Skip to main content
Log in

Simulation of the Growth Kinetics of FeB and Fe2B Layers on AISI D2 Steel by the Integral Method

  • STRUCTURE, PHASE TRANSFORMATIONS, AND DIFFUSION
  • Published:
Physics of Metals and Metallography Aims and scope Submit manuscript

Abstract

In the present study, a new diffusion model based on the integral method was suggested to investigate the boriding kinetics of pack-borided AISI D2 steel. This diffusion model considered the effect of boride incubation time of the total boride layer (FeB + Fe2B). Firstly, the diffusion coefficients of boron in the FeB and Fe2B layers were estimated using a simple approach derived from the integral method. Secondly, the values of boron activation energies for the FeB and Fe2B layers were determined and compared with the literature data. The formulated diffusion model has been validated by using additional boriding conditions. The total boride layer thicknesses, obtained experimentally at 1243 K for 2, 4 and 6 h, were compared to the predicted thicknesses. Finally, a good agreement was observed between the experimental and the predicted results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1.
Fig. 2.
Fig. 3.

Similar content being viewed by others

REFERENCES

  1. A. K. Sinha, “Boriding (boronizing) of steels,” J. Heat Treat. 437, 437–446 (1991).

    Google Scholar 

  2. M. Ortiz-Domínguez, M. Elias-Espinosa, M. Keddam, O. A. Gómez-Vargas, R. Lewis, E. E. Vera-Cárdenas, and J. Zuno-Silva, “Growth kinetics and mechanical properties of Fe2B layers formed on AISI D2 steel,” Indian J. Eng. Mater. Sci. 22, 231–243 (2015).

    Google Scholar 

  3. M. Elias-Espinosa, M. Ortiz-Domínguez, M. Keddam, O. A. Gómez-Vargas, A. Arenas-Flores, F. R. Barrientos-Hernández, R. West Anthony, and C. Sinclair Derek, “Boriding kinetics and mechanical behaviour of AISI O1 steel,” Surf. Eng. 31, 588–597 (2015).

    Article  Google Scholar 

  4. R. Kouba, M. Keddam, and M. Kulka, “Modelling of paste boriding process,” Surf. Eng. 31, 563–569 (2015).

    Article  Google Scholar 

  5. M. Ortiz-Domínguez, J. Zuno-Silva, M. Keddam, O. Damián-Mejía, and M. Elias-Espinosa, “Diffusion model and characterisation of Fe2B layers on AISI 1018 steel,” J. Surf. Sci. Eng. 9, 281–297 (2015).

    Article  Google Scholar 

  6. I. Campos-Silva, M. Ortiz-Dominguez, H. Cimenoglu, R. Escobar-Galindo, M. Keddam, M. Elias-Espinosa, and N. López-Perrusquia, “Diffusion model for growth of Fe2B layer in pure iron,” Surf. Eng. 27, 189–195 (2011).

    Article  Google Scholar 

  7. Z. Nait Abdellah, M. Keddam, and A. Elias, “Evaluation of the effective diffusion coefficient of boron in the Fe2B phase in the presence of chemical stresses,” Int. J. Mater. Res. 104, 260–265 (2013).

    Article  Google Scholar 

  8. M. Keddam, “Computer simulation of monolayer growth kinetics of Fe2B phase during the paste-boriding process: Influence of the paste thickness,” Appl. Surf. Sci. 253, 757–761 (2006).

    Article  Google Scholar 

  9. M. Keddam, M. Ortiz-Domínguez, I. Campos-Silva, and J. Martínez-Trinidad, A simple model for the growth kinetics of Fe2B iron boride on pure iron substrate, Appl. Surf. Sci. 256, 3128–3132 (2010).

    Article  Google Scholar 

  10. M. Bendaoud, D. Madouri, A. Zanoun, and A. Belaidi, “Simulation model of monolayer growth kinetics of Fe2B phase,” Matér. Techn. 103 (7), 703 (2015).

    Google Scholar 

  11. Z. Nait Abdellah, M. Keddam, R. Chegroune, B. Bouarour, H. Lillia, and A. Elias, “Simulation of the boriding kinetics of Fe2B layers on iron substrate by two approaches,” Matér. Techn. 100, 581–588 (2012).

    Google Scholar 

  12. I. Campos-Silva, N. López-Perrusquia, M. Ortiz-Domínguez, U. Figueroa-López, O. A. Gómes-Vargas, A. Meneses-Amador, and G. Rodríguez-Castro, “Characterization of boride layers formed at the surface of gray cast irons,” Kovove Mater. 47, 75–81 (2009).

