Kinetic Model for the Phase Transformation of High-Strength Steel Under Arbitrary Cooling Conditions

  • Hao Zhao
  • Xiuli Hu
  • Junjia Cui
  • Zhongwen Xing


To meet the demands of energy conservation and security improvement, high-strength steel (HSS) is widely used to produce safety-related automotive components. In addition to fully high-strength parts, HSS is also used to manufacture components with tailored properties. In this work, a computational model is presented to predict the austenite decomposition into ferrite, pearlite, bainite and martensite during arbitrary cooling paths in HSS. First, a kinetic model for both diffusional and martensite transformations under isothermal or non-isothermal with constant cooling rate cooling conditions is proposed based on the well-known Johnson–Mehl–Avrami–Kolmogorov and Kamamoto models. The model is then modified for arbitrary cooling conditions through the introduction of the effects of the cooling rate, and the influence of diffusional transformations on martensite transformation is considered. Next, the detailed kinetics parameters are identified by fitting experimental data from BR1500HS steel. The model is further verified by several experiments conducted outside of the fit domain. The results obtained by calculation are found to be in good agreement with the corresponding experimental data, including the transformation histories, volume fraction microconstituents and Vickers hardness. Additionally, the model is also implemented as a subroutine in ABAQUS to simulate a tailored-strength hot stamping process of HSS, and the results are consistent with the test data. Thus, this computational model can be used as a guideline to design manufacturing processes that achieve the desired microstructure and material properties.


Kinetic model for phase transformation HSS Arbitrary cooling conditions Microstructure Hot stamping 



This project was supported by the National Natural Science Foundation of China (Grant No. 51405149).


