Skip to main content
SpringerLink
Log in

Modeling of transport phenomena and solidification cracking in laser spot bead-on-plate welding of AA6063-T6 alloy. Part I—the mathematical model

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

In this study, a transient unified model including simulation of the temperature, velocity, solute (Mg2Si) concentration and stress fields, free surface, and laser-induced plasma, has been developed to predict the transport phenomena and solidification cracking susceptibility during laser spot bead-on-plate welding of aluminum alloy. The model consists of the modeling of heat, momentum and mass transports in the metal and plasma zones, thermomechanical modeling, and evaluation of solidification cracking. The full set of mathematical equations and numerical methods are presented. The main challenges and the corresponding solutions for the modeling are discussed. In this model, the lever-rule based on the phase diagram was used to deal with the macroscale segregation at the solid–liquid interface, while the solute transfer due to the diffusion and convection were calculated by the conservation equations for transport phenomena. The solute redistribution in the weldment is coupled with the changes of liquidus and solidus temperatures of the material. The total strain consists of the elastic, viscoplastic, and thermal parts that are coupled with the calculated temperature, velocity, and solute in the weldment. The criterion for the weld solidification cracking was established based on the strain theory, in which the cracking initiates only when the strain exceeds the threshold strain in the brittle temperature range (btr).

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

Similar content being viewed by others

References

  1. Mazumder J (1990) Laser–beam welding. In: ASM handbook, Volume 6, welding, brazing, and soldering. ASM international, pp 262–269

  2. Kawahito Y, Mizutani M, Katayama S (2007) Elucidation of high–power fiber laser welding phenomena of stainless steel and effect of factors on weld geometry. J Phys D Appl Phys 40:5854–5859

    Article  Google Scholar 

  3. Pastor M, Zhao H, Martukanitz RP, DebRoy T (1999) Porosity, underfill and magnesium lose during continuous wave Nd: YAG laser welding of thin plates of aluminum alloys 5182 and 5754. Weld J 78:207s–216s

    Google Scholar 

  4. Zhao H, White DR, DebRoy T (1999) Current issues and problems in laser welding of automotive aluminum alloys. Int Mater Rev 44:238–266

    Article  Google Scholar 

  5. Kou S (2003) Solidification and liquation cracking issues in welding. JOM 55:37–42

    Article  Google Scholar 

  6. Cross CE (2005) On the origin of weld solidification cracking, in: Thomas Böllinghaus, Horst Herolded, Hot cracking phenomena in welds, Volume 1, Springer

  7. Thomas BG (2009) Modeling of hot tearing and other defects in casting processes. In: ASM Handbook, Volume 22A, Fundamentals of Modeling for Metals Processing. ASM International, pp 362–374

  8. Cicală E, Duffetb G, Andrzejewski H, Grevey D, Ignata S (2005) Hot cracking in Al–Mg–Si alloy laser welding–operating parameters and their effects. Mater Sci Eng A 395:1–9

    Article  Google Scholar 

  9. Kim HT, Nam SW, Hwang SH (1996) Study on the solidification cracking behavior of high strength aluminum alloy welds: effects of alloying elements and solidification behaviors. J Mater Sci 31:2859–2864

    Article  Google Scholar 

  10. Yang YP, Dong P, Zhang J, Tian X (2000) A hot-cracking mitigation technique for welding high-strength aluminum alloy. Weld J 79:9s–17s

    Google Scholar 

  11. Ploshikhin V, Zoch HW (2005) Integrated mechanical-metallurgical approach to modeling of solidification cracking in Welds, Hot Crack Phenom Welds 223–244

  12. Ploshikhin V, Prikhodovsky A, Ilin A, Makhutin M, Heimerdinger C, Palm F (2006) Influence of the weld metal chemical composition on the solidification cracking susceptibility of AA6056-T4 alloy. Weld World 50:46–50

    Article  Google Scholar 

  13. Rao ZH, Liao SM, Tsai HL (2011) Modeling of hybrid laser-GMA welding: a review and challenges. Sci Technol Weld Join 16:300–305

    Article  Google Scholar 

  14. Beck M, Berger P, Hügel H (1995) The effect of plasma formation on beam focusing in deep penetration welding with CO2 lasers. J Phys D Appl Phys 28:2430–2442

