Simulation of the growth of an ensemble of austenite grains considering the inhibition by particles of the second phases

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription Access

Abstract

Methods to simulate the grain growth in alloys considering the inhibition of this growth by second-phases particles have been proposed. The presented approaches are primarily focused on low-alloyed steels with carbonitride strengthening. The calculation results have been compared with the experimental data available in the literature and their satisfactory agreement has been shown.

Full Text

Restricted Access

About the authors

I. I. Gorbachev

Miheev Institute of Metal Physics, Ural Branch, Russian Academy, Sciences

Author for correspondence.
Email: gorbachev@imp.uran.ru
Russian Federation, 620108, Ekaterinburg

References

  1. Harker D., Parker E.R. Grain shape and grain growth // Trans. American Soc. Metals. 1945. V. 34. P. 156–195.
  2. Burke J.E. Some factors affecting the rate of grain growth in metals // Aime Trans. 1949. V. 180. V. 73–91.
  3. Hillert M. On the theory of normal and abnormal grain growth // Acta Metal. 1965. V. 13. № 3. P. 227–238.https://doi.org/10.1016/0001-6160(65)90200-2
  4. Maire L., Scholtes B., Moussa C., Bozzolo N., Muñoz D.P., Bernacki M. Improvement of 3D mean field models for capillarity-driven grain growth based on full field simulations // J. Mar. Sci. 2016. V. 51. № 24. P. 10970–10981. https://doi.org/10.1007/s10853-016-0309-6
  5. Miyoshi E., Takaki T., Ohno M., Shibuta Y., Sakane S., Shimokawabe T., Aoki T. Ultra-large-scale phase-field simulation study of ideal grain growth //npj Computational Materials. 2017. V. 3. № 1. Р. 25. https://doi.org/10.1038/s41524–017–0029–8
  6. Rios P.R., Dalpian T.G., Brandão V.S., Castro J.A., Oliveira A.C.L. Comparison of analytical grain size distributions with three-dimensional computer simulations and experimental data // Scripta Mater. 2006. V. 54. № 9. P. 1633–1637. https://doi.org/10.1016/j.scriptamat.2006.01.007
  7. Svoboda J., Zickler G.A., Kozeschnik E., Fischer F.D. Generalization of classical Hillert's grain growth and LSW theories to a wide family of kinetic evolution equations and stationary distribution functions // Acta Mater. 2022. V. 235. Р. 118085. https://doi.org/10.1016/j.actamat.2022.118085
  8. Lifshitz I.M., Slyozov V.V. The kinetics of precipitation from supersaturated solid solutions //J. Phys. Chem. Solids. 1961. V. 19. № 1–2. P. 35–50. https://doi.org/10.1016/0022-3697(61)90054-3
  9. Liu Y., Baudin T., Penelle R. Simulation of normal grain growth by cellular automata // Scripta Mater. 1996. V. 34. № 11. P. 1679–1683. https://doi.org/10.1016/1359-6462(96)00055-3
  10. Raghavan S., Sahay Satyam S. Modeling the grain growth kinetics by cellular automaton // Mater. Sci. Eng.: A. 2007. V. 445–446. P. 203–209. https://doi.org/10.1016/j.msea.2006.09.023
  11. Sieradzki L., Madej L. A perceptive comparison of the cellular automata and Monte Carlo techniques in application to static recrystallization modeling in polycrystalline materials // Comp. Mater. Sci. 2013. V. 67. P. 156–173. https://doi.org/10.1016/j.commatsci.2012.08.047
  12. Ogawa J., Natsume Y. Three-dimensional large-scale grain growth simulation using a cellular automaton model // Comp. Mater. Sci. 2021. V. 199. 110729. https://doi.org/10.1016/j.commatsci.2021.110729
  13. Fischer F.D., Svoboda J., Fratzl P. A thermodynamic approach to grain growth and coarsening // Philosoph. Magazine. 2003. V. 83. № 9. P. 1075–1093. https://doi.org/10.1080/0141861031000068966
