Study of phase transformations in complex phase steel using a mesoscale cellular automaton model Part 1: Modeling fundamentals

• Autorzy: Opara Jarosław , Kuziak Roman

Identyfikatory

DOI

10.32730/imz.2657-747.20.3.2

Warianty tytułu

PL

Badania przemian fazowych w stali wielofazowej za pomocą mezoskalowego modelu automatu komórkowego Cz. 1: Podstawy modelowania

• Języki publikacji: EN

Abstrakty

EN

A two-dimensional mesoscale model based on the concept of hybrid cellular automata is developed to study phase transformations in a complex phase steel during continuous cooling. The model is capable of simulating microstructure evolution with carbon diffusion in the volume and along grain boundaries, γ/α interfaces migration into austenite, as well as formation of bainite and martensite islands during intensive cooling in lower temperatures. In contrast to the classic statistical approaches which are based on the assumption of modeling one point in the material with homogeneous microstructure, the proposed phase transformations’ model in the mesoscale accounts for material heterogeneity. The simulation results in the form of a digital material representation with microstructures and maps showing the carbon concentration field as well as microhardness distribution are presented. One of the main advantages of the model is that has only seven adjustment coefficients that are used in the fitting process.

PL

Dwuwymiarowy mezoskalowy model oparty na koncepcji hybrydowych automatów komórkowych został opracowany w celu badania przemian fazowych w stali wielofazowej podczas ciągłego chłodzenia. Model umożliwia symulację rozwoju mikrostruktury wraz z dyfuzją węgla w objętości, jak i wzdłuż granic ziaren oraz migracją powierzchni międzyfazowych γ/α do austenitu, a także powstawaniem wysp bainitu i martenzytu podczas intensywnego chłodzenia w niższych temperaturach. W odróżnieniu od klasycznych podejść statystycznych, które bazują na założeniu modelowania jednego punktu w materiale o jednorodnej mikrostrukturze, zaproponowany model przemian fazowych w mezoskali umożliwia uwzględnienie warunków niejednorodności materiału. Zaprezentowano wyniki symulacji w postaci cyfrowej reprezentacji materiału z mikrostrukturami oraz mapami przedstawiającymi pola stężenia węgla oraz rozkłady mikrotwardości. Jedną z głównych zalet modelu jest to, że regulowany jest tylko za pomocą siedmiu współczynników w procesie dopasowania.

Słowa kluczowe

EN

phase transformations; complex phase steel; cellular automata; mesoscale model

PL

przemiany fazowe; stal wielofazowa; automat komórkowy; model mezoskalowy

• Wydawca: Sieć Badawcza Łukaszewicz - Instytut Metalurgii Żelaza im. Stanisława Staszica
• Czasopismo: Journal of Metallic Materials
• Rocznik: 2020
• Tom: Vol. 72, no. 3
• Strony: 17--31
• Opis fizyczny: Bibliogr. 80 poz., rys., tab.

