Mean field and full field modelling of microstructure evolution and  phase transformations during hot forming and cooling of low carbon steels

Danuta Szeliga¹, Krzysztof Bzowski¹, Łukasz Rauch¹, Roman Kuziak², Maciej Pietrzyk¹

¹AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland.

²Łukasiewicz Research Network, Institute for Ferrous Metallurgy, ul. K. Miarki 12, 44-100 Gliwice, Poland.

DOI:

https://doi.org/10.7494/cmms.2020.3.0727

Abstract:

The paper describes a critical comparison of mean field and full field approaches to modelling hot deformation/controlled cooling sequences for steels. Classification of the models, based on the balance between predictive capabilities and computing costs, is presented. Mean field models, which describe microstructure evolution and phase transformations were connected with thermomechanical finite element program and applied to simulation of the hot strip rolling process and cooling of tubes after hot rolling. Full field model described in the paper is a connection of the finite element (FE) and level set (LSM) methods. These methods were used to simulate heating/cooling sequence in the continuous annealing line. A suggestion to use a stochastic model as a bridge between mean field and full field approaches is made.

Cite as:

Szeliga, D., Bzowski, K., Rauch, L., Kuziak, R., & Pietrzyk, M. (2020). Mean field and full field modelling of microstructure evolution and phase transformations during hot forming and cooling of low carbon steels. Computer Methods in Materials Science, 20(3), 121-132. https://doi.org/10.7494/cmms.2020.3.0727

Article (PDF):

Keywords:

Mean field models, Full field models, Finite element method, Level set method

References:

Abinandanan, T.A., Haider, F., & Martin, G. (1998). Computer simulations of diffusional phase transformations: Monte Carlo algorithm and application to precipitation of ordered phases. Acta Materialia, 46(12), 4243–4255.

Allix, O. (2006). Multiscale Strategy for Solving Industrial Problems. In: Motasoares, C.A., Martins, J.A.C., Rodrigues, H.C., Ambrósio, J.A.C., Pina, C.A.B., Motasoares, C.M., Pereira, E.B.R., Folgado, J. (Eds.), III European Conference on Computational Mechanics. Solids, Structures and Coupled Problems in Engineering: Book of Abstracts (pp. 107–126). Springer.

Avrami, M. (1939). Kinetics of phase change. I. General theory. Journal of Chemical Physics, 7(12), 1103–1112.

Bargmann, S., Klusemann, B., Markmann, J., Schnabel, J.E., Schneider, K., Soyarslan, C., & Wilmers, J. (2018). Generation of 3D representative volume elements for heterogeneous materials: A review. Progress in Materials Science, 96, 322–384.

Bernacki, M., Chastel, Y., Coupez, T., & Logé, R.E. (2008). Level set framework for the numerical modelling of primary recrystallization in polycrystalline materials. Scripta Materialia, 58(12), 1129–1132.

Bhadeshia, H.K.D.H., & Honeycombe, R.W.K. (2006). Steels. Microstructure and properties (3rd ed.). Elsevier, Butterworth-Heinemann. Bollada, P.C., Goodyer, C.E., Jimack, P.K., Mullis, A.M., & Yang, F.W. (2015). Three dimensional thermal-solute phase field simulation of binary alloy solidification. Journal of Computational Physics, 287, 130–150.

Bzowski, K. (2019). Wykorzystanie statystycznej reprezentacji mikrostruktury do modelowania przemian fazowych w stalach DP poprzez rozwiązanie równania dyfuzji [PhD thesis]. Akademia Górniczo-Hutnicza, Kraków.

Bzowski, K., Kitowski, J., Kuziak, R., Uranga, P., Gutierrez, I., Jacolot, R., Rauch, Ł., & Pietrzyk, M. (2017). Development of the material database for the VirtRoll computer system dedicated to design of an optimal hot strip rolling technology. Computer Methods in Materials Science, 17(4), 225–246.

Bzowski, K., Rauch, Ł., & Pietrzyk, M. (2018). Application of statistical representation of the microstructure to modeling of phase transformations in DP steels by solution of the diffusion equation. Procedia Manufacturing, 15, 1847–1855.

Choudhury, A.N. (2013). Quantitative phase-field model for phase transformations in multi-component alloys. KIT Scientific Publishing.

Christian, J.W. (1975). The theory of transformations in metals and alloys. Pergamon Press.

Clouet, E., & Soisson, F. (2010). Atomic simulations of diffusional phase transformations. Comptes Rendus Physique, 11(3–4), 226–235.

Contieri, R.J., Zanotello, M., & Caram, R. (2017). Simulation of CP-Ti recrystallization and grain growth by a cellular automata algorithm: simulated versus experimental results. Materials Research, 20(3), 688–701.

