Dybkov model for the estimation of boron diffusion in the FeB/Fe2B bilayer on AISI 316 steel

Authors

  • Naima Hadjadj 1Département Sciences de la Matière, Faculté des Sciences et Technologie, Université de Tissemsilt, BP 182, 38000 Tissemsilt, Algérie, 2Laboratoire d’Etudes Physique des Matériaux, Université des Sciences et de Technologies USTO-MB, BP 1505 El M’Naouar, Oran, Algérie Author
  • Bendaoud Mebarek Laboratoire de Recherche en Intelligence Artificielle et Systèmes (LRIAS), University of Tiaret, Algeria Author
  • Yassine El Guerri Research laboratory of industrial technologies, University of Tiaret, Algeria Author
  • Mourad Keddam Laboratoire de Technologie des Matériaux, Faculté de Génie Mécanique et Génie des Procédés, USTHB, B.P No. 32, 16111, El-Alia, Bab-Ezzouar, Alger, Algérie Author

DOI:

https://doi.org/10.62638/ZasMat1125

Keywords:

Boriding, diffusion, Iron borides, Dybkov model, Integral method

Abstract

The aim of this work is to apply three models to simulate the boron diffusion in AISI 316 steel, with an approach based on classical mass balance equations, the Dybkov model and the integral method. From the numerical solutions of both models, the predicted values of thickness have been compared to the experimental results. In addition, in order to improve the predictability of the two models, it is necessary to find precise measurements on the diffusion of boron in each phase. The comparison of experimental and theoretical results allows us to confirm the validity of both models. After validation, the root mean square error and the diffusion coefficient were calculated to achieve good performance and better accuracy. The comparison of the results from the two simulation models with confronted with the experimental data to verify the validity of this theoretical study. Finally, the comparison of the derived results gave the values of the root mean square error equal to 1.6μm for Fe2B and 0.75μm for FeB.

References

M.Kulka (2019) Current Trends in Boriding. Techniques, Engineering Materials book series, Springer International Publishing. https://doi.org/ 10.1007/978-3-030-06782-3

A.G.Matuschka (1980) Boronizing, Hayden and Son Inc, Philadelphia.

A.K.Sinha, N.Boronizing (1991) ASM Int. handbook, The Materials International Society, Materials Park, OH, USA, 4 ,437-447.

O.Allaoui, N.Bouaouadja, G.Saindernan (2006) Characterization of boronized layers on a XC38 steel, Surf. Coat. Tech. 201, 3475-3483. https://doi.org/10. 1016/ j.surfcoat.2006.07.238

S.A.Bouaziz, N.Boudaoud, A.Zanoun (2009) Boruration thermochimique d'un acier C38 dans un bain de sels borax-SiC, Matériaux et Techniques, 97, 253-261. https://doi.org/10.1051/mattech/2009036

M Keddam, SM Chentouf (2005) A diffusion model for describing the bilayer growth (FeB/Fe2B) during the ironpowder-packboriding ;Applied Surface Science, 252(2),393-399. https://doi.org/10.1016/j.apsusc.2005.01.016

B.Mebarek, D.Madouri, A.Zanoun, A.Belaidi (2015) Simulation model of monolayer growth kinetics of Fe2B phase, Matériaux et Techniques, 103, 703 . https://doi.org/10.1051/mattech/2015058

B.Mebarek, A.Benguelloula, A.Zanoun (2018) Efect of Boride Incubation Time During the Formation of Fe2B Phase, Materials Research, 21(1), 23-32. http://dx.doi.org/10.1590/1980-5373-MR-2017-0647.

L.G.Yu, X.J.Chen, K.A.Khor, G.Sundararajan (2005) FeB/Fe2B phase transformation during SPSpack-boronizing:Boride layer growth kinetics, Acta Materialia 53, 2361-2368. https://doi.org/10.1016/j.actamat.2005.01.043

B.Mebarek, M.Keddam, M.Kulka (2021) Simulation of the incubation time for the formation of (FeB/Fe2B) bilayer on pure iron , KOM – Corrosion and Material Protection Journal, 65(2)49-56. https://doi.org/10.2478/kom-2021-0006

B.Mebarek, S.A.Bouaziz, A.Zanoun (2012) Modèle de simulation pour l’étude de la boruration thermochimique de l’acier inoxydable «AISI 316» (X5CrNiMo17-12-2),Matériaux & Techniques,100, 167-175, https://doi.org/10.1051/mattech/2012009

S.Şahin (2009) Effects of boronizing process on the surface roughness and dimensions of AISI 1020, AISI 1040 and AISI 2714, Journal of Materials Processing Technology, 209(4),1736-1741, https://doi.org/10.1016/j.jmatprotec.2008.04.040

B.Mebarek (2012) thèse de doctorat, Ecole Nationale Polytechnique d'Oran Maurice Audin.

