Skip to main content

Combined crystal plasticity and phase-field method for recrystallization in a process chain of sheet metal production


In sheet metal production, a typical process chain contains hot rolling, cold rolling and annealing as a sequence of consecutive processing steps. We investigate the grain structure evolution of body centered cubic low carbon steel and focus on recrystallization, by employing different computational methods which operate across the process chain and across length scales. In particular, we combine finite element crystal plasticity with phase-field simulations to study the effect of deformation of the grain structure by hot and cold rolling on recrystallization during annealing. The overall goal is to represent the most important technological quantities such as texture evolution and the fraction of recrystallization. The results of grain quantities are validated by a comparison of the orientation distribution functions with experimental electron backscatter measurements. The coupling of the simulation methods has shown that the effects of recrystallization can be recovered well, depending on the preceding processing conditions.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10


  1. 1.

    Abdolvand H, Daymond M, Mareau C (2011) Incorporation of twinning into a crystal plasticity finite element model: Evolution of lattice strains and texture in zircaloy-2. Int J Plast 27:1721–1738

    Article  MATH  Google Scholar 

  2. 2.

    Abrivard G, Busso E, Forest S, Appolaire B (2012) Phase field modelling of grain boundary motion driven by curvature and stored energy gradients. Part I: theory and numerical implementation. Philos Mag 92(28–30):3618–3642. doi:10.1080/14786435.2012.713135

    Article  Google Scholar 

  3. 3.

    Asaro RJ (1983) Crystal plasticity. J Appl Mech 50(4b):921–934. doi:10.1115/1.3167205

    Article  MATH  Google Scholar 

  4. 4.

    (1983) Micromechanics of crystals and polycrystals, advances in applied mechanics. Elsevier, Amsterdam, pp 1–115. doi:10.1016/S0065-2156(08)70242-4

  5. 5.

    Aurenhammer F (1991) Voronoi diagrams—a survey of a fundamental data structure. Computing 23(3):345–405. doi:10.1145/116873.116880

    Google Scholar 

  6. 6.

    Avrami M (1939) Kinetics of phase change. I general theory. J Chem Phys 7(12):1103. doi:10.1063/1.1750380

    Article  Google Scholar 

  7. 7.

    Baiker M, Helm D, Butz A (2014) Determination of mechanical properties of polycrystals by using crystal plasticity and numerical homogenization schemes. Steel Res Int 85(6):988–998

    Article  Google Scholar 

  8. 8.

    Barbe F, Decker L, Jeulin D, Cailletaud G (2001) Intergranular and intragranular behavior of polycrystalline aggregates. part 1: F.e. model. Int J Plast 17(4):513–536. doi:10.1016/S0749-6419(00)00061-9

    Article  MATH  Google Scholar 

  9. 9.

    Chen Y, Lee W, To S (2007) Influence of initial texture on formability of aluminum sheet metal by crystal plasticity fe simulation. J Mater Process Technol 192:397–403

    Article  Google Scholar 

  10. 10.

    Crumbach M, Goerdeler M, Gottstein G, Neumann L, Aretz H, Kopp R (2004) Through-process texture modelling of aluminium alloys. Model Simul Mater Sci Eng 12(1):S1–S18. doi:10.1088/0965-0393/12/1/S01

    Article  Google Scholar 

  11. 11.

    Doherty R, Hughes D, Humphreys F, Jonas J, Jensen D, Kassner M, King W, Mcnelley T, Mcqueen H, Rollett A (1997) Current issues in recrystallization: a review. Mater Sci Eng A 238(2):219–274. doi:10.1016/S0921-5093(97)00424-3

    Article  Google Scholar 

  12. 12.

    Eisenlohr P, Roters F (2008) Selecting a set of discrete orientations for accurate texture reconstruction. Comput Mater Sci 42(4):670–678. doi:10.1016/j.commatsci.2007.09.015

    Article  Google Scholar 

  13. 13.

    Eisenlohr P, Tjahjanto DD, Hochrainer T, Roters F, Raabe D (2009) Comparison of texture evolution in fcc metals predicted by various grain cluster homogenization schemes. Int J Mater Res 100(4):500–509. doi:10.3139/146.110071

    Article  Google Scholar 

  14. 14.

    Folch R, Casademunt J, Hernández-Machado a, Ramírez-Piscina L (1999) Phase-field model for Hele-Shaw flows with arbitrary viscosity contrast. I. Theoretical approach. Phys Rev E 60(2 Pt B):1724–1733 Statistical physics, plasmas, fluids, and related interdisciplinary topics

    Article  Google Scholar 

  15. 15.

