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Science China Technological Sciences

, Volume 55, Issue 2, pp 341–356 | Cite as

Progress in mesoscopic modeling of microstructure evolution in steels

  • NaMin Xiao
  • Yun Chen
  • DianZhong LiEmail author
  • YiYi Li
Article

Abstract

The mesoscopic modeling developed rapidly in the past three decades is a promising tool for predicting and understanding the microstructure evolution at grain scale. In this paper, the recent development of mesoscopic modeling and its application to microstructure evolution in steels is reviewed. Firstly, some representative computational models are briefly introduced, e.g., the phase field model, the cellular automaton model and the Monte Carlo model. Then, the emphasis is put on the application of mesoscopic modeling of the complex features of microstructure evolution, including solidification, solid-state phase transformation, recrystallization and grain growth. Finally, some issues in the present mesoscopic modeling and its perspective are discussed.

Keywords

microstructure evolution steel phase field cellular automaton Monte Carlo 

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References

  1. 1.
    Sellars C M, Whiteman J A. Recrystallization and grain growth in hot rolling. Met Sci, 1979, 13: 187–194CrossRefGoogle Scholar
  2. 2.
    Senuma T. Present status of and future prospects for precipitation research in the steel industry. ISIJ Int, 2002, 42: 1–12CrossRefGoogle Scholar
  3. 3.
    Militzer M. Computer simulation of microstructure evolution in low carbon sheet steels. ISIJ Int, 2007, 47: 1–15CrossRefGoogle Scholar
  4. 4.
    Chen L Q. Phase-field models for microstructure evolution. Ann Rev Mater Res, 2002, 32: 113–140CrossRefGoogle Scholar
  5. 5.
    Rollett A D, Manohar P. The monte carlo method. Cont Scale Simul Eng Mat, 2004. 77–114Google Scholar
  6. 6.
    Anderson M P, Srolovitz D J, Grest G S, et al. Computer simulation of grain growth-I. Kinetics. Acta Metall, 1984, 32: 783–791Google Scholar
  7. 7.
    Srolovitz D J, Grest G S, Anderson M P. Computer simulation of recrystallization-I. Homogeneous nucleation and growth. Acta Metall, 1986, 34: 1833–1845CrossRefGoogle Scholar
  8. 8.
    Rollett A D, Luton M J, Srolovitz D J. Microstructural simulation of dynamic recrystallization. Acta Metall Mater, 1992, 40: 43–55CrossRefGoogle Scholar
  9. 9.
    Tong M M, Li D Z, Li Y Y, et al. Modeling the austenite-ferrite isothermal transformation in an Fe-C binary system and experimental verification. Metall Mater Trans A, 2002, 33: 3111–3115CrossRefGoogle Scholar
  10. 10.
    Raabe D. Scaling Monte Carlo kinetics of the Potts model using rate theory. Acta Mater, 2000, 48: 1617–1628CrossRefGoogle Scholar
  11. 11.
    Marx V, Reher F R, Gottstein G. Simulation of primary recrystallization using a modified three-dimensional cellular automaton. Acta Mater, 1999, 47: 1219–1230CrossRefGoogle Scholar
  12. 12.
    Raabe D. Cellular automata in materials science with particular reference to recrystallization simulation. Ann Rev Mater Res, 2002, 32: 53–76CrossRefGoogle Scholar
  13. 13.
    Raabe D. Computational materials science: the simulation of materials microstructures and properties. Wiley-VCH Weinheim, 1998Google Scholar
  14. 14.
    Kim S G, Kim W T, Suzuki T. Phase-field model for binary alloys. Phys Rev E, 1999, 60: 7186–7186CrossRefGoogle Scholar
  15. 15.
    Boettinger W J, Warren J A, Beckermann C, et al. Phase-field simulation of solidifcation. Ann Rev Mater Res, 2002, 32: 163–194CrossRefGoogle Scholar
  16. 16.
    Li J J, Wang J C, Yang G C. Phase field simulation of the columnar dendritic growth and microsegregation in a binary alloy. Chin Phys B, 2008, 17: 3516–3522CrossRefGoogle Scholar
  17. 17.
    Guo J, Li X, Su Y, et al. Phase-field simulation of structure evolution at high growth velocities during directional solidification of Ti55Al45 alloy. Intermetallics, 2005, 13: 275–279CrossRefGoogle Scholar
  18. 18.
