1,004
Views
1
CrossRef citations to date
0
Altmetric
Full Critical Reviews

Modelling of the diffusional austenite-ferrite transformation

, , &
Pages 725-754 | Received 20 Mar 2021, Accepted 03 Sep 2022, Published online: 28 Sep 2022

References

  • Pereloma E, Edmonds D. Phase transformations in steels: fundamentals and diffusion-controlled transformations. Cambridge: Woodhead; 2012.
  • Yoshie A, Fujioka M, Watanabe Y, et al. Modelling of microstructural evolution and mechanical properties of steel plates produced by thermo–mechanical control process. ISIJ Int. 1992;32:395–404.
  • Senuma T, Suehiro M, Yada H. Mathematical models for predicting microstructural evolution and mechanical properties of hot strips. ISIJ Int. 1992;32:423–432.
  • Militzer M. Computer simulation of microstructure evolution in low carbon sheet steels. ISIJ Int. 2007;47:1–15.
  • Gouné M, Danoix F, Ågren J, et al. Overview of the current issues in austenite to ferrite transformation and the role of migrating interfaces therein for low alloyed steels. Mater Sci Eng R: Reports. 2015;92:1–38.
  • Gamsjäger E, Wiessner M, Schider S, et al. Analysis of the mobility of migrating austenite–ferrite interfaces. Philos Mag. 2015;95:2899–2917.
  • Wits JJ, Kop TA, van Leeuwen Y, et al. A study on the austenite–to–ferrite phase transformation in binary substitutional iron alloys. Mater Sci Eng A. 2000;283:234–241.
  • Zhu JN, Luo HW, Yang ZG, et al. Determination of the intrinsic α/γ interface mobility during massive transformations in interstitial free Fe–X alloys. Acta Mater. 2017;133:258–268.
  • Liu ZQ, Miyamoto G, Yang ZG, et al. Carbon enrichment in austenite during bainite transformation in Fe–3Mn–C alloy. Metall Mater Trans A. 2015;46:1544–1549.
  • Yamashita T, Enomoto M, Tanaka Y, et al. Analysis of carbon partitioning at an early stage of proeutectoid ferrite transformation in a low carbon Mn–Si steel by high accuracy FE–EPMA. ISIJ Int. 2018;58:1079–1085.
  • Danoix F, Sauvage X, Huin D, et al. A direct evidence of solute interactions with a moving ferrite/austenite interface in a model Fe–C–Mn alloy. Scripta Mater. 2016;121:61–65.
  • Langelier B, Van Landeghem HP, Botton GA, et al. Interface segregation and nitrogen measurement in Fe–Mn–N steel by atom probe tomography. Microsc Microanal. 2017;23:385–395.
  • Van Landeghem HP, Langelier B, Gault B, et al. Investigation of solute/interphase interaction during ferrite growth. Acta Mater. 2017;124:536–543.
  • Phillion A, Zurob HS, Hutchinson CR, et al. Studies of the influence of alloying elements on the growth of ferrite from austenite under decarburization conditions: Fe–C–Ni alloys. Metall Mater Trans A. 2004;35:1237–1242.
  • Hutchinson CR, Zurob HS, Bréchet Y. The growth of ferrite in Fe–C–X alloys: The role of thermodynamics, diffusion, and interfacial conditions. Metall Mater Trans A. 2006;37:1711–1720.
  • Beche A, Zurob HS, Hutchinson CR. Quantifying the solute drag effect of Cr on ferrite growth using controlled decarburization experiments. Metall Mater Trans A. 2007;38:2950–2955.
  • Chen H, Appolaire B, van der Zwaag S. Application of cyclic partial phase transformations for identifying kinetic transitions during solid–state phase transformations: experiments and modeling. Acta Mater. 2011;59:6751–6760.
  • Chen H, Gamsjäger E, Schider S, et al. In situ observation of austenite–ferrite interface migration in a lean Mn steel during cyclic partial phase transformations. Acta Mater. 2013;61:2414–2424.
  • Chen H, van der Zwaag S. An overview of the cyclic partial austenite–ferrite transformation concept and its potential. Metall Mater Trans A. 2017;48:2720–2729.
  • Borgenstam A, Hillert M. Massive transformation in the Fe–Ni system. Acta Mater. 2000;48:2765–2775.
  • Purdy G, Ågren J, Borgenstam A, et al. ALEMI: a ten–year history of discussions of alloying–element interactions with migrating interfaces. Metall Mater Trans A. 2011;42:3703–3718.
  • Ashby MF. Physical modelling of materials problems. Mater Sci Technol. 1992;8:1574–1573.
  • Kolmogorov AN. On the statistical theory of the crystallization of metals. Bull Acad Sci URSS (Cl Sci Math Nat). 1937;3:335–359.
  • Johnson WA, Mehl RF. ‘Reaction kinetics in processes of nucleation and growth. Trans Am Inst Min Metall Engin. 1939;135:416–442.
  • Avrami M. Kinetics of phase change: I. General theory. J Chem Phys. 1939;7:1103–1112.