Twórcy

autor

Opara Jarosław

• Sieć Badawcza Łukasiewicz - Instytut Metalurgii Żelaza

autor

Kuziak Roman

• Sieć Badawcza Łukasiewicz - Instytut Metalurgii Żelaza

Bibliografia

• [1] C.W. Zheng, N. Xiao, L. Hao, D. Li, Y. Li. Numerical simulation of dynamic strain-induced austenite-ferrite transformation in a low carbon steel. Acta Materialia, 2009, 57, p. 2956-2968.
• [2] M.G. Mecozzi, C. Bos, J. Sietsma. 3D cellular automata modelling of solid-state transformations relevant in low-alloy steel production. Solid State Phenomena, 2011, 172-174, p. 1140-1145.
• [3] C. Bos, M.G. Mecozzi, D.N. Hanlon, M.P. Aarnts, J. Sietsma. Application of a Three-Dimensional Microstructure Evolution Model to Identify Key Process Settings for the Production of Dual-Phase Steels. Metallurgical and Materials Transactions A, 2011, 42, p. 3602- 3610.
• [4] M.J. Santofimia, L. Zhao, J. Sietsma. Overview of Mechanisms Involved During the Quenching and Partitioning Process in Steels. Metallurgical and Materials Transactions A, 2011, 42, p. 3620-3626.
• [5] M. Pernach, K. Bzowski, M. Pietrzyk. Application of numerical solution of the diffusion equation to modelling phase transformation during heating of DP steels in the continuous annealing process. Computer Methods in Materials Science, 2012, 12 (3), p. 183-196.
• [6] M. Pernach, K. Bzowski, M. Pietrzyk. Numerical modeling of phase transformation in dual phase (DP) steel after hot rolling and laminar cooling. Journal for Multiscale Computational Engineering, 2014, 12 (5), p. 397-410.
• [7] K. Nakashima, T. Nagai, K. Kawasaki. Scaling behavior of two-dimensional domain growth: Computer simulation of vertex models. Journal of Statistical Physics, 1989, 57, p. 759-787.
• [8] D. Weygand, Y. Bréchet, J. Lépinoux. Reduced Mobility of Triple Nodes and Lines on Grain Growth in Two and Three Dimensions. Interface Science, 1999, 7, p. 285-295.
• [9] S. Maddali, S. Ta’asan, R.M. Suter. Topology-faithful nonparametric estimation and tracking of bulk interface networks. Computational Materials Science, 2016, 125, p. 328-340.
• [10] E. Javierre, C. Vuik, F. Vermolen, A. Segal, S. van der Zwaag. The Level Set Method for Solid-Solid Phase Transformations. Numerical Mathematics and Advanced Applications, 2006, 18, p. 712-719.
• [11] T. Iwamoto, M. Cherkaoui, E.P. Busso. A finite element-based level-set method of an interface motion driven by a diffusion field: Application to a phase transformation problem. Computational Materials Science, 2008, 44, p. 792-801.
• [12] Y. Saito, M. Enomoto. Monte Carlo Simulation of Grain Growth. ISIJ International, 1992, 32 (3), p. 267-274.
• [13] N. Xiao, M. Tong, Y. Lan, D. Li, Y. Li. Coupled simulation of the influence of austenite deformation on the subsequent isothermal austenite-ferrite transformation. Acta Materialia, 2006, 54, p. 1265-1278.
• [14] D. Zöllner. Treating grain growth in thin films in three dimensions: A simulation study. Computational Materials Science, 2016, 125, p. 51-60.
• [15] A.A. Wheeler, W.J. Boettinger, G.B. McFadden. Phase-field model for isothermal phase transitions in binary alloys. Physical Review A, 1992, 45, p. 7424-7439.
• [16] I. Steinbach, F. Pezzolla, B. Nestler, M. Sedklberg, R. Ptieler, G.J. Schmitz, J.L.L. Rezende. A phase field concept for multiphase systems. Physica D, 1996, 94, p. 135-147.
• [17] J. Tiaden, B. Nestler, H.J. Diepers, I. Steinbach. The multiphase-field model with an integrated concept for modelling solute diffusion. Physica D, 1998, 115, p. 73-86.
• [18] C.-J. Huang, D.J. Browne, S. McFadden. A phase-field simulation of austenite to ferrite transformation kinetics in low carbon steels. Acta Materialia, 2006, 54, p. 11-21.
• [19] M. Militzer, M.G. Mecozzi, J. Sietsma, S. van der Zwaag. Threedimensional phase field modelling of the austenite-to-ferrite transformation. Acta Materialia, 2006, 54, p. 3961-3972.
