МЕТОДЫ МОДЕЛИРОВАНИЯ ФАЗОВЫХ ПРЕВРАЩЕНИЙ В БЕЙНИТНЫХ СТАЛЯХ

К механическим свойствам и эксплуатационным характеристикам рельсовых сталей предъявляются повышенные требования. В связи с этим разработка новых марок рельсовых сталей на сегодняшний день является актуальной задачей. Бейнитные стали, не содержащие карбидов, являются своего рода потенциальными кандидатами для применения на железных дорогах, благодаря своей более высокой вязкости разрушения, сопротивлению усталости и износостойкости. Процесс термической обработки оказывает существенное влияние на механические свойства бейнитных рельсовых сталей. Решающим фактором, определяющим технологию производства рельсовых сталей, является прогнозирование микроструктуры. Для того, чтобы отойти от метода перебора, необходимо создавать математические модели охлаждения рельсов, учитывающие химический состав стали. Для моделирования структурно-фазовых превращений в рельсах для неизотермических условий разрабатываются два подхода: Аврами-Колмогорова с учетом правила Шейля и модель фазового поля. Настоящий обзор посвящен современным исследованиям по компьютерному моделированию структурно-фазовых превращений по этим двум подходам. Первый подход был предложен в 30-е годы XX века для изотермических условий, позднее был развит для неизотермического случая в рамках правила Шейля. В настоящее время к этому подходу интерес со стороны исследователей не ослабевает из-за малого времени расчета. Однако описать пространственное распределение фаз и структур этот метод не может, поэтому активно развиваются методы фазового поля, расчеты по которому могут занимать от нескольких часов до нескольких суток. В представленном обзоре проведен анализ указанных подходов, а также продемонстрированы их ограничения.

1. Garnham J.E., Davis C.L. Rail materials. In: Wheel-rail interface handbook. 2009. P. 125–171. https://doi.org/10.1533/9781845696788.1.125

2. Vickerman R. International Encyclopedia of Transportation. Elsevier, 2021. P. 4569–4418.

3. Mićić M., Brajović L., Lazarević L., Popović Z. Inspection of RCF rail defects – Review of NDT methods // Mechanical Systems and Signal Processing. 2023. Vol. 182. Article 109568.

4. Królicka A., Lesiuk G., Radwański K., Ku-ziak R., et al. Comparison of fatigue crack growth rate: Pearlitic rail versus bainitic rail // International Journal of Fatigue. 2021. Vol. 149. Article 106280. http://dx.doi.org/10.1016/j.ijfatigue. 2021.106280

5. Aglan H.A. Fatigue crack growth and frac-ture behavior of bainitic rail steels. United States. Federal Railroad Administration. Office of Railroad Policy and Development, 2011.

6. Ruijie Z., Chunlei Z., Bo L., Xubiao W., Xiaofeng L., et al. Research progress on rolling contact fatigue damage of bainitic rail steel // Engineering Failure Analysis. 2022. Article 106875. http://dx.doi.org/10.56748/ejse. 131621

7. Hasan S.M., Chakrabarti D., Singh S.B. Dry rolling/sliding wear behaviour of pearlitic rail and newly developed carbide-free bainitic rail steels // Wear. 2018. Vol. 408. P. 151–159. https://doi.org/10.1016/j.wear.2018.05.006

8. Tung P.Y., Zhou X., Morsdorf L., Morsdorf L., et al. Formation mechanism of brown etching layers in pearlitic rail steel // Mate-rialia. 2022. Vol. 26. Article 101625. http://dx.doi.org/ 10.1016/j.mtla.2022.101625

9. Wang K., Tan Z., Gao G., Gui X., Misra, Bingzhe Baia. 2016. “Ultrahigh strength-toughness combination in Bainitic rail steel: The determining role of austenite stability during tempering” // Materials Science and Engineering A..2016. Vol. 662. P. 162–168. http://dx.doi.org/10.1016/j.msea.2016.03.043

10. Zhang R., Zheng C., Chen C., Lv B., et al. Study on fatigue wear competition mecha-nism and microstructure evolution on the surface of a bainitic steel rail // Wear. 2021. Vol. 482. Article 203978. http://dx.doi.org/10.1016/j. wear.2021.203978

