International Journal of Material Forming

, Volume 12, Issue 2, pp 173–183 | Cite as

Introduction to the level-set full field modeling of laths spheroidization phenomenon in α/β titanium alloys

  • D . PolychronopoulouEmail author
  • N. Bozzolo
  • D. Pino Muñoz
  • J. Bruchon
  • M. Shakoor
  • Y. Millet
  • C. Dumont
  • I. Freiherr von Thüngen
  • R. Besnard
  • M. Bernacki
Thematic Issue: Advances in Material Forming Simulation


The fragmentation of α lamellae and the subsequent spheroidization of α laths, in α/β titanium alloys, are well known phenomena, occurring during and after deformation. We will illustrate the development of a new finite element methodology to model these phenomena. This new methodology is based on a level set framework modeling the deformation and the ad hoc concurrent or subsequent interfaces kinetics. In the current paper, we will focus on the modeling of the surface diffusion at the α/β phase interfaces and the motion by mean curvature at the α/α grain interfaces.


spheroidization grooving α laths surface diffusion α/β titanium alloys 



The authors would like gratefully to thank AUBERT & DUVAL, CEA, TIMET and SAFRAN for funding this research through the SPATIALES project of the DIGIMU consortium.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Lütjering G, Williams J (2007) Titanium. Springer, HeidelbergGoogle Scholar
  2. 2.
    Semiatin SL, Furrer DU (2008) Modeling of microstructure evolution during the thermomechanical processing of titanium alloys. Technical paper preprint. Air Force Research LabGoogle Scholar
  3. 3.
    Li X, Bottler F, Spatschek R, Schmitt A, Heilmaier M, Stein F (2017) Coarsening kinetics of lamellar microstructures: Experiments and simulations on a fully-lamellar Fe-Al in situ composite. Acta Mater 127:230–243CrossRefGoogle Scholar
  4. 4.
    Voorhees PW (1985) The theory of Ostwald ripening. J Stat Phys 38:231–252CrossRefGoogle Scholar
  5. 5.
    Mullins W (1958) The effect of thermal grooving on grain boundary motion. Acta Metall 6:414–427CrossRefGoogle Scholar
  6. 6.
    Bruchon J, Pino Muñoz D, Valdivieso F, Drapier S, Pacquaut G (2010) 3D simulation of the matter transport by surface diffusion within a Level-Set context. Eur J Comp Mech 19:281–292CrossRefzbMATHGoogle Scholar
  7. 7.
    Derkach V (2010) Surface evolution and grain boundary migration in a system of 5 grains. M.Sc. thesis, Department of Mathematics, Technion–Israel Institute of TechnologyGoogle Scholar
  8. 8.
    Derkach V, Novick-Cohen A, Vilenkin A, Rabkin E (2014) Grain boundary migration and grooving in thin 3-D systems. Acta Mater 65:194–206CrossRefGoogle Scholar
  9. 9.
    Smereka P (2003) Semi-implicit level set methods for curvature and surface diffusion motion. J Sci Comput 19:439–456MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Osher S, Fedkiw F (2001) Level Set Methods: An Overview and Some Recent Results. J Comput Phys 169:463–502MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Sethian JA (1999) Level set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science, vol 3. Cambridge University Press, CambridgeGoogle Scholar
  12. 12.
    Bernacki M, Logé R, Coupez T (2011) Level set framework for the finite-element modelling of recrystallization and grain growth in polycrystalline materials. Scr Mater 64:525–528CrossRefGoogle Scholar
  13. 13.
    Bernacki M, Chastel Y, Coupez T, Logé R (2008) Level set framework for the numerical modelling of primary recrystallization in polycrystalline materials. Scr Mater 58:1129–1132CrossRefGoogle Scholar
  14. 14.
    Burger M, Hausser F, Stocker C, Voigt A (2007) A level-set approach to anisotropic flows with curvature regularization. J Comput Phys 225:183–205MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Bruchon J, Drapier S, Valdivieso F (2011) 3D finite element simulation of the matter flow by surface diffusion using a level set method. Int J Numer Methods Eng 86:845–861CrossRefzbMATHGoogle Scholar
  16. 16.
    Bernacki M, Resk H, Coupez T, Logé R (2009) Finite element model of primary recrystallization in polycrystalline aggregates using a level set framework. Model Simul Mater Sci Eng 17:064006CrossRefGoogle Scholar
  17. 17.
    Shakoor M, Scholtes B, Bouchard P-O, Bernacki M (2015) An efficient and parallel level set reinitialization method - application to micromechanics and microstructural evolutions. Appl Math Model 39:7291–7302MathSciNetCrossRefGoogle Scholar
  18. 18.
    Scholtes B, Boulais-Sinou R, Settefrati A, Pino Muñoz D, Poitrault I, Montouchet A, Bozzolo N, Bernacki M (2016) 3D level set modeling of static recrystallization considering stored energy fields. Comput Mater Sci 122:57–71CrossRefGoogle Scholar
  19. 19.
    Gruau C, Coupez T (2005) 3D tetrahedral, unstructured and anisotropic mesh generation with adaptation to natural and multidomain metric. Comput Methods Appl Mech Eng 194:4951–4976MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Shakoor M, Bernacki M, Bouchard P-O (2015) A new body-fitted immersed volume method for the modeling of ductile fracture at the microscale: analysis of void clusters and stress state effects on coalescence. Eng Fract Mech 147:398–417CrossRefGoogle Scholar
  21. 21.
    Shakoor M, Bouchard P-O, Bernacki M (2017) An adaptive level-set method with enhanced volume conservation for simulations in multiphase domains. Int J Numer Methods Eng 109:555–576MathSciNetCrossRefGoogle Scholar
  22. 22.
    Digonnet H, Silva L, Coupez T (2007) Cimlib: a fully parallel application for numerical simulations based on components assembly. Proceedings of the 9th International Conference on Numerical Methods in Industrial Forming ProcessesGoogle Scholar
  23. 23.
    Resk H, Delannay L, Bernacki M, Coupez T, Logé R (2009) Adaptive mesh refinement and automatic remeshing in crystal plasticity finite element simulations. Model Simul Mater Sci Eng 17:075012CrossRefGoogle Scholar

Copyright information

© Springer-Verlag France SAS 2017

Authors and Affiliations

  • D . Polychronopoulou
    • 1
    Email author
  • N. Bozzolo
    • 1
  • D. Pino Muñoz
    • 1
  • J. Bruchon
    • 2
  • M. Shakoor
    • 1
  • Y. Millet
    • 3
  • C. Dumont
    • 4
  • I. Freiherr von Thüngen
    • 5
  • R. Besnard
    • 6
  • M. Bernacki
    • 1
  1. 1.MINES ParisTechPSL Research University, CEMEF - Centre de mise en forme des matériauxSophia Antipolis CedexFrance
  2. 2.École Nationale Supérieure des Mines de Saint-Étienne, Centre Sciences des Matériaux et des Structures, Département Mécanique et Procédés d’ElaborationSaint-Etienne Cedex 02France
  3. 3.Timet SavoieUgineFrance
  4. 4.Aubert & DuvalLes Ancizes-CompsFrance
  5. 5.Safran, SafranTech - Pôle Matériaux et procédésMagny-Les-HameauxFrance
  6. 6.CEA ValducIs-Sur-TilleFrance

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