  • Militzer M, Pandi R, Hawbolt EB. Ferrite nucleation and growth during continuous cooling. Metall Mater Trans A. 1996;27:1547–1556.
  • Christian JW. The theory of transformation in metals and alloys. Oxford: Pergamon; 2002.
  • van Leeuwen Y, Vooijs S, Sietsma J, et al. The effect of geometrical assumptions in modeling solid-state transformation kinetics. Metall Mater Trans A. 1998;29:2925–2931.
  • Garcin T, Militzer M, Poole WJ, et al. Microstructure model for the heat–affected zone of X80 linepipe steel. Mater Sci Technol. 2016;32:708–721.
  • Bhadeshia HKDH. Bainite in steels. London: The Institute of Materials; 1992.
  • Quidort D, Brechet YJM. Isothermal growth kinetics of bainite in 0.5% C steels. Acta Mater. 2001;49:4161–4170.
  • Jägle EA, Mittemeijer EJ. The kinetics of grain-boundary nucleated phase transformations: simulations and modelling. Acta Mater. 2011;59:5775–5786.
  • Umemoto M, Komatsubara N, Tamura I. Prediction of hardenability effects from isothermal transformation kinetics. J Heat Treat. 1980;1:57–64.
  • Militzer M, Hawbolt EB, Meadowcroft TR. Microstructural model for hot strip rolling of high–strength low–alloy steels. Metall Mater Trans A. 2000;31:1247–1259.
  • Tamura I, Sekine H, Tanaka T, et al. Thermomechanical processing of high strength low alloy steels. London: Butterworths; 1988.
  • Suehiro M, Sato K, Tsukano Y, et al. Computer modeling of microstructural change and strength of low carbon steel in hot strip rolling. Trans Iron Steel Inst Japan. 1987;27:439–445.
  • Roy S. Austenite decomposition in the coarse grain heat affected zone of X80 line pipe steel. M.A.Sc. Thesis. The University of British Columbia, Vancouver, BC; 2020.
  • Vandermeer RA, Masumura RA, Rath BB. Microstructural paths of shape–preserved nucleation and growth transformations. Acta Metall. 1991;39:383–389.
  • Vandermeer RA, Masumura RA. The microstructural path of grain–boundary–nucleated phase transformations. Acta Metall. 1992;40:877–886.
  • Song SJ, Che WK, Zhang JB, et al. Kinetics and microstructural modeling of isothermal austenite–to–ferrite transformation in Fe–C–Mn–Si steels. J Mater Sci Technol. 2019;35:1753–1766.
  • Kelton KF, Greer AF. Nucleation in condensed matter – applications in materials and biology. Amsterdam: Pergamon; 2010.
  • Kwiatkowski da Silva A, Darvishi Kamachali R, Ponge D, et al. Thermodynamics of grain boundary segregation, interfacial spinodal and their relevance for nucleation during solid-solid phase transitions. Acta Mater. 2019;168:109–120.
  • Deschamps A, Hutchinson CR. Precipitation kinetics in metallic alloys: experiments and modelling. Acta Mater. 2021;220:117338.
  • Fang H, van der Zwaag S, van Dijk NH. A novel 3D mixed-mode multigrain model with efficient implementation of solute drag applied to austenite-ferrite phase transformations in Fe-C-Mn alloys. Acta Mater. 2021;212:116897.
  • Lange WF, Enomoto M, Aaronson HI. The kinetics of ferrite nucleation at austenite grain boundaries in Fe–C alloys. Metall Trans A. 1988;19:427–440.
  • Offerman SE, van Dijk NH, Sietsma J, et al. Grain nucleation and growth during phase transformations. Sci. 2002;298:1003–1005.
  • Aaronson HI, Lange III, Purdy GR. Discussion to “Grain nucleation and growth during phase transformations” by S.E. Offerman et al., Science, 298, 1003 (November 1, 2002). Scripta Mater. 2004;51:931–935.
  • Aaronson HI. Decomposition of austenite by diffusional processes. New York: Interscience; 1962.
  • Aaronson HI, Boswell PG, Kinsman KR. Symposium on structure property relationships. In: EL Parker, editor. Mech. Prop. Phase Transform. Eng. Mater. Warrendale (PA): TMS–AIME; 1986. p. 467–473.
  • Krahe PR, Kinsman KR, Aaronson HI. Influence of austenite grain size upon the Widmanstätten–start (Ws) temperature for the proeutectoid ferrite reaction. Acta Metall. 1972;20:1109–1121.
  • Leach L, Kolmskog P, Höglund L, et al. Use of Fe-C information as reference for alloying effects on BS. Metall Mater Trans A. 2019;50:4531–4540.
  • Leach L, Kolmskog P, Höglund L, et al. Critical driving forces for formation of bainite. Metall Mater Trans A. 2018;49:4509–4520.
  • Howe JM, Pond RC, Hirth JP. The role of disconnections in phase transformations. Prog Mater Sci. 2009;54:792–838.
  • Townsend RD, Kirkaldy JS. Widmanstaetten ferrite formation in Fe-C alloys. Trans Am Soc Met. 1968;61:605–619.
  • Mullins WW, Sekerka RF. Morphological stability of a particle growing by diffusion or heat flow. J Appl Phys. 1963;34:323–329.