O.Delai, C.Xia, L.Shiqiang (2021) Growth kinetics of the FeB/Fe2B boride layer on the surface of 4Cr5MoSiV1 steel: experiments and modelling, Journal of Materials Research and Technology, 11, 1272-1280, https://doi.org/10.1016/j.jmrt. 2021. 01.109

M.X.Wei, S.Q.Wang, L.Wang, X.H.Cui, K.M.Chen (2011) Effect of tempering conditions on wear resistance in various wear mechanisms of H13 steel, Tribol Int, 44(7), 898-905, https://doi.org/ 10.1016/j.triboint.2011.03.005

A.Günen et al (2019) Properties and Corrosion Resistance of AISI H13 Hot-Work Tool Steel with Borided B4C Powders. Metals and Materials International. 26(9), 329-1340. doi.org/10.1007/ s12540-019-00421-0

I.E.Campos-Silva, G.A.Rodriguez-Castro (2015) Boriding to improve the mechanical properties and corrosion resistance of steels, in Thermochemical surface engineering of steels Elsevier. 651-702. https://doi.org/10.1533/9780857096524.5.651

B.Mebarek, M.Keddam (2019) Prediction model for studying the growth kinetics of Fe2B boride layers during boronizing. Ingénierie des Systèmes d’Information, 24(2), 201-205. https://doi.org/ 10.18280/isi.240212

S.Sahin, C.Meric (2002) Investigation of the effect of boronizing on cast irons, Materials Research Bulletin, 37(5), 971-979, https://doi.org/10. 1016/S0025-5408(02)00697-9.

B.Mebarek, M.Keddam, H.Boussebha (2020) Simulation model of the Growth Kinetics of Fe2B Layers with Consideration of the Boride Incubation Time Effect, Surface Review and Letters, 27(04), 1950127 https://doi.org/10.1142/S0218625X19501270

Ch.Kapfenberger, A.Barbara, P.Rainer, H.Hubert (2006) Structure refinements of iron borides Fe2B and FeB; ZeitschriftfürKristallographie - Crystalline Materials, 221(5-7), 477-481. https://doi.org/10. 1524/ zkri.2006.221.5-7.477

M.Keddam (2004) A kinetic model for the borided layers by the paste-boronizing process, Applied Surface Science, 236, 451-455. https://doi.org/ 10.1016/j.apsusc.2004.05.141

M.Keddam, M.Kulka (2018) Simulation of the growth kinetics of FeB and Fe2B layers on AISI D2 steel by the integral method. Physics of Metals and Metallography, 119(9), 842-851. doi.org/10.1134/S0031918X18090065

I.Campos, M.Islas, G.Ramírez, C. Villa Velázquez, C.Mota (2007) Growth kinetics of borided layers: Artificial neural network and least square appro-aches, Applied Surface Science, 253(14), 6226-6231, https://doi.org/10.1016/j.apsusc.2007.01.070

I.Campos-Silva, E.J.Hernández-Ramirez, A. Contreras-Hernández, J.L.Rosales-Lopez, E. Valdez-Zayas, I.Mejía-Caballero, J.Martínez-Trinidad (2021) Pulsed-DC powder-pack boriding: Growth kinetics of boride layers on an AISI 316 L stainless steel and Inconel 718 superalloy,Surface and Coatings Technology, 421, 127-404, https://doi.org/10.1016/j.surfcoat.2021.127404

B.Mebarek, M.Keddam (2018) A fuzzy neural network approach for modeling the growth kinetics of FeB and Fe2B layers during the boronizing process, Matériaux et Techniques, 06, 603-609. 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, Revue des Sciences et Technologie de l’information, 23 (5), 29-41. https://doi.org/10.3166/ISI.23.5.29-41