11. Stock R., Pippan R. RCF and wear in theory and practice-The influence of rail grade on wear and RCF // Wear. 2011. Vol. 271. No. 1-2. P. 125–133. http://dx.doi.org/10.1016/j. wear.2010.10.015

12. Ueda M., Matsuda K. Effects of carbon content and hardness on rolling contact fatigue resistance in heavily loaded pearlitic rail steels // Wear. 2020. Vol. 444. Article 203120. https://doi.org/10.1016/j.wear.2019.203120

13. Kumar A., Dutta A., Makineni S.K., Herbig M., et al. In-situ observation of strain partitioning and damage development in continuously cooled carbide-free bainitic steels using micro digital image correlation // Materials Science and Engineering: A. 2019. Vol. 757. P. 107–116. http://dx.doi.org/10.1016/j.msea.2019.04.098

14. Sourmail T., Caballero F.G., García-Mateo C., Smanio V., et al. Evaluation of potential of high Si high C steel nanostructured bainite for wear and fa-tigue applications // Materials Science and Technol-ogy. 2013. Vol. 29. No. 10. P. 1166–1173. http://dx.doi.org/10.1179/1743284713Y.0000000242

15. Kumar A., Makineni S.K., Dutta A., Goulas C., et al. Design of high-strength and dam-age-resistant carbide-free fine bainitic steels for railway crossing applications // Materials Science and Engineering: A. 2019. Vol. 759. P. 210–223.

16. Leiro A., Kankanala A., Vuorinen E., Pra-kash B. Tribological behaviour of carbide-free bainitic steel under dry rolling/sliding conditions // Wear. 2011. Vol. 273. No. 1. P. 2–8. http://dx.doi.org/10.1016/j.wear.2011.03.025

17. Hu F., Wu K.M., Hodgson P.D. Effect of retained austenite on wear resistance of nanostructured dual phase steels // Materials Science and Technology. 2016. Vol. 32. No. 1. P. 40–48.

18. Liu J., Li Y., Zhang Y., Hu Y., et al. Dry rolling/sliding wear of bainitic rail steels under different contact stresses and slip ratios // Materials. 2020. Vol. 13. No. 20. P. 4678. http://dx.doi.org/10.3390/ma13204678

19. Masoumi M., Ariza E.A., Sinatora A., Goldenstein H. Role of crystallographic orientation and grain boundaries in fatigue crack propagation in used pearlitic rail steel // Materials Science and Engineering: A. 2018. Vol. 722. P. 147–155. http://dx.doi.org/10.1016/j.msea. 2018.03.028

20. Zhou Y., Wang S., Wang T., Xu Y., Li Z. Field and laboratory investigation of the re-lationship between rail head check and wear in a heavy-haul railway // Wear. 2014. Vol. 315. No. 1–2. P. 68–77. http://dx.doi.org/10.1016/j.wear. 2014.04.004

21. Ding H.H., Fu Z.K., Wang W.J., Guo J., et al. Investigation on the effect of rotational speed on rolling wear and damage behaviors of wheel/rail materials // Wear. 2015. Vol. 330. P. 563–570. http://dx.doi.org/10.1016/j. wear.2014.12.043

22. Huang Y.B., Shi L.B., Zhao X.J., Cai Z.B., et al. On the formation and damage mecha-nism of rolling contact fatigue surface cracks of wheel/rail under the dry condition // Wear. 2018. Vol. 400. P. 62–73. http://dx.doi.org/ 10.1016/j.wear.2017.12.020

23. Guo L.C., Zhu W.T., Shi L.B., Liu Q.Y., et al. Study on wear transition mechanism and wear map of CL60 wheel material under dry and wet conditions // Wear. 2019. Vol. 426. P. 1771–1780. http://dx.doi.org/10.1016/j.wear.2018. 12.049

24. Maya-Johnson S., Santa J. F., Toro A. Dry and lubricated wear of rail steel under rolling contact fatigue-Wear mechanisms and crack growth // Wear. 2017. Vol. 380. P. 240–250. http://dx.doi.org/10.1016/j.wear.2017.03.025

25. Benoît D., Salima B., Marion R. Multiscale characterization of head check initiation on rails under rolling contact fatigue: Mechan-ical and microstructure analysis // Wear. 2016. Vol. 366. P. 383–391. http://dx.doi.org/10.1016/j. wear.2016.06.019

26. Messaadi M., Oomen M., Kumar A. Friction modifiers effects on tribological behaviour of bainitic rail steels // Tribology international. 2019. Vol. 140. Article 105857.