  • Yang ZN, Xu W, Yang ZG, et al. A 2D analysis of the competition between the equiaxed ferritic and the bainitic morphology based on a Gibbs energy balance approach. Acta Mater. 2016;105:317–327.
  • Aaronson HI, Eylon D, Cooke CM, et al. The Widmanstätten–start (Ws) temperature, as affected by matrix grain size, in Ti–6% Al–4% V and in Fe–C alloys. Scripta Metall. 1989;23:435–440.
  • Chakrabarty AK, Jacob KT. Isothermal transformation of β-phase in Cu-rich Cu-Al-Sn alloys. Int J Mater Res. 2013;104:430–441.
  • Steven W, Haynes AG. The temperature of formation of martensite and bainite in low–alloy steels. J Iron Steel Inst. 1956;183:349–359.
  • Swallow E, Bhadeshia HKDH. High resolution observations of displacements caused by bainitic transformation. Mater Sci Technol. 1996;12:121–125.
  • Bhadeshia HKDH. The lower bainite transformation and the significance of carbide precipitation. Acta Metall. 1980;28:1103–1114.
  • Bhadeshia HKDH. BCC–BCC orientation relationships, surface relief and displacive phase transformations in steels. Scripta Metall. 1980;14:821–824.
  • Aaronson HI, Furuhara T, Hall MG, et al. On the mechanism of formation of diffusional plate–shaped transformation products. Acta Mater. 2006;54:1227–1232.
  • Hillert M, Borgenstam A. Centennial of the diffusionless paradigm of bainite. Metall Mater Trans A. 2012;43:4487–4495.
  • Hillert M, Höglund L. Mobility of α/γ phase interfaces in Fe alloys. Scripta Mater. 2006;54:1259–1263.
  • Krielaart GP, van der Zwaag S. Simulations of pro–eutectoid ferrite formation using a mixed control growth model. Mater Sci Eng A. 1998;246:104–116.
  • Sietsma J, van der Zwaag S. A concise model for mixed–mode phase transformations in the solid state. Acta Mater. 2004;52:4143–4152.
  • Chen H, van der Zwaag S. A general mixed–mode model for the austenite–to–ferrite transformation kinetics in Fe–C–M alloys. Acta Mater. 2014;72:1–12.
  • Hillert M. Phase equilibrium in steel. Jernkontorets Ann. 1957;141:757.
  • Hillert M. Paraequilibrium. Internal Report, Swedish Institute for Metal Research, 1953, Stockholm, Sweden.
  • Hillert M. The growth of ferrite, bainite and martensite. Internal Report, Swedish Institute for Metal Research, 1960, Stockholm, Sweden.
  • Purdy GR, Kirkaldy JS. Kinetics of the proeutectoid ferrite reaction at an incoherent interface, as determined by a diffusion couple. Trans TMS-AIME. 1963;227:1255–1256.
  • Kamat RG, Hawbolt EB, Brown LC, et al. The principle of additivity and the proeutectoid ferrite transformation. Metall Trans A. 1992;23:2469–2480.
  • Zener C. Theory of growth of spherical precipitates from solid solution. J Appl Phys. 1949;20:950–953.
  • Aaronson HI, Enomoto M, Lee JK. Mechanisms of diffusional phase transformations in metals and alloys. Boca Raton (FL): CRC Press; 2010.
  • Ågren J. A revised expression for the diffusivity of carbon in binary Fe-C austenite. Scripta Metall. 1986;20:1507–1510.
  • van der Ven A, Delaey L. Models for precipitate growth during the γ → α + γ transformation in Fe–C and Fe–C–M alloys. Prog Mater Sci. 1996;40:181–264.
  • Kinsman KR, Eichen E, Aaronson HI. Thickening kinetics of proeutectoid ferrite plates in Fe-C alloys. Metall Trans A. 1975;6:303–317.
  • Enomoto M. Computer modeling of the growth-kinetics of ledged interphase boundaries–I. Single step and infinite train of steps. Acta Metall. 1987;35:935–945.
  • Zener C. Kinetics of the decomposition of austenite. Trans Met Soc AIME. 1946;167:550–595.
  • Leach L, Ågren J, Höglund L, et al. Diffusion-controlled lengthening rates of bainitic ferrite: a part of the steel genome. Metall Mater Trans A. 2019;50:2613–2618.
  • Ivantsov GP. Temperature field around spherical, cylindrical and needle-shaped crystals which grow in supercooled melt. G. Horvay (Trans). Dokl Akad Nauk SSSR. 1947;58:567–569.
  • Horvay G, Cahn JW. Dendritic and spheroidal growth. Acta Metall. 1961;9:695–705.
  • Trivedi R. The role of interfacial free energy and interface kinetics during the growth of precipitate plates and needles. Metall Trans. 1970;1:921–927.
  • Yin JQ, Leach L, Hillert M, et al. C–curves for lengthening of Widmanstätten and bainitic ferrite. Metall Mater Trans A. 2017;48:3997–4005.
