Skip to main content
SpringerLink
Log in

Inverse Thermal Analysis of Ti-6Al-4V Laser Welds Using Solidification and Heat-Affected Zone Boundaries

  • Published:
Journal of Materials Engineering and Performance Aims and scope Submit manuscript

Abstract

Temperature histories of Ti-6Al-4V laser welds are presented, which are calculated using numerical-analytical basis functions and boundary constraints based on measured solidification and heat-affected zone cross sections. These weld temperature histories can be adopted as input data to various types of computational procedures, which include numerical models for prediction of solid-state phase transformations and mechanical response. In addition, these temperature histories can be used parametrically for inverse thermal analysis of welds corresponding to other welding processes whose process conditions are within similar regimes. The present study applies an inverse thermal analysis procedure that uses three-dimensional constraint conditions whose two-dimensional projections are mapped within transverse cross sections of experimentally measured solidification and heat-affected zone boundaries.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

References

  1. S. Kou, Welding Metallurgy, 2nd ed., Wiley, New York, 2003, doi:10.1002/0471434027

    Google Scholar 

  2. O. Grong, Metallurgical Modelling of Welding, 2 ed., Materials Modelling Series, (H.K.D.H. Bhadeshia, ed.), published by The Institute of Materials, UK, (1997), chapter 2: pp. 1–115

  3. S.V. Patankar, Numerical Heat Transfer and Fluid Flow, Series in Computational Methods in Mechanics and Thermal Sciences Hemisphere Publishing Corporation, London, 1980

    Google Scholar 

  4. W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Numerical Recipes in Fortran 77, The Art of Scientific Computing, Vol 1, 2nd ed., Fortran Numerical Recipes Cambridge University Press, New York, 1997

    Google Scholar 

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

    Book  Google Scholar 

  6. C.R. Vogel, Computational Methods for Inverse Problems, SIAM, Philadelphia, 2002

    Book  Google Scholar 

  7. A.G. Ramm, Inverse Problems, Mathematical and Analytical Techniques with Applications to Engineering, Springer, New York, 2005

    Google Scholar 

  8. J.V. Beck, B. Blackwell, and C.R. St, Clair, Inverse Heat Conduction: Ill-Posed Problems, Wiley Interscience, New York, 1995

    Google Scholar 

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

    Book  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  12. 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, pp. 427–437

  13. J.V. Beck, Inverse Problems in Heat Transfer, Mathematics of Heat Transfer, G.E. Tupholme and A.S. Wood eds., Clarendon Press, (1998), pp. 13–24

  14. A.N. Tikhonov, Inverse Problems in Heat Conduction, J. Eng. Phys., 1975, 29(1), p 816–820

    Article  Google Scholar 

  15. O.M. Alifanov, Solution of an Inverse Problem of Heat-Conduction by Iterative Methods, J. Eng. Phys., 1974, 26(4), p 471–476

    Article  Google Scholar 

  16. O.M. Alifanov and V.Y. Mikhailov, Solution of the Overdetermined Inverse Problem of Thermal Conductivity Involving Inaccurate Data, High Temp., 1985, 23(1), p 112–117

    Google Scholar 

  17. E.A. Artyukhin and A.V. Nenarokomov, Coefficient Inverse Heat Conduction Problem, J. Eng. Phys., 1988, 53, p 1085–1090

    Article  Google Scholar 

  18. T.J. Martin and G.S. Dulikravich, Inverse Determination of Steady Convective Local Heat Transfer Coefficients, ASME J. Heat Transf., 1998, 120, p 328–334

    Article  Google Scholar 

  19. S.G. Lambrakos and S.G. Michopoulos, Algorithms for Inverse Analysis of Heat Deposition Processes, Mathematical Modelling of Weld Phenomena, Volume 8, 847, Published by Verlag der Technischen Universite Graz, Austria (2007)

  20. S.W. Smith, The Scientist and Engineer’s Guide to Digital Signal Processing, California Technical Publishing, San Diego, 1997

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  24. S.G. Lambrakos and J.O. Milewski, Analysis of Welding and Heat Deposition Processes using an Inverse-Problem Approach, Mathematical Modelling of Weld Phenomena, 7, 1025, Published by Verlag der Technischen Universite Graz, Austria 2005, pp. 1025–1055