    Zhang R, Jing T, Jie W, et al. Phase-field simulation of solidification in multicomponent alloys coupled with thermodynamic and diffusion mobility databases. Acta Mater, 2006, 54: 2235–2239CrossRefGoogle Scholar
  19. 19.
    Chen Y, Bogno A A, Billia B, et al. Phase-field Modeling of the Initial Transient in Directional Solidification of Al-4 wt% Cu Alloy. ISIJ Int, 2010, 50: 1895–1900CrossRefGoogle Scholar
  20. 20.
    Chen L Q, Yang W. Computer simulation of the domain dynamics of a quenched system with a large number of nonconserved order parameters: The grain-growth kinetics. Phys Rev B, 1994, 50: 15752–15756CrossRefGoogle Scholar
  21. 21.
    Steinbach I, Pezzolla F, Nestler B, et al. A phase field concept for multiphase systems. Physica D, 1996, 94: 135–147zbMATHCrossRefGoogle Scholar
  22. 22.
    Nestler B, Wheeler A A. A multi-phase-field model of eutectic and peritectic alloys: numerical simulation of growth structures. Physica D, 2000, 138: 114–133MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Hecht U, Gránásy L, Pusztai T, et al. Multiphase solidification in multicomponent alloys. Mater Sci Eng R, 2004, 46: 1–49CrossRefGoogle Scholar
  24. 24.
    Choudhury A, Nestler B, Telang A, et al. Growth morphologies in peritectic solidification of Fe-C: A phase-field study. Acta Mater, 2010, 58: 3815–3823CrossRefGoogle Scholar
  25. 25.
    Tiaden J. Phase field simulations of the peritectic solidification of Fe-C. J Cryst Growth, 1999, 198–199: 1275–1280CrossRefGoogle Scholar
  26. 26.
    Takatani H, Gandin C A, Rappaz M. EBSD characterisation and modelling of columnar dendritic grains growing in the presence of fluid flow. Acta Mater, 2000, 48: 675–688CrossRefGoogle Scholar
  27. 27.
    Wang B, Zhang J Y, Li X M, et al. Simulation of solidification microstructure in twin-roll casting strip. Comput Mater Sci, 2010, 49: S135–S139CrossRefGoogle Scholar
  28. 28.
    Yamazaki M, Satoh J, Ohsasa K, et al. Numerical model of solidification structure formation in Fe-C alloy with peritectic transformation. ISIJ Int, 2008, 48: 362–367CrossRefGoogle Scholar
  29. 29.
    Michelic S C, Thuswaldner J M, Bernhard C. Polydimensional modelling of dendritic growth and microsegregation in multicomponent alloys. Acta Mater, 2010, 58: 2738–2751CrossRefGoogle Scholar
  30. 30.
    Ode M, Suzuki T, Kim S G, et al. Phase-field model for solidification of Fe-C alloys. Sci Technol Adv Mater, 2000, 1: 43–49CrossRefGoogle Scholar
  31. 31.
    Lipton J, Glicksman M E, Kurz W. Dendritic growth into undercooled alloy metals. Mater Sci Eng, 1984, 65: 57–63CrossRefGoogle Scholar
  32. 32.
    Lipton J, Kurz W, Trivedi R. Rapid dendrite growth in undercooled alloys. Acta Metall, 1987, 35: 957–964CrossRefGoogle Scholar
  33. 33.
    Zhang Y, Li D, Wang C, et al. Simulation of dendrite growth of Fe-C alloy using phase field method. Chin J of Mate Res, 2009, 23: 317–322MathSciNetGoogle Scholar
  34. 34.
    Niu Y, Yan W, Feng X, et al. Phase-field simulation of Fe-C alloy in the isothermal solidification. Found Technol, 2008, 29: 244–249Google Scholar
  35. 35.
    Oguchi K, Suzuki T. Three-dimensional phase-field simulation of free dendrite growth of iron. ISIJ Int, 2007, 47: 277–281CrossRefGoogle Scholar
  36. 36.
    Oguchi K, Suzuki T. Free dendrite growth of Fe-0.5mass%C alloy three-dimensional phase-field simulation and LKT model. ISIJ Int, 2007, 47: 1432–1435CrossRefGoogle Scholar
  37. 37.