  • Dong H, Zhang Y, Miyamoto G, et al. A comparative study on intrinsic mobility of incoherent and semicoherent interfaces during the austenite to ferrite transformation. Scripta Mater. 2020;188:59–63.
  • Simonen EP, Aaronson HI, Trivedi R. Lengthening kinetics of ferrite and bainite sideplates. Metall Trans A. 1973;4:1239–1245.
  • Hultgren A. Isothermal transformation of austenite. Trans ASM. 1947;39:915–1005.
  • Kirkaldy JS. Diffusion in multicomponent metallic systems III. The motion of planar phase interfaces. Can J Phys. 1958;36(7):917–925.
  • Coates DE. Diffusion-controlled precipitate growth in ternary systems I. Metall Trans. 1972;3:1203–1212.
  • Gilmour JB. The role of manganese in the formation of proeutectoid ferrite. PhD Thesis, 1970, Queen's University, Kingston, ON.
  • Coates DE. Diffusion controlled precipitate growth in ternary systems II. Metall Trans. 1973;4:1077–1086.
  • Bradley JR, Aaronson HI. Growth kinetics of grain boundary ferrite allotriomorphs in Fe–C–X alloys. Metall Trans A. 1981;12:1729–1741.
  • Hutchinson CR, Fuchsmann A, Bréchet Y. The diffusional formation of ferrite from austenite in Fe–C–Ni alloys. Metall Mater Trans A. 2004;35:1211–1221.
  • Odqvist J, Hillert M, Ågren J. Effect of alloying elements on the γ to α transformation in steel. I. Acta Mater. 2002;50:3213–3227.
  • Purdy GR, Bréchet YJM. A solute drag treatment of the effects of alloying elements on the rate of the proeutectoid ferrite transformation in steels. Acta Metall. 1995;43:3763–3774.
  • Liu ZK. The transformation phenomenon in Fe–Mo–C alloys: A solute drag approach. Metall Mater Trans A. 1997;28:1625–1631.
  • Enomoto M. Influence of solute drag on the growth of proeutectoid ferrite in Fe–C–Mn alloy. Acta Mater. 1999;47:3533–3540.
  • Zurob HS, Panahi D, Hutchinson CR, et al. Self–consistent model for planar ferrite growth in Fe–C–X alloys. Metall Mater Trans A. 2013;44:3456–3471.
  • Qiu C, Zurob HS, Panahi D, et al. Quantifying the solute drag effect on ferrite growth in Fe–C–X alloys using controlled decarburization experiments. Metall Mater Trans A. 2013;44:3472–3483.
  • Miyamoto G, Yokoyama K, Furuhara T. Quantitative analysis of Mo solute drag effect on ferrite and bainite transformations in Fe–0.4C–0.5Mo alloy. Acta Mater. 2019;177:187–197.
  • Hillert M, Sundman B. A solute–drag treatment of the transition from diffusion-controlled to diffusionless solidification. Acta Metall. 1977;25:11–18.
  • Odqvist J, Sundman B, Ågren J. A general method for calculating deviation from local equilibrium at phase interfaces. Acta Mater. 2003;51:1035–1043.
  • Larsson H, Borgenstam A. Trans–interface diffusivity in the Fe–Ni system. Scripta Mater. 2007;56:61–64.
  • Sun WW, Zurob HS, Hutchinson CR. Coupled solute drag and transformation stasis during ferrite formation in Fe–C–Mn–Mo. Acta Mater. 2017;139:62–74.
  • Zhang YJ, Miyamoto G, Shinbo K, et al. Quantitative measurements of phase equilibria at migrating α/γ interface and dispersion of VC interphase precipitates: evaluation of driving force for interphase precipitation. Acta Mater. 2017;128:166–175.
  • Aaronson HI, Reynolds Jr WT, Purdy GR. The incomplete transformation phenomenon in steel. Metall Mater Trans A. 2006;37:1731–1745.
  • Wu KM, Kagayama M, Enomoto M. Kinetics of ferrite transformation in an Fe–0.28mass%C–3mass%Mo alloy. Mater Sci Eng A. 2003;343:143–150.
  • Bréchet Y, Purdy G. A self–consistent treatment of precipitate growth via ledge migration in the presence of interfacial dissipation. Scripta Mater. 2005;52:7–10.
  • Yang ZN, Xu W, Yang ZG, et al. Predicting the transition between upper and lower bainite via a Gibbs energy balance approach. J Mater Sci Technol. 2017;33:1513–1521.
  • Miyamoto G, Hori R, Poorganji B, et al. Crystallographic analysis of proeutectoid ferrite/austenite interface and interphase precipitation of vanadium carbide in medium-carbon steel. Metall Mater Trans A. 2013;44:3436–3443.
  • Chen H, Zhu KY, Zhao L, et al. Analysis of transformation stasis during the isothermal bainitic ferrite formation in Fe–C–Mn and Fe–C–Mn–Si alloys. Acta Mater. 2013;61:5458–5468.
  • Jin H, Elfimov I, Militzer M. Study of the interaction of solutes with Σ5 (013) tilt grain boundaries in iron using density–functional theory. J Appl Phys. 2014;115:093506.
