Accounting for the random character of nucleation in the modelling of phase transformations in steels

• Autorzy: Poloczek Łukasz , Kuziak Roman , Foryś Jakub , Szeliga Danuta , Pietrzyk Maciej

Identyfikatory

DOI

10.7494/cmms.2023.2.0806

• Języki publikacji: EN

Abstrakty

EN

In our earlier work, a stochastic model of multi-stage deformation at elevated temperatures was developed. The model was applied to calculate histograms of dislocation density and grain size at the onset of phase transformation. The histograms were used as input data for the simulation of phase transitions using the traditional deterministic model. Following this approach, microstructural inhomogeneity was predicted for different cooling conditions. The results obtained, showing the effect of dislocation density and inhomogeneity of austenite grain size on the microstructural inhomogeneity of the final product, can be considered reliable as they are based on material models determined in previous publications and validated experimentally. The aim of the present work was to extend the model by taking into account the stochastic nature of nucleation during phase transitions. The analysis of existing stochastic models of nucleation was performed, and a model for ferritic transformation in steels was proposed. Simulations for constant cooling rates as well as for industrial cooling processes of steel rods were performed. In the latter case, uncertainties in defining the boundary conditions and segregation of elements were also considered. The reduction of the computing costs is an important advantage of the model, which is much faster when compared to full field models with explicit microstructure representation.

Słowa kluczowe

EN

stochastic model; grain size; phase transformations; dislocation density; cooling of rods; heterogeneity of the microstructure

• Wydawca: Wydawnictwa AGH
• Czasopismo: Computer Methods in Materials Science
• Rocznik: 2023
• Tom: Vol. 23, No. 2
• Strony: 17--28
• Opis fizyczny: Bibliogr. 34 poz., rys.

Twórcy

autor

Poloczek Łukasz

• Łukasiewicz Research Network, Upper Silesian Institute of Technology, ul. K. Miarki 12, 44-100 Gliwice, Poland

• https://orcid.org/0000-0002-0676-9932

autor

Kuziak Roman

• Łukasiewicz Research Network, Upper Silesian Institute of Technology, ul. K. Miarki 12, 44-100 Gliwice, Poland

