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Metal science and metallography
ArticleName Simulation of phase transformations in high carbon pearlite steel at various cooling rates
DOI 10.17580/cisisr.2020.02.12
ArticleAuthor S. A. Nevskii, Yu. N. Simonov, V. E. Kormyshev, S. V. Konovalov

Siberian State Industrial University (Novokuznetsk, Russia):

S. A. Nevskii, Cand. Eng., Assistant Prof., Dept. of Natural Science

V. E. Kormyshev, Cand. Eng., Researcher, Research Dept.


Perm National Research Polytechnic University (Perm, Russia):

Yu. N. Simonov, Dr. Eng., Prof., Dept. of Metal Science, Laser and Thermal Treatment


Samara National Research University (Samara, Russia):

S. V. Konovalov, Dr. Eng., Prof., Dept. of Materials Technology and Aviation Material Science, E-mail:


The paper reports on the experimental research into the austenite decomposition in high carbon steel at a constant temperature and rates of cooling. The study was carried out by the methods of dilatometry, micro-durometry, optical and scanning microscopy. From the dilatometric curves it is apparent they are sufficiently presented by the Kolmogorov-Avrami equation in a temperature range from 700 to 550 °С, and by the logistic function for temperatures ranging 500 to 250 °С. The data of the dilatometric analysis were used to draw isothermal and continuous cooling transformation diagrams of phase conversions. It has been pointed out an isothermal diagram to comprise four C-curves of pearlite and bainite transformations, which are approximated by second- and third-degree polynomials. The critical temperatures of austenite, bainite, and martensite transformations have been determined, being 711, 550 and 196 °С, respectively. Considering the data obtained experimentally, a mathematical model of austenite decomposition has been developed for a constant cooling rate, and volume fractions of structure-phase components estimated theoretically, demonstrating the congruence with experimental results. The suggested mathematical model can be adopted to calculate a structure-phase composition in industrial differential heat treatment of rails.

The authors are grateful to Vladimir Sarychev, Egor Polevoy and Victor Gromov who took an active part in the preparation of the manuscript. This work is supported by the Russian Foundation for Basic Research (RFBR) [project number 19-32-60001] and President grant for State Support to young researches [grant number МK-118.2019.2].

keywords High carbon steel, continuous cooling transformation, transformation equilibrium temperature, volume fraction, dilatometric curves, simulation, Kolmogorov-Avrami equation

1. Fronstein N. Advanced High Strength Sheet Steels. Berlin: Springer, 2015. 396 p.
2. Zhao M., Song L., Fan X. The Boundary Theory of Phase Diagrams and Its Application, Berlin: Springer, 2011. 238 p.