  • Wu RQ, Freeman AJ, Olson GB. Effects of carbon on Fe–grain–boundary cohesion: first–principles determination. Phys Rev B. 1996;53:7504–7509.
  • Wachowicz E, Kiejna A. Effect of impurities on structural, cohesive and magnetic properties of grain boundaries in α–Fe. Modell Simul Mater Sci Eng. 2011;19:025001.
  • Jin H, Elfimov I, Militzer M. First–principles simulations of binding energies of alloying elements to the ferrite–austenite interface in iron. J Appl Phys. 2018;123:085303.
  • Zhang X, Hickel T, Rogal J, et al. Structural transformations among austenite, ferrite and cementite in Fe–C alloys: A unified theory based on ab initio simulations. Acta Mater. 2015;99:281–289.
  • Maresca F, Curtin WA. The austenite/lath martensite interface in steels: structure, athermal motion, and in–situ transformation strain revealed by simulation and theory. Acta Mater. 2017;134:302–323.
  • Lejček P. Grain boundary segregation in metals. Dordrecht, London, New York: Springer Heidelberg; 2010.
  • Wicaksono AT, Militzer M. Interaction of C and Mn in a ∑3 grain boundary of bcc iron. IOP Conf Ser: Mater Sci Eng. 2017;219:012044.
  • Gornostyrev YN, Urtsev VN, Zalalutdinov MK, et al. Reconstruction of grain boundaries during austenite–ferrite transformation. Scripta Mater. 2005;53:153–158.
  • Ou X, Sietsma J, Santofimia MJ. Molecular dynamics simulations of the mechanisms controlling the propagation of bcc/fcc semi-coherent interfaces in iron. Modell Sim Mater Sci Eng. 2016;24:055019.
  • Ou X. Molecular dynamics simulations of fcc-to-bcc transformation in pure iron: a review. Mat Sci Techn. 2017;33:822–835.
  • Karewar S, Sietsma J, Santofimia MJ. Effect of pre-existing defects in the parent fcc phase on atomistic mechanisms during the martensitic transformation in pure Fe: A molecular dynamics study. Acta Mater. 2017;142:71–81.
  • Karewar S, Sietsma J, Santofimia MJ. Effect of C on the martensitic transformation in Fe-C alloys in the presence of pre-existing defects: A molecular dynamics study. Crystals. 2019;9:99.
  • Dickel DE, Barrett CD. Methods for the determination of diffusionless transformation conditions from atomistic simulations. Modell Sim Mater Sci Eng. 2019;27:023001.
  • Meiser J, Urbassek HM. Ferrite-to-austenite and austenite-to-martensite phase transformations in the vicinity of a cementite particle: A molecular dynamics approach. Metals. 2019;8:837.
  • Meiser J, Urbassek HM. Dislocations help initiate the α–γ phase transformation in iron – an atomistic study. Metals. 2019;9:90.
  • Tripathi PK, Karewar S, Lo YC, et al. Role of interface morphology on the martensitic transformation in pure Fe. Materialia. 2021;16:101085.
  • Song H, Hoyt JJ. A molecular dynamics simulation study of the velocities, mobility and activation energy of an austenite–ferrite interface in pure Fe. Acta Mater. 2012;60:4328–4335.
  • Song H, Hoyt JJ. An atomistic simulation study of the migration of an austenite–ferrite interface in pure Fe. Acta Mater. 2013;61:1189–1196.
  • Song H, Hoyt JJ. A molecular dynamics study of heterogeneous nucleation at grain boundaries during solid–state phase transformations. Comput Mater Sci. 2016;117:151–163.
  • Song H, Hoyt JJ. A molecular dynamics study of the nucleus interface structure and orientation relationships during the austenite–to–ferrite transformation in pure Fe. Can Metall Q. 2018;57:12–19.
  • Song H, Shi R, Wang Y, et al. Simulation study of heterogeneous nucleation at grain boundaries during the austenite–ferrite phase transformation: comparing the classical model with the multi–phase field nudged elastic band method. Metall Mater Trans A. 2017;48:2730–2738.
  • Tripathi PK, Maurya SK, Bhowmick S. Role of disconnections in mobility of the austenite-ferrite interphase boundary in Fe. Phys Rev Mater. 2018;2:113403.
  • Sun ZP, Dai FZ, Xu B, et al. Three-dimensional growth of coherent ferrite in austenite: a molecular dynamics study. Acta Metall Sinica. 2019;32:669–676.
  • Ackland GJ, Bacon DJ, Calder AF, et al. Computer simulation of point defect properties in dilute Fe–Cu alloy using a many–body interatomic potential. Philos Mag A. 1997;75:713–732.
  • van Dijk NH, Offerman E, Sietsma J, et al. Barrier-free heterogeneous grain nucleation in polycrystalline materials: the austenite to ferrite phase transformation in steel. Acta Mater. 2007;55:4489–4498.
  • Steinbach I, Pezzolla F, Nestler B, et al. A phase field concept for multiphase systems. Physica D. 1996;94:135–147.
  • Böttger B, Apel M, Eiken J, et al. Phase–field simulation of solidification and solid-state transformations in multicomponent steels. Steel Res. Int. 2008;79:608–616.
