Open Access
Manufacturing Rev.
Volume 5, 2018
Article Number 10
Number of page(s) 18
Published online 27 July 2018
  1. Y.J. Lan et al., Mesoscale simulation of deformed austenite decomposition into ferrite by coupling a cellular automaton method with a crystal plasticity finite element model, Acta Materialia 53 (2005) 991–1003 [CrossRef] [Google Scholar]
  2. H. Yang et al., Review on cellular automata simulations of microstructure evolution during metal forming process: Grain coarsening, recrystallization and phase transformation, Sci. China Technol. Sci. 54 (2011) 2107–2118 [CrossRef] [Google Scholar]
  3. Y.H. Jiang et al., Solid-state phase transformation kinetics in the near-equilibrium regime, J. Mater. Sci. 50 (2015) 662–677 [CrossRef] [Google Scholar]
  4. K.J. Song et al., Cellular automaton-based study of factors that affect dynamic solid phase transformation kinetics, Appl. Math. Model. 39 (2015) 5058–5072 [CrossRef] [Google Scholar]
  5. H. Li et al., Non-isothermal phase-transformation kinetics model for evaluating the austenization of 55 CrMo steel based on Johnson–Mehl–Avrami equation, Materials & Design 92 (2016) 731–741 [CrossRef] [Google Scholar]
  6. Y.H. Jiang, F. Liu, S.J. Song, Extension of analytical model of solid-state phase transformation, Trans. Nonferrous Metals Soc. China 22 (2012) 1176–1181 [CrossRef] [Google Scholar]
  7. M. Meng et al., On the modeling of diffusion-controlled growth of primary alpha in heat treatment of two-phase Ti-alloys, J. Alloys & Compounds 691 (2016) 67–80 [CrossRef] [Google Scholar]
  8. R. Shi et al., Microstructure and transformation texture evolution during α, precipitation in polycrystalline α/β, titanium alloys − A simulation study, Acta Materialia 94 (2015) 224–243 [CrossRef] [Google Scholar]
  9. S. Cui et al., Interface stress evolution of martensitic transformation in MnCu alloys: a phase-field study, Materials & Design 109 (2016) 88–97 [CrossRef] [Google Scholar]
  10. Y. Deng, S. Xiu, Research on microstructure evolution of austenitization in grinding hardening by cellular automata simulation and experiment, Int. J. Adv. Manuf. Technol. 93 (2017) 2599–2612 [CrossRef] [Google Scholar]
  11. C. Halder, L. Madej, M. Pietrzyk, Discrete micro-scale cellular automata model for modelling phase transformation during heating of dual phase steels, Archives Civil & Mech. Eng. 14 (2014) 96–103 [CrossRef] [Google Scholar]
  12. D.S. Svyetlichnyy, Three-dimensional frontal cellular automata model of microstructure evolution phase transformation module, ISIJ Int. 54 (2014) 1386–1395 [CrossRef] [Google Scholar]
  13. B.J. Kooi, Monte Carlo simulations of phase transformations caused by nucleation and subsequent anisotropic growth: extension of the Johnson-Mehl-Avrami-Kolmogorov theory, Phys. Rev. B 70 (2004) 155–163 [Google Scholar]
  14. H. Song, J.J. Hoyt, A molecular dynamics study of heterogeneous nucleation at grain boundaries during solid-state phase transformations, Comput. Mater. Sci. 117 (2016) 151–163 [CrossRef] [Google Scholar]
  15. G.Z. Quan, J. Pan, Z.H. Zhang, Phase transformation and recrystallization kinetics in space-time domain during isothermal compressions for Ti-6Al-4V analyzed by multi-field and multi-scale coupling FEM, Materials & Design 94 (2016) 523–535 [CrossRef] [Google Scholar]
  16. N.M. Xiao et al., Progress in mesoscopic modeling of microstructure evolution in steels, Sci. China Technol. Sci. 55 (2012) 341–356 [CrossRef] [Google Scholar]
  17. N. Moelans, B. Blanpain, P. Wollants, An introduction to phase-field modeling of microstructure evolution, Calphad-Comput. Coupling Phase Diagrams & Thermochemistry 32 (2008) 268–294 [CrossRef] [Google Scholar]
