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Purpose: The primary aim of this research was to develop a mathematical and computational model of the nitriding process for steel using CA cellular automata theory, which enables the modelling of spatial hardness distributions and nitrogen concentrations within the material. Design/methodology/approach: The proposed mathematical model consists of two interacting cellular automata: one representing the surface layer of the nitride material and the other describing the spatial distribution of nitrogen. The developed algorithm and model based on CA were implemented in the MATLAB environment, enabling more effective and efficient testing of the created model and its further use. Findings: The developed computer model enabled, by changing the values of the CA model parameters, which correspond to the nitrogen diffusion coefficient in alloy steel, nitrogen solubility in iron and the enthalpy of formation and decomposition of iron nitrides, to adapt the model to the description of the nitriding process of 1.2343 (WCL) steel. The model was experimentally verified by comparing predicted hardness profiles with those measured after nitriding. Research limitations/implications: The main limitation of the developed model is the size of the material fragment in which the nitriding process is simulated. Practical implications: High compliance of the results of numerical calculations with the results obtained by experimental measurements was obtained, which predestines the potential usage of CA-based models for scientific and practical applications. The model can be used as part of an optimisation procedure for designing hybrid composite layers for tribological applications, comprising a nitride layer and a coating deposited via Physical Vapor Deposition (PVD) techniques. Originality/value: The added value of the developed model of the nitriding process, based on the concept of CA, is the author’s modification of the transition rules (both for cells in the Moore and von Neumann neighbourhood) in the automaton related to the structural and phase transformations in the nitride material.
Wydawca
Rocznik
Tom
Strony
58--65
Opis fizyczny
Bibliogr. 29 poz., rys., tab., wykr.
Twórcy
autor
- Department of Biomedical Engineering, Faculty of Mechanical Engineering and Energy, Koszalin University of Technology, Śniadeckich 2 Street, 75-453 Koszalin, Poland
autor
- Department of Biomedical Engineering, Faculty of Mechanical Engineering and Energy, Koszalin University of Technology, Śniadeckich 2 Street, 75-453 Koszalin, Poland
Bibliografia
- [1] L.A. Dobrzański, Engineering materials with the basics of material process technology. Part 1, PWN, Warszawa, 2024 (in Polish).
- [2] L.A. Dobrzański, Engineering materials with the basics of material process technology. Part 2, PWN, Warszawa, 2024 (in Polish).
- [3] L.A. Dobrzański, A.D. Dobrzańska-Danikiewicz, Shaping the structure and surface properties of engineering materials, Silesian University of Technology Publishing House, Gliwice, 2013 (in Polish).
- [4] L.A. Dobrzański, Shaping the structure and properties of engineering and biomedical materials, International OCSCO World Press, Gliwice, 2009 (in Polish).
- [5] M. Polok-Rubiniec, L.A. Dobrzański, M. Adamiak, Comparison of the PVD coatings deposited onto plasma nitrited steel, Journal of Achievements in Materials and Manufacturing Engineering 42/1-2 (2010) 172-179.
- [6] E. Wołowiec-Korecka, Case hardening development review (2001-2020), Archives of Materials Science and Engineering 120/2 (2023) 70-85. DOI: https://doi.org/10.5604/01.3001.0053.6922
- [7] J. Ratajski, R. Olik, T. Suszko, J. Dobrodziej, J. Michalski, A. Gilewicz, Precise formation the phase composition and the thickness of nitrided layers, Journal of Achievements in Materials and Manufacturing Engineering 37/2 (2009) 675-689.
- [8] E. Wolowiec, P, Kula, B. Januszewicz, M. Korecki, Mathematical modelling the low-pressure nitriding process, Applied Mechanics and Materials 421 (2013) 377-383. DOI: https://doi.org/10.4028/www.scientific.net/AMM.421.377
- [9] E. Wołowiec-Korecka, J. Michalski, B. Januszewicz, The Stability of the Layer Nitrided in Low-Pressure Nitriding Process, Coatings 13/2 (2023) 257. DOI: https://doi.org/10.3390/coatings13020257
- [10] E. Wołowiec-Korecka, J. Michalski, B. Kucharska, Kinetic aspects of low-pressure nitriding process, Vacuum 155 (2018) 292-299. DOI: https://doi.org/10.1016/j.vacuum.2018.06.025
- [11] J. Ratajski, T. Suszko, Modelling of the nitriding process, Journal of Materials Processing Technology 195/1-3 (2008) 212-217. DOI: https://doi.org/10.1016/j.jmatprotec.2007.04.133
- [12] J. Ratajski, Relation between phase composition of compound zone and growth kinetics of diffusion zone during nitriding of steel, Surface and Coatings Technology 203/16 (2009) 2300-2306. DOI: https://doi.org/10.1016/j.surfcoat.2009.02.021
- [13] J. Ratajski, R. Olik, T. Suszko, J. Dobrodziej, J. Michalski, Design, control and in situ visualization of gas nitriding processes, Sensors 10/1 (2010) 218-240. DOI: https://doi.org/10.3390/s100100218
- [14] B. Mortimer, P. Griveson, K.H. Jack, Precipitation of Nitrides in Ferritic Iron Alloys containing chromium, Scandinavian Journal of Metallurgy 1 (1972) 203-209.