  • Yeon DH, Cha PR, Yoon JK. A phase field study for ferrite–austenite transitions under paraequilibrium. Scripta Mater. 2001;45:661–668.
  • Pariser G, Schaffnit P, Steinbach I, et al. Simulation of the (-(-transformation using the phase-field method. Steel Res. Int. 2001;72:354–360.
  • Loginova I, Odqvist J, Amberg G, et al. The phase–field approach and solute drag modeling of the transition to massive γ→ α transformation in binary Fe-C alloys. Acta Mater. 2003;51:1327–1339.
  • Loginova I, Ågren J, Amberg G. On the formation of Widmanstätten ferrite in binary Fe–C–phase–field approach. Acta Mater. 2004;52:4055–4063.
  • Yamanaka A, Takaki T, Tomita Y. Phase–field simulation of austenite to ferrite transformation and Widmanstätten ferrite formation in Fe–C alloy. Mater Trans. 2006;47:2725–2731.
  • Yan W, Xiao NM, Chen Y, et al. Phase–field modeling of Widmanstätten ferrite formation during isothermal transformation in low carbon steels. Comput Mater Sci. 2014;81:503–509.
  • Bhattacharya A, Ankit K, Nestler B. Phase–field simulations of curvature–induced cascading of Widmanstätten–ferrite plates. Acta Mater. 2017;123:317–328.
  • Zhang LJ, Stratmann M, Du Y, et al. Incorporating the CALPHAD sublattice approach of ordering into the phase–field model with finite interface dissipation. Acta Mater. 2015;88:156–169.
  • Cottura M, Appolaire B, Finel A, et al. Phase field study of acicular growth: role of elasticity in Widmanstätten structure. Acta Mater. 2014;72:200–210.
  • Amos PGK, Schoof E, Schneider D, et al. Chemo–elastic phase–field simulation of the cooperative growth of mutually–accommodating Widmanstätten plates. J Alloys Compd. 2018;767:1141–1154.
  • Lin C, Wan J, Ruan H. Phase field modeling of Widmanstätten ferrite formation in steel. J Alloys Compd. 2018;769:620–630.
  • Bhattacharya A, Mondal K, Upadhyay CS, et al. A phase-field study on the evolution of Widmanstätten-ferrite plates under mixed-mode of transformation. Comput Mater Sci. 2020;180:109718.
  • Song WW, Prahl U, Bleck W, et al. Phase–field simulations of bainitic phase transformations in 100CR6. In: TMS 2011 140th Annual Meeting and Exhibition: Supplemental Proceedings: Materials Fabrication, Properties, Characterization, and Modeling, Vol. 2, The Minerals, Metals & Materials Society (TMS), Pittsburgh, PA.
  • Ramazani A, Pinard PT, Richter S, et al. Characterisation of microstructure and modelling of flow behaviour of bainite–aided dual–phase steel. Comput Mater Sci. 2013;80:134–141.
  • Arif TT, Qin RS. A phase–field model for bainitic transformation. Comput Mater Sci. 2013;77:230–235.
  • Düsing M, Mahnken R. A thermodynamic framework for coupled multiphase field and diffusion models for lower bainite transformation. PAMM Proc Appl Math Mech. 2016;16:321–322.
  • Toloui M, Militzer M. Phase field modeling of the simultaneous formation of bainite and ferrite in TRIP steel. Acta Mater. 2018;144:786–800.
  • Düsing M, Mahnken R. A coupled phase field/diffusion model for upper and lower bainitic transformation. Int J Solids Struct. 2018;135:172–183.
  • Song WW, Prahl U, Ma Y, et al. Multiphase–field simulation of cementite precipitation during isothermal lower bainitic transformation. Steel Res Int. 2018;89:28–33.
  • Elhigazi F, Artemev A. The interaction between the displacive transformation and the diffusion process in the bainitic type transformation. Comput Mater Sci. 2019;169:109079.
  • Elhigazi F, Artemev A. Interaction between carbon partitioning and carbide nucleation inside austenite during a bainitic type transformation. Comput Mater Sci. 2020;184:109846.
  • Mecozzi MG, Sietsma J, van der Zwaag S, et al. Analysis of the γ→ α transformation in a C-Mn steel by phase-field modeling. Metall Mater Trans A. 2005;36:2327–2340.
  • Mecozzi MG, Sietsma J, van der Zwaag S. Phase field modelling of the interfacial condition at the moving interphase during the γ→ α transformation in C-Mn steels. Comput. Mater. Sci. 2005;34:290–297.
  • Mecozzi MG, Sietsma J, van der Zwaag S. Analysis of γ→ α transformation in a Nb micro-alloyed C-Mn steel by phase field modelling. Acta Mater. 2006;54:1431–1440.
  • Militzer M, Mecozzi MG, Sietsma J, et al. Three–dimensional phase field modelling of the austenite–to–ferrite transformation. Acta Mater. 2006;54:3961–3972.
  • Mecozzi MG, 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;39:1237–1247.
  • Huang CJ, Browne DJ, McFadden S. A phase–field simulation of austenite to ferrite transformation kinetics in low carbon steels. Acta Mater. 2006;54:11–21.