    Article  Google Scholar 

  15. Tix C, Simon G (1994) Model of a laser heated plasma interacting with walls arising in laser keyhole welding. Phys Rev E 50:453–462

    Article  Google Scholar 

  16. Tix C, Simon G (1993) A transport theoretical model of the keyhole plasma in penetration laser welding. J Phys D Appl Phys 26:2066–2074

    Article  Google Scholar 

  17. Dilthey U, Goumeniouk A, Lopota V, Turichin G (2000) Kinetic description of keyhole plasma in laser welding. J Phys D Appl Phys 33:2747–2753

    Article  Google Scholar 

  18. Fabbro R, Chouf K (2000) Keyhole modeling during laser welding. J Appl Phys 87:4075–4083

    Article  Google Scholar 

  19. Solana P, Negro G (1997) A study of the effect of multiple reflections on the shape of keyhole in the laser processing of materials. J Phys D Appl Phys 30:3216–3222

    Article  Google Scholar 

  20. Semak V, Matsunawa A (1997) The role of recoil pressure in energy balance during laser materials processing. J Phys D Appl Phys 30:2541–2552

    Article  Google Scholar 

  21. Dowden J, Chang WS, Kapadia P, Strange C (1991) Dynamics of the vapor flow in the keyhole in penetration welding with a laser at medium welding speeds. J Phys D Appl Phys 24:519–532

    Article  Google Scholar 

  22. Meng C, Lu FG, Cui HC, Tang XH (2013) Research on formation and stability of keyhole in stationary laser welding on aluminum MMCs reinforced with particles. Int J Adv Manuf Technol 67:2917–2925

    Article  Google Scholar 

  23. Postacioglu N, Kapadia P, Davis M, Dowden J (1987) A keyhole model in penetration welding with a laser. J Phys D Appl Phys 29:340–345

    Article  Google Scholar 

  24. Gao ZG, Wu YX, Huang J (2009) Analysis of weld pool dynamics during stationary laser-MIG hybrid welding. Int J Adv Manuf Technol 44:870–879

    Article  Google Scholar 

  25. Rohde M, Markert C, Pfleging W (2010) Laser micro-welding of aluminum alloys: experimental studies and numerical modeling. Int J Adv Manuf Technol 50:207–215

    Article  Google Scholar 

  26. Zhou J, Tsai HL, Wang PC (2006) Transport phenomena and keyhole dynamics during pulsed laser welding. ASME J Heat Trans 128:680–690

    Article  Google Scholar 

  27. Duley W (1999) Laser welding. Wiley, New York

    Google Scholar 

  28. Martin CL, Favier D, Suéry M (1999) Fracture behavior in tension of viscoplastic porous metallic materials saturated with liquid. Int J Plast 15:981–1008

    Article  MATH  Google Scholar 

  29. Martin CL, Braccini M, Suéry M (2002) Rheological behavior of the mushy zone at small strains. Mater Sci Eng A 325A:293–302

    Google Scholar 

  30. Ni J, Beckermann C (1990) A volume-averaged two-phase model for transport phenomena during solidification. Metall Trans B 22:349–361

    Article  Google Scholar 

  31. Farup I, Mo A (2000) Two-phase modeling of mushy zone parameters associated with hot tearing. Metall Mater Trans A 31A:1461–1472

    Article  Google Scholar 

  32. Nicolli LC, Mo A, M’Hamdi M (2005) Modeling of macrosegregation caused by volumetric deformation in a coherent mushy zone. Metall Mater Trans A 36A:433–441

    Article  Google Scholar 

  33. Suyitno KWH, Katgerman L (2005) Hot tearing criteria evaluation for direct-chill casting of an Al-4.5 Pct Cu alloy. Metall Mater Trans A 36A:1537–1546

    Article  Google Scholar 

  34. Fjaer HG, Mo A (1990) ALSPEN-A mathematical model for thermal stresses in direct chill casting of aluminum billets. Metall Trans B 21B:1049–1061

    Google Scholar 

  35. Tan L, Zabaras N (2005) A thermomechanical study of the effects of mold topography on the solidification of aluminum alloys. Mater Sci Eng A 404:197–207