    Gruber J, Ma N, Wang Y, Rollett AD, Rohrer GS (2006) Sparse data structure and algorithm for the phase field method. Model Simul Mater Sci Eng 14(7):1189–1195. doi:10.1088/0965-0393/14/7/007

    Article  Google Scholar 

  16. 16.

    Güvenc O, Henke T, Laschet G (2013) Modeling of static recrystallization kinetics by coupling crystal plasticity FEM and multiphase field calculations. Comput Methods Mater Sci 13(2):368–374

    Google Scholar 

  17. 17.

    Güvenç O, Bambach M, Hirt G (2014) Coupling of crystal plasticity finite element and phase field methods for the prediction of SRX kinetics after hot working. Steel Res Int 85(6):999–1009. doi:10.1002/srin.201300191

    Article  Google Scholar 

  18. 18.

    Han F, Tang B, Kou H, Cheng L, Li J, Feng Y (2014) Static recrystallization simulations by coupling cellular automata and crystal plasticity finite element method using a physically based model for nucleation. J Mater Sci 49(8):3253–3267. doi:10.1007/s10853-014-8031-8

    Article  Google Scholar 

  19. 19.

    Haupt P (2002) Continuum mechanics and theory of materials. Springer, Berlin

    Book  MATH  Google Scholar 

  20. 20.

    Helm D (2010) Thermomechanical representation of the stored energy during plastic deformation. Int J Mater Res 101(8):972–980

  21. 21.

    Helm D, Butz A, Raabe D, Gumbsch P (2011) Microstructure-based description of the deformation of metals: theory and application. JOM J Miner Met Mater Soc 63(4):26–33

    Article  Google Scholar 

  22. 22.

    Holm EA, Battaile CC (2001) The computer simulation of microstructural evolution. JOM 53(9):20–23. doi:10.1007/s11837-001-0063-2

    Article  Google Scholar 

  23. 23.

    Huang Y (1991) A user-material subroutine incorporating single crystal plasticity in the ABAQUS finite element program. Mech Report 178

  24. 24.

    Humphreys F (1997) A unified theory of recovery, recrystallization and grain growth, based on the stability and growth of cellular microstructures-I. The basic model. Acta Mater 45:4231–4240. doi:10.1016/S1359-6454(97)00070-0

    Article  Google Scholar 

  25. 25.

    Humphreys F, Hatherly M (1995) Recrystallization and related annealing phenomena. Pergamon, New York

    Google Scholar 

  26. 26.

    Hutchinson JW (1970) Elastic-plastic behaviour of polycrystalline metals and composites. Proc Roy Soc A Math Phys Eng Sci 319(1537):247–272

    Article  Google Scholar 

  27. 27.

    Kim SG, Kim DI, Kim WT, Park YB (2006) Computer simulations of two-dimensional and three-dimensional ideal grain growth. Phys Rev E 74(6 Pt 1):061,605 Statistical, nonlinear and soft matter physics

    Article  Google Scholar 

  28. 28.

    Kröner E (1959) Allgemeine kontinuumstheorie der versetzungen und eigenspannungen. Arch Ration Mech Anal 4(1):273–334. doi:10.1007/BF00281393

    Article  Google Scholar 

  29. 29.

    Lan Y, Pinna C (2012) Modelling textures formed during the plane strain compression and subsequent static recrystallisation of body-centred cubic (BCC) metals. Mater Sci Forum 709:3040–3045. doi:10.4028/

    Google Scholar 

  30. 30.

    Le K, Günther C (2014) Nonlinear continuum dislocation theory revisited. Int J Plast 53:164–178. doi:10.1016/j.ijplas.2013.08.003

    Article  Google Scholar 

  31. 31.

    Lebensohn RA, Tome CN (1993) A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals: application to zirconium alloys. Acta Metal Mater 41(9):2611–2624. doi:10.1016/0956-7151(93)90130-K

    Article  Google Scholar 

  32. 32.

    Lee EH (1967) Finite-strain elastic-plastic theory with application to plane-wave analysis. J Appl Phys 38(1):19. doi:10.1063/1.1708953

    Article  Google Scholar 

  33. 33.

    Li H, Wu C, Yang H (2013) Crystal plasticity modeling of the dynamic recrystallization of two-phase titanium alloys during isothermal processing. Int J Plast 51:271–291. doi:10.1016/j.ijplas.2013.05.001

    Article  Google Scholar 

  34. 34.

    Liu Z, Liu X, Zhuang Z, You X (2009) A multi-scale computational model of crystal plasticity at submicron-to-nanometer scales. Int J Plast 25(8):1436–1455

    Article  MATH  Google Scholar 

  35. 35.

    Ma A, Roters F, Raabe D (2006) A dislocation density based constitutive model for crystal plasticity FEM including geometrically necessary dislocations. Acta Mater 54(8):2169–2179. doi:10.1016/j.actamat.2006.01.005

    Article  Google Scholar 

  36. 36.