27. Lee K.M., Polycarpou A.A. Wear of conventional pearlitic and improved bainitic rail steels // Wear. 2005. Vol. 259. No. 1–6. P. 391–399. http://dx.doi.org/10.1016/j.wear.2005.02.058

28. Hasan S.M., Chakrabarti D., Singh S.B. Dry rolling/sliding wear behaviour of pearlitic rail and newly developed carbide-free bainitic rail steels // Wear. 2018. Vol. 408. P. 151–159. http://dx.doi.org/10.1016/j.wear.2018.05.006

29. Liu J.P., Li Y.Q., Zhou Q.Y., Zhang Y. H., et al. New insight into the dry rolling-sliding wear mechanism of carbide-free bainitic and pearlitic steel // Wear. 2019. Vol. 432. Article 202943. https://doi.org/10.1016/j.wear. 2019.202943

30. Chen Y., Ren R., Pan J., Pan R., et al. Microstructure evolution of rail steels under different dry sliding conditions: A compari-son between pearlitic and bainitic microstructures // Wear. 2019. Vol. 438. Article 203011. https://doi.org/10.1016/j.wear.2019.203011

31. Li Q., Guo J., Zhao A. Effect of upper bain-ite on wear behaviour of high-speed wheel steel // Tribology Letters. 2019. Vol. 67. P. 1–9.

32. Kuziak R., Pidvysotskyy V., Pernach M., Rauch L., et al. Selection of the best phase transformation model for optimization of manufacturing processes of pearlitic steel rails //Archives of Civil and Mechanical Engineering. 2019. Vol. 19. P. 535–546. http://dx.doi. org/10.1016/j.acme.2018.12.004

33. Tehler M. Modeling phase transformations and volume changes during cooling of case hardening steels. KTH, 2009.

34. Bzowski K., Rauch L., Pietrzyk M. Applica-tion of statistical representation of the microstructure to modeling of phase trans-formations in DP steels by solution of the diffusion equation // Procedia Manufactur-ing. 2018. Vol. 15. P. 1847–1855. http://dx.doi.org/10.1016/j. promfg.2018.07.205

35. Rauch L., Kuziak R., Pietrzyk M. From high accuracy to high efficiency in simulations of processing of Dual-Phase steels // Metallurgical and Materials transactions B. 2014 Vol. 45. P. 497–506. http://dx.doi.org/10.1007/s11663-013-9926-5

36. Rheingans B., Mittemeijer E.J. Phase trans-formation kinetics: advanced modeling strategies // JOM. 2013. Vol. 65. P. 1145–1154.

37. Starink M.J. On the meaning of the impinge-ment parameter in kinetic equations for nucleation and growth reactions // Journal of Materials Science. 2001. Vol. 36. No. 18. P. 4433–4441.

38. Todinov M.T. On some limitations of the Johnson–Mehl–Avrami–Kolmogorov equa-tion // Acta materialia. 2000. Vol. 48. No. 17. P. 4217–4224.

39. Kempen A.T.W., Sommer F., Mittemeijer E.J. Determination and interpretation of iso-thermal and non-isothermal transformation kinetics; the effective activation energies in terms of nucleation and growth // Journal of materials science. 2002. Vol. 37. P. 1321–1332. https://doi.org/ 10.1023/a:1014556109351

40. Liu F., Sommer F., Bos C., Mittemeijer E.J. Analysis of solid state phase transformation kinetics: models and recipes // International materials reviews. 2007. Vol. 52. No. 4. P. 193–212. http://dx.doi.org/10.1179/174328007X160308

41. Robson J.D. Modeling competitive continu-ous and discontinuous precipitation // Acta Materialia. 2013. Vol. 61. No. 20. P. 7781–7790. http://dx.doi.org/10.1016/j.actamat.2013.09.017

42. Ranganathan S., Von Heimendahl M. The three activation energies with isothermal transformations: applications to metallic glasses // Journal of Materials Science.1981. Vol. 16. P. 2401–2404.

