Adomian decomposition method for modelling the growthof FeB/Fe2B layer in boronizing process
DOI:
https://doi.org/10.62638/ZasMat1090Keywords:
Adomian decomposition method, Diffusion, Boronizing, kinetic simulation, ModelAbstract
The main objective of this paper is to explore the practical implementation of the Adomian decomposition method (ADM) in effectively solving the system of equations governing boron diffusion during the boronizing process. This study uses ADM to investigate the kinetics of the boronizing process, assess the influence of various parameters on the growth of the layer thickness, and determine the boron concentration in FeB and Fe2B phases. To validate the simulation results, data obtained from the literature were utilized. Overall, this research contributes to understanding the boronizing process and demonstrates the effectiveness of ADM as a mathematical tool for solving complex diffusion equations.
References
A. G. Von Matuschka (1980) Boronizing,Carl Hansen Verlag, Germany. ISBN: 9783446131767
A.K.Sinha (1991)Boronizing, ASM Handbook, OH, USA, Journal of Heat Treating, 4, 437-447.
G.Wahl (1975) Boronizing, A Method for the Production of Hard Surfaces for Extreme Wear, Durferrit-Technical Information, Germany: Reprint from VDI-Z117, 785-789.
W.Fichtl (1980) Boronizing and its practical applications,Materials & Design,2(6), 276-286.https://doi.org/10.1016/0261-3069(81)90034-0
M. Kulka (2019) Current Trends in Boriding, Switzerland, Springer.https://doi.org/10.1007/978-3-030-06782-3
O. Allaoui, N. Bouaouadja, G. Saindernan (2006) Characterization of Boronized layers on a XC38 steel,Surface and Coatings Technology,201(6) 3475-3482.https://doi.org/10.1016/j.surfcoat.2006.07.238
B.Mebarek (2012) Etude numérique de la cinétique de boruration de l'acier inoxydable, Doctorat Science Physique, ENP d'Oran, Algeria.
V. I.Dybkov (2016) Basics of Formation of Iron Boride Coatings, Journal of Mineral, Metal and Material Engineering, 2, 30-46. ISSN: 2414-2115. https://doi.org/10.20941/2414-2115.2016.02.5
A.S. Dehlinger, J.F. Pierson, A. Roman, P.Bauer (2003) Properties of iron boride films prepared by magnetron sputtering, Surface and Coatings Technology, 174-175,331-337.https://doi.org/10.1016/S0257-8972(03)00399-2
B.Mebarek, S.A.Bouaziz, A.Zanoun (2012) Simulation model to study the thermochemical boriding of stainless steel «AISI 316» (X5CrNiMo17-12-2),Matériaux& Techniques, 100(2), 167-175.https://doi.org/10.1051/mattech/2012009
L.Casteletti, A.N.Lombardi,G.E.Totten(2013) Boriding. In:Q.J. Wang, Y. W. Chung (Eds.) Encyclopedia of Tribology, Springer, Boston. https://doi.org/10.1007/978-0-387-92897-5_727
C. Zimmerman (2013) Boriding (boronizing) of metals, in: J.L. Dossett, G.E. Totten (Eds.) Steel Heat Treating Fundamentals and Processes, ASM International, Ohio, 709-724.https://doi.org/10.31399/asm.hb.v04a.a0005772
A.Calik, N.Ucar, M.S.Karakas, and H.Tanis (2019) Pack-Boriding of Pure Iron with Powder Mixtures Containing ZrB2, High Temperature Materials and Processes, 38(2019), 342-346.https://doi.org/10.1515/htmp-2017-0081
V.Jain, G.Sundararajan (2002) Influence of the pack thickness of the boronizing mixture on the boriding of steel, Surface and Coatings Technology, 149(1), 21-26.https://doi.org/10.1016/S0257-8972(01)01385-8
J. Subrahmanyam and K. Gopinath (1984), Wear studies on boronized mild steel, Wear, 95(3), 287‑292.https://doi.org/10.1016/0043-1648(84)90143-1
B. Mebarek, D. Madouri, A.Zanoun, A.Belaidi (2015) Simulation model of monolayer growth kinetics of Fe2B phase, Matériaux& Techniques, 103(7), 703.https://doi.org/10.1051/mattech/2015058
M.Keddam, S. M.Chentouf (2005)A diffusion model for describing the bilayer growth (FeB/Fe2B) during the iron powder-pack boriding, Applied Surface Science, 252 (2), 393-399.https://doi.org/10.1016/j.apsusc.2005.01.016