    Mandel J (1973) Plasticite classique et viscoplasticite, cism inter edn. Springer, Berlin

    Google Scholar 

  37. 37.

    Message Passing Interface Forum: MPI (2012) A Message-Passing Interface Standard Version 3.0. High-Performance Computing Center Stuttgart, Stuttgart

  38. 38.

    Miodownik M (2002) A review of microstructural computer models used to simulate grain growth and recrystallisation in aluminium alloys. J Light Met 2(3):125–135. doi:10.1016/S1471-5317(02)00039-1

    Article  Google Scholar 

  39. 39.

    Muramatsu M, Aoyagi Y, Tadano Y, Shizawa K (2014) Phase-field simulation of static recrystallization considering nucleation from subgrains and nucleus growth with incubation period. Comput Mater Sci 87:112–122. doi:10.1016/j.commatsci.2014.02.003

    Article  Google Scholar 

  40. 40.

    Muramatsu M, Tadano Y, Shizawa K (2008) A phase-field simulation of nucleation from subgrain and grain growth in static recrystallization. Mater Sci Forum 584–586:1045–1050. doi:10.4028/

    Article  Google Scholar 

  41. 41.

    Nestler B, Garcke H, Stinner B (2005) Multicomponent alloy solidification: phase-field modeling and simulations. Phys Rev E 71(4):1–6

    Article  Google Scholar 

  42. 42.

    Potts RB (1952) Some generalized order-disorder transformations. Math Proc Camb Philos Soc 48(01):106–109. doi:10.1017/S0305004100027419

    Article  MATH  MathSciNet  Google Scholar 

  43. 43.

    Raabe D (1999) Introduction of a scalable three-dimensional cellular automaton with a probabilistic switching rule for the discrete mesoscale simulation of recrystallization phenomena. Philos Mag A 79(10):2339–2358. doi:10.1080/01418619908214288

    Article  Google Scholar 

  44. 44.

    Raabe D (2002) Cellular automata in materials science with particular reference to recrystallization simulation. Ann Rev Mater Res 32(1):53–76. doi:10.1146/annurev.matsci.32.090601.152855

    Article  Google Scholar 

  45. 45.

    Raabe D (2007) Multiscale recrystallization models for the prediction of crystallographic textures with respect to process simulation. J Strain Anal Eng Design 42(4):253–268. doi:10.1243/03093247JSA219

    Article  MathSciNet  Google Scholar 

  46. 46.

    Raabe D, Becker RC (2000) Coupling of a crystal plasticity finite-element model with a probabilistic cellular automaton for simulating primary static recrystallization in aluminium. Model Simul Mater Sci Eng 4:445–462

    Article  Google Scholar 

  47. 47.

    Raabe D, Hantcherli L (2005) 2D cellular automaton simulation of the recrystallization texture of an IF sheet steel under consideration of Zener pinning. Comput Mater Sci 34(4):299–313. doi:10.1016/j.commatsci.2004.12.067.

  48. 48.

    Raabe D, Lücke K (1994) Rolling and annealing textures of BCC metals. Mater Sci Forum 157–162:597–610. doi:10.4028/

    Article  Google Scholar 

  49. 49.

    Radhakrishnan B, Sarma G (2004) Simulating the deformation and recrystallization of aluminum bicrystals. JOM 56(4):55–62. doi:10.1007/s11837-004-0074-x

    Article  Google Scholar 

  50. 50.

    Radhakrishnan B, Sarma G, Weiland H, Baggethun P (2000) Simulations of deformation and recrystallization of single crystals of aluminium containing hard particles. Model Simul Mater Sci Eng 8(5):737–750. doi:10.1088/0965-0393/8/5/307

    Article  Google Scholar 

  51. 51.

    Read WT, Shockley W (1950) Dislocation models of crystal grain boundaries. Phys Rev 78(3):275–289. doi:10.1103/PhysRev.78.275

  52. 52.

    Rios P Jr, Sandim F, Plaut R (2005) Nucleation and growth during recrystallization. Mater Res 8(3):225–238

    Article  Google Scholar 

  53. 53.

    Schmid E, Boas W (1935) Kristallplastizität mit besonderer Berücksichtigung der Metalle. Angewandte Chemie 48(30). doi:10.1002/ange.19350483008

  54. 54.

    Schulz K, Dickel D, Schmitt S, Sandfeld S, Weygand D, Gumbsch P (2014) Analysis of dislocation pile-ups using a dislocation-based continuum theory. Model Simul Mater Sci Eng 22(2):025,008. doi:10.1088/0965-0393/22/2/025008

  55. 55.