  1. 1.
    P. Åkerström, G. Bergman, M. Oldenburg, Numerical implementation of a constitutive model for simulation of hot stamping. Model. Simul. Mater. Sci. Eng. 15(2), 105–119 (2007)CrossRefGoogle Scholar
  2. 2.
    G. Georgiadis, A.E. Tekkaya, P. Weigert, S. Horneber, P.A. Kuhnleal, Formability analysis of thin press hardening steel sheets under isothermal and non-isothermal conditions. Int.J. Mater. Form. 10(3), 1–15 (2016)Google Scholar
  3. 3.
    H. Karbasian, A.E. Tekkaya, A review on hot stamping. J. Mater. Process. Technol. 210(15), 2103–2118 (2010)CrossRefGoogle Scholar
  4. 4.
    P. Hippchen, A. Lipp, H. Grass, P. Craighero, M. Fleischer, M. Merklein, Modelling kinetics of phase transformation for the indirect hot stamping process to focus on car body parts with tailored properties. J. Mater. Process. Technol. 228(8), 59–67 (2016)CrossRefGoogle Scholar
  5. 5.
    R. George, A. Bardelcik, M.J. Worswick, Hot forming of boron steels using heated and cooled tooling for tailored properties. J. Mater. Process. Technol. 212(11), 2386–2399 (2012)CrossRefGoogle Scholar
  6. 6.
    K. Omer, R. George, A. Bardelcik, M. Worswick, S. Malcolm, D. Detwiler, Development of a hot stamped channel section with axially tailored properties–experiments and models. Int. J. Mater. Form. 11(1), 1–16 (2017)Google Scholar
  7. 7.
    B.A. Hay, B. Bourouga, C. Dessain, Thermal contact resistance estimation at the blank/tool interface: experimental approach to simulate the blank cooling during the hot stamping process. Int. J. Mater. Form. 3(3), 147–163 (2010)CrossRefGoogle Scholar
  8. 8.
    P. Åkerström, M. Oldenburg, Austenite decomposition during press hardening of a boron steel—computer simulation and test. J. Mater. Process. Technol. 174(1), 399–406 (2006)CrossRefGoogle Scholar
  9. 9.
    H.H. Bok, S.N. Kim, D.W. Suh, F. Barlat, M.G. Lee, Non-isothermal kinetics model to predict accurate phase transformation and hardness of 22MnB5 boron steel. Mater. Sci. Eng., A 626, 67–73 (2015)CrossRefGoogle Scholar
  10. 10.
    W.A. Johnson, R.F. Mehl, Reaction kinetics in processes of nucleation and growth. Trans. Am. Inst. Min. Metall. Eng. 135, 416–458 (1939)Google Scholar
  11. 11.
    M. Avrami, Kinetics of phase change. III: granulation, phase change and microstructure. J. Chem. Phys. 9(2), 177–184 (1941)CrossRefGoogle Scholar
  12. 12.
    A.N. Kolmogorov, On the statistical theory of metal crystallization. Izv. Akad. Nauk. SSSR Ser. Mat. 3, 355–359 (1937)Google Scholar
  13. 13.
    Kirkaldy J.S., Venugopalan D. Prediction of microstructure and hardenability in low-alloy steels, in Phase Transformation in Ferrous Alloys, ed. by A.R. Marder, J.I. Goldstein, 1983, pp. 125–148Google Scholar
  14. 14.
    J.W. Cahn, The kinetics of grain boundary nucleated reactions. Acta Metall. 4(5), 449–459 (1956)CrossRefGoogle Scholar
  15. 15.
    M. Umemoto, N. Nishioka, Prediction of hardenability from isothermal transformation diagrams. J. Heat. Treat. 2(2), 130–138 (1981)CrossRefGoogle Scholar
  16. 16.
    F. Liu, F. Sommer, E.J. Mittemeijer, An analytical model for isothermal and isochronal transformation kinetics. J. Mater. Sci. 39(5), 1621–1634 (2004)CrossRefGoogle Scholar
  17. 17.
    A. Pohjonen, M. Somani, D. Porter, Modelling of austenite transformation along arbitrary cooling paths. Comput. Mater. Sci. 150, 244–251 (2018)CrossRefGoogle Scholar
  18. 18.
    M.V. Li, D.V. Niebuhr, L.L. Meekisho, D.G. Atteridge, A computational model for the prediction of steel hardenability. Metall. Mater. Trans. B 29(3), 661–672 (1998)CrossRefGoogle Scholar
  19. 19.
    N. Saunders, Z. Guo, X. Li, A.P. Miodownik, J.P. Schillé, The Calculation of TTT and CCT diagrams for General Steels. Sente Software Ltd, 2004Google Scholar
  20. 20.
    S.J. Lee, E.J. Pavlina, C.J.V. Tyne, Kinetics modeling of austenite decomposition for an end-quenched 1045 steel. Mater. Sci. Eng., A 527(13), 3186–3194 (2010)CrossRefGoogle Scholar
  21. 21.
    D.P. Koistinen, R.E. Marburger, A general equation prescribing the extent of the austenite-martensite transformation in pure iron-carbon alloys and plain carbon steels. Acta Metall. 7(1), 59–60 (1959)CrossRefGoogle Scholar
  22. 22.
    C.L. Magee, The nucleation of martensite, in Phase Transformations, ed. by H.I. Aaronson, V.F. Zackay, ASM International, 1970, pp. 115–156Google Scholar
  23. 23.
    K. Tanaka, A thermomechanical sketch of shape memory effect: one-dimensional tensile behavior. Res. Mech. 18, 251–263 (1986)Google Scholar
  24. 24.