- [15] D.H. Jack, P.C. Lidster, P. Grieveson, K.H. Jack, Kinetics of Nitriding Iron Alloys, Scandinavian Journal of Metallurgy 1 (1971) 374-379.
- [16] B.J. Lightfoot, D.H. Jack, H. Du, Kinetics of nitriding with and without white-layer formation, Proceedings of the Conference on Heat Treatment, London, 1973, 59-65.
- [17] G. Doolen, Lattice Gas Methods For Partial Differential Equations, 1 st Edition, CRC Press, Boca Raton, 1990.
- [18] B. Chopard, M. Droz, M. Kolb, Cellular automata approach to non-equilibrium diffusion and gradient percolation, Journal of Physics A: Mathematical and General 22/10 (1989) 1609. DOI: https://doi.org/10.1088/0305-4470/22/10/016
- [19] B. Chopard, M. Droz, Cellular automata approach to non-equilibrium phase transitions in a surface reaction model: static and dynamic properties, Journal of Physics A: Mathematical and General 21/1 (1988) 205. DOI: https://doi.org/10.1088/0305-4470/21/1/025
- [20] D. Dab, J.-P. Boon, Cellular automata approach to reaction-diffusion systems, in: P. Manneville, N. Boccara, G.Y. Vichniac, R. Bidaux (eds), Cellular Automata and Modeling of Complex Physical Systems, Springer Proceedings in Physics, vol 46, Springer, Berlin, Heidelberg, 1989, 257-273. DOI: https://doi.org/10.1007/978-3-642-75259-9_23
- [21] J.R. Weimar, Cellular automata for reaction-diffusion systems, Parallel Computing 23/11 (1997) 1699-1715. DOI: https://doi.org/10.1016/S0167-8191(97)00081-1
- [22] C. Halder, L. Madej, M. Pietrzyk, Discrete micro-scale cellular automata model for modelling phase transformation during heating of dual phase steels, Archives of Civil and Mechanical Engineering 14/1 (2014) 96-103. DOI: https://doi.org/10.1016/j.acme.2013.07.001
- [23] S. Kundu, M. Dutta, S. Ganguly, S. Chandra, Prediction of phase transformation and microstructure in steel using cellular automaton technique, Scripta Materialia 50/6 (2004) 891-895. DOI: https://doi.org/10.1016/j.scriptamat.2003.12.007
- [24] K. Jahns, M. Landwehr, J. Wübbelmann, U. Krupp, Numerical analysis of internal oxidation and nitridation by the cellular automata approach, Oxidation of Metals 79/1-2 (2013) 107-120. DOI: https://doi.org/10.1007/s11085-012-9334-2
- [25] K. Jahns, K. Balinski, M. Landwehr, J. Wübbelmann, U. Krupp, Prediction of high temperature corrosion phenomena by the cellular automata approach, Materials and Corrosion 68/2 (2017) 125-132. DOI: https://doi.org/10.1002/maco.201508777
- [26] B. Chopard, M. Droz, Cellular automata model for the diffusion equation, Journal of Statistical Physics 64/3-4 (1991) 859-892. DOI: https://doi.org/10.1007/BF01048321
- [27] B. Chopard, Cellular automata modeling of physical systems, in: R. Meyers (eds), Computational Complexity, Springer, New York, NY, 2012, 407-433. DOI: https://doi.org/10.1007/978-1-4614-1800-9_27
- [28] T. Belmonte, M. Gouné, H. Michel, Numerical modeling of interstitial diffusion in binary systems. Application to iron nitriding, Materials Science and Engineering: A 302/2 (2001) 246-257. DOI: https://doi.org/10.1016/S0921-5093(00)01830-X
- [29] T.L. Christiansen, M.A.J. Somers, Determination of the concentration dependent diffusion coefficient of nitrogen in expanded austenite, International Journal of Materials Research 99/9 (2008) 999-1005. DOI: https://doi.org/10.3139/146.101729
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-46c01bbb-c74b-41ba-84ae-6691b6ecb37e
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