  18. M.A. Miodownik, A review of microstructural computer models used to simulate grain growth and recrystallisation in aluminium alloys, J. Light Metals 2 (2002) 125–135 [CrossRef] [Google Scholar]
  19. H. Hallberg, Approaches to modeling of recrystallization, Metals 1 (2011) 16–48 [CrossRef] [Google Scholar]
  20. J.M. Haile, Molecular dynamics simulation: elementary methods, Comput. Phys. 7 (1993) 625 [CrossRef] [Google Scholar]
  21. J. Svoboda et al., Kinetics of interfaces during diffusional transformations, Acta Materialia 49 (2001) 1249–1259 [CrossRef] [Google Scholar]
  22. A.K. Jena, M.C. Chaturvedi, Phase transformation in materials, Prentice Hall, 1992 [Google Scholar]
  23. W.A. Soffa, D.E. Laughlin, Diffusional phase transformations in the solid state. Phys. Metall. (2014) 0851–1020 [CrossRef] [Google Scholar]
  24. E. Kozeschnik, Modeling solid-state diffusion − Computational Materials Engineering − 5. Comput. Mater. Eng., 2007 151–177 [CrossRef] [Google Scholar]
  25. H.I. Aaronson, M. Enomoto, J.K. Lee, Mechanisms of diffusional phase transformations in metals and alloys, 2010 [CrossRef] [Google Scholar]
  26. J. Sietsma, S.V.D. Zwaag, A concise model for mixed-mode phase transformations in the solid state, Acta Materialia 52 (2004) 4143–4152 [CrossRef] [Google Scholar]
  27. C. Zener, Theory of growth of spherical precipitates from solid solution, J. Appl. Phys. 20 (1949) 950–953 [CrossRef] [Google Scholar]
  28. J.W. Christian, The theory of transformations in metals and alloys, Newnes, 2002 [Google Scholar]
  29. J. Sietsma et al., Evolution of the mixed-mode character of solid-state phase transformations in metals involving solute partitioning, Zeitschrift Für Metallkunde 97 (2006) 356–361 [CrossRef] [Google Scholar]
  30. E.D. Schmidt, E.B. Damm, S.A. Sridhar, Study of diffusion- and interface-controlled migration of the austenite/ferrite front during austenitization of a case-hardenable alloy steel, Metall. & Mater. Trans. A 38 (2007) 698–715 [CrossRef] [Google Scholar]
  31. H. Chen, B. Appolaire, S.V.D. Zwaag, Application of cyclic partial phase transformations for identifying kinetic transitions during solid-state phase transformations: experiments and modeling, Acta Materialia 59 (2011) 6751–6760 [CrossRef] [Google Scholar]
  32. M. Hillert, Solute drag, solute trapping and diffusional dissipation of Gibbs energy 1, Acta Materialia 47 (1999) 4481–4505 [CrossRef] [Google Scholar]
  33. G.P. Krielaart, J. Sietsma, S.V.D. Zwaag, Ferrite formation in Fe–C alloys during austenite decomposition under non-equilibrium interface conditions, Mater. Sci. & Eng. A 237 (1997) 216–223 [CrossRef] [Google Scholar]
  34. A. Salwén, A new model for diffusional growth, Metallurgical Transactions A 24 (1993) 1507–1516 [CrossRef] [Google Scholar]
  35. G. Eriksson, K. Hack, ChemSage—a computer program for the calculation of complex chemical equilibria, Metall. Trans. B 21 (1990) 1013–1023 [CrossRef] [Google Scholar]
  36. J.W. Gibbs, On the equilibrium of heterogeneous substances, Trans Connecticut Acad, 1967 [Google Scholar]
  37. R. Becker, W. Döring, Kinetische Behandlung der Keimbildung in übersättigten Dämpfen, Annalen Der Physik 416 (1935) 719–752 [NASA ADS] [CrossRef] [Google Scholar]
  38. J.W. Cahn, J.E. Hilliard, Free energy of a nonuniform system. I. Interfacial free energy, J. Chem. Phys. 28 (1958) 258–267 [CrossRef] [Google Scholar]
  39. J.W. Cahn, J.E. Hilliard, Free energy of a nonuniform system, III. Nucleation in a two-component incompressible fluid. The Selected Works of John W. Cahn, 2013, pp. 39–50 [CrossRef] [Google Scholar]