    Ode M, Suzuki T. Numerical simulation of initial microstructure evolution of Fe-C alloys using a phase-field model. ISIJ Int, 2002, 42: 368–374CrossRefGoogle Scholar
  38. 38.
    Suzuki T, Ode M, Kim S G, et al. Phase-field model of dendritic growth. J Cryst Growth, 2002, 237: 125–131CrossRefGoogle Scholar
  39. 39.
    Cha P R, Yeon D H, Yoon J K. A phase field model for isothermal solidification of multicomponent alloys. Acta Mater, 2001, 49: 3295–3307CrossRefGoogle Scholar
  40. 40.
    Cui H X, Zhang Y T, Sun Q, et al. Simulation of dendrite growth in Fe-C-Mn ternary alloy during isothermal solidification by phase field method. Res Stu Found Equip, 2008. 39–41Google Scholar
  41. 41.
    Tiaden J, Grafe U. In: Proceedings of the International Conference on Solid-Solid Phase Transfor-mations: JIMIC-3, 1999Google Scholar
  42. 42.
    Lee J S, Kim S G, Kim W T, et al. Numerical simulation of peritectic reaction using a multi-phase-field model. ISIJ Int, 1999, 39: 730–736CrossRefGoogle Scholar
  43. 43.
    Phelan D, Reid M, Dippenaar R. Kinetics of the peritectic phase transformation: In-situ measurements and phase field modeling. Metall Mater Trans A, 2006, 37A: 985–994CrossRefGoogle Scholar
  44. 44.
    Ode M, Kim S G, Kim W T, et al. Numerical simulation of peritectic reaction in Fe-C alloy using a multi-phase-field model. ISIJ Int, 2005, 45: 147–149CrossRefGoogle Scholar
  45. 45.
    Böttger B, Grafe U, Ma D. Mater Sci Technol, 2000, 16: 1425CrossRefGoogle Scholar
  46. 46.
    Nestler B, Choudhury A. Phase-field modeling of multi-component systems. Curr Opin Solid State Mater Sci, 2011, 15: 93–105CrossRefGoogle Scholar
  47. 47.
    Heike E, Ricardo S. Investigating heterogeneous nucleation in peritectic materials via the phase-field method. J Phys: Condens Matter, 2006, 18: 11121CrossRefGoogle Scholar
  48. 48.
    Kumar M, Sasikumar R, Nair P K. Competition between nucleation and early growth of ferrite from austenite-Studies using cellular automaton simulations. Acta Mater, 1998, 46: 6291–6303CrossRefGoogle Scholar
  49. 49.
    Kundu S, Dutta M, Ganguly S, et al. Prediction of phase transformation and microstructure in steel using cellular automaton technique. Scr Mater, 2004, 50: 891–895CrossRefGoogle Scholar
  50. 50.
    Zhang L, Zhang C B, Wang Y M, et al. Cellular automaton model to simulate nucleation and growth of ferrite grains for low-carbon steels. J Mater Res, 2002, 17: 2251–2259CrossRefGoogle Scholar
  51. 51.
    Zhang L, Zhang C B, Wang Y M, et al. A cellular automaton investigation of the transformation from austenite to ferrite during continuous cooling. Acta Mater, 2003, 51: 5519–5527CrossRefGoogle Scholar
  52. 52.
    Lan Y J, Li D Z, Huang C J, et al. A cellular automaton model for austenite to ferrite transformation in carbon steel under non-equilibrium interface conditions. Model Simul Mater Sci Eng, 2004, 12: 719–729CrossRefGoogle Scholar
  53. 53.
    Lan Y, Li D, Li Y. Modeling austenite-ferrite transformation in low carbon steel using the cellular automaton method. J Mater Res, 2004, 19: 2877–2886CrossRefGoogle Scholar
  54. 54.
    Lan Y J, Li D Z, Li Y Y. Modeling austenite decomposition into ferrite at different cooling rate in low-carbon steel with cellular automaton method. Acta Mater, 2004, 52: 1721–1729CrossRefGoogle Scholar
  55. 55.
    Lange W F, Enomoto M, Aaronson H I. The kinetics of ferrite nucleation at austenite grain-boundaries in Fe-C alloys. Metall Mater Trans A, 1988, 19: 427–440CrossRefGoogle Scholar
  56. 56.