3. Fucheng Zhang, Zhinan Yang. Development of and Perspective on High-Performance Nanostructured Bainitic Bearing Steel. Engineering. 2019. Vol. 5. pp. 319–328. DOI: 10.1016/j.eng.2018.11.024
4. Sha W. Steels. Berlin: Springer, 2013. 268 p.
5. Ji-Cheng Zhao, Notis M.R. Continuous cooling transformation kinetics versus isothermal transformation kinetics of steels: a phenomenological rationalization of experimental observations. Materials Science and Engineering: R: Reports. 1995. Vol. 15. pp. 135–207. DOI: 10.1016/0927-796X(95)00183-2
6. Fei Peng, Yunbo Xu, Jiayu Li, Xingli Gu, Xu Wang. Interaction of martensite and bainite transformations and its dependence on quenching temperature in intercritical quenching and partitioning steels. Materials & Design. 2019. Vol. 181. p. 107921. DOI: 10.1016/j.matchar.2020.110244
7. Hehemann R. F., Kinsman K. R., Aaronson H. I. A debate on the bainite reaction. Metall. Trans. 1972. Vol. 3. No. 5. pp. 1077–1094. DOI: 10.1007/BF02642439
8. Bhadeshia H. K. D. H., Bainite In Steels. Transformations, Microstructure and Properties, Cambridge University Press, Cambridge, 2001. 454 p.
9. Caballero F. G., Miller M. K., Garcia-Mateo C., et al. New experimental evidence of the diffusionless transformation nature of bainite. J. Alloy. Compd. 2013. Vol. 577 (5). pp. S626–S630. DOI: 10.1016/j.jallcom.2012.02.130
10. Borgenstam A., Hillert M.,     gren J. Metallographic evidence of carbon diffusion in the growth of bainite. Acta Mater. 2009. Vol. 57 (11). pp. 3242–3252. DOI: 10.1016/j.actamat.2009.03.026
11. Jun Lu, Hao Yu, Xiaoni Duan, Chenghao Song. Investigation of microstructural evolution and bainite transformation kinetics of multi-phase steel. Materials Science and Engineering: A. 2020. Vol. 774. pp. 138868 DOI: 10.1016/j.msea.2019.138868
12. Liu Z. C., Wang H. Y., Ren H. P. Shear-diffusion conformity mechanism of bainite transformation. In: Heat Treatment of Metals. 2006, pp. 36–42.
13. Razumov I. K. Possible Mechanisms of the Formation of Bainitic Colonies. Physics of the Solid State. 2019. Vol. 61. pp. 80–83. DOI: 10.1134/S1063783419020203
14. Johnson W. A., Mehl R. F. Reaction kinetics in processes of nucleation and growth. Trans. Am. Inst. Min. Metall. Eng. 1939. Vol. 135. pp. 416–458.
15. Avrami M. Kinetics of phase change. III: granulation, phase change and microstructure. J. Chem. Phys. 1941. Vol. 9. No. 2. pp. 177–184.
16. Kolmogorov A. N. On the statistical theory of metal crystallization. Izv. Akad. Nauk. SSSR Ser. Mat. 1937. No. 3. pp. 355–359.
17. Kirkaldy J. S., Venugopalan D. Prediction of microstructure and hardenability in low alloy steels, in: A. R. Marder, J. I. Goldstein (Eds.), International Conference on Phase Transformations in Ferrous Alloys. 1983. pp. 125–148.
18. Hao Zhao, Xiuli Hu, Junjia Cui, Zhongwen Xing. Kinetic model for the phase transformation of high-strength steel under arbitrary cooling conditions. Metals and Materials International. 2019. Vol. 25. pp. 381–395. DOI: 10.1007/s12540-018-0196-2
19. Lee S. J., Pavlina E. J., Tyne C. J. V. Kinetics modeling of austenite decomposition for an end-quenched 1045 steel. Mater. Sci. Eng. A. 2010. Vol. 527. No. 13. pp. 3186–3194. DOI: 10.1016/j.msea.2010.01.081
20. Lee S. J., Lee Y. K. Finite element simulation of quench distortion in a low-alloy steel incorporating transformation kinetics. Acta Mater. 2008. Vol. 56 (7). pp. 1482–1490. DOI: 10.1016/j.actamat.2007.11.039
21.     kerstrm P., Bergman G., Oldenburg M. Numerical implementation of a constitutive model for simulation of hot stamping. Model. Simul. Mater. Sci. Eng. 2007. Vol. 15 (2). pp. 105–119. DOI: 10.1088/0965-0393/15/2/007