• [20] A. Yamanaka, T. Takaki, Y. Tomita. Coupled simulation of microstructural formation and deformation behavior of ferrite-pearlite steel by phase-field method and homogenization method. Materials Science and Engineering A, 2008, 480, p. 244-252.
• [21] J. Rudnizki, B. Bӧttger, U. Prahl, W. Bleck. 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, 2011, 42, p. 2516-2525.
• [22] M. Düsing, R. Mahnken. A coupled phase-field - Cahn-Hilliard model for lower bainitic transformation. Proceedings in Applied Mathematics and Mechanics, 2015, 15, p. 285-286.
• [23] K.R. Elder. M. Katakowski, M. Haataja, M. Grant. Modeling Elasticity in Crystal Growth. Physical Review Letters, 2002, 88, p. 245701-245704.
• [24] N. Provatas, J.A. Dantzig, B. Athreya, P. Chan, P. Stefanovic, N. Goldenfeld, K.R. Elder. Using the Phase-Field Crystal Method in the Multi-Scale Modeling of Microstructure Evolution. JOM, 2007, 59 (7), p. 83-90.
• [25] M. Greenwood, N. Provatas, J. Rottler. Free Energy Functionals for Efficient Phase Field Crystal Modeling of Structural Phase Transformations. Physical Review Letters, 2010, 105, p. 045702-045704.
• [26] M. Kumar, R. Sasikumar, P. Kesavan Nair. Competition between nucleation and early growth of ferrite from austenite - studies using cellular automaton simulations. Acta Materialia, 1998, 46, p. 6291-6303.
• [27] L. Zhang, C.B. Zhang, Y.M. Wang, S.Q. Wang, H.Q. Ye. A cellular automaton investigation of the transformation from austenite to ferrite during continuous cooling. Acta Materialia, 2003, 51, p. 5519-5527.
• [28] S. Kundu, M. Dutta, S. Ganguly, S. Chandra. Prediction of phase transformation and microstructure in steel using cellular automaton technique. Scripta Materialia, 2004, 50, p. 891-895.
• [29] Y.J. Lan, D.Z. Li, Y.Y. Li. Modeling austenite decomposition into ferrite at different cooling rate in low-carbon steel with cellular automaton method. Acta Materialia, 2004, 52, p. 1721-1729.
• [30] Y.J. Lan, N.M. Xiao, D.Z. Li, Y.Y. Li. Mesoscale simulation of deformed austenite decomposition into ferrite by coupling a cellular automaton method with a crystal plasticity finite element model. Acta Materialia, 2005, 53, p. 991-1003.
• [31] D.Z. Li, N.M., Xiao, Y.J. Lan, C.W. Zheng, Y.Y. Li. Growth modes of individual ferrite grains in the austenite to ferrite transformation of low carbon steels. Acta Materialia, 2007, 55, p. 6234-6249.
• [32] M. Pietrzyk, Ł. Madej, Ł. Rauch, R. Gołąb. Multiscale modelling of microstructure evolution during laminar cooling of hot rolled DP steels. Archives of Civil and Mechanical Engineering, 2010, 10 (4), p. 57-67.
• [33] J. Opara, R. Kuziak, H. Chen, S. van der Zwaag. A two-dimensional CA model to simulate microstructure development and carbon redistribution during the phase transformation of austenite to ferrite using realistic angular starting microstructures. Computer Methods in Materials Science, 2012, 12 (3), p. 207-217.
• [34] B.L. Ennis, E. Jimenez-Melero, R. Mostert, B. Santillana, P.D. Lee. The role of aluminium in chemical and phase segregation in a TRIP-assisted dual phase steel. Acta Materialia, 2016, 115, p. 132-142.
• [35] B.J. Yang, L. Chuzhoy, M.L. Johnson. Modeling of reaustenitization of hypoeutectoid steels with cellular automaton method. Computational Materials Science, 2007, 41 (2), p. 186-194.
• [36] C.W. Zheng, D. Raabe. Interaction between recrystallization and phase transformation during intercritical annealing in a coldrolled dual-phase steel: A cellular automaton model. Acta Materialia, 2013, 61, p. 5504-5517.
• [37] C. Jiaa, C.W. Zheng, D., Li. Cellular automaton modeling of austenite formation from ferrite plus pearlite microstructures during intercritical annealing of a C-Mn steel. Journal of Materials Science & Technology, 2020, 47, p. 1-9.