  14. Onsager L. Reciprocal relations in irreversible processes. I // Phys. Rev. 1931. V. 37. № 4. P. 405–426. https://doi.org/10.1103/PhysRev.37.405
  15. Onsager L. Reciprocal relations in irreversible processes. II // Phys. Rev. 1931. V. 38. № 12. P. 2265–2279. https://doi.org/10.1103/PhysRev.38.2265
  16. Svoboda J., Fischer F.D. Abnormal grain growth: a non-equilibrium thermodynamic model for multi-grain binary systems // Model. Simulation Mater. Sci. Eng. 2013. V. 22. № 1. Р. 015013. https://dx.doi.org/10.1088/0965-0393/22/1/015013
  17. Zener C. цитируется по Gladman T. On the theory of the effect of precipitate particles on grain growth in metals // Proc. R. Soc. Lond. A. 1966. V. 294. P. 298–309. https://doi.org/10.1098/rspa.1966.0208
  18. Maalekian M., Radis R., Militzer M., Moreau A., Poole W.J. In situ measurement and modelling of austenite grain growth in a Ti/Nb microalloyed steel // Acta Mater. 2012. V. 60. P. 1015–1026. https://doi.org/10.1016/j.actamat.2011.11.016
  19. Khalaj G., Yoozbashizadeh H., Khodabandeh A., Tamizifar M. Austenite grain growth modelling in weld heat affected zone of Nb/Ti microalloyed linepipe Steel // Mater. Sci. Techn. 2014. V. 30. № 2. P. 424–433. https://doi.org/10.1179/1743284713Y.0000000364
  20. Banerjee K., Militzer M., Perez M., Wang X. Nonisothermal austenite grain growth kinetics in a microalloyed X80 linepipe steel // Metal. Mater. Trans. A. 2010. V. 41A. № 12. P. 3161–3172. https://doi.org/10.1007/s11661-010-0376-2
  21. Dépinoy S., Marini B., Toffolon-Masclet C., Roch F., Gourgues-Lorenzon A.-F. Austenite grain growth in a 2.25Cr-1Mo vanadium-free steel accounting for Zener pinning and solute drag: experimental study and modeling // Metal. Mater. Trans. A. 2017. V. 48. № 5. P. 2289–2300. https://doi.org/10.1007/s11661-017-4002-4
  22. Sandström R., Lagneborg R. A model for hot working occurring by recrystallization // Acta Metall. 1975. V. 23. P. 387–398. https://doi.org/10.1016/0001-6160(75)90132-7
  23. Roucoules C., Pietrzyk M., Hodgson P.D. Analysis of work hardening and recrystallization during the hot working of steel using a statistically based internal variable model // Mater. Sci. Eng. A. 2003. V. 339. № 1–2. P. 1–9. https://doi.org/10.1016/S0921-5093(02)00120-X
  24. Rath M., Kozeschnik E. Coupled grain growth and precipitation modeling in multi-phase systems // Mater. Sci. Forum. 2013. V. 753. P. 357–360. https://doi.org/10.4028/www.scientific.net/MSF.753.357
  25. Горбачёв И.И., Пасынков А.Ю., Попов В.В. Прогнозирование размера аустенитного зерна микролегированных сталей на основе моделирования эволюции карбонитридных выделений // ФММ. 2015. Т. 116. № 11. С. 1184–1191. https://doi.org/10.1134/S0031918X1511006X
  26. Горбачев И.И., Пасынков А.Ю., Попов В.В. Моделирование влияния горячей деформации на размер аустенитного зерна низколегированных сталей с карбонитридным упрочнением // ФММ. 2018. Т. 119. № 6. С. 582–589. https://doi.org/10.1134/S0031918X18060078
  27. Горбачев И.И., Пасынков А.Ю., Попов В.В. Моделирование эволюции карбонитридных частиц сложного состава при горячей деформации низколегированной стали // Физика металлов и металловедение. 2018. Т. 119. № 8. С. 817–826. https://doi.org/10.1134/S0031918X18080021
  28. Горбачев И.И., Корзунова Е.И., Попов В.В., Хабибулин Д.М., Урцев Н.В. Моделирование роста аустенитного зерна в низколегированных сталях при аустенитизации // ФММ. 2023. T. 124. № 3. С. 303–309. https://doi.org/10.1134/S0031918X23600100
