Skip to main content
SpringerLink
Log in

An ALE approach for large-deformation thermoplasticity with application to friction welding

  • Original Paper
  • Published:
Computational Mechanics Aims and scope Submit manuscript

Abstract

This work describes the development and implementation of a large-deformation solver with thermomechanical friction contact for numerical simulation in applications such as friction welding processes. A finite strain associative coupled thermoplasticity model is used: this resolves the viscoplastic deformations in the thermomechanically affected zone as well as the elastic stresses in the parent material. An arbitrary Lagrangian–Eulerian (ALE) formulation for coupled finite strain thermoplasticity is developed and incorporated into the solver, in which the motion of the reference configuration is represented incrementally through a reference velocity field. Thus, the deformation from the material configuration is required neither explicitly in terms of a deformation field, nor implicitly in terms of the deformation gradient. While the finite element formulation and the solver are derived for the general 3D setting, the axisymetric approximation is made for application to a range of benchmark problems. These serve to elucidate features of the model and computational procedure, also through comparison with a fully Lagrangian approach. Simulation of a direct drive friction welding problem illustrates the robustness and reliability of the new numerical approach.

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

Similar content being viewed by others

References

  1. AgeletdeSaracibar C (1998) Numerical analysis of coupled thermomechanical frictional contact problems. Computational model and applications. Arch Comput Methods Eng 5(3):243–301

    Article  MathSciNet  Google Scholar 

  2. Argyris J, Doltsinis JS (1979) On the large strain inelastic analysis in natural formulation part I: quasistatic problems. Comput Methods Appl Mech Eng 20(2):213–251

    Article  MATH  Google Scholar 

  3. Armero F, Love E (2003) An arbitrary Lagrangian–Eulerian finite element method for finite strain plasticity. Int J Numer Methods Eng 57(4):471–508

    Article  MathSciNet  MATH  Google Scholar 

  4. Bangerth W, Hartmann R, Kanschat G (2007) deal.II—a general purpose object oriented finite element library. ACM Trans Math Softw 33(4):24/1-24/27

    Article  MathSciNet  MATH  Google Scholar 

  5. Bendzsak G, North T, Li Z (1997) Numerical model for steady-state flow in friction welding. Acta Mater 45(4):1735–1745

    Article  Google Scholar 

  6. Buffa G, Fratini L (2017) Strategies for numerical simulation of linear friction welding of metals: a review. Prod Eng Res Devel 11(3):221–235

    Article  Google Scholar 

  7. Chung J, Hulbert GM (1993) A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-\(\alpha \) method. J Appl Mech 60(2):371–375

    Article  MathSciNet  MATH  Google Scholar 

  8. Crossland B (1971) Friction welding. Contemp Phys 12(6):559–574

    Article  Google Scholar 

  9. Frigaard Ø, Grong Ø, Midling OT (2001) A process model for friction stir welding of age hardening aluminum alloys. Metall Mater Trans A 32(5):1189–1200

    Article  Google Scholar 

  10. Fu L, Duan L, Du S (2003) Numerical simulation of inertia friction welding process by finite element method. Weld J 82(3):65S-70S

    Google Scholar 

  11. Grujicic M, Arakere G, Pandurangan B, Ochterbeck JM, Yen CF, Cheeseman BA, Reynolds AP, Sutton MA (2011) Computational analysis of material flow during friction stir welding of AA5059 aluminum alloys. J Mater Eng Perform 21(9):1824–1840

    Article  Google Scholar 

  12. He X, Gu F, Ball A (2014) A review of numerical analysis of friction stir welding. Prog Mater Sci 65(3):1–66

    Article  Google Scholar 

  13. Johnson G, Cook W (1983) A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. In: Proceedings of the 7th international symposium on ballistics, The Hague, The Netherlands

  14. Lacy J, Novascone S, Richins W, Larson T (2008) A method for selecting software for dynamic event analysis: II-the Taylor anvil and dynamic Brazilian tests. In: Proceedings of the 16th international conference on nuclear engineering, vol 48175, pp 261–270

  15. Landell R, Kanan LF, Buzzatti D, Vicharapu B, De A, Clarke T (2020) Material flow during friction hydro-pillar processing. Sci Technol Weld Join 25(3):228–234

    Article  Google Scholar 

  16. Laursen T, Simo J (1993) A continuum-based finite element formulation for the implicit solution of multibody, large deformation-frictional contact problems. Int J Numer Methods Eng 36(20):3451–3485

    Article  MathSciNet  MATH  Google Scholar 

  17. Lehmann T, Blix U (1985) On the coupled thermo-mechanical process in the necking problem. Int J Plast 1(2):175–188

    Article  Google Scholar 

  18. Li W, Shi S, Wang F, Zhang Z, Ma T, Li J (2012) Numerical simulation of friction welding processes based on ABAQUS environment. J Eng Sci Technol Rev 5(3):10–19