  25. S.G. Lambrakos, Inverse Thermal Analysis of 304L Stainless Steel Laser Welds, J. Mater. Eng. Perform., 2013, 22(8), p 2141

    Google Scholar 

  26. S.G. Lambrakos, Inverse Thermal Analysis of Stainless Steel Deep-Penetration Welds Using Volumetric Constraints, J. Mater. Eng. Perform., 2014, 23(6), p 2219–2232. doi:10.1007/s11665-014-1023-7

  27. S.G. Lambrakos, Inverse Thermal Analysis of Welds Using Multiple Constraints and Relaxed Parameter Optimization, J. Mater. Eng. Perform., 2015, 24(8), p 2925–2936

    Article  Google Scholar 

  28. D. Rosenthal, The Theory of Moving Sources of Heat and Its Application to Metal Treatments, Trans. ASME, 1946, 68, p 849–866

    Google Scholar 

  29. J. Goldak, A. Chakravarti, and M. Bibby, A New Finite Element Model for Welding Heat Source, Metall. Trans. B, 1984, 15, p 299–305

    Article  Google Scholar 

  30. R.O. Myhr and O. Grong, Acta Metall. Mater., 1990, 38, p 449–460

    Article  Google Scholar 

  31. R.C. Reed and H.K.D.H. Bhadeshia, A Simple Model for Multipass Welds, Acta Metall. Mater., 1994, 42(11), p 3663–3678

    Article  Google Scholar 

  32. V.A. Karkhin, P.N. Homich, and V.G. Michailov, Models for Volume Heat Sources and Functional-Analytic Technique for Calculating the Temperature Fields in Butt Welding, Mathematical Modelling of Weld Phenomena, Volume 8, 847, Published by Verlag der Technischen Universite Graz, Austria (2007)

  33. A.A. Deshpande, A. Short, W. Sun, D.G. McCartney, L. Xu, and T.H. Hyde, Finite-Element Analysis of Experimentally Identified Parametric Envelopes for Stable Keyhole Plasma Arc Welding of a Titanium Alloy, J. Strain Anal. Eng. Des., 2012, 47(5), p 266–275

    Article  Google Scholar 

  34. I.S. Leoveanu, G. Zgura, and D. Birsan, Modeling the Heat and Fluid Flow in the Welded Pool, Bulletin of the Transilvania University of Brasov, Vol. 3, p. 363–368, ISSN 1223-9631, 2007

  35. I.S. Leoveanu and G. Zgura, Modelling the Heat and Fluid Flow in the Welded Pool from High Power Arc Sources, Materials Science Forum, Editors: C. Lee, J.-B. Lee, D.-H. Park, and S.-J. Na, vols. 580–582, p. 443–446, 2008

  36. E. Akman, A. Demir, T. Canel, and T. Sinmazcelik, Laser Welding of Ti6Al4V Titanium, J. Mater. Proc. Technol., 2009, 209, p 3705–3713

    Article  Google Scholar 

  37. R. Bracwell, The Fourier Transform and Its Applications, McGraw Hill, New York, 2000

    Google Scholar 

  38. R. Haberman, Applied Partial Differential Equations with Fourier Series and Boundary Value Problems, 5th ed., Pearson, 2012

  39. S.G. Lambrakos, Parametric Modeling of Welding Processes Using Numerical-Analytical Basis Functions and Equivalent Source Distributions, J. Mater. Eng. Perform., 2016, 25(4), p 1360–1375

    Article  Google Scholar 

  40. E.A. Metzbower, D.W. Moon, C.R. Feng, S.G. Lambrakos, and R.J. Wong, Modelling of HSLA-65 GMAW Welds, Mathematical Modelling of Weld Phenomena, 7, Published by Verlag der Technischen Universite Graz, Austria, p. 327–339 (2005)

  41. Welding Handbook, 9th Edition, Volume 1, Welding Science and Technology, Publication of the American Welding Society (2017)

Download references

Acknowledgments

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

Author information

Authors and Affiliations

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

    S. G. Lambrakos

Authors
  1. S. G. Lambrakos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. G. Lambrakos.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lambrakos, S.G. Inverse Thermal Analysis of Ti-6Al-4V Laser Welds Using Solidification and Heat-Affected Zone Boundaries. J. of Materi Eng and Perform 26, 1195–1208 (2017). https://doi.org/10.1007/s11665-017-2546-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11665-017-2546-5

Keywords

Search

Navigation