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. SolidState Phenomena. 138, 181-188.https://doi.org/10.4028/www.scientific.net/SSP.138.181

M. Keddam, B. Bouarour, Z.Nait Abdellah, R. Chegroune (2013) The effective diffusion coefficient of boron in the Fe2B layers formed on the iron substrate, MATEC Web of Conferences 3, 01012, doi.org/ 10.1051/matecconf/20130301012

S.Taktak (2006) A study on the diffusion kinetics of borides on boronized Cr-basedteels, J. Mater. Sci., 41, 7590–7596. https://doi.org/10.1007/s10853-006-0847-4

Y.ElGuerri, B.Mebarek, M.Keddam (2022) Impact of the diffusion coefficient calculation on predicting Fe2B boride layer thickness, KOM – Corrosion and Material Protection Journal, 66(1), 25-35. https://doi.org/10.2478/kom-2022-0005

J.S.Kirkaldy (1958) diffusion in multicomponent metallic systems: iii. The motion of planar phase interfaces, Can. J. Phys. 36 , 917-926.

T.R.Goodman (1964) Application of integral methods to transient nonlinear heat transfer. Adv. Heat Transfer, 1,51-122. https://doi.org/10.1016/ S0065-2717(08)70097-2

V.I.Dybkov (2010) Reaction Diffusion and Solid-State Chemical, Kinetics, 2nd ed., Trans Tech Publications, Zuerich.ISBN, 3038134457

V.I.Dybkov (2013) Chemical Kinetics, IPMS Publications, Kyiv, Free online version http://www.dybkov.kiev.ua

I.Campos-Silva, M.Ortiz-Domínguez, O.Bravo Bárcenas, M.A.Doñu-Ruiz, D.Bravo-Bárcenas, C. Tapia-Quintero, M.Y. Jiménez-Reyes (2010) Formation and kinetics of FeB/Fe2B layers and diffusion zone at the surface of AISI 316 borided steels, Surf. Coat.Technol. 205, 403-214. https://doi. org/10.1016/j.surfcoat.2010.06.068

I.Campos-Silva, M.Ortiz-Domínguez, C.Tapia-Quintero et al (2012) Kinetics and Boron Diffusion in the FeB/Fe2B Layers Formed at the Surface of Borided High-Alloy Steel. J. of MateriEng and Perform, 21, 1714–1723. https://doi.org/10.1007/ s11665-011-0088-9

Z.NaitAbellah, M.Keddam (2014) Estimation of the boron diffusion coefficients in the FeB and Fe2B layers during the pack-boriding of a high-alloy steel. Mater. Tehnol., 48, 237–242. http://mit.imt.si/ Revija/izvodi/mit142/abdellah.pdf

M.Keddam, M.Kulka ( 2020) Simulation of Boriding kinetics of AISID2 steel by using two different approaches, Met,Sci,Heat Treat; 61,756–763. https://doi.org/10.1007/s11041-020-00496-2

M.Keddam, R.Chegroune, M.Kulka, N.Makuch, D.Panfil, P.Siwak, S.Taktak (2018) Characterization tribological and mechanical properties of plasma paste boridedAISI 316 steel. Trans. Indian Inst. Met. 71, 79–90. doi:10.1007/s12666-017-1142-6

P.Orihel, M.Drienovský, Z.Gabalcová, P.Jurči, M.Keddam (2023) Characterization and Boron Diffusion Kinetics on the Surface-Hardened Layers of Royalloy Steel, Coatings, 13,113-122. https://doi.org/10.3390/coatings13010113

I.Campos, R.Torres, O.Bautista, G.Ramírez, L. Zúñiga (2006) Effect of boron paste thickness on the growth kinetics of polyphase boride coatings during the boriding process. Appl. Surf,Sci. 252, 2396–2403. http://dx.doi.org/10.1016/j.apsusc.2005. 04.022

T.B.Massalski, H.Okamoto, P.R.Subramanian, L. Kacprzak (1990) Binary Alloy Phase Diagrams, Eds. ASM,480. ISBN: 978-0-87170-403-0

M.Keddam (2011) Simulation of the growth kinetics of the (FeB/Fe2B) bilayer obtained on a borided stainless steel,Applied Surface Science, 257(6), 2004-2010, https://doi.org/10.1016/j.apsusc. 2010. 09.043

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15-06-2024

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