• https://orcid.org/0000-0003-4965-5123

autor

Foryś Jakub

• AGH University of Krakow, al. A. Mickiewicza 30, 30-059 Krakow, Poland

autor

Szeliga Danuta

• AGH University of Krakow, al. A. Mickiewicza 30, 30-059 Krakow, Poland

• https://orcid.org/0000-0002-2915-8317

autor

Pietrzyk Maciej

• AGH University of Krakow, al. A. Mickiewicza 30, 30-059 Krakow, Poland

• https://orcid.org/0000-0002-1473-4625

Bibliografia

• Alekseechkin, N.V. (2000). On calculating volume fractions of competing phases. Journal of Physics: Condensed Matter, 12, 9109–9122. https://doi.org/10.1088/0953-8984/12/43/301.
• Avrami, M. (1939). Kinetics of phase change. I. General theory. Journal of Chemical Physics, 7, 1103–1112. https://doi.org/10.1063/1.1750380.
• Bruna, P., Crespo, D., González-Cinca, R., & Pineda, E. (2006). On the validity of Avrami formalism in primary crystallization. Journal of Applied Physics, 100, 054907.
• Bzowski, K., Rauch, Ł., Pietrzyk, M., Kwiecień, M., & Muszka, K. (2021). Numerical modeling of phase transformations in dual-phase steels using Level Set and SSRVE approaches. Materials, 14(18), 5363. https://doi.org/10.3390/ma14185363.
• Czarnecki, M., Sitko, M., & Madej, Ł. (2021). The role of neighborhood density in the random cellular automata model of grain growth. Computer Methods in Materials Science, 21(3), 129–137. https://doi.org/10.7494/cmms.2021.3.0760.
• Gladman, T. (1997). The physical metallurgy of microalloyed steels. Institute of Materials.
• Helbert, C., Touboul, E., Perrin, S., Carraro, L., & Pijolat, M. (2004). Stochastic and deterministic models for nucleation and growth in non-isothermal and/or non-isobaric powder transformations. Chemical Engineering Science, 59(7), 1393–1401. https://doi.org/10.1016/j.ces.2003.12.004.
• Heo, T.W., & Chen, L.Q. (2014). Phase-field modeling of nucleation in solid-state phase transformations. JOM, 66, 1520–1528. https://doi.org/10.1007/s11837-014-1033-9.
• Hodgson, P.D., & Gibbs, R.K. (1992). A mathematical model to predict the mechanical properties of hot rolled C-Mn and microalloyed steels. ISIJ International, 32(12), 1329–1338. https://doi.org/10.2355/isijinternational.32.1329.
• Isasti, N., Jorge-Badiola, D., Taheri, M.L., & Uranga, P. (2014). Microstructural and precipitation characterization in Nb-Mo microalloyed steels: estimation of the contributions to the strength. Metals and Materials International, 20, 807–817. https://doi.org/10.1007/s12540-014-5002-1.
• Izmailov, A.F., Myerson, A.S., & Arnold, S. (1999). A statistical understanding of nucleation. Journal of Crystal Growth, 196, 234–242. https://doi.org/10.1016/S0022-0248(98)00830-6.
• Johnson, W.A., & Mehl, R.F. (1939). Reaction kinetics in processes of nucleation and growth. Transactions AIME, 135, 416–442.
• Klimczak, K., Oprocha, P., Kusiak, J., Szeliga, D., Morkisz, P., Przybyłowicz, P., Czyżewska, N., & Pietrzyk, M. (2022). Inverse problem in stochastic approach to modelling of microstructural parameters in metallic materials during processing. Mathematical Problems in Engineering, 9690742. https://doi.org/10.1155/2022/9690742.
• Koistinen, D.P., & Marburger, R.E. (1959). A general equation prescribing the extent of the austenite-martensite transformation in pure iron-carbon alloys and plain carbon steels. Acta Metallurgica, 7(1), 59–60. https://doi.org/10.1016/0001-6160(59)90170-1.
• Kolmogorov, A. (1937). K statisticheskoy teorii kristallizatsii metallov. Izvestiya Akademii Nauk SSS. Seriya matematicheskaya, 1(3), 355–359 [Колмогоров, А.Н. (1937). К статистической теории кристаллизации металлов. Известия Академии Наук СССР. Серия математическая, 1(3), 355–359].
• Lenard, J.G., Pietrzyk, M., & Cser, L. (1999). Mathematical and Physical Simulation of the Properties of Hot Rolled Products. Elsevier.
• Liu, X., Li, H., & Zhan, M. (2018). A review on the modeling and simulations of solid-state diffusional phase transformations in metals and alloys. Manufacturing Review, 5, 10. https://doi.org/10.1051/mfreview/2018008.