  40. R. Poduri, L.Q. Chen, Non-classical nucleation theory of ordered intermetallic precipitates—application to the Al–Li alloy, Acta Materialia 44 (1996) 4253–4259 [CrossRef] [Google Scholar]
  41. D.A. Porter, K.E. Easterling, Phase transformations in metal and alloys, 2nd edition. Chapman & Hall, 1992 [CrossRef] [Google Scholar]
  42. F. Liu, F. Sommer, E.J. Mittemeijer, An analytical model for isothermal and isochronal transformation kinetics, J. Mater. Sci. 39 (2004) 1621–1634 [CrossRef] [Google Scholar]
  43. F. Liu et al., Analysis of solid state phase transformation kinetics: models and recipes, Metall. Rev. 52 (2013) 193–212 [CrossRef] [Google Scholar]
  44. M. Avrami, Kinetics of phase change. II Transformation-time relations for random distribution of nuclei, J. Chem. Phy. 8 (1940) 212–224 [NASA ADS] [CrossRef] [Google Scholar]
  45. M. Avrami, Granulation, phase change, and microstructure kinetics of phase change. III, J. Chem. Phys. 9 (1941) 177–184 [NASA ADS] [CrossRef] [Google Scholar]
  46. Y. Liu et al., Isothermal austenite–ferrite transformation of Fe–0.04 at.% C alloy: dilatometric measurement and kinetic analysis, Acta Materialia 56 (2008) 3833–3842 [CrossRef] [Google Scholar]
  47. G. Meyrick, G.W. Powell, Phase transformations in metals and alloys, Annu. Rev. Mater. Sci. 74 (2003) 299–301 [Google Scholar]
  48. T.W. Heo, L.Q. Chen, Phase-field modeling of nucleation in solid-state phase transformations, JOM 66 (2014) 1520–1528 [CrossRef] [Google Scholar]
  49. Y.V. Leeuwen, Moving interfaces in low-carbon steel − a phase transformation model, Appl. Sci. 29 (2000) 223–230 [Google Scholar]
  50. R.D. Doherty, Diffusive phase transformations in the solid state − Physical Metallurgy (Fourth Edition) − Chapter 15[J]. Phys. Metall. (1996) 1363–1505 [CrossRef] [Google Scholar]
  51. Ø. Grong, H.R. Shercliff, Microstructural modelling in metals processing, Progr. Mater. Sci. 47 (2002) 163–282 [CrossRef] [Google Scholar]
  52. H.S. Carslaw, J.C. Jaeger, Conduction of heat in solids/by H. S. Carslaw and J. C. Jaeger[J], 1959 [Google Scholar]
  53. H.B. Aaron, D. Fainstein, G.R. Kotler, Diffusion-limited phase transformations: a comparison and critical evaluation of the mathematical approximations, J. Appl. Phys. 41 (1970) 4404–4410 [CrossRef] [Google Scholar]
  54. S.L. Semiatin et al., Microstructure evolution during alpha-beta heat treatment of Ti-6Al-4V, Metall. & Mater. Trans. A 34 (2003) 2377–2386 [CrossRef] [Google Scholar]
  55. M. Avrami, Kinetics of phase change. I general theory, J. Chem. Phys. 7 (1939) 1103–1112 [NASA ADS] [CrossRef] [Google Scholar]
  56. K. Fan et al., Analysis of soft impingement in nonisothermal precipitation, J. Mater. Res. 24 (2009) 3664–3673 [CrossRef] [Google Scholar]
  57. C. Wert, C. Zener, Interference of growing spherical precipitate particles, J. Appl. Phys. 21 (1950) 5–8 [CrossRef] [Google Scholar]
  58. K. Fan et al., Modeling of isothermal solid-state precipitation using an analytical treatment of soft impingement, Acta Materialia 56 (2008) 4309–4318 [CrossRef] [Google Scholar]
  59. S.E. Offerman et al., Solid-state phase transformations involving solute partitioning: modeling and measuring on the level of individual grains, Acta Materialia 52 (2004) 4757–4766 [CrossRef] [Google Scholar]
  60. D. Crespo et al., Microstructural evaluation of primary crystallization with diffusion-controlled grain growth, Phys. Rev. B Condens. Matter 55 (1997) 3435–3444 [CrossRef] [Google Scholar]