    Semiatin S, Piehler H (1979) Formability of sandwich sheet materials in plane strain compression and rolling. Metal Mater Trans A 10(1):97–107

    Article  Google Scholar 

  56. 56.

    Srolovitz DJ, Crest GS, Anderson MP (1986) Computer simulation of recrystallization-I. Homogeneous nucleation and growth. Acta Metal Mater 34:1833–1845

    Article  Google Scholar 

  57. 57.

    Suwa Y, Saito Y, Onodera H (2008) Phase-field simulation of recrystallization based on the unified subgrain growth theory. Comput Mater Sci 44(2):286–295. doi:10.1016/j.commatsci.2008.03.025

    Article  Google Scholar 

  58. 58.

    Takaki T, Hisakuni Y, Hirouchi T, Yamanaka A, Tomita Y (2009) Multi-phase-field simulations for dynamic recrystallization. Comput Mater Sci 45(4):881–888. doi:10.1016/j.commatsci.2008.12.009

    Article  Google Scholar 

  59. 59.

    Takaki T, Tomita Y (2010) Static recrystallization simulations starting from predicted deformation microstructure by coupling multi-phase-field method and finite element method based on crystal plasticity. Int J Mech Sci 52(2):320–328. doi:10.1016/j.ijmecsci.2009.09.037

    Article  Google Scholar 

  60. 60.

    Takaki T, Yamanaka A, Higa Y, Tomita Y (2007) Phase-field model during static recrystallization based on crystal-plasticity theory. J Comput Aided Mater Design 14:75–84

    Article  Google Scholar 

  61. 61.

    Takaki T, Yoshimoto C, Yamanaka A, Tomita Y (2014) Multiscale modeling of hot-working with dynamic recrystallization by coupling microstructure evolution and macroscopic mechanical behavior. Int J Plast 52:105–116. doi:10.1016/j.ijplas.2013.09.001

    Article  Google Scholar 

  62. 62.

    Taylor GI (1938) Plastic strain in metals. J Inst Met 62(1):307–324

    Google Scholar 

  63. 63.

    Vedantam S, Patnaik BSV (2006) Efficient numerical algorithm for multiphase field simulations. Phys Rev E Stat Nonlinear Soft Matter Phys 73(1 Pt 2):016,703

    Article  Google Scholar 

  64. 64.

    Von Neumann J (1966) Theory of self-reproducing automata. doi:10.2307/2005041

  65. 65.

    Vondrous a, Selzer M, Hotzer J, Nestler B (2013) Parallel computing for phase-field models. Int J High Perform Comput Appl 28(1):61–72

    Article  Google Scholar 

  66. 66.

    Wawszczak R, Baczmański A, Braham C, Seiler W, Wróbel M, Wierzbanowski K (2010) Evolution of residual stresses and stored elastic energy in ferritic steel during recovery process. Mater Sci Forum 652:279–284. doi:10.4028/

    Article  Google Scholar 

  67. 67.

    Wegst C, Wegst M (2010) Stahlschlüssel - Key to Steel 2010. Stahlschlüssel Wegst GmbH

  68. 68.

    Weygand D, Bréchet Y, Lépinoux J, Gust W (1999) Three-dimensional grain growth: a vertex dynamics simulation. Philos Mag Part B 79(5):703–716. doi:10.1080/13642819908205744

    Article  Google Scholar 

  69. 69.

    Lee Won H, Im YT (2010) Numerical modeling of dynamic recrystallization during nonisothermal hot compression by cellular automata and finite element analysis. Int J Mech Sci 52(10):1277–1289. doi:10.1016/j.ijmecsci.2010.06.003

    Article  Google Scholar 

  70. 70.

    Yamaki N, Aoyagi Y, Shizawa K (2007) Multiscale modeling and simulation of crystal plasticity based on dislocation patterning in polycrystal. Key Eng Mater 340–341:205–210. doi:10.4028/

    Article  Google Scholar 

Download references


We thank the DFG for funding our investigations and voestalpine for providing hot rolled, cold rolled and heat treated steel sheets for our studies in the framework of the Graduate School 1483. The authors gratefully acknowledge the national supercomputing center HLRS (University of Stuttgart) for providing computing time on the supercomputer HERMIT, funded by the German Federal Ministry of Education and Research (BMBF), and the German State Ministry for Research of Baden-Württemberg (MWK). We thank Jan Hoffmann for productive discussions.

Author information



Corresponding author

Correspondence to Alexander Vondrous.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Vondrous, A., Bienger, P., Schreijäg, S. et al. Combined crystal plasticity and phase-field method for recrystallization in a process chain of sheet metal production. Comput Mech 55, 439–452 (2015).

Download citation


  • Plasticity
  • Static recrystallization
  • Finite element method
  • Finite difference method
  • Phase-field method
  • Orientation distributions