    Tong M M, Li D Z, Li Y Y. A q-state Potts model-based Monte Carlo method used to model the isothermal austenite-ferrite transformation under non-equilibrium interface condition. Acta Mater, 2005, 53: 1485–1497CrossRefGoogle Scholar
  57. 57.
    Huang C J, Browne D J, McFadden S. A phase-field simulation of austenite to ferrite transformation kinetics in low carbon steels. Acta Mater, 2006, 54: 11–21CrossRefGoogle Scholar
  58. 58.
    Huang C J, Browne D J. Phase-field model prediction of nucleation and coarsening during austenite/ferrite transformation in steels. Metall Mater Trans A, 2006, 37: 589–598CrossRefGoogle Scholar
  59. 59.
    Mecozzi M G, Sietsma J, Van der Zwaag S. Phase field modelling of the interfacial condition at the moving interphase during the gamma → alpha transformation in C-Mn steels. Comput Mater Sci, 2005, 34: 290–297CrossRefGoogle Scholar
  60. 60.
    Mecozzi M G, Sietsma J, Van der Zwaag S, et al. Analysis of the gamma →alpha transformation in a C-Mn steel by phase-field modeling. Metall Mater Trans A, 2005, 36A: 2327–2340CrossRefGoogle Scholar
  61. 61.
    Mecozzi M G, Sietsma J, Van der Zwaag S. Analysis of gamma → alpha transformation in a Nb micro-alloyed C-Mn steel by phase field modelling. Acta Mater, 2006, 54: 1431–1440CrossRefGoogle Scholar
  62. 62.
    Takahama Y, Sietsma J. Mobility analysis of the Austenite to ferrite transformation in nb microalloyed steel by phase field modelling. ISIJ Int, 2008, 48: 512–517CrossRefGoogle Scholar
  63. 63.
    Militzer M. Phase field modeling of microstructure evolution in steels. Curr Opin Solid State Mater Sci, 2011, 15: 106–115CrossRefGoogle Scholar
  64. 64.
    Militzer M, Mecozzi M G, Sietsma J, et al. Three-dimensional phase field modelling of the austenite-to-ferrite transformation. Acta Mater, 2006, 54: 3961–3972CrossRefGoogle Scholar
  65. 65.
    Mecozzi M G, Militzer M, Sietsma J, et al. The role of nucleation behavior in phase-field simulations of the austenite to ferrite transformation. Metall Mater Trans A, 2008, 39A: 1237–1247CrossRefGoogle Scholar
  66. 66.
    Thiessen R G, Sietsma J, Palmer T A, et al. Phase-field modelling and synchrotron validation of phase transformations in martensitic dual-phase steel. Acta Mater, 2007, 55: 601–614CrossRefGoogle Scholar
  67. 67.
    Santofimia M J, Takahama Y, Zhao L, et al. Analysis of the Quenching and Partitioning (Q&P) Process with Partial Austenitisation in a Low Carbon Steel by Phase Field Modelling. Warrendale: Minerals, Metals & Materials Soc, 2008Google Scholar
  68. 68.
    Bos C, Mecozzi M, Sietsma J. A microstructure model for recrystallisation and phase transformation during the dual-phase steel annealing cycle. Comput Mater Sci, 2010, 48: 692–699CrossRefGoogle Scholar
  69. 69.
    Tong M M, Ni J, Zhang Y T, et al. Monte Carlo-method simulation of the deformation-induced ferrite transformation in the Fe-C system. Metall Mater Trans A, 2004, 35A: 1565–1577CrossRefGoogle Scholar
  70. 70.
    Tong M M, Ni J, Zhang Y T, et al. Temporal oscillatory behavior in deformation induced ferrite transformation in an Fe-C binary system. Scr Mater, 2004, 50: 909–913CrossRefGoogle Scholar
  71. 71.
    Lan Y J, Xiao N M, Li D Z, et al. Mesoscale simulation of deformed austenite decomposition into ferrite by coupling a cellular automaton method with a crystal plasticity finite element model. Acta Mater, 2005, 53: 991–1003CrossRefGoogle Scholar
  72. 72.
    Xiao N M, Tong M M, Lan Y J, et al. Coupled simulation of the influence of austenite deformation on the subsequent isothermal austenite-ferrite transformation. Acta Mater, 2006, 54: 1265–1278CrossRefGoogle Scholar
  73. 73.