• Lyrio, M.S., Alves, A.L.M., Silveira de Sá, G.M., da Silva Ventura, H., da Silva Assis, W.L., & Rios, P.R. (2019). Comparison of transformations with inhomogeneous nucleation and transformations with inhomogeneous growth velocity. Journal of Materials Research and Technology, 8(5), 4682–4686. https://doi.org/10.1016/j.jmrt.2019.08.012.
• Maggioni, G.M. (2018). Modelling and data analysis of stochastic nucleation in crystallization (Doctoral thesis, ETH Zurich). https://doi.org/10.3929/ethz-b-000250375.
• Militzer, M. (2012). Phase field modelling of phase transformations in steels. In: E. Pereloma, & D.V. Edmonds (Eds.), Phase Transformations in Steels (Vol. 2: Diffusionless Transformations, High Strength Steels, Modelling and Advanced Analytical Techniques, pp. 405–432). Woodhead Publishing.
• Ou, X., Sietsma, J., & Santofimia, M.J. (2022). Fundamental study of nonclassical nucleation mechanisms in iron. Acta Materialia, 226, 117655. https://doi.org/10.1016/j.actamat.2022.117655.
• Pietrzyk, M., Madej, Ł., Rauch, Ł., & Szeliga, D. (2015). Computational Materials Engineering: Achieving High Accuracy and Efficiency in Metals Processing Simulations. Butterworth-Heinemann, Elsevier.
• Rauch, Ł., Bachniak, D., Kuziak, R., Kusiak, J., & Pietrzyk, M. (2018). Problem of identification of phase transformation models used in simulations of steels processing. Journal of Materials Engineering and Performance, 27, 5725–5735. https://doi.org/10.1007/s11665-018-3651-9.
• Rios, P.R., & Villa, E. (2009). Transformation kinetics for inhomogeneous nucleation. Acta Materialia, 57, 1199–1208.
• Rios, P.R., Jardim, D., Assis, W.L.S., Salazar, T.C., & Villa, E. (2009). Inhomogeneous Poisson point process nucleation: comparison of analytical solution with Cellular Automata simulation. Materials Research, 12(2), 219–224. https://doi.org/10.1590/S1516-14392009000200017.
• Rivera-Díaz-Del-Castillo, P.E.J., Sietsma, J., & Van Der Zwaag, S. (2004). A model for ferrite/pearlite band formation and prevention in steels. Metallurgical and Materials Transactions A, 35(2), 425–433.
• Song, K.J., Wei, Y.H., Dong, Z.B., Wang, X.Y., Zheng, W.J., & Fang, K. (2015). Cellular automaton modeling of diffusion, mixed and interface controlled phase transformation. Journal of Phase Equilibria and Diffusion, 36, 136–148. https://doi.org/10.1007/s11669-015-0369-3.
• Stoyan, D., Kendall, W.S., & Mecke, J. (1987). Stochastic Geometry and Its Applications. Wiley.
• Szeliga, D., Chang, Y., Bleck, W., & Pietrzyk, M. (2019). Evaluation of using distribution functions for mean field modelling of multiphase steels. Procedia Manufacturing, 27, 72–77.
• Szeliga, D., Czyżewska, N., Klimczak, K., Kusiak, J., Kuziak, R., Morkisz, P., Oprocha, P., Pietrzyk, M., Poloczek, Ł., & Przybyłowicz, P. (2022a). Stochastic model describing evolution of microstructural parameters during hot rolling of steel plates and strips. Archives of Mechanical and Civil Engineering, 22, 139. https://doi.org/10.1007/s43452-022-00460-2.
• Szeliga, D., Czyżewska, N., Klimczak, K., Kusiak, J., Kuziak, R., Morkisz, P., Oprocha, P., Pidvysotsk’yy, V., Pietrzyk, M., & Przybyłowicz, P. (2022b). Formulation, identification and validation of a stochastic internal variables model describing the evolution of metallic materials microstructure during hot forming. International Journal of Material Forming, 15, 53. https://doi.org/10.1007/s12289-022-01701-8.
• Tagami, T., & Tanaka, S.-I. (1997). Stochastic modeling of nucleation and growth in a thin layer between two interfaces. Acta Materialia, 45(8), 3341–3347. https://doi.org/10.1016/S1359-6454(97)00021-9.
• Tomellini, M., & Fanfoni, M. (2014). Comparative study of approaches based on the differential critical region and correlation functions in modeling phase-transformation kinetics. Physical Review E, 90, 052406. https://doi.org/10.1103/Phys-RevE.90.052406.
• Wang, Z.-J., Luo, S., Song, H.-W., Deng, W.-D., & Li W.-Y. (2014). Simulation of microstructure during laser rapid forming solidification based on cellular automaton. Mathematical Problems in Engineering, 627528. https://doi.org/10.1155/2014/627528.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).