Journal of Materials Science

, Volume 53, Issue 9, pp 6911–6921 | Cite as

Modeling the growth of austenite in association with cementite during continuous heating in low-carbon martensite

  • M. Enomoto
  • K. Hayashi


The growth of austenite during continuous heating in plain low-carbon martensite is simulated extending the analytical model by Judd and Paxton to include the carbon diffusion through the matrix. It is assumed that cementite is fully precipitated at an early stage of heating so that austenite is nucleated above the eutectoid temperature either on cementite or away from it, e.g., on prior austenite grain boundary. The austenite grows fast until all cementite particles vanish and thereafter continues to grow at a gradually increasing rate with temperature. Cementite particles remain up to a higher temperature with the increase in heating rate, initial particle size of cementite and the decrease in the number of austenite nuclei. Due to slow carbon diffusivity in austenite, the cementite free of austenite tends to dissolve faster than the cementite on which austenite was nucleated except when the particle size of cementite and/or the number of austenite nuclei is small.



The work was done under the collaborative project with Nippon Steel & Sumitomo Metal Corporation, entitled ‘Modeling austenitization in steel during non-isothermal heat treatment’ (2015).

Compliance with ethical standards

Conflicts of interest

The authors have no conflicts of interest.

Ethical standards

The current manuscript is not under consideration for publication anywhere else. Its publication has been agreed by the co-author.