  61. C. Hao, S.V.D. Zwaag, Modeling of soft impingement effect during solid-state partitioning phase transformations in binary alloys, J. Mater. Sci. 46 (2011) 1328–1336 [CrossRef] [Google Scholar]
  62. M. Tomellini, Soft impingement in diffusion-controlled growth of binary alloys: moving boundary effect in one-dimensional system, J. Mater. Sci. 48 (2013) 5653–5663 [CrossRef] [Google Scholar]
  63. H. Chen, V.D.Z. Sybrand, A mixed-mode model considering soft impingement effects for solid-state partitioning phase transformations, Solid State Phenom. 172–174 (2011) 561–566 [CrossRef] [Google Scholar]
  64. R.E. Lyon, An integral method of nonisothermal kinetic analysis, Thermochimica Acta 297 (1997) 117–124 [CrossRef] [Google Scholar]
  65. J. Málek, Crystallization kinetics by thermal analysis, J. Therm. Anal & Calorim. 56 (1999) 763–769 [CrossRef] [Google Scholar]
  66. W.A. Johnson, Reaction kinetics in process of nucleation and growth, Trans. AIME 135 (1939) 416–458 [Google Scholar]
  67. S.J. Song et al., Kinetics of solid-state transformation subjected to anisotropic effect: model and application, Acta Materialia 59 (2011) 3276–3286 [CrossRef] [Google Scholar]
  68. F. Liu et al., Analytical description for solid-state phase transformation kinetics: extended works from a modular model, a review, J. Mater. Sci. & Technol. 32 (2016) 97–120 [CrossRef] [Google Scholar]
  69. V.V. Sessa, M. Fanfoni, M. Tomellini, Validity of Avrami's kinetics for random and nonrandom distributions of germs, Phys. Rev. B Condens. Matter 54 (1996) 836–841 [CrossRef] [Google Scholar]
  70. G. Tegze et al., Diffusion-controlled anisotropic growth of stable and metastable crystal polymorphs in the phase-field crystal model, Phys. Rev. Lett. 103 (2009) 035702 [CrossRef] [PubMed] [Google Scholar]
  71. J.W. Cahn, The kinetics of grain boundary nucleated reactions, Acta Metallurgica 4 (1956) 449–459 [CrossRef] [Google Scholar]
  72. K.F. Kelton, A.L. Greer, C.V. Thompson, Transient nucleation in condensed systems, J. Chem. Phys. 79 (1983) 6261–6276 [CrossRef] [Google Scholar]
  73. M. Tomellini, M. Fanfoni, M. Volpe, Spatially correlated nuclei: how the Johnson-Mehl-Avrami-Kolmogorov formula is modified in the case of simultaneous nucleation, Phys. Rev. B 62 (2000) 11300 [CrossRef] [Google Scholar]
  74. P.R. Rios, E. Villa, Simultaneous and sequential transformations, Acta Materialia 59 (2011) 1632–1643 [CrossRef] [Google Scholar]
  75. B.J. Kooi, Monte Carlo simulations of phase transformations caused by nucleation and subsequent anisotropic growth: extension of the Johnson-Mehl-Avrami-Kolmogorov theory, Physical Review B 70 (2004) 155–163 [Google Scholar]
  76. V.A. Shneidman, M.C. Weinberg, The effects of transient nucleation and size-dependent growth rate on phase transformation kinetics, J. Non-Crystalline Solids 160 (1993) 89–98 [CrossRef] [Google Scholar]
  77. A. Bhattacharya, C.S. Upadhyay, S. Sangal, A quantitative phase-field simulation of soft-impingement in austenite to ferrite transformation with mixed-mode, Metall. & Mater. Trans. A (2017) 1–14 [Google Scholar]
  78. M. Tomellini, Impingement factor in the case of phase transformations governed by spatially correlated nucleation, Phys. Rev. B 78 (2008) 1436–1446 [CrossRef] [Google Scholar]
  79. M.C. Weinberg, D.P.B. Iii, Avrami exponents for transformations producing anisotropic particles, J. Non-Crystalline Solids 202 (1996) 290–296 [CrossRef] [Google Scholar]
  80. B.J. Kooi. Extension of the Johnson–Mehl–Avrami–Kolmogorov theory incorporating anisotropic growth studied by Monte Carlo simulations, Phys. Rev. B 73 (2006) 054103 [CrossRef] [Google Scholar]
