Abstract
The technique of solving the inverse heat conduction problem (IHCP) to find the steady state welding conditions by observable or desired weld features is outlined. The objective function is an augmented sum of weighted squares of differences in value between calculated and measured temperature-related functions, constraints and regularisation of unknown parameters. The algorithm for finding the minimum of the objective function is based on the Gauss-Newton method. As examples, the heat input distributions during laser edge welding of aluminium alloys AC 120 (authors’ experiments), electron beam welding of low-carbon and stainless steel and as well as laser welding of aluminium alloy Al-Mg-Li-Cu-Mn-Zn (experimental data found in the published literature) (thin sheets and thick plates) are found. The weld interface, molten pool boundary and weld texture orientation have been used as the temperature-related functions. The results of simulation are directly compared with the experimental evidence. The suggested technique allows evaluating the heat efficiency of the welding process. It can be applied to an optimisation problem.
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References
A.N. Tikhonov and V.Y. Arsenin, Solutions of III-Posed Problems, V.H. Winston and Sons, New York, Wiley, Washington, D.C., 1977.
L.A. Kozdoba and P.G. Krukovsky, Methods of Solution to Inverse Heat Transfer Problems, Naukova Dumka, Kiev, 1982.
J.V. Beck, B. Blackwell and C.R. St. Clair, Inverse Heat Conduction: III-Posed Problems, Wiley-International, New York, 1985.
A.N. Tikhonov, V.D. Kalner and V.B. Glasko, Mathematical Modelling of Technological Processes and Method of Inverse Problems in Machinery, Machinostroenie, Moscow, 1990.
A.N. Tikhonov, A.V. Goncharsky, V.V. Stepanov and A.G. Yagola, Numerical Methods of Solution to Ill-Posed Problems, Nauka, Moscow, 1990.
O.M. Alifanov, Inverse Heat Transfer Problems, Springer, Berlin, 1994.
K. Kurpisz and A.J. Nowak, Inverse Thermal Problems, Computational Mechanics Publications, Southampton, UK and Boston, USA, 1995.
A.N. Tikhonov, A.S. Leonov and A.G. Yagola, Nonlinear Ill-Posed Problems, Chapman & Hall, London, 1998.
J.V. Beck, “Inverse Problems in Heat Transfer”, Mathematics of Heat Transfer, G.E. Tupholme and A.S. Wood ed., Clarendon Press, Oxford, 1998, p. 13–24.
J.V. Beck, “Inverse Problems in Heat Transfer with Application to Solidification and Welding”, Modeling of Casting, Welding and Advanced Solidification Processes V, M. Rappaz, M.R. Ozgu and K.W. Mahin ed., The Minerals, Metals and Materials Society, 1991, 503–514.
N. Zabaras, “Inverse Modeling of Solidification and Welding Processes”, Modeling of Casting, Welding and Advanced Solidification Processes V, M. Rappaz, M.R. Ozgu and K.W. Mahin ed., The Minerals, Metals and Materials Society, 1991, 523–530.
N. Al-Khalidy, “Two-Dimensional Inverse Phase Change Problem”, Advanced Computational Methods in Heat Transfer IV, L.C. Wrobel, G. Comini, C.A. Brebbia and A.J. Nowak ed., Computational Mechanics Publications, Southampton, Boston, 1996, 427–437.
V.A. Karkhin, V.V. Plochikhine and H.W. Bergmann, “Solution of the Inverse Heat Conduction Problem for Determining the Heat Input, Weld Shape and Grain Structure during Laser Welding”, Science and Technology of Welding and Joining (to be published).
V.A. Karkhin, V.V. Plochikhine, A.S. Ilyin and H.W. Bergmann, “Reconstruction of the Heat Distribution and Grain Structure during Laser Beam Welding”, Conference “Lasers in Engineering”, 15 June 2001, Munich, Germany (to be published).
V.A. Karkhin, A.S. Ilyin, V.V. Ploshikhine and H.W. Bergmann, “Inverse Modelling of the Heat Input Distribution during Deep Penetration Laser and Electron Beam Welding”, 8th Nordic Conference on Laser Materials Processing, Copenhagen, Denmark, 2001, 289–300.