    Article  Google Scholar 

  19. Li W, Wang F, Shi S, Ma T (2014) Numerical simulation of linear friction welding based on ABAQUS environment: challenges and perspectives. J Mater Eng Perform 23(2):384–390

    Article  Google Scholar 

  20. Maalekian M (2007) Friction welding-critical assessment of literature. Sci Technol Weld Join 12(8):738–759

    Article  Google Scholar 

  21. Maurya RR, Kauzlarich JJ (1969) Reciprocating friction bonding apparatus. US Patent 3,420,428

  22. Moal A, Massoni E (1995) Finite element simulation of the inertia welding of two similar parts. Eng Comput 12(6):497–512

    Article  MATH  Google Scholar 

  23. Needleman A (1972) A numerical study of necking in circular cylindrical bar. J Mech Phys Solids 20(2):111–127

    Article  MATH  Google Scholar 

  24. Neto DM, Neto P (2013) Numerical modeling of friction stir welding process: a literature review. Int J Adv Manuf Technol 65(1–4):115–126

    Article  Google Scholar 

  25. Rodríguez-Ferran A, Pérez-Foguet A, Huerta A (2002) Arbitrary Lagrangian–Eulerian (ALE) formulation for hyperelastoplasticity. Int J Numer Methods Eng 53(8):1831–1851

    Article  MATH  Google Scholar 

  26. Schmicker D, Naumenko K, Strackeljan J (2013) A robust simulation of direct drive friction welding with a modified carreau fluid constitutive model. Comput Methods Appl Mech Eng 265(1):186–194

    Article  MathSciNet  MATH  Google Scholar 

  27. Schmidt H, Hattel J (2005) A local model for the thermomechanical conditions in friction stir welding. Model Simul Mater Sci Eng 13(1):77–93

    Article  Google Scholar 

  28. Simo J, Laursen T (1992) An augmented Lagrangian treatment of contact problems involving friction. Comput Struct 42(1):97–116

    Article  MathSciNet  MATH  Google Scholar 

  29. Simo JC, Laursen TA (1992) An augmented Lagrangian treatment of contact problems involving friction. Comput Struct 42(1):97–116

    Article  MathSciNet  MATH  Google Scholar 

  30. Simo J, Miehe C (1992) Associative coupled thermoplasticity at finite strains: Formulation, numerical analysis and implementation. Comput Methods Appl Mech Eng 98(1):41–104

    Article  MATH  Google Scholar 

  31. Taylor GI (1948) The use of flat-ended projectiles for determining dynamic yield stress I theoretical considerations. Proc R Soc Lond. Ser A Math Phys Sci 194(1038):289–299

    Google Scholar 

  32. Thomas W, Nicholas E, Needham J, Murch M, Temple-Smith P, Dawes C (1991) Friction stir welding, international patent application. GB Patent Application PCT/GB92/02203

  33. Vairis A, Frost M (2000) Modelling the linear friction welding of titanium blocks. Mater Sci Eng, A 292(1):8–17

    Article  Google Scholar 

  34. Veljic D, Rakin M, Perovic M, Medjo B, Radakovic Z, Todorovic P, Pavisic M (2013) Heat generation during plunge stage in friction stir welding. Therm Sci 17(2):489–496

    Article  Google Scholar 

  35. Vill VI (1962) Friction welding of metals, vol 1. American Welding Society; Trade Distributor: Reinhold Pub. Co

  36. Wriggers P, Miehe C, Kleiber M, Simo J (1992) On the coupled thermomechanical treatment of necking problems via finite element methods. Int J Numer Methods Eng 33(4):869–883

    Article  MATH  Google Scholar 

  37. Xu Y, Jing H, Han Y, Xu L (2015) Numerical simulation of the effects of various stud and hole configurations on friction hydro-pillar processing. Int J Mech Sci 90:44–52

  38. Zhang Q, Zhang L, Liu W, Zhang X, Zhu W, Qu S (2006) 3D rigid viscoplastic fe modelling of continuous drive friction welding process. Sci Technol Weld Join 11(6):737–743

    Article  Google Scholar 

Download references

Acknowledgements

The work reported in this article has been carried out with the support of the National Research Foundation through the South African Research Chair in Computational Mechanics.

Author information

Authors and Affiliations

  1. Centre for Research in Computational Mechanics, University of Cape Town, 7701, Rondebosch, South Africa

    M. M. O. Hamed & B. D. Reddy

  2. Glasgow Computational Engineering Centre, University of Glasgow, Glasgow, G12 8LT, UK

    A. T. McBride

Authors
  1. M. M. O. Hamed
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. T. McBride
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. B. D. Reddy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. M. O. Hamed.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hamed, M.M.O., McBride, A.T. & Reddy, B.D. An ALE approach for large-deformation thermoplasticity with application to friction welding. Comput Mech 72, 803–826 (2023). https://doi.org/10.1007/s00466-023-02303-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00466-023-02303-0

Keywords

Search

Navigation