    S.J. Lee, Y.K. Lee, Finite element simulation of quench distortion in a low-alloy steel incorporating transformation kinetics. Acta Mater. 56(7), 1482–1490 (2008)CrossRefGoogle Scholar
  25. 25.
    R.F. Hehemann, K.R. Kinsman, H.I. Aaronson, A debate on the bainite reaction. Metall. Trans. 3(5), 1077–1094 (1972)CrossRefGoogle Scholar
  26. 26.
    H.K.D.H. Bhadeshia, D.V. Edmonds, The bainite transformation in a silicon steel. Metall. Trans. A 10(7), 895–907 (1979)CrossRefGoogle Scholar
  27. 27.
    F.G. Caballero, M.K. Miller, C. Garcia-Mateo et al., New experimental evidence of the diffusionless transformation nature of bainite. J. Alloy. Compd. 577(5), S626–S630 (2013)CrossRefGoogle Scholar
  28. 28.
    A. Borgenstam, M. Hillert, J. Ågren, Metallographic evidence of carbon diffusion in the growth of bainite. Acta Mater. 57(11), 3242–3252 (2009)CrossRefGoogle Scholar
  29. 29.
    Z.C. Liu, H.Y. Wang, H.P. Ren, Shear-diffusion conformity mechanism of bainite transformation. in Heat Treatment of Metals, 2006Google Scholar
  30. 30.
    S. Kamamoto, T. Nishimori, S. Kinoshita, Analysis of residual stress and distortion resulting from quenching in large low-alloy steel shafts. Met. Sci. J. 1(10), 798–804 (1985)Google Scholar
  31. 31.
    W. Piekarska, M. Kubiak, Z. Saternus, Numerical modelling of thermal and structural strain in laser welding process/Modelowanie Numeryczne Odkształceń Cieplnych I Strukturalnych W Procesie Spawania Techniką Laserową. Arch. Metall. Mater. 57(4), 1219–1227 (2012)CrossRefGoogle Scholar
  32. 32.
    F. Liu, F. Sommer, C. Bos et al., Analysis of solid state phase transformation kinetics: models and recipes. Metall. Rev. 52(4), 193–212 (2007)CrossRefGoogle Scholar
  33. 33.
    J. Rohde, A. Jeppsson, Literature review of heat treatment simulations with respect to phase transformation, residual stresses and distortion. Scand. J. Metall. 29(2), 47–62 (2010)CrossRefGoogle Scholar
  34. 34.
    E.B. Hawbolt, B. Chau, J.K. Brimacombe, Kinetics of austenite-ferrite and austenite-pearlite transformations in a 1025 carbon steel. Metall. Trans. A 16(4), 565–578 (1985)CrossRefGoogle Scholar
  35. 35.
    M. Lusk, H. Jou, On the rule of additivity in phase transformation kinetics. Metall. Mater. Trans. A 28(2), 287–291 (1997)CrossRefGoogle Scholar
  36. 36.
    Y.T. Zhu, T.C. Lowe, Application of, and precautions for the use of, the Rule of additivity, in phase transformation. Metall. Mater. Trans. B 31(4), 675–682 (2000)CrossRefGoogle Scholar
  37. 37.
    M. Naderi, A. Saeed-Akbari, W. Bleck, The effects of non-isothermal deformation on martensitic transformation in 22MnB5 steel. Mater. Sci. Eng., A 487(1), 445–455 (2008)CrossRefGoogle Scholar
  38. 38.
    M. Nikravesh, M. Naderi, G.H. Akbari, Influence of hot plastic deformation and cooling rate on martensite and bainite start temperatures in 22MnB5 steel. Mater. Sci. Eng., A 540(4), 24–29 (2012)CrossRefGoogle Scholar
  39. 39.
    H.C. Kang, B.J. Park, H.J. Ji et al., Determination of the continuous cooling transformation diagram of a high strength low alloyed steel. Met. Mater. Int. 22(6), 949–955 (2016)CrossRefGoogle Scholar
  40. 40.
    T.T. Pham, E.B. Hawbolt, J.K. Brimacombe, Predicting the onset of transformation under noncontinuous cooling conditions: Part II: application to the austenite pearlite transformation. Metall. Mater. Trans. A 26(8), 1993–2000 (1995)CrossRefGoogle Scholar
  41. 41.
    J.L. Lee, Y.T. Pan, K.C. Hsieh, Assessment of ideal TTT diagram in C–Mn steels. Mater. Trans. 39(1), 196–202 (1998)CrossRefGoogle Scholar
  42. 42.
    J.S. Kirkaldy, Prediction of alloy hardenability from thermodynamic and kinetic data. Metall. Trans. 4(10), 2327–2333 (1973)CrossRefGoogle Scholar
  43. 43.
    A. Malakizadi, S. Hatami, L. Nyborg, Simulation of cooling behavior and microstructure development of PM steels. Int. J. Oncol. 37(4), 829–835 (2010)Google Scholar
  44. 44.
    K. Omer, R. George, A. Bardelcik, M. Worswick, S. Malcolm, D. Detwiler, Development of a hot stamped channel section with axially tailored properties–experiments and models. Int. J. Mater. Form. 11(1), 1–16 (2017)Google Scholar

Copyright information

© The Korean Institute of Metals and Materials 2018

Authors and Affiliations

  1. 1.School of Mechanical and Electrical EngineeringHarbin Institute of TechnologyHarbinChina
  2. 2.State Key Laboratory of Advanced Design and Manufacturing for Vehicle BodyHunan UniversityChangshaChina

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