Das, S., Palmiere, E.J., & Howard, I.C. (2002). CAFE: a tool for modelling thermomechanical processes, In E.J. Palmiere, M. Mahfouf, C. Pinna (Eds.), Conference proceedings. International Conference on Thermomechanical Processing: Mechanics, Microstructure & Control. 23–26 June 2002, The University of Sheffield, England (pp. 296–301).

Donnay, B., Herman, J.C., Leroy, V., Lotter, U., & Grossterlinden, R. (1996). Microstructure evolution of C-Mn Steels in the hot deformation process: The STRIPCAM model. In J.H. Beynon, P. Ingham, H. Teichert, K. Waterson, H. Pircher (eds.), Proceedings of 2nd Conference on Modelling of Metal Rolling Processes, 23–35.

Estrin, Y., & Mecking, H. (1984). A unified phenomenological description of work hardening and creep based on one-parameter model. Acta Metallurgica, 32(1), 57–70.

Fang, H., Mecozzi, M.G., Brück, E., Zwaag, S., van der, & Dijk, N.H., van (2018). Analysis of the grain size evolution for ferrite formation in Fe-C-Mn steels using a 3D Model under a mixed-mode interface condition. Metallurgical and Materials Transactions A, 49(1), 41–53.

Fausty, J., Murgas, B., Florez, S., Bozzolo, N., & Bernacki, M. (2020). A new analytical test case for the anisotropic grain growth problem – first calculations with a Finite Element Level Set model. Applied Mathematical Modelling, 93, 28–52.

Fish, J. (Ed.) (2009). Multiscale methods: bridging the scales in science and engineering. Oxford University Press.

Fish, J. (2013). Practical multiscaling. Wiley.

Furstoss, J., Bernacki, M., Petit, C., Fausty, J., Muñoz, D.P., & Ganino, C. (2020). Full field and mean field modeling of grain growth in a multiphase material under dry conditions: application to peridotites. JGR Solid Earth, 125(1), e2019JB018138.

Håkan, H. (2013). A modified level set approach to 2D modeling of dynamic recrystallization. Modelling and Simulation in Materials Science and Engineering, 21(8), 085012.

Halder, C., Madej, L., & Pietrzyk, M. (2014). Discrete micro-scale cellular automata model for modelling phase transformation during heating of dual phase steels. Archives of Civil and Mechanical Engineering, 14(1), 96–103.

Janssens, K.G.F., Raabe, D., Kozeschnik, E., Miodownik, M.A., & Nestler, B. (2007). Computational materials engineering: An introduction to microstructure evolution. Elsevier, Academic Press.

Johnson, W.A., & Mehl, R.F. (1939). Reaction kinetics in processes of nucleation and growth. Transactions AIME, 135, 416–442.

Karhausen, K., & Kopp, R. (1992). Model for integrated process and microstructure simulation in hot forming. Steel Research, 63(6), 247–256.

Kobayashi, S., Oh, S.I., & Altan, T. (1989). Metal forming and the finite element method. Oxford University Press.

Колмогоров, A.H. (1937). К статистической теории кристаллизации металлов. Известия Академии Наук СССР. Серияматематическая, 1(3), 355–359.

Kuziak, R., Radwański, K., Molenda, R., Mazur, A., Broll, J., & Pietrzyk, M. (2018). Identification of phase transformation model for the simulation of controlled cooling of bainitic steel tubes. Prace Instytutu Metalurgii Żelaza, 70, 24–33.

Lan, Y.J., Li, D.Z., & Li, Y.Y. (2004). Modeling austenite decomposition into ferrite at different cooling rate in low-carbon steel with cellular automaton method. Acta Materialia, 52(6), 1721–1729.

Le, C.T., Nguyen, Trang T., Nguyen, Thao T., & Le, V.V. (2019). Molecular dynamics simulation of phase transformation and mechanical behavior in Al2O3 model. Vacuum, 167, 175–181.

Leblond, J.B., & Devaux, J. (1984). A new kinetic model for anisothermal metallurgical transformations in steel including effect of austenite grain size. Acta Metallurgica, 32(1), 137–146.

Lian, Y., Lin, S., Yan, W., Liu, W.K., & Wagner, G.J. (2018). A parallelized three-dimensional cellular automaton model for grain growth during additive manufacturing. Computational Mechanics, 61(5), 543–558.

Liu, E.Y., Zhang, D.H., Sun, J., Peng, L.G., Gao, B.H., & Su L.T. (2012). Algorithm design and application of laminar cooling feedback control in hot strip mill. Journal of Iron and Steel Research, International, 19(4), 39–42.

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).

Madej, L. (2017). Digital/virtual microstructures in application to metals engineering – A review. Archives of Civil and Mechanical Engineering, 17(4), 839–854.

Madej, Ł., Mrozek, A., Kuś, W., Burczyński, T., & Pietrzyk, M. (2008). Concurrent and upscaling methods in multi scale modelling – case studies. Computer Methods in Materials Science, 8(1), 1–10.

Maire, L. (2018). Full field and mean field modeling of dynamic and post-dynamic recrystallization in 3D – Application to 304L steel [PhD thesis], MINES ParisTech.