    Google Scholar 

  13. M. Keddam, M. Ortiz-Domínguez, O. A. Gómez-Vargas, A. Arenas-Flores, M. A. Flores-Rentería, M. Elias-Espinosa, and A. García-Barrientos, “Kinetic study and characterization of borided AISI 4140 steel,” Mater. Technol. 49, 665–672 (2015).

    Google Scholar 

  14. I. Campos, M. Islas, E. González, P. Ponce, and G. Ramírez, “Use of fuzzy logic for modeling the growth of Fe2B boride layers during boronizing,” Surf. Coat. Technol. 201, 2717–2723 (2006).

    Article  Google Scholar 

  15. I. Campos, M. Islas, G. Ramírez, C. VillaVelázquez, and C. Mota, “Growth kinetics of borided layers: Artificial neural network and least square approaches,” Appl. Surf. Sci. 253, 6226–6231 (2007).

    Article  Google Scholar 

  16. M. Bendaoud, A. Zanoun, and A. Rais, “Comparaison de deux approches numériques pour le traitement de boruration thermochimique de l’acier XC38,” Metall. Res. Technol. 113, 104 (2016).

    Article  Google Scholar 

  17. M. Kulka, N. Makuch, A. Pertek, and L. Maldzinski, “Simulation of the growth kinetics of boride layers formed on Fe during gas boriding in H2–BCl3 atmosphere,” J. Solid State Chem. 199, 196–203 (2013).

    Article  Google Scholar 

  18. I. Campos-Silva, M. Ortiz-Dominguez, C. Tapia-Quintero, G. Rodríguez-Castro, M. Y. Jiménez-Reyes, and E. Chávez-Gutiérrez, “Kinetics and boron diffusion in the FeB/Fe2B layers formed at the surface of borided high-alloy steel,” J. Mater. Eng. Perform. 21, 1714–1723 (2012).

    Article  Google Scholar 

  19. M. Keddam, Z. Nait Abdellah, M. Kulka, and R. Chegroune, “Determination of the diffusion coefficients of boron in the FeB and Fe2B layers formed on AISI D2 steel,” Acta Phys. Pol., A 128, 740–745 (2015).

    Article  Google Scholar 

  20. Z. Nait Abdellah and M. Keddam, “Estimation of the boron diffusion coefficients in FeB and Fe2B layers during the pack-boriding of a high-alloy steel,” Mater. Technol. 48, 237–242 (2014).

    Google Scholar 

  21. L. G. Yu, X. J. Chen, K. A. Khor, and G. Sundararajan, “FeB/Fe2B phase transformation during SPS pack-boriding: Boride layer growth kinetics,” Acta Mater. 53, 2361–2368 (2005).

    Article  Google Scholar 

  22. I. Campos-Silva, R. Tadeo-Rosas, H. D. Santos-Medina, and C. Lopez-Garcıa, Boride layers: growth kinetics and mechanical characterization, encyclopedia of iron, steel, and their alloys, Five-Volume Set, Eds. R. Colás, G. E. Totten (2015). doi 10.1081 / E-EISA-120052666.

  23. I. Campos-Silva, M. Ortiz-Domínguez, O. Bravo-Bárcenas, M. A. Doñu-Ruiz, D. Bravo-Bárcenas, C. Tapia-Quintero, and M. Y. Jiménez-Reyes, “Formation and kinetics of FeB/Fe2B layers and diffusion zone at the surface of AISI 316 borided steels,” Surf. Coat. Technol. 205, 403–412 (2010).

    Article  Google Scholar 

  24. E. Chavez–Gutiérrez, Endurecimiento superficial por diffusion de boro en un acero AISI D2: Caracterizacion mecanica y cinética de crecimiento do compuestos FeB y Fe 2 B, Master thesis (IPN, Mexico, 2012) [in Spanish].

  25. M. Keddam, M. Kulka, N. Makuch, A. Pertek, and L. Małdziński, “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. 298, 155–163 (2014).

    Article  Google Scholar 

  26. B. Sarma, N. M. Tikekar, and K. S. Ravi Chandran, “Kinetics of growth of superhard boride layers during solid state diffusion of boron into titanium,” Ceram. Int. 38, 6795–6805 (2012).

    Article  Google Scholar 

  27. B. Sarma, and K. S. Ravi Chandran, “Accelerated kinetics of surface hardening by diffusion near phase transition temperature: Mechanism of growth of boride layers on titanium,” Acta Mater. 59, 4216–4228 (2011).