  81. A.T.W. Kempen, F. Sommer, E.J. Mittemeijer, The kinetics of the austenite-ferrite phase transformation of Fe-Mn: differential thermal analysis during cooling, Acta Materialia 50 (2002) 3545–3555 [CrossRef] [Google Scholar]
  82. S.J. Song, F. Liu, Y.H. Jiang, Generalized additivity rule and isokinetics in diffusion-controlled growth, J. Mater. Sci. 49 (2014) 2624–2629 [CrossRef] [Google Scholar]
  83. M. Hillert, Role of interfacial energy during solid-state phase transformations, Jernkontorets Annaler 141 (1957) 757–789 [Google Scholar]
  84. G.P. Ivantsov, The temperature field around a spherical, cylindrical, or pointed crystal growing in a cooling solution, Dokl. Akad. Nauk SSSR 58 (1947) 567–569 [Google Scholar]
  85. G. Horvay, J.W. Cahn, Dendritic and spheroidal growth, Acta Metallurgica 9 (1961) 695–705 [CrossRef] [Google Scholar]
  86. R. Trivedi, The role of interfacial free energy and interface kinetics during the growth of precipitate plates and needles, Metall. Mater. Trans. B 1 (1970) 921–927 [Google Scholar]
  87. L.Q. Chen, W. Yang, 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 Condens. Matter 50 (1994) 15752 [CrossRef] [Google Scholar]
  88. L.Q. Chen, A.G. Khachaturyan, Dynamics of simultaneous ordering and phase separation and effect of long-range Coulomb interactions, Phys. Rev. Lett. 70 (1993) 1477 [CrossRef] [Google Scholar]
  89. J.D.V.D. Waals, The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density, J. Stat. Phys. 20 (1979) 200–244 [CrossRef] [Google Scholar]
  90. V.L. Ginzburg, L.D. Landau, On the theory of superconductivity, J. Exp. Theor. Phys. 20 (1950) 35 [Google Scholar]
  91. V.L. Ginzburg, L.D. Landau, Phenomenological theory, J. Exp. Theor. Phys. 20 (1950) 1064 [Google Scholar]
  92. L.Q. Chen, Phase-field models for microstructure evolution, Annu. Rev. Mater. Res. 32 (2002) 113–140 [CrossRef] [Google Scholar]
  93. L.Q. Chen, Y. Wang, The continuum field approach to modeling microstructural evolution, JOM 48 (1996) 13–18 [CrossRef] [Google Scholar]
  94. L. Zhang, L.Q. Chen, Q. Du, Simultaneous prediction of morphologies of a critical nucleus and an equilibrium precipitate in solids, Commun. Comput. Phys. 7 (2010) 674–682 [Google Scholar]
  95. T.W. Heo et al., Incorporating diffuse-interface nuclei in phase-field simulations, Scripta Materialia 63 (2010) 8–11 [CrossRef] [Google Scholar]
  96. W. Yan et al., Phase-field modeling of Widmanstätten ferrite formation during isothermal transformation in low carbon steels, Comput. Mater. Sci. 81 (2014) 503–509 [CrossRef] [Google Scholar]
  97. T.W. Heo, L.Q. Chen, Phase-field modeling of nucleation in solid-state phase transformations, JOM 66 (2014) 1520–1528 [CrossRef] [Google Scholar]
  98. Y. Jin et al., 2D finite element modeling of misorientation dependent anisotropic grain growth in polycrystalline materials: level set versus multi-phase-field method, Comput. Mater. Sci. 104 (2015) 108–123 [CrossRef] [Google Scholar]
  99. E. Miyoshi, T. Takaki, Extended higher-order multi-phase-field model for three-dimensional anisotropic-grain-growth simulations, Comput. Mater. Sci. 120 (2016) 77–83 [CrossRef] [Google Scholar]
  100. A.G. Khachaturyan, Theory of structural transformations in solids, Courier Corporation, 2013 [Google Scholar]
  101. F. Peter, P. Oliver, L.L. Joel, Modelling of phase separation in alloys with coherent elastic misfit, J. Stat. Phys. 95 (1999) 1429–1503 [CrossRef] [MathSciNet] [Google Scholar]
  102. L. Q. Chen, S. Hu, Phase-field method applied to strain-dominated microstructure evolution during solid-state phase transformations. Continuum scale simulation of engineering materials: fundamentals-microstructures-process applications, 2004, pp. 271–296 [Google Scholar]