22. Hippchen P., Lipp A., Grass H., Craighero P. et al. Modelling kinetics of phase transformation for the indirect hot stamping process to focus on car body parts with tailored properties. Journal of Materials Processing Technology. 2016. Vol. 228. pp. 59–67. DOI: 10.1016/j.jmatprotec.2015.01.003
23. Koistinen D. P., Marburger R. E. A general equation prescribing the extent of the austenite-martensite transformation in pure iron carbon alloys and plain carbon steels. Acta Metall. 1959. Vol. 7 (1). pp. 59–60. DOI: 10.1016/0001-6160(59)90170-1
24. Yudin Yu. V., Maisuradze M. V., Kuklina A. A. Describing the isothermal bainitic transformation in structural steels by a logistical function. Steel in Translation. 2017. Vol. 47. pp. 213–218. DOI: 10.3103/S0967091217030160
25. Yudin Yu. V., Kuklina A. A., Lebedev P. D., Maisuradze M. V. Simulation of Isothermal Austenite Transformation in Steel. Steel in Translation. 2018. Vol. 48. pp. 684–689. DOI: 10.3103/S0967091218100133
26. Maisuradze M. V., Ryzhkov M. A., Yudin Yu. V., Kuklina A. A. Transformations of supercooled austenite in a promising highstrength steel under continuous cooling. Metal Science and Heat Treatment. 2017. Vol. 59. pp. 486–490. DOI: 10.1007/s11041-017-0176-z
27. Sidhu Gaganpreet, Srinivasan Seshasai, Bhole Sanjiwan. A Model for bainite formation at isothermal heat treatment conditions. Journal of Thermal Science and Engineering Applications. 2020. Vol. 12. p. 011006. DOI: 10.1115/1.4042861
28. Razumov I. K., Gornostyrev Yu. N., Katsnelson M. I. Effect of magnetism on kinetics of γ → α transformation and pattern formation in iron. J. Phys.: Condens. Matter. 2013. Vol. 25. pp. 135401. DOI: 10.1088/0953-8984/25/13/135401
29. Razumov I. K., Gornostyrev Yu. N., Katsnelson M. I. Autocatalytic mechanism of pearlite transformation in steel. Physical Review Applied. 2017. Vol. 7. pp. 014002. DOI: 10.1103/PhysRevApplied.7.014002
30. Loginova I., Odqvist J., Amberg G., Agren J. The phase-field approach and solute drag modeling of the transition to massive γ → α transformation in binary Fe–C alloys. Acta Materialia. 2003. Vol. 51. pp. 1327–1339. DOI: 10.1016/S1359-6454(02)00527-X
31. Loginova I., Amberg G., Agren J. On the formation of Widmanstatten ferrite in binary Fe–C phase-field approach. Acta Materialia. 2004. Vol. 52. pp. 4055–4063. DOI: 10.1016/j.actamat.2004.05.033
32. Kuziak R., Pidvysots’kyy V., Pernach M., Rauch L., Zygmunt T., Pietrzyk M. Selection of the best phase transformation model for optimization of manufacturing processes of pearlitic steel rails. Archives of Сivil and Mechanical Engineering. 2019. Vol. 19. pp. 535–546.
33. Shah S. M. A., Khattak M. A., Asad M., Iqbala J., Badshahd S., Khan M. S. Numerical modeling of phase transformation during grinding process. Jurnal Teknologi. 2017. Vol. 79. pp. 33 – 41, DOI: 10.11113/jt.v79.10573
34. Sarychev V. D., Khaimzon B. B., Nevskii S. A., Il’yashchenko A. V., Grishunin V. A. Mathematical models of mechanisms for rolled products accelerated cooling. Izvestiya vuzov. Chernaya metallurgiya. 2018. Vol. 61. pp. 326–332. DOI: 10.17073/0368-0797-2018-4-326-332
35. Konovalov S., Chen X., Sarychev V., Nevskii S., Gromov V., Trtica M. Mathematical modeling of the concentrated energy flow effect on metallic materials. Metals. 2017. Vol. 7 (1). No. 4. pp. 1–18. DOI: 10.3390/met7010004
36. Voronov A. N., Kvachkai T, Zadan V. T., Pavlush M. Computer modelling of austenite transformation at steel cooling. Izvestiya AN SSSR. Metally. 1991, Iss. 2. pp. 81–89.
37. Reti T., Fried Z., Felde I. Computer simulation of steel quenching process using a multi-phase transformation model. Computational Materials Science. 2001. Vol. 22. pp. 261–278. DOI: 10.1016/S0927-0256(01)00240-3

Full content Simulation of phase transformations in high carbon pearlite steel at various cooling rates