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Experimental and theoretical cooling velocity profile inside laser welded metals using keyhole approximation and Boubaker polynomials expansion

  • Asma Belhadj
  • Jamel Bessrour
  • Mahmoud Bouhafs
  • Laurent Barrallier
Article

Abstract

In this paper we are concerned with the t-dependent cooling velocity during laser welding sequences. The temperature profile has been yielded by using keyhole approximation for the melted zone and solving the heat transfer equation. A polynomial expansion has been adopted as a guide to determining the cooling velocity during welding cut-off stage. A thorough comparison with experimental results and recently published profiles has been carried out.

Keywords

Laser welding Keyhole model Cooling velocity Boubaker polynomials Temperature profiling 

PACS

02.00.00 02.30.Jr 02.60.Lj 

Notes

Acknowledgements

The authors would like to acknowledge help and assistance from Associate Prof. Dr K. Boubaker from University of Tunis (Tunisia).

References

  1. 1.
    Singh RK, Narayan J. Pulsed-laser evaporation technique for deposition of thin films: physics and theoretical model. Phys Rev B. 1990;41:8843–59.CrossRefGoogle Scholar
  2. 2.
    Anisimov SI, Luk’yanchuk BS, Luches A. An analytical model for three-dimensional laser plume expansion into vacuum in hydrodynamic regime. Appl Surf Sci. 1996;96–98:24–32.CrossRefGoogle Scholar
  3. 3.
    Koopman DW. Langmuir probe and microwave measurements of streaming plasmas generated by focused laser pulses. Phys Fluids. 1971;14:1707–16.CrossRefGoogle Scholar
  4. 4.
    Toftmann B, Schou J, Hansen TN, Lunney JG. Evolution of the plasma parameters in the expanding laser ablation plume of silver. Phys Rev Lett. 2000;84:3998–4001.CrossRefGoogle Scholar
  5. 5.
    Weaver I, Martin GW, Graham WG, Morrow T, Lewis CLS. The Langmuir probe as a diagnostic of the electron component within low temperature laser ablated plasma plumes. Rev Sci Instrum. 1999;70:1801–5.CrossRefGoogle Scholar
  6. 6.
    Doggett B, Budtz-Joergensen C, Lunney JG, Sheerin P, Turner MM. Behaviour of a planar Langmuir probe in a laser ablation plasma. Appl Surf Sci. 2005;247:134–8.CrossRefGoogle Scholar
  7. 7.
    Chaouachi A, Boubaker K, Amlouk M, Bouzouita H. Enhancement of pyrolysis spray disposal performance using thermal time-response to precursor uniform deposition. Eur Phys J Appl Phys. 2007;37:105–9.CrossRefGoogle Scholar
  8. 8.
    Ghanouchi J, Labiadh H, Boubaker K. An attempt to solve the heat transfer equation in a model of pyrolysis spray using 4q-order Boubaker polynomials. Int J Heat Technol. 2008;26:49–53.Google Scholar
  9. 9.
    Awojoyogbe OB, Boubaker K. A solution to Bloch NMR flow equations for the analysis of homodynamic functions of blood flow system using m-Boubaker polynomials. Curr Appl Phys. 2009;9:278–83.CrossRefGoogle Scholar
  10. 10.
    Boubaker K. On modified Boubaker polynomials: some differential and analytical properties of the new polynomials issued from an attempt for solving bi-varied heat equation. Trends Appl Sci Res. 2007;2:540–4.CrossRefGoogle Scholar
  11. 11.
    Labiadh H. A Sturm-Liouville shaped characteristic differential equation as a guide to establish a quasi-polynomial expression to the Boubaker polynomials. J Differ Equ Control Process. 2007;2:117–33.Google Scholar
  12. 12.
    Gallusser R, Dressler K. Application of the coulomb approximation to the Rydberg transitions of the NO molecule. Z Angew Math Phys. 1971;22:792–4.CrossRefGoogle Scholar
  13. 13.
    Armstrong BH, Purdum KL. Extended use of the Coulomb approximation: mean powers of r, a sum rule, and improved transition integrals. Phys Rev. 1966;150:51–8.CrossRefGoogle Scholar
  14. 14.
    Paul A, Debroy T. Free surface flow and heat transfer in conduction mode laser welding. Metall Mater Trans B. 1988;19:851–8.Google Scholar
  15. 15.
