Simulation of the incubation time for the formation of (FeB/Fe2B) bilayer on pure iron

Mebarek, B.; Keddam, M.; Kulka, M.

doi:10.2478/kom-2021-0006

Abstract

In this work, a mathematical model was used in order to study the growth kinetics of (Fe₂B/FeB) bilayer during bori-ding process basing on the second Fick’s law and mass balance equation. The run of the numerical simulation allowed calculating the incubation time (τ) of each boronized layer (Fe₂B or FeB), and estimating the effect of this parameter on the growth of the boronized layer. The boride incubation time for forming the FeB or Fe₂B layer on the pure iron substrate was incorporated into the present mathematical model. To simulate the value of the growth rate constant and the incubation time for the bilayer configuration, the experimental data available in the literature concerning the boronizing of pure iron were considered. Based on the experimental and simulation results, it was shown that the incubation time decreases with increasing temperature in the FeB and Fe₂B phases.

It was concluded from this study that the thickness of each boride layer depended on its growth rate constant and on another parameter k_τ which was the rate constant of incubation time.The obtained results confirmed the validity of the present mathematical model and gave a good estimate of the incubation time during the formation of each boride layer as well as formulated the variation of this parameter with a mathematical equation. Furthermore, the comparison of experimental data with the simulated results of boronized layer thickness allowed to validate the present model.

