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Inverse Thermal Analysis of Refractory Metal Laser Welds

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Abstract

Case study inverse thermal analyses of Vanadium and Tantalum laser welds are presented. These analyses employ a methodology that is in terms of analytic basis functions for inverse thermal analysis of steady-state energy deposition in plate structures. The results of the case studies presented provide parametric representations of weld temperature histories that can be adopted as input data to various types of computational procedures, such as those for prediction of solid-state phase transformations. In addition, these temperature histories can be used to construct parametric-function representations for inverse thermal analysis of welds corresponding to other process parameters or welding processes process conditions of which fall within similar regimes. This study also discusses specific aspects the inverse-analysis methodology relevant to further development of algorithms for its application in practice.

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References

  1. R.W. Farebrother, Linear Least Square Computations, Marcel Dekker, New York, 1988

    Google Scholar 

  2. Y.B. Bard, Nonlinear Parameter Estimation, Academic Press, New York, 1974

    Google Scholar 

  3. K. Levenberg, A Method for the Solution of Certain Non-linear Problems in Least-Squares, Q. Appl. Math., 1944, 2, p 164–168

    Google Scholar 

  4. D.W. Marquardt, An Algorithm for Least Squares Estimation of Nonlinear Parameters, J. Soc. Ind. Appl. Math., 1963, 11, p 431–441

    Article  Google Scholar 

  5. S. Mishra and T. DebRoy, Tailoring Gas Tungsten Arc Weld Geometry using a Genetic Algorithm and a Neural Network Trained with Convective Heat Flow Calculations, Mater. Sci. Eng. A, 2007, 454-455, p 477–486

    Article  Google Scholar 

  6. A. Tarantola, Inverse Problem Theory and Methods for Model Parameter Estimation, SIAM, Philadelphia, PA, 2005

    Book  Google Scholar 

  7. M.N. Ozisik and H.R.B. Orlande, Inverse Heat Transfer, Fundamentals and Applications, Taylor and Francis, New York, 2000

    Google Scholar 

  8. K. Kurpisz and A.J. Nowak, Inverse Thermal Problems, Computational Mechanics Publications, Boston, USA, 1995

    Google Scholar 

  9. O.M. Alifanov, Inverse Heat Transfer Problems, Springer, Berlin, 1994

    Book  Google Scholar 

  10. J.V. Beck, B. Blackwell, and C.R. St, Clair, Inverse Heat Conduction: Ill-Posed Problems, Wiley, New York, 1985

    Google Scholar 

  11. 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, Eds., The Minerals, Metals and Materials Society, 1991, p 427–437

  12. J.V. Beck, Inverse Problems in Heat Transfer, Mathematics of Heat Transfer, G.E. Tupholme and A.S. Wood, Eds., Clarendon Press, 1998, p 13–24

  13. S.G. Lambrakos, A.D. Zervaki, G.N. Haidemenopoulos, and V. Stergiou, Basis Functions and Parameterizations for Inverse Analysis of Welding Processes, Mathematical Modelling of Weld Phenomena, Vol. 9, H.H. Cerjak, Ed., Verlag der Technischen Universite Graz, Austria, 2011, p 793

  14. A.D. Zervaki, G.N. Haidemenopoulos, and S.G. Lambrakos, Analysis of Heat Affected Zone using Direct and Inverse Modelling in 6XXX Aluminum Alloys, Mathematical Modelling of Weld Phenomena, Vol. 8, H.H. Cerjak, Ed., Verlag der Technischen Universite Graz, Austria, 2007, p 907

  15. S.G. Lambrakos and S.G. Michopoulos, Algorithms for Inverse Analysis of Heat Deposition Processes, Mathematical Modelling of Weld Phenomena, Vol. 8, H.H. Cerjak, Ed., Verlag der Technischen Universite Graz, Austria, 2007, p 847

  16. S.G. Lambrakos and J.O. Milewski, Analysis of Welding and Heat Deposition Processes using an Inverse-Problem Approach, Mathematical Modelling of Weld Phenomena, Vol. 7, H.H. Cerjak, Ed., Verlag der Technischen Universite Graz, Austria, 2005, p 1025–1055

  17. J. Xie and J. Zou, Numerical Reconstruction of Heat Fluxes, SIAM J. Numer. Anal., 2005, 43(4), p 1504–1535

    Article  Google Scholar 

  18. H.S. Carslaw and J.C. Jaegar, Conduction of Heat in Solids, 2nd ed., Clarendon Press, Oxford, 1959, p 374

  19. T.A. Palmer, B. Wood, J.W. Elmer, C. Westrich, J.O. Milewski, M. Piltch, and R. Carpenter: Characterization of Stainless Steel and Refractory Metal Welds Made Using a Diode-Pumped, Continuous Wave Nd:YAG Laser, Report UCRL-ID-146005, Lawrence Livermore.

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Acknowledgment

This study was supported by a Naval Research Laboratory (NRL) internal core program.

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Authors and Affiliations

  1. Center for Computational Materials, Code 6390, Materials Science and Technology Division, Naval Research Laboratory, Washington, DC, USA

    S. G. Lambrakos

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  1. S. G. Lambrakos
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Correspondence to S. G. Lambrakos.

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Lambrakos, S.G. Inverse Thermal Analysis of Refractory Metal Laser Welds. J. of Materi Eng and Perform 22, 2467–2476 (2013). https://doi.org/10.1007/s11665-013-0571-6

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  • DOI: https://doi.org/10.1007/s11665-013-0571-6

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