43. Liu F., Sommer F., Mittemeijer E.J. Analysis of the kinetics of phase transformations; roles of nucleation index and temperature dependent site saturation, and recipes for the extraction of kinetic parameters // Journal of Materials Science. 2007. Vol. 42. P. 573–587.

44. Dill E.D., Folmer J.C.W., Martin J.D. Crystal growth simulations to establish physically relevant kinetic parameters from the empirical Kolmogorov–Johnson–Mehl–Avrami model // Chemistry of Materials. 2013. Vol. 25. No. 20. P. 3941–3951.

45. Weinberg M.C. A test of the Johnson-Mehl-Avrami equation // Journal of crystal growth. 1987. Vol. 82. No. 4. P. 779–780. https://doi.org/10.1016/S0022-0248(87)80025-8

46. Weinberg M.C., Birnie III D.P., Shneidman V.A. Crystallization kinetics and the JMAK equation // Journal of non-crystalline solids. 1997. Vol. 219. P. 89–99. https://doi.org/10.1016/S0022-3093%2897%2900261-5

47. Kelton K.F., Spaepen F.A study of the devitrification of Pd82Si18 over a wide temperature range // Acta Metallurgica. 1985. Vol. 33. No. 3. P. 455–464.

48. Yinnon H., Uhlmann D.R. Applications of thermoanalytical techniques to the study of crystallization kinetics in glass-forming liq-uids, part I: theory // Journal of Non-Crystalline Solids. 1983. Vol. 54. No. 3. P. 253–275.

49. Levine L.E., Narayan K.L., Kelton K.F. Fi-nite size corrections for the Johnson-Mehl-Avrami-Kolmogorov equation // Journal of Materials Research. 1997. Vol. 12. P. 124–132.

50. Chen L.Q. Annu Rev Mater Res // Annu. Rev. Mater. Res. 2002. Vol. 32. P. 113–140.

51. Fallah V., Amoorezaei M., Provatas N., Corbin S.F., et al. Phase-field simulation of solidification morphology in laser powder deposition of Ti–Nb alloys // Acta Materi-alia. 2012. Vol. 60. No. 4. P. 1633–1646. http://dx.doi.org/ 10.1016/j.actamat.2011.12.009

52. Beckermann C., Diepers H.J., Steinbach I., Karma A., et al. Modeling melt convection in phase-field simulations of solidification // Journal of Computational Physics. 1999. Vol. 154. No. 2. P. 468–496.

53. Böttger B., Apel M., Eiken J., Schaffnit P., et al. Phase‐Field simulation of solidification and solid‐state transformations in mul-ticomponent steels // Steel Research International. 2008. Vol. 79. No. 8. P. 608–616. http://dx.doi.org/ 10.2374/SRI08SP021-79-2008-608

54. Tiaden J. Phase-field simulations of the peritectic solidification of Fe-C // Journal of Crystal Growth. 1999. Vol. 198. P. 1275–1280.

55. Steinbach I., Pezzolla F., Nestler B., Seeßel-berg M., et al. A phase field concept for multiphase systems // Physica D: Nonlinear Phenomena. 1996. Vol. 94. No. 3. P. 135–147.

56. Militzer M. Phase field modeling of micro-structure evolution in steels // Current Opin-ion in Solid State and Materials Science. 2011. Vol. 15. No. 3. P. 106–115. https://doi.org/10.1016/j.cossms.2010.10.001

57. Pariser G., Schaffnit P., Steinbach I., Bleck, W. Simulation of the γ–α‐transformation using the phase‐field method // Steel Research. 2001. Vol. 72. No. 9. P. 354–360. http://dx.doi.org/10.1002/srin.200100130

58. Elder K.R., Grant M., Provatas N., Kosterlitz J. M. Sharp interface limits of phase-field models // Physical Review E. 2001. Vol. 64. No. 2. Article 021604. http://dx.doi.org/10.1103/ PhysRevE.64.021604

59. Jou H.J., Lusk M.T. Comparison of John-son-Mehl-Avrami-Kologoromov kinetics with a phase-field model for microstructural evolution driven by substructure energy // Physical Review B. 1997. Vol. 55. No. 13. P. 8114. http://dx.doi.org/10.1103/PhysRevB.55.8114