  103. B. Appolaire et al., Non-coherent interfaces in diffuse interface models, Philos. Magazine 90 (2010) 461–483 [CrossRef] [Google Scholar]
  104. K. Ammar et al., Combining phase field approach and homogenization methods for modelling phase transformation in elastoplastic media, European J. Comput. Mech. 18 (2009) 485–523 [CrossRef] [Google Scholar]
  105. K. Ammar et al., Modelling inheritance of plastic deformation during migration of phase boundaries using a phase field method, Meccanica 49 (2014) 2699–2717 [CrossRef] [Google Scholar]
  106. V. De Rancourt et al., Homogenization of viscoplastic constitutive laws within a phase field approach, J. Mech. & Phys. Solids 88 (2016) 291–319 [CrossRef] [Google Scholar]
  107. J.P. Simmons et al., Microstructural development involving nucleation and growth phenomena simulated with the phase field method, Mater Sci. & Eng. A 365 (2004) 136–143 [CrossRef] [Google Scholar]
  108. G. Wang, D.C. Zeng, Z.W. Liu, Phase field study of concurrent nucleation and growth in a diffusion-controlled solid-state phase transformation, Adv. Mater. Res. 490–495 (2012) 1140–1144 [CrossRef] [Google Scholar]
  109. A. Yamanaka, T. Takaki, Y. Tomita, Multi-phase-field modeling of diffusive solid phase transition in carbon steel during continuous cooling transformation, J. Crys. Growth 310 (2008) 1337–1342 [CrossRef] [Google Scholar]
  110. M. Militzer et al., Three-dimensional phase field modelling of the austenite-to-ferrite transformation, Acta Materialia 54 (2006) 3961–3972 [CrossRef] [Google Scholar]
  111. Q. Chen et al., Quantitative phase field modeling of diffusion-controlled precipitate growth and dissolution in Ti–Al–V , Scripta Materialia 50 (2004) 471–476 [CrossRef] [Google Scholar]
  112. N. Ofori-Opoku, N. Provatas, A quantitative multi-phase field model of polycrystalline alloy solidification, Acta Materialia 58 (2010) 2155–2164 [CrossRef] [Google Scholar]
  113. I. Steinbach et al., CALPHAD and phase-field modeling: a successful liaison, J. Phase Equilibria & Diffusion 28 (2007) 101–106 [CrossRef] [Google Scholar]
  114. M. Militzer et al., Three-dimensional phase field modelling of the austenite-to-ferrite transformation, Acta Materialia 54 (2006) 3961–3972 [CrossRef] [Google Scholar]
  115. S. Cui, J. Wan, X. Zuo et al., Three-dimensional, non-isothermal phase-field modeling of thermally and stress-induced martensitic transformations in shape memory alloys, Int. J. Solids & Struc. 109 (2017) 1–11 [CrossRef] [Google Scholar]
  116. I. Steinbach, F. Pezzolla, A generalized field method for multiphase transformations using interface fields, Physica D: Nonlinear Phenomena 134 (1999) 385–393 [CrossRef] [MathSciNet] [Google Scholar]
  117. S.B. Biner, Programming phase- field modeling, Springer, 2017 T. Takaki et al., Two-dimensional phase- field simulations of dendrite competitive growth during the directional solidification of a binary alloy bicrystal, Acta Materialia 81 (2014) 272–283 [CrossRef] [Google Scholar]
  118. T. Takaki et al., Two-dimensional phase-field simulations of dendrite competitive growth during the directional solidification of a binary alloy bicrystal, Acta Materialia 81 (2014) 272–283 [CrossRef] [Google Scholar]
  119. C. Yang, Q. Xu, B. Liu, GPU-accelerated three-dimensional phase-field simulation of dendrite growth in a nickel-based superalloy, Comput. Mater. Sci. 136 (2017) 133–143 [CrossRef] [Google Scholar]
  120. Rolling of advanced high strength steels: theory, simulation and practice, CRC Press, 2017 [Google Scholar]