  • Huang CJ, Browne DJ. Phase–field model prediction of nucleation and coarsening during austenite/ferrite transformation in steels. Metall Mater Trans A. 2006;37:589–598.
  • Takahama Y, Sietsma J. Mobility analysis of the austenite to ferrite transformation in Nb microalloyed steel by phase field modelling. ISIJ Int. 2008;48:512–517.
  • Zhu BQ, Militzer M. Phase–field modeling for intercritical annealing of a dual–phase steel. Metall Mater Trans A. 2015;46:1073–1084.
  • Shahandeh S, Militzer M. Modelling of particle pinning in dual scale using phase field method. Mater Sci Forum. 2012;715–716:764–769.
  • Zhu BQ, Chen H, Militzer M. Phase–field modeling of cyclic phase transformations in low–carbon steels. Comput Mater Sci. 2015;108:333–341.
  • Suwanpinij P, Rudnizki J, Prahl U, et al. Investigation of the effect of deformation on γ→ α transformation kinetics in hot-rolled dual phase steel by phase field approach. Steel Res Int. 2009;80:616–622.
  • Thiessen RG, Sietsma J, Palmer TA, et al. Phase–field modelling and synchrotron validation of phase transformations in martensitic dual–phase steel. Acta Mater. 2007;55:601–614.
  • Thiessen RG, Richardson IM, Sietsma J. Physically based modelling of phase transformations during welding of low–carbon steel. Mater Sci Eng A. 2006;427:223–231.
  • Santofimia MJ, Zhao L, Sietsma J. Model for the interaction between interface migration and carbon diffusion during annealing of martensite–austenite microstructures in steels. Scripta Mater. 2008;59:159–162.
  • Mecozzi MG, Eiken J, Santofimia MJ, et al. Phase field modelling of microstructural evolution during the quenching and partitioning treatment in low–alloy steels. Comput Mater Sci. 2016;112:245–256.
  • Toloui M, Militzer M. Phase field modelling of microstructure evolution in the HAZ of X80 linepipe steel. Proceedings of International Pipeline Conference 2012 (IPC 2012), 2012, Calgary, 323–328.
  • Toloui M. Microstructure evolution in the HAZ of X80 linepipe steel: Phase field modelling [PhD thesis]. , Vancouver, BC: The University of British Columbia; 2015.
  • Kumar M, Sasikumar R, Nair PK. Competition between nucleation and early growth of ferrite from austenite-studies using cellular automaton simulations. Acta Mater. 1998;46:6291–6303.
  • Varma MR, Sasikumar R, Pillai SGK, et al. Cellular automaton simulation of microstructure evolution during austenite decomposition under continuous cooling conditions. Bull Mater Sci. 2001;24:305–312.
  • Reed RC, Bhadeshia HKDH. A simple model for multipass steel welds. Acta Metall Mater. 1994;42:3663–3678.
  • Zhang L, Zhang CB, Wang YM, et al. A cellular automaton investigation of the transformation from austenite to ferrite during continuous cooling. Acta Mater. 2003;51:5519–5527.
  • Lan YJ, Li DZ, Li YY. Modeling austenite decomposition into ferrite at different cooling rate in low–carbon steel with cellular automaton method. Acta Mater. 2004;52:1721–1729.
  • Lan YJ, Li DZ, Huang CJ, et al. A cellular automaton model for austenite to ferrite transformation in carbon steel under non–equilibrium interface conditions. Modelling Simul Mater Sci Eng. 2004;12:719–729.
  • Lan YJ, Li DZ, Li YY. Modeling austenite–ferrite transformation in low carbon steel using the cellular automaton method. J Mater Res. 2004;19:2877–2886.
  • Lan YJ, Li DZ, Li YY. Mesoscale simulation of ferrite transformation from deformed austenite during continuous cooling in a C–Mn steel using a cellular automaton method. Comput Mater Sci. 2005;32:47–155.
  • Lan YJ, Xiao NM, Li DZ, 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;53:991–1003.
  • Li X, Zhang Y, Liu Y, et al. Multi-pass transformation kinetics of HSLA steels during continuous cooling: experiments and cellular automaton (CA) simulation. Philos Mag Lett. 2020;100:2001–2007.
  • Offerman SE, van Dijk NH, Sietsma J, et al. Solid–state phase transformations involving solute partitioning: modeling and measuring on the level of individual grains. Acta Mater. 2004;52:4757–4766.
  • Bos C, Mecozzi MG, Sietsma J. A microstructure model for recrystallisation and phase transformation during the dual–phase steel annealing cycle. Comput Mater Sci. 2010;48:692–699.
  • Svyetlichnyy DS, Muszka K, Majta J. Three–dimensional frontal cellular automata modeling of the grain refinement during severe plastic deformation of microalloyed steel. Comput Mater Sci. 2015;102:159–166.
  • Bos C, Sietsma J. A mixed–mode model for partitioning phase transformations. Scripta Mater. 2007;57:1085–1088.
  • Tong MM, Li DZ, Li YY. Modeling the austenite–ferrite diffusive transformation during continuous cooling on a mesoscale using Monte Carlo method. Acta Mater. 2004;52:1155–1162.