    Article  Google Scholar 

  28. M. Keddam, S. Taktak, and S. Tasgetiren, “A diffusion model for the titanium borides on pure titanium,” Surf. Eng. 32, 802–808 (2016).

    Article  Google Scholar 

  29. M. Makuch, M. Kulka, M. Keddam, S. Taktak, V. Ataibis, and P. Dziarski, “Growth kinetics and some mechanical properties of two-phase boride layers produced on commercially pure titanium during plasma paste boriding,” Thin Solid Films. 626, 25–37 (2017).

    Article  Google Scholar 

  30. M. Keddam and S. Taktak, “Characterization and diffusion model for the titanium boride layers formed on the Ti6Al4V alloy by plasma paste boriding,” Appl. Surf. Sci. 399, 229–236 (2017).

  31. I. Campos-Silva, D. Bravo-Bárcenas, A. Meneses-Amador, M. Ortiz-Dominguez, H. Cimenoglu, U. Figueroa-López, and J. Andraca-Adame, “Growth kinetics and mechanical properties of boride layers formed at the surface of the ASTM F-75 biomedical alloy,” Surf. Coat. Technol. 237, 402–414 (2013).

    Article  Google Scholar 

  32. F. Leon Cazares, A. Jimenez Ceniceros, J. Oseguera Pena, and F. Castillo Aranguren, “Modeling surface processes and kinetics of compound layer formation during plasma nitriding of pure iron,” Rev. Mex. Fis. 60, 257–268 (2014).

    Google Scholar 

  33. F. Castillo, J. Oseguera, A. Gómez, and A. Fraguela, “Mathematical simulation of the layer growth kinetics during post-discharge nitriding: From early stage to quasi-steady stage,” Surf. Coat. Technol. 203, 876–882 (2008).

    Article  Google Scholar 

  34. U. Ascher and L. Petzold, Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations (SIAM, Philadelphia, 1998).

    Book  Google Scholar 

  35. W. H. Press, B. P. Flannery, and S. A. Teukolsky, Numerical Recipes in Pascal: The Art of Scientific Computing (Cambridge University, 1989).

    Google Scholar 

  36. M. Elias-Espinosa, M. Ortiz-Domínguez, M. Keddam, M. A. Flores-Rentería, O. Damián-Mejía, J. Zuno-Silva, J. Hernández-Ávila, E. Cardoso-Legorreta, and A. Arenas-Flores, “Growth kinetics of the Fe2B layers and adhesion on armco iron substrate,” J. Mater. Eng. Perform. 23, 2943–2952 (2014).

    Article  Google Scholar 

  37. M. Ortiz-Domínguez, M. Keddam, M. Elias-Espinosa, O. Damián-Mejía, M. A. Flores-Rentería, A. Arenas-Flores, and J. Hernández-Ávila, “Investigation of boriding kinetics of AISI D2 steel,” Surf. Eng. 30, 490–497 (2014).

    Article  Google Scholar 

  38. K. Genel, “Boriding kinetics of H13 steel,” Vacuum 80, 451–457 (2006).

    Article  Google Scholar 

  39. M. Keddam and M. Kulka, “A kinetic model for the boriding kinetics of AISI D2 steel during the diffusion annealing process,” Prot. Met. Phys. Chem. Surf. 54, 282–290 (2018).

    Article  Google Scholar 

  40. P. Goeuriot, R. Fillit, F. Thevenot, J. H. Driver, and H. Bruyas, “The influence of alloying element additions on the boriding of steels,” Mater. Sci. Eng. 55, 9–19 (1982).

    Article  Google Scholar 

  41. M. Carbucicchio and G. Palombarini, “Effects of alloying elements on the growth of iron boride coatings,” J. Mater. Sci. Lett. 6, 1147–1149 (1987).

    Article  Google Scholar 

  42. K. Matiasovsky, M. Chrenkova-Paucirova, P. Fellner, and M. Makyta, “Electrochemical and thermochemical boriding in molten salts,” Surf. Coat. Technol. 35, 133–149 (1988).

    Article  Google Scholar 

  43. C. Martini, C. Palombarini, and M. Carbucicchio, “Mechanism of thermochemical growth of iron borides on iron,” J. Mater. Sci. 39, 933–937 (2004).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. Keddam.

Additional information

1The article is published in the original.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Keddam, M., Kulka, M. Simulation of the Growth Kinetics of FeB and Fe2B Layers on AISI D2 Steel by the Integral Method. Phys. Metals Metallogr. 119, 842–851 (2018). https://doi.org/10.1134/S0031918X18090065

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0031918X18090065

Keywords:

Navigation