B. Mebarek, A. Benguelloula, A. Zanoun (2018) Efect of Boride Incubation Time During the For-mation of Fe2B Phase, Materials Research, 21(1), 1-7.https://doi.org/10.1590/1980-5373-mr-2017-0647
C. M. Brakman, A.W. J. Gommers and E. J. Mittemeijer (1989)Boriding of Fe and Fe-C, Fe-Cr, and Fe-Ni alloys; Boride-layer growth kinetics, Journal of Materials Research, 4(6),1354-1370. https://doi.org/10.1557/JMR.1989.1354
I.Campos-silva, M.Ortiz-Domínguez, C.Tapia-Quintero, G.Rodriguez-Castro, M.Y. Jiménez-Reye, E.Chavez-Gutiérrez(2012) Kinetics and boron diffusion in the FeB/Fe2B layers formed at the surface of borided high-alloy steel. Journal of Materials Engineering and Performance, 21(8),1714-1723.https://doi.org/10.1007/s11665-011-0088-9
M.G.Albayrak, E.Evi̇n, O.Yi̇ği̇t, M.Toğaçar, B.Ergen (2023) Experimental and artificial intelligence approaches to measuring the wear behavior of DIN St28 steel boronized by the box boronizing method using a mechanically alloyed powder source, Engineering Applications of Artificial Intelligence, 120,105-910.https://doi.org/10.1016/j.engappai.2023.105910
C. Bindal, A. Erdemir (1996) Ultralow friction behavior of borided steel surfaces after flash annealing, App. Phys. Lett, 68(7), 923-925. https://doi.org/10.1063/1.116232
M. Keddam, M. Kulka (2018) Analysis of the growth kinetics of Fe2B layers by the integral method, Journal of Mining and Metallurgy, 54(3), 361-367.https://doi.org/10.2298/JMMB180405026K
V.I.Dybkov, L.V.Goncharuk, V.G.Khoruzha, K.A.Meleshevich, A.V.Samelyuk, V.R.Sidorko (2008)Diffusional growth kinetics of boride layers on iron-chromium alloys,Solid State Phenomena, 138, 181-188. https://doi.org/10.4028/www.scientific.net/SSP.138.181
B. Mebarek, M. Keddam (2019) Prediction model for studying the growth kinetics of Fe2B boride layers during boronizing, Ingénierie des Systèmesd'Information, 24(2),201-205.https://doi.org/10.18280/isi.240212
B.Mebarek and M.Keddam (2018), A fuzzy neural network approach for modeling the growth kinetics of FeB and Fe2B layers during the boronizing process, Matériaux& Techniques, 106(6),603.https://doi.org/10.1051/mattech/2019002
B.Mebarek, M.Keddam, H.Aboshighiba (2018) LS-SVM approach for modeling the growth kinetics of FeB and Fe2B layers formed on Armco iron, Ingénierie des Systèmes d'Information,23(5),29-41.https://doi.org/10.3166/isi.23.5.29-41
B.Mebarek, M.Keddam (2020) Fuzzy logic approach for modelling the formation kinetics of Fe2B layer, International Journal of Computational Materials Science and SurfaceEngineering,9(2),147-156. https://doi.org/10.1504/IJCMSSE.2020.109563
O.Belguendouz, B.Mebarek, Y.El Guerri, M.Keddam, N.Hadjadj, Y.Djafri (2023) Simple model and integral method for simulating the growth of the borided layer FeB/Fe2B on the AISI H13 steel, Zaštita materijala (Material Protection),64(4), 491-502. https://doi.org/10.5937/zasmat2304491B
V.I.Dybkov, W.Lengauer, K.Barmak(2005) Forma-tion of boride layers at the Fe-10% Cr alloy-boron interface, Journal of Alloys and Compounds, 398(1-2),113-122.https://doi.org/10.1016/j.jallcom.2005.02.033
G.Adomian (1998) A review of the decomposition method in applied mathematics, Journal of Mathematical Analysis and Applications 135(2), 501-544.https://doi.org/10.1016/0022-247X(88)90170-9
Y. Cherruault (1989) Convergence of Adomian's Method, Kybenetes, 18(2), 31-38.https://doi.org/10.1108/eb005812
G. Adomian (1990) A review of decomposition method and some recent results for nonlinear equations, Mathematical and Computer Modelling, 13(7) 17-43.https://doi.org/10.1016/0895-7177(90)90125-7
K. Abbaoui and Y. Cherruault (1994) Convergence of Adomian's Method Applied to Differential Equations, Computers & Mathematics with Applications,28(5),103-109.https://doi.org/10.1016/0898-1221(94)00144-8
H. Fatoorehchia and R. Rach(2021) Decomposition Solution for Nonlinear Model Describing Diffusional Growth of Intermetallic Layers, Acta Physica Polonica A, 1(140),91-96.https://doi.org/10.12693/APhysPolA.140.91