References

1. Matuschka A. G. Boronizing, Hayden and Son Inc, Philadelphia, 1980.
Search in Google Scholar Back to article
2. Sinha A. K. Boronizing, ASM Handbook, OH, USA, J. Heat. Treat 1999, 4, 437-447.
Search in Google Scholar Back to article
3. Kulka M. Current Trends in Boriding. Techniques, Engineering Materials book series, Springer International Publishing, 2019.10.1007/978-3-030-06782-3
Search in Google Scholar Back to article
4. Mebarek B. et al. Simulation model of monolayer growth kinetics of Fe2B phase, Matériaux et Techniques 2015, 103, 703-710.10.1051/mattech/2015058
Search in Google Scholar Back to article
5. Mebarek B. et al. Simulation model to study the thermochemical boriding of stainless steel “AISI 316” (X5CrNiMo17-12-2). Matériaux et Techniques 2012, 100, 167-175.10.1051/mattech/2012009
Search in Google Scholar Back to article
6. Allaoui O. et al. Characterization of boronized layers on a XC38 steel, Surf Coat Tech 2006, 201, 3475-3482.10.1016/j.surfcoat.2006.07.238
Search in Google Scholar Back to article
7. Mebarek B. et al. Effect of boride incubation time during the formation of Fe2B phase, Materials Research 2017. https://dx.doi.org/10.1590/1980-5373-mr-2017-064710.1590/1980-5373-mr-2017-0647
Search in Google Scholar Back to article
8. Campos-Silva I. et al. Formation and kinetics of FeB/Fe2B layers and diffusion zone at the surface of AISI 316 borided steels, Surf. Coat. Technol 2010, 205, 403-412.10.1016/j.surfcoat.2010.06.068
Search in Google Scholar Back to article
9. Dong X. et al. Microstructure and Properties of Boronizing Layer of Fe-based Powder Metallurgy Compacts Prepared by Boronizing and Sintering Simultaneously, Science of Sintering 2009, 41, 199-207.10.2298/SOS0902199D
Search in Google Scholar Back to article
10. Karakaş M.S. et al. boride layer growth kinetics of AISI H13 steel borided with nano-sized powders, Arch. Metall. Mater 2018, 63, 159-165.
Search in Google Scholar Back to article
11. Bartkowska A. et al. the influence of the laser beam fluence on change in microstructure, microhardness and phase composition of FeB-Fe2B surface layers produced on vanadis-6 steel, Arch. Metall. Mater 2018, 63,791-800.
Search in Google Scholar Back to article
12. Azouani O. et al. Diffusion kinetics of boron in the X200 CrMoV12 high-alloy steel, J. Min. Metall. Sect. B-Metall 2015, 51 (1), 49-54.10.2298/JMMB140404009A
Search in Google Scholar Back to article
13. Kul M. et al. Effect of boronizing compositions on boride layer of boronized GGG-60 ductile cast iron, Vacuum 2016, 126, 80-83.10.1016/j.vacuum.2016.01.021
Search in Google Scholar Back to article
14. Keddam M., Chentouf S.M. A diffusion model for describing the bilayer growth (FeB/Fe2B) during the iron powder-pack boriding, Appl.Surf.Sci 2005,252,393-399.10.1016/j.apsusc.2005.01.016
Search in Google Scholar Back to article
15. Ortiz-Domínguez M. et al. A kinetic model for analyzing the growth kinetics of Fe2B layers in AISI 4140 steel, Kovove Mater 2010,48,285-290.10.4149/km_2010_5_285
Search in Google Scholar Back to article
16. Mebarek B. et al. “Comparaison de deux approches numériques pour le traitement de boruration thermochimique de l’acier XC38,” Metall. Res. Technol 2016, 113, 104.10.1051/metal/2015046
Search in Google Scholar Back to article
17. Brakman C. M. et al. Boronizing of Fe and Fe–C,Fe–Cr and Fe–Ni alloys : boride-layer growth kinetics, J. Mater. Res. 1989, 4, 1354-1370.
Search in Google Scholar Back to article
18. Campos I. et al. Kinetic study of boron diffusion in the paste-boriding process, Mater. Sci. Eng. A 2003, 352, 261-265.10.1016/S0921-5093(02)00910-3
Search in Google Scholar Back to article
19. Keddam M. et al. Modeling of the Growth Kinetics of Boride Layers during the Diffusion Annealing Process, Physics of Metals and Metallography 2018, 119, 927-935.10.1134/S0031918X1810006X
Search in Google Scholar Back to article
20. Keddam M. A diffusion model for the Fe2B layers formed on a ductile cast iron, Acta Physica Polonica A 2018, 133, 1174-117710.12693/APhysPolA.133.1174
Search in Google Scholar Back to article
21. Raden Dadan Ramdan, Tomohiro Takaki and Yoshihiro Tomita, Free energy problem for the simulations of the growth of Fe2B phase using phase-field method, Materials Transactions 2008, 49, 2625-2631.10.2320/matertrans.MRA2008158
Search in Google Scholar Back to article
22. Kubaschewski O. Iron-Binary Phase Diagrams, Springer Verlag, Berlin, 1982.
Search in Google Scholar Back to article
23. Casadesus P., Frantz C. La boruration du fer et des aciers par bombardement ionique avec le diborane, Mémoire scientifiques de la revue de métallurgie 1978, 81-91.
Search in Google Scholar Back to article
24. Keddam M. et al. The effective diffusion coefficient of boron in the Fe2B layers formed on the iron substrate, MATEC Web of Conferences 2013, 3, 01012.10.1051/matecconf/20130301012
Search in Google Scholar Back to article
25. Kulka M. et al. Simulation of the growth kinetics of boride layers formed on Fe during gas boriding in H2–BCl3 atmosphere, Journal of Solid State Chemistry 2013, 199, 196–203.10.1016/j.jssc.2012.12.029
Search in Google Scholar Back to article
26. Keddam M. et al. A kinetic model for estimating the boron activation energies in the FeB and Fe2B layers during the gas-boriding of Armco iron: Effect of boride incubation times, Appl Surf Sci 2014, 298, 155-163.10.1016/j.apsusc.2014.01.151
Search in Google Scholar Back to article
27. Guiraldenq P. Diffusion dans les métaux, Techniques de l’ingénieur MB1 (M 55), 1978.
Search in Google Scholar Back to article
28. Keddam M., A simple model for the growth kinetics of Fe2B iron boride on iron substrate, Applied Surface Science 2010, 256, 3128-3132.10.1016/j.apsusc.2009.11.085
Search in Google Scholar Back to article
29. Campos-Silva I. Properties and Characterization of Hard Coatings obtained by Boriding: An Overview, Defect and Diffusion Forum 2010, 297, 1284-1289.10.4028/www.scientific.net/DDF.297-301.1284
Search in Google Scholar Back to article
30. Nait Abdellah Z., Keddam M. Estimation of the boron diffusion coefficients in FeB and Fe2B layers during the pack-boriding of a high-alloy steel, MTAEC 2014, 48, 237.
Search in Google Scholar Back to article
31. Keddam M. and Kulka M. Simulation of the Growth Kinetics of FeB and Fe2B Layers on AISI D2 Steel by the Integral Method, Physics of Metals and Metallography 2018, 119, 842–851.10.1134/S0031918X18090065
Search in Google Scholar Back to article
32. Keddam M. et al. Determination of the Diffusion Coefficients of Boron in the FeB and Fe2B Layers Formed on AISI D2 Steel, Acta physica polonica A 2015, 128, 740-745.10.12693/APhysPolA.128.740
Search in Google Scholar Back to article

Simulation of the incubation time for the formation of (FeB/Fe2B) bilayer on pure iron

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