Marx, V., Reher, F.R., & Gottstein, G. (1999). Simulation of primary recrystallization using a modified three-dimensional cellular automaton. Acta Materialia, 47(4), 1219–1230.

Mecking, H., & Kocks, U.F. (1981). Kinetics of flow and strain-hardening. Acta Metallurgica, 29(11), 1865–1875.

Mecozzi, M.G., Militzer, M., Sietsma, J., & Zwaag, S., van der (2008). The role of nucleation behavior in phase-field simulations of the austenite to ferrite transformation. Metallurgical and Materials Transactions A, 39(6), 1237–1247.

Mecozzi, M.G., Eiken, J., Santofimia, M.J., & Sietsma, J. (2016). Phase field modelling of microstructural evolution during the quenching and partitioning treatment in low-alloy steels. Computational Materials Science, 112, part A,
245–256.

Milenin, I., Pernach, M., & Pietrzyk, M. (2015). Application of the control theory for modelling austenite-ferrite phase transformation in steels. Computer Methods in Materials Science, 15(2), 327–335.

Morkisz, P., Oprocha, P., Przybyłowicz, P., Czyzewska, N., Kusiak, J., Szeliga, D., Rauch, Ł., & Pietrzyk, M. (2019). Prediction of distribution of microstructural parameters in metallic materials described by differential equations with recrystallization term. International Journal for Multiscale Computational Engineering, 17(3), 361–371.

Niño, O., Martínez, D.I., Lizcano, C., Guerrero-Mata, M., & Colás, R. (2007). Study of the Tempcore process for the production of high resistance reinforcing rods. Materials Science Forum, 537–538, 533–540.

Osher, S., & Sethian, J.A. (1988). Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics, 79(1), 12–49.

Pereloma, E., & Edmonds, D. (2012). Phase transformations in steels. Fundamentals and diffusion-controlled transformations, (1st ed., vol. 1), Woodhead Publishing.

Pietrzyk, M. (1990). Finite element based model of structure development in the hot rolling process. Steel Research, 61(12), 603–607.

Pietrzyk, M. (2000). Finite-element simulation of large plastic deformation. Journal of Materials Processing Technology,106(1–3), 223–229.

Pietrzyk, M., & Kuziak, R. (2012). Modelling phase transformations in steel. In J. Lin, D. Balint, M. Pietrzyk (Eds.), Microstructure evolution in metal forming processes (pp. 145–179). Woodhead Publishing.

Pietrzyk, M., & Madej, L. (2017). Perceptive review of ferrous micro/macro material models for thermo-mechanical processing applications. Steel Research International, 88(10), 1700193.

Pietrzyk, M., Madej, L., Rauch, L., & Szeliga, D. (2015). Computational Materials Engineering: Achieving high accuracy and efficiency in metals processing simulations. Butterworth-Heinemann, Elsevier.

Raabe, D. (2002). Cellular automata in materials science with particular reference to recrystallization simulation. Annual Review of Materials Research, 32, 53–76.

Raghavan, S., & Sahay, S.S. (2007). Modeling the grain growth kinetics by cellular automaton. Materials Science and Engineering: A, 445–446, 203–209.

Roh, W., & Kikuchi, N. (2002). Analysis of Stefan problem with level set method. In 8th AIAA/ASME Joint Thermophysics and Heat Transfer Conference. American Institute of Aeronautics and Astronautics.

Rudnizki J., Böttger B., Prahl U., & Bleck W. (2011). Phase-field modeling of austenite formation from a ferrite plus pearlite microstructure during annealing of cold-rolled dual-phase steel. Metallurgical and Materials Transactions A, 42(8), 2516–2525.

Scheil, E. (1935). Anlaufzeit der Austenitumwandlung. Archiv für Eissenhüttenwesen, 8(12), 565–67.

Schröder, J. (2014). A numerical two-scale homogenization scheme: the FE2-method. In J. Schröder, K. Hackl (Eds.), Plasticity and beyond. Microstructures, crystal-plasticity and phase transitions (pp. 1–64). Springer.

Schröder, J., Balzani, D., & Brands, D. (2011). Approximation of random microstructures by periodic statistically similar representative volume elements based on lineal-path functions. Archives of Applied Mechanics, 81(7), 975–997.

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(2), 136–148.

Steinbach, I., & Apel, M. (2006). Multi phase field model for solid state transformation with elastic strain. Physica D: Nonlinear Phenomena, 217(2), 153–160.

Strangwood, M. (2012). Chapter 6. Fundamentals of ferrite formation in steels. In E. Pereloma, D.V. Edmonds (Eds.), Phase transformations in steels (pp. 187–224), Woodhead Publishing.

Urcola, J.J., & Sellars, C.M. (1987). Influence of changing strain rate on microstructure during hot deformation. Acta Metallurgica, 35(11), 2649–2657.