  29. Горбачев И.И., Корзунова Е.И., Попов В.В., Хабибулин Д.М., Урцев Н.В. Модель для прогнозирования размера аустенитного зерна при горячей деформации низколегированных сталей с учётом эволюции дислокационной структуры // ФММ. 2023. T. 124. № 12. С. 1244–1252.
  30. Горбачев И.И., Корзунова Е.И., Попов В.В., Хабибулин Д.М., Урцев Н.В. Моделирование эволюции фазового состава и размера аустенитного зерна при многопроходной горячей деформации низколегированных сталей // ФММ. 2024. Т. 125. № 3. С. 293–305.
  31. Горбачев И.И., Попов В.В., Пасынков А.Ю. Моделирование эволюции выделений двух карбонитридных фаз в сталях с Nb и Ti при изотермическом отжиге // ФММ. 2013. Т. 114. № 9. С. 807–817. https://doi.org/10.1134/S0031918X13090068
  32. Popov V.V., Gorbachev I.I., Pasynkov A. Yu. Simulation of precipitates evolution in multiphase multicomponent systems with consideration of nucleation // Philosoph. Magazine. 2016. V. 96. № 35. P. 3632–3653. https://doi.org/10.1080/14786435.2016.1232867
  33. Buken H., Kozeschnik E. A model for static recrystallization with simultaneous precipitation and solute drag // Metal. Mater. Trans. A. 2017. V. 48. P. 2812–2818. https://doi.org/10.1007/s11661-016-3524-5
  34. Hillert M. Inhibition of grain growth by second-phase particles // Acta Metal. 1988. V. 36. № 12. P. 3177–3181. https://doi.org/10.1016/0001-6160(88)90053-3
  35. Горбачев И.И., Попов В.В., Пасынков А.Ю. Термодинамическое моделирование карбонитридообразования в сталях с Nb и Ti // ФММ. 2012. Т. 113. № 7. С. 727–735. https://doi.org/10.1134/S0031918X1207006X
  36. Rios P.R. Overview no. 62: A theory for grain boundary pinning by particles // Acta Metal. 1987. V. 35. № 12. P. 2805–2814. https://doi.org/10.1016/0001-6160(87)90280-X
  37. Uhm S., Moon J., Lee Ch., Yoon J., Lee B. Prediction model for the austenite grain size in the coarse grained heat affected zone of Fe–C–Mn steels: Considering theeffect of initial grain size on isothermal growth behavior // ISIJ International. 2004. V. 44. № 7. P. 1230–1237. https://doi.org/10.2355/isijinternational.44.1230

Supplementary files

Supplementary Files
Action
1. JATS XML
Download
2. Fig. 1. Change in the size of austenitic grains during annealing according to data [18]. Symbols are experimental data based on metallographic measurements; dotted lines are the results of ultrasonic measurements; solid lines are the results of modeling based on PTE.

Download (87KB)
Indexing metadata
3. Fig. 2. Change in the size of austenitic grains during annealing according to data [19]. Symbols and dotted lines are experimental data; solid lines are the results of modeling based on PTE.

Download (103KB)
Indexing metadata
4. Fig. 3. Change in grain size distribution during annealing at 1150 °C (PTE-based simulation results corresponding to the data [18]).

Download (59KB)
Indexing metadata
5. Fig. 4. Change in the size of austenitic grains during annealing according to data [18]. Symbols are experimental data based on metallographic measurements; dotted lines are the results of ultrasonic measurements; solid lines are the results of modeling the behavior of an array of individual grains.

Download (93KB)
Indexing metadata
6. Fig. 5. Change in grain size distribution during annealing at 1150 °C (simulation results for an array of individual grains corresponding to the data [18]).

Download (213KB)
Indexing metadata