrectly formulated problems and the regularization method, Soviet Math. Dokl., 1963, 4, pp. 1035–1038.
Fletcher R., Reeves C.M.: Function minimization by conjugate gradients, Computer J., 1964, 7, pp. 149–154.
Tikhonov N.: Regularization of incorrectly posed problems, Soviet Math. Dokl., 1963, 4, pp. 1624–1627.
Alifanov M.: Inverse heat transfer problems, Springer-Verlag, NY, 1994.
Masubuchi K.: Analysis of welded structures, Pergamon, Oxford, 1980.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kumar, A., Zhang, W., Kim, C.H. et al. A Smart Bi-Directional Model of Heat Transfer and Free Surface Flow in Gas-Metal-Arc Fillet Welding for Practising Engineers. Weld World 49, 32–48 (2005). https://doi.org/10.1007/BF03266488
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03266488