Adomian decomposition method for modelling the growthof FeB/Fe2B layer in boronizing process
DOI:
https://doi.org/10.62638/ZasMat1090Abstract
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.
Keywords:
Adomian decomposition method, Diffusion, Boronizing, kinetic simulation, ModelReferences
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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: https://doi.org/10.12693/APhysPolA.140.91
Downloads
Published
Issue
Section