  • Tong MM, Li DZ, Li YY, et al. Monte Carlo–method simulation of the deformation–induced ferrite transformation in the Fe–C system. Metall Mater Trans A. 2004;35:1565–1577.
  • Tong MM, Li DZ, Li YY. 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;53:1485–1497.
  • Tong MM, Li DZ, Li YY, et al. Modeling the austenite–ferrite isothermal transformation in an Fe–C binary system and experimental verification. Metall Mater Trans A. 2002;33:3111–3115.
  • Fang Z, Tomiko Y, Hideyuki I, et al. Monte Carlo simulation of γ→ α transformation during continuous cooling. J Japan Inst Metals. 2009;73:495–501.
  • Xiao N, Tong MM, Lan Y, et al. Coupled simulation of the influence of austenite deformation on the subsequent isothermal austenite-ferrite transformation. Acta Mater. 2006;54:1265–1278.
  • Olson GB. Genomics materials design: the ferrous frontier. Acta Mater. 2013;61:771–781.
  • Olson GB, Kuehmann CJ. Materials genomics: from CALPHAD to flight. Scripta Mater. 2014;70:25–30.
  • Militzer M, Hoyt JJ, Provatas N, et al. Multiscale modeling of phase transformations in steels. JOM. 2014;66:740–746.
  • Suhane A, Scheiber D, Popov M, et al. Solute drag assessment of grain boundary migration in Au. Acta Mater. 2022;223:117473.
  • Henriksson KOE, Nordlund K. Simulations of cementite: An analytical potential for the Fe–C system. Phys Rev B. 2009;79:144107.
  • Swinburne TD, Perez D. Self–optimized construction of transition rate matrices from accelerated atomistic simulations with Bayesian uncertainty quantification. Phys Rev Mater. 2018;2:053802.
  • Perez D, Huang R, Voter A. Long–time molecular dynamics simulations on massively parallel platforms: A comparison of parallel replica dynamics and parallel trajectory splicing. J Mater Res. 2018;33:813–822.
  • Dontsova E, Rottler J, Sinclair CW. Solute–defect interactions in Al–Mg alloys from diffusive variational Gaussian calculations. Phys Rev B. 2014;90:174102.
  • Béland LK, Brommer P, El–Mellouhi F, et al. Kinetic activation–relaxation technique. Phys Rev E. 2011;84:046704.
  • Kapikranian O, Zapolsky H, Domain C, et al. Atomic structure of grain boundaries in iron modeled using the atomic density function. Phys Rev B. 2014;89:01411.
  • Kapikranian O, Zapolsky H, Patte R, et al. Point defect absorption by grain boundaries in α–iron by atomic density function modeling. Phys Rev B. 2015;92:224106.
  • Zapolsky H, Demange G, Abdank–Kozubski R. From the atomistic to the mesoscopic scale modeling of phase transition in solids. Diff Found. 2017;12:111–126.
  • Greenwood M, Provatas N, Rottler J. Free energy functionals for efficient phase field crystal modeling of structural phase transformations. Phys Rev Lett. 2010;105:045702.
  • Greenwood M, Rottler J, Provatas N. Phase–field–crystal methodology for modeling of structural transformations. Phys Rev E. 2011;83:031601.
  • Greenwood M, Sinclair C, Militzer M. Phase field crystal model of solute drag. Acta Mater. 2012;60:5752–5761.
  • Ofori–Opoku N, Fallah V, Greenwood M, et al. Multicomponent phase–field crystal model for structural transformations in metal alloys. Phys Rev B. 2013;87:134105.
  • Qui C, Zurob HS, Hutchinson CR. The coupled solute drag effect during ferrite growth in Fe-C-Mn-Si alloys using controlled decarburization. Acta Mater. 2015;100:333–343.
  • Chen H, Kuziak R, van der Zwaag S. Experimental evidence of the effect of alloying additions on the stagnant stage length during cyclic partial phase transformations. Metall Mater Trans A. 2013;44:5617–5621.
  • Mathevon A, Perez M, Massardier V, et al. Gibbs energy minimisation model for the austenite-ferrite phase transformation in Fe-C-X-Y alloys. Phil Mag Lett. 2021;101:232–241.
  • Huber L, Hadian R, Grabowski B, et al. A machine learning approach to model solute grain boundary segregation. npj Comput Mater. 2018;4:64–71.
  • Wagih M, Larsen PM, Schuh CA. Learning grain boundary segregation energy spectra in polycrystals. Nat Commun. 2020;11:6376.
  • Suzuki A, Mishin Y. Atomistic modeling of point defects and diffusion in copper grain boundaries. Interface Sci. 2003;11:131–148.
  • Dai Z, Chen H, Ding R, et al. Fundamentals and application of solid-state phase transformations for advanced high strength steels containing metastable retained austenite. Mater Sci Eng R. 2021;143:100590.
  • Sun WW, Wu YX, Yang SC, et al. Advanced high strength steel (AHSS) development through chemical patterning of austenite. Scripta Mater. 2018;146:60–63.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.