• [38] C. Bos, M.G. Mecozzi, J. Sietsma. A microstructure model for recrystallisation and phase transformation during the dual-phase steel annealing cycle. Computational Materials Science, 2010, 48, p. 692-699.
• [39] C.W. Zheng, D. Raabe, D.Z. Li. Prediction of post-dynamic austenite-to-ferrite transformation and reverse transformation in a low-carbon steel by cellular automaton modeling. Acta Materialia, 2012, 60, p. 4768-4779.
• [40] D. An, S. Pan, L. Huang, T. Dai, B. Krakauer, M. Zhu. Modeling of Ferrite-Austenite Phase Transformation Using a Cellular Automaton Model. ISIJ International, 2014, 54, p. 422-429.
• [41] D.S. Svyetlichnyy, A.I. Mikhalyov. Three-dimensional Frontal Cellular Automata Model of Microstructure Evolution - Phase Transformation Module. ISIJ International, 2014, 54, p. 1386-1395.
• [42] G. Jabłoński, B. Pawłowski, M. Pietrzyk. Application of the Cellular Automata method to modelling lower bainite in steels. Computer Methods in Materials Science, 2012, 12, p. 51-62.
• [43] J. Opara, G. Jabłoński, D. Rudzki, M. Pietrzyk. Modelowanie metodą automatów komórkowych cyklu przemian fazowych w stalach. Hutnik - Wiadomości Hutnicze, 2012, 79, p. 447-451.
• [44] W. Kapturkiewicz, E. Fraś, A.A. Burbelko. Why is the computer modelling needed in casting? Przegląd Odlewnictwa, 2005, 1, p. 15-23.
• [45] M. Militzer. Computer Simulation of Microstructure Evolution in Low Carbon Sheet Steels. ISIJ International, 2007, 47, p. 1-15.
• [46] Future Steel Vehicle. Final Engineering Report, Steel Market Development Institute, Washington, DC, 2011. [Online] Available at: www.autosteel.org [Accessed on: 28 August 2020].
• [47] K.G.F. Janssens, D. Rabbe, E. Kozeschnik, M.A. Miodownik, B. Nestler. Computational Materials Engineering. An Introduction to Microstructure Evolution. Oxford: Elsevier Academic Press, 2007.
• [48] J.P. Naylor. The influence of the lath morphology on the yield stress and transition temperature of martensitic-bainitic steels. Metallurgical and Materials Transactions A, 1979, 10, p. 861-873.
• [49] T.J. Chung. Computational Fluid Dynamics. Cambridge: Cambridge University Press, 2002.
• [50] G.P. Krielaart, J. Sietsma, S. van der Zwaag. Ferrite formation in Fe-C alloys during austenite decomposition under non-equilibrium interface conditions. Materials Science and Engineering A, 1997, 237, p. 216-223.
• [51] J. Sietsma, S. van der Zwaag. A concise model for mixed-mode phase transformations in the solid state. Acta Materialia, 2004, 52, p. 4143-4152.
• [52] J.C. Fisher. Calculation of Diffusion Penetration Curves for Surface and Grain Boundary Diffusion. Journal of Applied Physics, 1951, 22, p. 74-77.
• [53] S.-W.Seo, H.K.D.H. Bhadeshia, D.W. Suh. Pearlite growth rate in Fe-C and Fe-Mn-C Steels. Materials Science and Technology, 2015, 31, p. 487-493.
• [54] F. Vermolen, K. Vuik. A numerical method to compute the dissolution of second phases in ternary alloys. Journal of Computational and Applied Mathematics, 1998, 93, p. 123-143.
• [55] J.W. Christian. The theory of transformation in metals and alloys, Issue 2. Oxford: Pergamon Press, 1981.
• [56] M. Marek. Grid anisotropy reduction for simulation of growth processes with cellular automaton. Physica D, 2013, 253, p. 73-84.
• [57] J.W. Cahn. The kinetics of grain boundary nucleated reactions. Acta Metallurgica, 1956, 4, p. 449-459.
• [58] M. Umemoto, Z.H. Guo, I. Tamura. Effect of cooling rate on grain size of ferrite in a carbon steel. Materials Science and Technology, 1987, 3, p. 249-255.
• [59] L. Madej, M. Sitko, M. Pietrzyk. Perceptive comparison of mean and full field dynamic recrystallization models. Archives of Civil and Mechanical Engineering, 2016, 16, p. 569-589.