    Suwanpinij P, Rudnizki J, Prahl U, et al. Investigation of the Effect of Deformation on gamma-alpha Phase Transformation Kinetics in Hot-Rolled Dual Phase Steel by Phase Field Approach. Steel Res Int, 2009, 80: 616–622Google Scholar
  74. 74.
    Zheng C W, Xiao N M, Hao L H, et al. Numerical simulation of dynamic strain-induced austenite-ferrite transformation in a low carbon steel. Acta Mater, 2009, 57: 2956–2968CrossRefGoogle Scholar
  75. 75.
    Li D Z, Xiao N M, Lan Y J, et al. Growth modes of individual ferrite grains in the austenite to ferrite transformation of low carbon steels. Acta Mater, 2007, 55: 6234–6249CrossRefGoogle Scholar
  76. 76.
    Offerman S, Van Dijk N, Sietsma J, et al. Grain nucleation and growth during phase transformations. Science, 2002, 298: 1003CrossRefGoogle Scholar
  77. 77.
    Loginova I, Agren J, Arnberg G. On the formation of Widmanstdtten ferrite in binary Fe-C-phase-field approach. Acta Mater, 2004, 52: 4055–4063CrossRefGoogle Scholar
  78. 78.
    Loginova I, Odqvist J, Amberg G, et al. The phase-field approach and solute drag modeling of the transition to massive gamma →alpha transformation in binary Fe-C alloys. Acta Mater, 2003, 51: 1327–1339CrossRefGoogle Scholar
  79. 79.
    Yamanaka A, Takaki T, Tomita Y. Coupled simulation of microstructural formation and deformation behavior of ferritepearlite steel by phase-field method and homogenization method. Mater Sci Eng A, 2008, 480: 244–252CrossRefGoogle Scholar
  80. 80.
    Nakajima K, Apel M, Steinbach I. The role of carbon diffusion in ferrite on the kinetics of cooperative growth of pearlite: A multiphase field study. Acta Mater, 2006, 54: 3665–3672CrossRefGoogle Scholar
  81. 81.
    Steinbach I, Apel A. The influence of lattice strain on pearlite formation in Fe-C. Acta Mater, 2007, 55: 4817–4822CrossRefGoogle Scholar
  82. 82.
    Jacot A, Rappaz M. A two-dimensional diffusion model for the prediction of phase transformations: Application to austenitization and homogenization of hypoeutectoid Fe-C steels. Acta Mater, 1997, 45: 575–585CrossRefGoogle Scholar
  83. 83.
    Jacot A, Rappaz M, Reed R C. Modelling of reaustenitization from the pearlite structure in steel. Acta Mater, 1998, 46: 3949–3962CrossRefGoogle Scholar
  84. 84.
    Yang B, Chuzhoy L, Johnson M. Modeling of reaustenitization of hypoeutectoid steels with cellular automaton method. Comput Mater Sci, 2007, 41: 186–194CrossRefGoogle Scholar
  85. 85.
    Yang B, Hattiangadi A, Li W, et al. Simulation of steel microstructure evolution during induction heating. Mater Sci Eng A, 2010, 527: 2978–2984CrossRefGoogle Scholar
  86. 86.
    Thiessen R G, Richardson I M, Sietsma J. Physically based modelling of phase transformations during welding of low-carbon steel. Mater Sci Eng A, 2006, 427: 223–231CrossRefGoogle Scholar
  87. 87.
    Savran V I. Austenite Formation in C-Mn Steel. Netherlands: The Delft University of Technology, 2009Google Scholar
  88. 88.
    Militzer M, Azizi Alizamini H. Phase field modelling of austenite formation in low carbon steels. Solid State Phenom, 2011, 172: 1050–1059CrossRefGoogle Scholar
  89. 89.
    Azizi-Alizamini H, Militzer M. Phase field modelling of austenite formation from ultrafine ferrite-carbide aggregates in Fe-C. Int J Mat Res, 2010, 101: 534–541CrossRefGoogle Scholar
  90. 90.
    Chang K N, Feng W M, Chen L Q. Effect of second-phase particle morphology on grain growth kinetics. Acta Mater, 2009, 57: 5229–5236CrossRefGoogle Scholar
  91. 91.
    Ding R, Guo Z X. Coupled quantitative simulation of microstructural evolution and plastic flow during dynamic recrystallization. Acta Mater, 2001, 49: 3163–3175CrossRefGoogle Scholar
  92. 92.