    Article  Google Scholar 

  36. Gao ZH (2012) Numerical modeling to understand liquation cracking propensity during laser and laser hybrid welding (I). Int J Adv Manuf Technol 63:291–303

    Article  Google Scholar 

  37. Chiang KC, Tsai HL (1992) Shrinkage-induced fluid flow and domain change in two-dimensional alloy solidification. Int J Heat Mass Tran 35:1763–1769

    Article  Google Scholar 

  38. Wang Y, Tsai HL (2001) Impingement of filler droplets and weld pool dynamics during gas metal arc welding process. Int J Heat Mass Transf 44:2067–2080

    Article  MATH  Google Scholar 

  39. Flemings MC, Nereo GE (1967) Macrosegregation. Trans AIME 239:1449–1461

    Google Scholar 

  40. Flemings MC (1974) Solidification process. Metall Trans 5:2121–2134

    Article  Google Scholar 

  41. Flemings MC (1990) Behavior of metal alloys in the semisolid state. Metall Trans A 22A:957–982

    Google Scholar 

  42. Beckermann C (2002) Modeling of macrosegregation: applications and future needs. Int Mater Rev 47:243–261

    Article  Google Scholar 

  43. Lesoult G, Gandin CA, Niane NT (2003) Segregation during solidification with spongy deformation of the mushy zone. Acta Mater 51:5263–5283

    Article  Google Scholar 

  44. Kumar KCH, Chakraborti N, Lukas H, Bodak O, Rokhlin L (2005) Aluminum–magnesium–silicon, In: Materials science international team MSIT, light metal ternary systems: phase diagrams. Crystallographic and thermodynamic data

  45. Zhang J, Fan Z, Wang YQ, Zhou BL (2001) Equilibrium pseudobinary Al–Mg2Si phase diagram. Mater Sci Technol 17:494–496

    Article  MATH  Google Scholar 

  46. Torrey MD, Cloutman LD, Mjolsness RC, Hirt CW (1985) NASA-VOF2D: a computer program for incompressible flows with free surfaces, LA-10612-MS, Los Alamos National Laboratory

  47. Knight CJ (1979) Theoretical modeling of rapid surface vaporization with back pressure. AIAA J 17:519–523

    Article  Google Scholar 

  48. Landau LD, Lifshitz EM (1980) Statistical physics. Pergamon

  49. Kaplan A (1994) A model of deep penetration laser welding based on calculation of the keyhole profile. J Phys D Appl Phys 27:1805–1814

    Article  Google Scholar 

  50. Siegel R, Howell JR (1992) Thermal radiation heat transfer, third ed. Hemisphere Publishing Corp

  51. Pellini WS (1952) Strain theory of hot tearing. Foundry 80:125–199

    Google Scholar 

  52. Eskin DG, Katgerman SL (2004) Mechanical properties in the semi-solid state and hot tearing of aluminum alloys. Prog Mater Sci 49:629–711

    Article  Google Scholar 

  53. Mondolfo LF (1976) Aluminum alloys, structure and properties. Butterworth’s, London

    Google Scholar 

  54. Welch JE, Harlow FH, Shannon JP, Daly BJ (1966) The MAC method. A computing technique for solving viscous, incompressible, transient fluid-flow problems involving free surfaces. Los Alamos Report No LA-3425

Download references

Author information

Authors and Affiliations

  1. School of Energy Science and Engineering, Central South University, Changsha, 410083, China

    Jiangwei Liu, Zhenghua Rao & Shengming Liao

  2. Global Research & Development, General Motors Corporation, Warren, MI, 48090, USA

    Pei-Chung Wang

Authors
  1. Jiangwei Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhenghua Rao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shengming Liao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Pei-Chung Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhenghua Rao.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, J., Rao, Z., Liao, S. et al. Modeling of transport phenomena and solidification cracking in laser spot bead-on-plate welding of AA6063-T6 alloy. Part I—the mathematical model. Int J Adv Manuf Technol 73, 1705–1716 (2014). https://doi.org/10.1007/s00170-014-5924-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-014-5924-2

Keywords

Search

Navigation