• [60] H.K.D.H. Bhadeshia, D.V. Edmonds. The mechanism of bainite formation in steels. Acta Metalurgica, 1980, 28, p. 1265-1273.
• [61] H.K.D.H. Bhadeshia. A rationalisation of shear transformations in steels. Acta Metalurgica, 1981, 29, p. 1117-1130.
• [62] H.K.D.H. Bhadeshia. Thermodynamic extrapolation and martensite-start temperature of substitutionally alloyed steels. Metal Science, 1981, 15, p. 178-180.
• [63] J.W. Cahn. Transformation kinetics during continuous cooling. Acta Metallurgica, 1956, 4 (6), p. 572-575.
• [64] K.C. Russell. Grain boundary nucleation kinetics. Acta Metallurgica, 1969, 17, p. 1123-1131.
• [65] H.K.D.H. Bhadeshia. A Thermodynamic analysis of isothermal transformation diagrams. Metal Science, 1982, 16, p. 159-165.
• [66] M. Irani, S. Chung, M. Kim, K. Lee, M. Joun. Adjustment of Isothermal Transformation Diagrams Using Finite-Element Optimization of the Jominy Test. Metals, 2020, 10 (7), p. 931.
• [67] D.P. Koistinen, R.E. Marburger. A general equation prescribing the extent of the austenite-martensite transformation in pure iron-carbon alloys and plain carbon steels. Acta Metallurgica, 1959, 7 (1), p. 59-60.
• [68] E.J. Pavlina, C.J. Van Tyne. Correlation of yield strength and tensile strength with hardness for steels. Journal of Materials Engineering and Performance, 2008, 17, p. 888-893.
• [69] M.V. Li, D.V. Niebuhr, L.L. Meekisho, D.G. Atteridge. A computational model for the prediction of steel hardenability. Metallurgical and Materials Transactions B, 1998, 29, p. 661-672.
• [70] B. Smoljan, S. Smokvina Hanza, N. Tomašić, D. Iljkić. Computer simulation of microstructure transformation in heat treatment processes. Journal of Achievements in Materials and Manufacturing Engineering, 2007, 24, p. 275-282.
• [71] H. Yada. Prediction of microstructural changes and mechanical properties in hot strip rolling. Proceedings of the Metallurgical Society of the Canadian Institute of Mining and Metallurgy, 1988, 3, p. 105-119.
• [72] N. Yurioka, T. Kasuya, M. Okumura. Methods for Predicting Maximum Hardness of Heat-Affected Zone and Selecting Necessary Preheat Temperature for Steel Welding. Nippon Steel Technical Report, 1995, 65 p. 7-14.
• [73] J. Opara, A. Wrożyna. Zastosowanie metody automatów komórkowych do opracowania cyfrowej reprezentacji wybranych cech mikrostruktury w oparciu o obrazy binarne jej składników. Prace Instytutu Metalurgii Żelaza, 2013, 65 (4), p. 2-7.
• [74] J. Opara. Fizyczny model przemian fazowych w mezoskali do symulacji procesu wytwarzania blach cienkich ze stali wielofazowych (doctoral dissertation). Gliwice: Instytut Metalurgii Żelaza, 2019. [unpublished].
• [75] J. Opara, R. Kuziak. Study of phase transformations in complex phase steel using a mesoscale cellular automaton model. Part II: Experiments and Validation. Journal of Metallic Materials, 2020, 73 (3), p. 32-44.
• [76] J.O. Andersson, T. Helander, L. Höglund, P.F. Shi, B. Sundman. Thermo-Calc and DICTRA, Computational tools for materials science. Calphad, 2002, 26, p. 273-312.
• [77] Materials Algorithms Project. [Online] Available at: https://www.phase-trans.msm.cam.ac.uk/map/ [Accessed on: 28 August 2020].
• [78] H. Springer, M. Belde, D. Raabe. Bulk combinatorial design of ductile martensitic stainless steels through confined martensite-to-austenite reversion. Materials Science & Engineering A, 2013, 582, p. 235-244.
• [79] B.B. He, M.X. Huang. Revealing heterogeneous C partitioning in a medium Mn steel by nanoindentation. Materials Science and Technology, 2017, 33, p. 1-7.
• [80] M. Pietrzyk, J. Kusiak, R. Kuziak, L. Madej, D. Szeliga, R. Gołąb. Conventional and Multiscale Modeling of Microstructure Evolution During Laminar Cooling of DP Steel Strips. Metallurgical and Materials Transactions A, 2014, 45, p. 5835-5851.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).