    Andreassen E, Myhre OJ, Oldervoll F, Hinrichsen EL, Grøstad K, Braathen MD. Nonuniform cooling in multifilament melt spinning of polypropylene fibers: cooling air speed limits and fiber-to-fiber variations. J Appl Polym Sci. 1995;58:1619–32.CrossRefGoogle Scholar
  16. 16.
    Belcher SL. Practical guide to injection blow molding. Boca Raton, FL: CRC Press; 2007. ISBN 0824757912, 9780824757915.Google Scholar
  17. 17.
    Santos CAC, Quaresma JNN, Lima JA. Convective heat transfer in ducts: the integral transform approach. Brazil: E-papers Servicos Editoriais Ltd; 2001. ISBN 8587922238, 9788587922236.Google Scholar
  18. 18.
    Mughal MP, Fawad H, Mufti R. Finite element prediction of thermal stresses and deformations in layered manufacturing of metallic parts. Acta Mech. 2006;183:61–79.CrossRefGoogle Scholar
  19. 19.
    Dowden J, Postacioglu N, Davis M, Kapadia P. A keyhole model in penetration welding with a laser. J Phys D Appl Phys. 1987;20:36–44.CrossRefGoogle Scholar
  20. 20.
    Semak VV, Bragg WD, Damkroger B, Kempka S. Transient model for the keyhole during laser welding. J Phys D Appl Phys. 1999;32:61–4.CrossRefGoogle Scholar
  21. 21.
    Ki H, Mazumder J, Mohanty PS. Modeling of laser keyhole welding: Part II: simulation of keyhole evolution, velocity, temperature profile, and experimental verification. Metall Mater Trans A. 2002;33:1831–42.CrossRefGoogle Scholar
  22. 22.
    Rai R, Kelly SM, Martukanitz RP, DebRoy T. A convective heat-transfer model for partial and full penetration keyhole mode laser welding of a structural steel. Metall Mater Trans A. 2008;39:98–112.CrossRefGoogle Scholar
  23. 23.
    Al-Kazzaz H, Medraj M, Caoand X, Jahazi M. Nd:YAG laser welding of aerospace grade ZE41A magnesium alloy: modeling and experimental investigations. Mater Chem Phys. 2008;109:61–76.Google Scholar
  24. 24.
    Kaplan A. A model of deep penetration laser welding based on calculation of the keyhole profile. J Phys D Appl Phys. 1994;27:1805–14.CrossRefGoogle Scholar
  25. 25.
    Lampa C, Kaplan AFH, Powell J, Magnusson C. An analytical thermodynamic model of laser welding. J Phys D Appl Phys. 1997;30:1293–9.CrossRefGoogle Scholar
  26. 26.
    Jin X, Li L, Zhang Y. A study on fresnel absorption and reflections in the keyhole in deep penetration laser welding. J Phys D Appl Phys. 2002;35:2304–10.CrossRefGoogle Scholar
  27. 27.
    Solana P, Negro G. A study of the effect of multiple reflections on the shape of the keyhole of the keyhole in the laser processing of materials. J Phys D Appl Phys. 1997;30:3216–22.CrossRefGoogle Scholar
  28. 28.
    Wu CS, Wang HG, Zhang YM. A new heat source model for keyhole plasma arc welding in FEM analysis of the temperature profile. Weld J. 2006;85:284–9.Google Scholar
  29. 29.
    Puchert R, Menzel U, Bärwolff A, Voß M, Lier Ch. Influence of heat source distributions in GaAs/GaAlAs quantum-well high-power laser arrays on temperature profile and thermal resistance. J Therm Anal Calorim. 1997;48:1273–82.CrossRefGoogle Scholar
  30. 30.
    Hakvoort G, Hol CM. DSC calibration during cooling. J Therm Anal Calorim. 1999;56:717–22.CrossRefGoogle Scholar
  31. 31.
    Holender J, Solstroktys J, Kozubski R. Numerical method of non-isothermal curve analysis by means of electrical resistance measurement during cooling. J Therm Anal Calorim. 1988;33:223–8.CrossRefGoogle Scholar
  32. 32.
    Hidvégi É, Csetényi EK, Keébe Gy. The effects of concentration and heating or cooling rate on the DTA curves of Al-Ce alloys. J Therm Anal Calorim. 1977;11:221–9.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2009

Authors and Affiliations

  • Asma Belhadj
    • 1
  • Jamel Bessrour
    • 2
  • Mahmoud Bouhafs
    • 2
  • Laurent Barrallier
    • 3
  1. 1.U.R. MA2I - L. MECASURFENIT - Art et Métiers ParisTechAix-en-ProvenceFrance
  2. 2.U.R. MA2IENITTunisTunisia
  3. 3.L. MECASURF Art et Métiers ParisTechAix-en-ProvenceFrance

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