  1. 1.
    Senuma S (2012) Preface to the special issue on “cutting edge of mathematical models for predicting microstructures and mechanical properties of steels”. ISIJ Int 52:539CrossRefGoogle Scholar
  2. 2.
    Speich GR, Szirmae A (1969) Formation of austenite from ferrite and ferrite-carbide aggregates. Trans TMS AIME 245:1063–1074Google Scholar
  3. 3.
    Speich GR, Demarest VA, Miller RL (1981) Formation of austenite during intercritical annealing of dual-phase steels. Metall Trans A 12A:1419–1428CrossRefGoogle Scholar
  4. 4.
    Fridberg J, Törndahl LE, Hillert M (1969) Diffusion in iron. Jernkont Ann 153:263–276Google Scholar
  5. 5.
    Ågren J (1982) Computer simulations of the austenite/ferrite diffusional transformations in low alloyed steels. Acta Metall 30:841–851CrossRefGoogle Scholar
  6. 6.
    Wei R, Enomoto M, Hadian R, Zurob HS, Purdy GR (2013) Growth of austenite from as-quenched martensite during intercritical annealing in an Fe–0.1 C–3Mn–1.5 Si alloy. Acta Mater 61:697–707CrossRefGoogle Scholar
  7. 7.
    Nakada NN, Mizutani K, Tsuchiyama T, Takaki S (2014) Difference in transformation behavior between ferrite and austenite formations in medium manganese steel. Acta Mater 65:251–258CrossRefGoogle Scholar
  8. 8.
    Wei R, Enomoto M (2015) Growth of austenite from martensite at a late stage of austenitization in an Fe–0.1C–3Mn–1.5Si alloy. In: Militzer M, Botton G, Chen LQ, Howe J, Sinclair C, Zurob H (eds) Proceedings of the international conference on solid–solid phase transformations in inorganic materials (PTM2015). TMS, Warrendale, PA, Canada, pp 131–137Google Scholar
  9. 9.
    Judd RR, Paxton HW (1968) Kinetics of austenite formation from a spheroidized ferrite-carbide aggregate. Trans TMS AIME 242:206–215Google Scholar
  10. 10.
    Caballero FG, Capdevila C, De Andrès CG (2001) Influence of pearlite morphology and heating rate on the kinetics of continuously heated austenite formation in a eutectoid steel. Metall Mater Trans A 32:1283–1291CrossRefGoogle Scholar
  11. 11.
    Luo H, Shi J, Wang C, Cao W, Sun X, Dong H (2011) Experimental and numerical analysis on formation of stable austenite during the intercritical annealing of 5Mn steel. Acta Mater 59:4002–4014CrossRefGoogle Scholar
  12. 12.
    Azizi-Alizamini H, Militzer M, Poole WJ (2011) Austenite formation in plain low-carbon steels. Metall Mater Trans A 42:1544–1557CrossRefGoogle Scholar
  13. 13.
    Enomoto M, Hayashi K (2015) Simulation of the growth of austenite during continuous heating in low carbon iron alloys. J Mater Sci 50:6786–6793. CrossRefGoogle Scholar
  14. 14.
    Nagakura S, Hirotsu Y, Kusunoki M, Suzuki T, Nakamura Y (1983) Crystallographic study of the tempering of martensitic carbon steel by electron microscopy and diffraction. Metall Mater Trans A 14:1025–1031CrossRefGoogle Scholar
  15. 15.
    Danoix F, Zapolsky H, Allain S, Gouné M (2015) Segregation and redistribution from supersaturated virgin Fe–C martensites. In: Militzer M, Botton G, Chen LQ, Howe J, Sinclair C, Zurob H (eds) Proceedings of the international conference on solid–solid phase transformations in inorganic materials (PTM2015). TMS, Warrendale, PA, Canada, pp 537–538Google Scholar
  16. 16.
    Speich GR (1969) Tempering of low-carbon martensite. Trans TMS AIME 245:2553–2564Google Scholar
  17. 17.
    Hayashi K, Enomoto M (2017) Unpublished research, Nippon Steel and Sumitomo Metal CorporationGoogle Scholar
  18. 18.
    Zener C (1949) Theory of growth of spherical precipitates from solid solution. J Appl Phys 20:950–953CrossRefGoogle Scholar
  19. 19.
    Aaron HB, Fainstein D, Kotler GR (1970) Diffusion-limited phase transformations: a comparison and critical evaluation of the mathematical approximations. J Appl Phys 41:4404–4410CrossRefGoogle Scholar
  20. 20.
    Enomoto M, Aaronson HI (1980) On the linearized gradient approximation for diffusion-limited growth of a spherical precipitate. J Appl Phys 51:818–819CrossRefGoogle Scholar
  21. 21.
    Perez M (2005) Gibbs–Thomson effects in phase transformations. Scr Mater 52:709–712CrossRefGoogle Scholar
  22. 22.
    Okamoto H (1993) C–Fe (Carbon–Iron). In: Okamoto H (ed) Phase diagrams of binary iron alloys. ASM, Metals Park, pp 64–83Google Scholar
  23. 23.
    Qiu C, Sybrand Van der Zwaag S (1997) Dilatation measurements of plain carbon steels and their thermodynamic analysis. Steel Res Int 68:32–38CrossRefGoogle Scholar
  24. 24.
    Ågren J (1990) Kinetics of carbide dissolution. Scand J Metall 19:2–8Google Scholar
  25. 25.
    Aaronson HI, Enomoto M, Lee JK (2010) Mechanisms of diffusional phase transformations in metals and alloys. CRC Press/Taylor & Francis, Boca Raton, pp 49–248CrossRefGoogle Scholar
  26. 26.
    Van Vlack LH (1951) Intergranular energy of iron and some iron alloys. Trans TMS AIME 191:251–259Google Scholar
  27. 27.
    Smith CS (1953) Microstructure. Trans ASM 45:533–575Google Scholar
  28. 28.
    Gjostein NA, Domian HA, Aaronson HI, Eichen E (1966) Relative interfacial energies in Fe–C alloys. Acta Metall 14:1637–1644CrossRefGoogle Scholar
  29. 29.
    Lang WF, Enomoto M, Aaronson HI (1988) The kinetics of ferrite nucleation at austenite grain boundaries in Fe–C alloys. Metall Trans A 19A:427–440CrossRefGoogle Scholar
  30. 30.
    Offerman SE et al (2002) Grain nucleation and growth during phase transformations. Science 298:1003–1005CrossRefGoogle Scholar
  31. 31.
    Sharma H (2012) In-situ characterization of grain nucleation and coarsening in metallic microstructures using synchrotron radiation. PhD Dissertation, Delft University of TechnologyGoogle Scholar
  32. 32.
    Thermo-Calc is Trademark of Thermo-Calc Software.
  33. 33.
    Kozeschnik E, Svoboda J, Fisher FD (2006) Shape factors in modeling of precipitation. Mater Sci Eng A441:68–72CrossRefGoogle Scholar
  34. 34.
    Das SK, Biswas A, Ghosh RN (1993) Volume fraction dependent particle coarsening in plain carbon steel. Acta Metall 41:777–781CrossRefGoogle Scholar
  35. 35.
    Miyamoto G, Oh JC, Hono K, Furuhara T, Maki T (2007) Effect of partitioning of Mn and Si on the growth kinetics of cementite in tempered Fe–0.6 mass% C martensite. Acta Mater 55:5027–5038CrossRefGoogle Scholar
  36. 36.
    Enomoto M (1998) Nucleation of phase transformations at intragranular inclusions in steel. Metals Mater 4:115–123CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Ibaraki UniversityBunkyo, MitoJapan
  2. 2.Nippon Steel and Sumitomo Metal CorporationFuttsuJapan

Personalised recommendations