  121. K.G.F. Janssens. An introductory review of cellular automata modeling of moving grain boundaries in polycrystalline materials, Math. & Comput. Simul. 80 (2010) 1361–1381 [CrossRef] [Google Scholar]
  122. H.W. Hesselbarth, L. Kaps, F. Haessner, Two dimensional simulation of the recrystallization kinetics in the case of inhomogeneous stored energy. Mater. sci. Forum, (1993) 317–322 [CrossRef] [Google Scholar]
  123. P.J. Hurley, F.J. Humphreys, Modelling the recrystallization of single-phase aluminium, Acta Materialia 51 (2003) 3779–3793 [CrossRef] [Google Scholar]
  124. Y.C. Lin et al., Study of static recrystallization behavior in hot deformed Ni-based superalloy using cellular automaton model, Materials & Design 99 (2016) 107–114 [CrossRef] [Google Scholar]
  125. K.J. Song et al., Numerical simulation of β to α phase transformation in heat affected zone during welding of TA15 alloy, Comput. Mater. Sci. 72 (2013) 93–100 [CrossRef] [Google Scholar]
  126. C. Wu, Y. He, H.W. Li, Modeling of static coarsening of two-phase titanium alloy in the α+β two-phase region at different temperature by a cellular automata method. Chin. Sci. Bull. 58 (2013) 3023–3032 [CrossRef] [Google Scholar]
  127. M.F. Zhu, D.M. Stefanescu, Virtual front tracking model for the quantitative modeling of dendritic growth in solidification of alloys, Acta Materialia 55 (2007) 1741–1755 [CrossRef] [Google Scholar]
  128. L. Madej, P.D. Hodgson, M. Pietrzyk, Multi-scale rheological model for discontinuous phenomena in materials under deformation conditions, Comput. Mater. Sci. 38 (2007) 685–691 [CrossRef] [Google Scholar]
  129. J.L. He, M.T. Li, Cellular automata to simulate crack propagation of quasi-brittle materials, Appl. Mech. & Mater. 90–93 (2011) 748–751 [Google Scholar]
  130. D.S. Svyetlichnyy, Modelling of the microstructure: from classical cellular automata approach to the frontal one, Comput. Mater. Sci. 50 (2011) 92–97 [CrossRef] [Google Scholar]
  131. K.G.F. Janssens, I rregular cellular automata modeling of grain growth. Continuum scale simulation of engineering materials: fundamentals − microstructures − process applications, 2005, pp. 297–308 [Google Scholar]
  132. K.J. Song et al., Virtual front tracking cellular automaton modeling of isothermal β to α phase transformation with crystallography preferred orientation of TA15 alloy, Model. & Simul.Mater. Sci. & Eng. 22 (2014) 5006 [Google Scholar]
  133. D. Raabe et al., Continuum scale simulation of engineering materials: fundamentals − microstructures − process applications, Front. Psychol. 6 (2014) 885 [Google Scholar]
  134. L. Beltran-Sanchez, D.M. Stefanescu, Growth of solutal dendrites: a cellular automaton model and its quantitative capabilities, Metall. & Mater. Trans. A 34 (2003) 367–382 [CrossRef] [Google Scholar]
  135. K.G.F. Janssens, E.A. Holm, S.M. Foiles, Introducing solute drag in irregular cellular automata modeling of grain growth, Mater. Sci. Forum 467–470 (2004) 1045–1050 [CrossRef] [Google Scholar]
  136. D.S. Svyetlichnyy, Reorganization of cellular space during the modeling of the microstructure evolution by frontal cellular automata, Comput. Mater. Sci. 60 (2012) 153–162 [CrossRef] [Google Scholar]
  137. D.S. Svyetlichnyy, Modeling of grain refinement by cellular automata, Comput. Mater. Sci. 77 (2013) 408–416 [CrossRef] [Google Scholar]
  138. J.W. Cahn, The impurity-drag effect in grain boundary motion, Acta Metallurgica 10 (1962) 789–798 [CrossRef] [Google Scholar]