M. Rappaz, J.-L. Desbiolles, J.-M. Drezet, Ch.-A. Gandin, A. Jacot and Ph. Thevoz, “Application of Inverse Methods to the Estimation of Boundary Conditions and Properties”, Modelling of Casting, Welding and Advanced Solidification Processes VII, M. Cross and J. Campbell ed., The Minerals, Metals and Materials Society, 1995, 449–457.
H.W. Bergmann, S. Mayer, K. Mueller and V.V. Ploshikhin, “Texture Evolution in Laser Beam Welds Undergoing the Planar Solidification Mode”, Mathematical Modelling of Weld Phenomena 4, H. Cerjak ed., The Institute of Materials, London, 1998, 166–183.
N.N. Rykalin, Calculation of Heat Flow in Welding, Translated by Zvi Paley and CM. Adams, Moscow, 1951.
V.A. Karkhin, “Thermal Fundamentals of Welding”, Publ. LGTU, Leningrad, 1990.
V.V. Ploshikhin and H.W. Bergmann, “Simulation of Grain Structures in Laser Beam Welds Undergoing the Planar Solidification Mode”, Mathematical Modelling of Weld Phenomena 4, H. Cerjak ed., The Institute of Materials, London, 1998, 150–165.
F. Dausinger, Strahlwerkzeug Laser: Energeeinkopplung und Processeffektivitaet, Teubner Verlag, Stuttgart, 1995.
V.V. Bashenko and N.N. Detsik, “Effect of Weld Form in Electron Beam Welding on the Properties of the Welded Joint in Low Carbon Steels in Different Sections”, Welding International, 1988, 10, 878–880.
V.A. Karkhin and A.Y. Pilipenko, “Modelling Thermal Cycles in the Weld Metal and the Heat Affected Zone in Beam Methods of Welding Thick Plates”, Welding International, 1997, 11, 401–403.
S.G. Lambrakos and J.O. Milewski, “Analysis of Welding Processes Using a Method Based on Constrained Parameter-Optimization”, Trends in Welding Research, Proceedings of the 5th Intern. Conf., J.M. Vitek, S.A. David, J.A. Johnson, H.B. Smartt and T. DebRoy ed., Pine Mountain, USA, 1998, 37–42.
E.A. Metzbower, “Laser Beam Welding: Thermal Profiles and HAZ Hardness”, Welding Journal, 1990, 7, 272–s–278–s.
J.M. Dowden, P. Kapadia and R. Ducharme, “An Analytical Model of Deep Penetration Welding of Metals with a Continuous CO2 Laser”, Int. J. for the Joining of Materials, 7 (2/3), 1995, 54–61.
M. Davis, P. Kapadia and J. Dowden, “Modelling the Fluid Flow in Laser Beam Welding”, Welding Journal, 1986, 7, 167–s–174–s.
N. Postacioglu, P. Kapadia, M. Davis and J. Dowden, “Upwelling in the Liquid Region Surrounding the Keyhole in Penetration Welding with a Laser”, Journal of Physics D. Applied Physics, 1987, 20, 340–345.
I.S. Gradshteyn and I.M. Ryzhik, Tables of Integrals, Series, and Products, Academic Press, Orlando, 1980.
A.F. Norman, R. Ducharme, A. Mackwood, P. Kapadia and P.B. Prangnell, “Application of Thermal Modelling to Laser Beam Welding of a Aluminium Alloys”, Science and Technology of Welding and Joining, 1998, 3 (5), 260–266.
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2001 K. E. Easterling Award winning paper presented at the 6th International Seminar “Numerical Analysis of Weldability”, 1–3 October 2001, Graz-Seggau, Austria
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Karkhin, V.A., Plochikhine, V.V., Ilyin, A.S. et al. Inverse Modelling of Fusion Welding Processes. Weld World 46, 2–13 (2002). https://doi.org/10.1007/BF03263391
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DOI: https://doi.org/10.1007/BF03263391
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