    Fan D N, Geng C W, Chen L Q. Computer simulation of topological evolution in 2-D grain growth using a continuum diffuse-interface field model. Acta Mater, 1997, 45: 1115–1126CrossRefGoogle Scholar
  93. 93.
    Moelans N, Blanpain B, Wollants P. Pinning effect of second-phase particles on grain growth in polycrystalline films studied by 3-D phase field simulations. Acta Mater, 2007, 55: 2173–2182CrossRefGoogle Scholar
  94. 94.
    Takaki T, Hisakuni Y, Hirouchi T, et al. Multi-phase-field simulations for dynamic recrystallization. Comput Mater Sci, 2009, 45: 881–888CrossRefGoogle Scholar
  95. 95.
    Rollett A D, Srolovitz D J, Doherty R D, et al. Computer simulation of recrystallization in non-uniformly deformed metals. Acta Metall, 1989, 37: 627–639CrossRefGoogle Scholar
  96. 96.
    Choi S H, Barlat F, Chung J H. Modeling of textures and yield surfaces during recrystallization in IF steel sheets. Scr Mater, 2001, 45: 1155–1162CrossRefGoogle Scholar
  97. 97.
    Choi S H, Cho J H. Primary recrystallization modelling for interstitial free steels. Mater Sci Eng A, 2005, 405: 86–101CrossRefGoogle Scholar
  98. 98.
    Hayakawa Y, Szpunar J A. A new model of Goss texture development during secondary recrystallization of electrical steel. Acta Mater, 1997, 45: 4713–4720CrossRefGoogle Scholar
  99. 99.
    Montano-Zuniga I M, Sepulveda-Cervantes G, Lopez-Hirata V M, et al. Numerical simulation of recrystallization in BCC metals. Comput Mater Sci, 2010, 49: 512–517CrossRefGoogle Scholar
  100. 100.
    Okuda K, Rollett A D. Monte Carlo simulation of elongated recrystallized grains in steels. Comput Mater Sci, 2005, 34: 264–273CrossRefGoogle Scholar
  101. 101.
    Raabe D, Hantcherli L. 2D cellular automaton simulation of the recrystallization texture of an IF sheet steel under consideration of Zener pinning. Comput Mater Sci, 2005, 34: 299–313CrossRefGoogle Scholar
  102. 102.
    Zheng C W, Xiao N M, Li D Z, et al. Mesoscopic modeling of austenite static recrystallization in a low carbon steel using a coupled simulation method. Comput Mater Sci, 2009, 45: 568–575CrossRefGoogle Scholar
  103. 103.
    Yu X F, Chen S H, Wang L. Simulation of recrystallization in cold worked stainless steel and its effect on chromium depletion by cellular automaton. Comput Mater Sci, 2009, 46: 66–72CrossRefGoogle Scholar
  104. 104.
    Qian M, Guo Z X. Cellular automata simulation of microstructural evolution during dynamic recrystallization of an HY-100 steel. Mater Sci Eng A, 2004, 365: 180–185CrossRefGoogle Scholar
  105. 105.
    Yazdipour N, Davies C H J, Hodgson P D. Microstructural modeling of dynamic recrystallization using irregular cellular automata. Comput Mater Sci, 2008, 44: 566–576CrossRefGoogle Scholar
  106. 106.
    Chen F, Cui Z S, Liu J, et al. Modeling and simulation on dynamic recrystallization of 30Cr2Ni4MoV rotor steel using the cellular automaton method. Model Simul Mater Sci Eng, 2009, 17: 075015CrossRefGoogle Scholar
  107. 107.
    Chen F, Cui Z S, Liu J A, et al. Mesoscale simulation of the high-temperature austenitizing and dynamic recrystallization by coupling a cellular automaton with a topology deformation technique. Mater Sci Eng A, 2010, 527: 5539–5549CrossRefGoogle Scholar
  108. 108.
    Jin Z Y, Cui Z S. Investigation on strain dependence of dynamic recrystallization behavior using an inverse analysis method. Mater Sci Eng A, 2010, 527: 3111–3119CrossRefGoogle Scholar
  109. 109.
    Thiessen R G, Richardson I M. A physically based model for microstructure development in a macroscopic heat-affected zone: Grain growth and recrystallization. Metall Mater Trans B, 2006, 37: 655–663CrossRefGoogle Scholar
  110. 110.