  139. B. Su, Z. Han, B. Liu, Cellular automaton modeling of austenite nucleation and growth in hypoeutectoid steel during heating process, ISIJ Int. 53 (2013) 527–534 [CrossRef] [Google Scholar]
  140. R. Golab et al., Sensivity analysis of the cellular automata model for austenite-ferrite phase transformation in steels, Appl. Math. 4 (2013) 1531–1536 [CrossRef] [Google Scholar]
  141. C. Zheng, D. Raabe, D. Li, Prediction of post-dynamic austenite-to-ferrite transformation and reverse transformation in a low-carbon steel by cellular automaton modeling, Acta Materialia 60 (2012) 4768–4779 [CrossRef] [Google Scholar]
  142. C. Zheng, D. Raabe, Interaction between recrystallization and phase transformation during intercritical annealing in a cold-rolled dual-phase steel: a cellular automaton model, Acta Materialia 61 (2013) 5504–5517 [CrossRef] [Google Scholar]
  143. K.J. Song et al., Cellular automaton modeling of diffusion, mixed and interface controlled phase transformation, J. Phase Equilibria & Diffusion 36 (2015) 136–148 [CrossRef] [Google Scholar]
  144. F.Y. Wu, The Potts model, Rev. Modern Phys. 54 (1982) 235–268 [CrossRef] [Google Scholar]
  145. M.P. Anderson et al., Computer simulation of grain growth I. Kinetics, Acta Metallurgica 32 (1984) 783–791 [CrossRef] [Google Scholar]
  146. A.D. Rollett, Overview of modeling and simulation of recrystallization, Prog. Mater. Sci. 42 (1997) 79–99 [CrossRef] [Google Scholar]
  147. J.K. Mason, Grain boundary energy and curvature in Monte Carlo and cellular automata simulations of grain boundary motion, Acta Materialia 94 (2015) 162–171 [CrossRef] [Google Scholar]
  148. B.J. Alder, T.E. Wainwright, Studies in molecular dynamics. I. General method, J. Chem. Phys. 31 (1959) 459–466 [CrossRef] [MathSciNet] [Google Scholar]
  149. C.P. Chui et al., Molecular dynamics simulation of iron — a review, Spin 05 (2015) [Google Scholar]
  150. S. Okita et al., Molecular dynamics simulations investigating consecutive nucleation, solidification and grain growth in a twelve-million-atom Fe-system, J. Cryst. Growth 474 (2017) 140–145 [CrossRef] [Google Scholar]
  151. D.U. Furrer, Application of phase-field modeling to industrial materials and manufacturing processes, Current Opin. Solid State Mater. Sci. 15 (2011) 134–140 [CrossRef] [Google Scholar]
  152. M. Mamivand, M.A. Zaeem, H.E. Kadiri, A review on phase field modeling of martensitic phase transformation, Comput. Mater. Sci. 77 (2013) 304–311 [CrossRef] [Google Scholar]
  153. H. Li, X. Sun, H. Yang, A three-dimensional cellular automata-crystal plasticity finite element model for predicting the multiscale interaction among heterogeneous deformation, DRX microstructural evolution and mechanical responses in titanium alloys, Int. J. Plasti. 87 (2016) 154–180 [CrossRef] [Google Scholar]
  154. M.A. Miodownik, A review of microstructural computer models used to simulate grain growth and recrystallisation in aluminium alloys, J. Light Metals 2 (2002) 125–135 [CrossRef] [Google Scholar]
  155. P.W. Hoffrogge, L.A. Barrales-Mora, Grain-resolved kinetics and rotation during grain growth of nanocrystalline aluminium by molecular dynamics, Comput. Mater. Sci. 128 (2017) 207–222 [CrossRef] [Google Scholar]
  156. S. Tateyama, Y. Shibuta, T. Suzuki, A molecular dynamics study of the fcc-bcc phase transformation kinetics of iron, Scripta Materialia 59 (2008) 971–974 [CrossRef] [Google Scholar]
  157. S. Chakraborty, J. Zhang, S. Ghosh, Accelerated molecular dynamics simulations for characterizing plastic deformation in crystalline materials with cracks, Comput. Mater. Sci. 121 (2016) 23–34 [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.