    Zheng C W, Xiao N M, Li D Z, et al. Microstructure prediction of the austenite recrystallization during multi-pass steel strip hot rolling: A cellular automaton modeling. Comput Mater Sci, 2008, 44: 507–514CrossRefGoogle Scholar
  111. 111.
    Lan Y J, Li D Z, Sha X C, et al. Prediction of microstructure and mechanical properties of hot rolled steel strip: Part I-Description of models. Steel Res Int, 2004, 75: 462–467Google Scholar
  112. 112.
    Rajmohan N, Szpunar J A. Monte-Carlo simulation of Goss texture development in silicon steel in the presence of MnS particles. Mater Sci Eng A, 2000, 289: 99–108CrossRefGoogle Scholar
  113. 113.
    Maazi N, Penelle R. Introduction of preferential Zener drag effect in Monte Carlo simulation of abnormal Goss grain growth in the Fe-3%Si magnetic alloys. Mater Sci Eng A, 2009, 504: 135–140CrossRefGoogle Scholar
  114. 114.
    Ko K J, Park J T, Kim J K, et al. Morphological evidence that Goss abnormally growing grains grow by triple junction wetting during secondary recrystallization of Fe-3% Si steel. Scr Mater, 2008, 59: 764–767CrossRefGoogle Scholar
  115. 115.
    Ko K-J, Rollett A D, Hwang N-M. Abnormal grain growth of Goss grains in Fe-3% Si steel driven by sub-boundary-enhanced solid-state wetting: Analysis by Monte Carlo simulation. Acta Mater, 2010, 58: 4414–4423CrossRefGoogle Scholar
  116. 116.
    Ko K J, Cha P R, Srolovitz D, et al. Abnormal grain growth induced by sub-boundary-enhanced solid-state wetting: Analysis by phase-field model simulations. Acta Mater, 2009, 57: 838–845CrossRefGoogle Scholar
  117. 117.
    Kong F, Santhanakrishnan S, Lin D, et al. Modeling of temperature field and grain growth of a dual phase steel DP980 in direct diode laser heat treatment. J Mater Process Tech, 2009, 209: 5996–6003CrossRefGoogle Scholar
  118. 118.
    Zhang W, Elmer J, DebRoy T. Integrated modelling of thermal cycles, austenite formation, grain growth and decomposition in the heat affected zone of carbon steel. Sci Tech Weld Join, 2005, 10: 574–582CrossRefGoogle Scholar
  119. 119.
    Wei Y, Xu Y, Dong Z, et al. Three-dimensional Monte Carlo simulation of discontinuous grain growth in HAZ of stainless steel during GTAW process. J Mater Process Tech, 2009, 209: 1466–1470CrossRefGoogle Scholar
  120. 120.
    Lan Y, Li D, Li Y. A mesoscale cellular automaton model for curvature-driven grain growth. Metall Mater Trans B, 2006, 37: 119–129CrossRefGoogle Scholar
  121. 121.
    Schaffnit P, Stallybrass C, Konrad J, et al. Dual-scale phase-field simulation of grain growth upon reheating of a microalloyed line pipe steel. Int J Mat Res, 2010, 101: 549CrossRefGoogle Scholar
  122. 122.
    Toloui M, Militzer M. Phase field simulation of austenite grain growth in the HAZ of microalloyed linepipe steel. Int J Mat Res, 2010, 101: 542–548CrossRefGoogle Scholar
  123. 123.
    Godiksen R B, Trautt Z T, Upmanyu M, et al. Simulations of boundary migration during recrystallization using molecular dynamics. Acta Mater, 2007, 55: 6383–6391CrossRefGoogle Scholar
  124. 124.
    Janssens K G F, Olmsted D, Holm E A, et al. Computing the mobility of grain boundaries. Nat Mater, 2006, 5: 124–127CrossRefGoogle Scholar
  125. 125.
    Steinbach I, Apel M. Multi phase field model for solid state transformation with elastic strain. Physica D, 2006, 217: 153–160zbMATHCrossRefGoogle Scholar
  126. 126.
    Artemev A, Jin Y, Khachaturyan A G. Three-dimensional phase field model of proper martensitic transformation. Acta Mater, 2001, 49: 1165–1177CrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Shenyang National Laboratory for Materials Science, Institute of Metal ResearchChinese Academy of SciencesShenyangChina

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