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L. F. Spevak, O. A. Nefedova, A. V. Makarov, G. V. Samoilova


DOI: 10.17804/2410-9908.2015.6.068-079

Two mathematical models of diffusion are discussed as applied to the description of ion nitriding of austenitic stainless steel in electron beam plasma. One model is based on the assumption of the diffusion coefficient dependent on concentration, and this corresponds to the nonlinear boundary value problem of diffusion. The other model takes into account the effect of internal stresses, occurring in the surface layer and induced by introduced nitrogen atoms, on the diffusion process, and this leads to the inhomogeneous boundary value problems of diffusion. Algorithms for solving the boundary value problems are proposed, which are based on the boundary element method. Model examples have been solved to illustrate the functioning of the algorithms.

Keywords: mathematical modelling, nitrogen diffusion, plasma nitriding, boundary element method


  1. Berlin E.V., Koval N.N., Seidman L.A. Plazmennaya khimiko-termicheskaya obrabotka poverkhnosti stalnykh detalei [Plasma Thermochemical Treatment of Steel Part Surfaces]. Moscow, Tekhnosfera Publ., 2012, 464 p. (In Russian).
  2. Gavrilov N.V., Mamaev A.S. A Method for Plasma Nitriding of a Steel or Non-Ferrous Product. Russ. Federation Patent 2009100619/02. (In Russian).
  3. Gavrilov N.V., Men’shakov A.I. A source of broad electron beams with a self-heated hollow cathode for plasma nitriding of stainless steel. Instruments and Experimental Techniques, 2011, vol. 54, no. 5, pp. 732–739. DOI: 10.1134/S0020441211050046.
  4. Gavrilov N.V., Menshakov A.I. Low-temperature nitriding of stainless steel in electron beam plasma at 400 ºС. Fizika i khimiya obrabotki materialov, 2012. no. 5, pp. 31–36. (In Russian).
  5. Lo K.H., Shek C.H., Lai J.K.L. Recent developments in stainless steels. Materials Science and Engineering: R: Reports, 2009, vol. 65, iss. 4–6, pp. 39–104. DOI: 10.1016/j.mser.2009.03.001.
  6. Laleh M., Kargar F., Velashjerdi M. Low-Temperature Nitriding of Nanocrystalline Stainless Steel and Its Effect on Improving Wear and Corrosion Resistance. Journal of Material Engineering and Performance, 2013, vol. 22, iss. 5, pp. 1304–1310. DOI: 10.1007/s11665-012-0417-7.
  7. Makarov A.V., Skorynina P.A., Osintseva A.L., Yurovskikh A.S., Savray R.A. Improving the tribological properties of austenitic steel 12Kh18N10T by nanostructuring frictional treatment. Obrabotka metallov: tekhnologiya, oborudovanie, instrumenty, 2015, vol. 69, no. 4, pp. 80–92. (In Russian).
  8. Tikhonov A.N., Samarsky A.A. Uravneniya matematicheskoy fiziki [Equations of Mathematical Physics]. M., Moscow University Publ., 1999, 799 p. (In Russian).
  9. Brebbia C.A., Telles J.F.C., Wrobel L.C. Boundary Element Techniques. Berlin, Neidelberg, New-York, Tokyo, Springer–Verlag, 1984, 466 p. DOI: 10.1007/978-3-642-48860-3.
  10. Fedotov V.P., Spevak L.F. Modifitsirovannyi metod granichnykh elementov v zadachakh mekhaniki, teploprovodnosti i diffuzii [A Modified Boundary Element Method in Problems of Mechanics, Heat Conduction and Diffusion]. Ekaterinburg, UrO RAN Publ., 2009, 164 p. (In Russian).
  11. Christiansen T., Somers M.A.J. Avoiding ghost stress on reconstruction of stress- and composition-depth profiles from destructive X-ray diffraction depth profiling. Materials Science and Engineering: A, 2006, vol. 424, iss. 1–2, pp. 181–189. DOI: 10.1016/j.msea.2006.03.007.
  12. Galdikas A., Moskalioviene T. Stress induced nitrogen diffusion during nitriding of austenitic stainless steel. Computational Materials Science, 2010, vol. 50, iss. 2, pp. 796–799. DOI: 10.1016/j.commatsci.2010.10.018.
  13. Galdikas A., Moskalioviene T. Modeling of stress induced nitrogen diffusion in nitrided stainless steel. Surface & Coatings Technology, 2011, vol. 205, iss. 12, pp. 3742–3746. DOI: 10.1016/j.surfcoat.2011.01.040.
  14. Moskalioviene T., Galdikas A. Stress induced and concentration dependent diffusion of nitrogen in plasma nitrided austenitic stainless steel. Vacuum, 2012, vol. 86, iss. 10, pp. 1552–1557. DOI: 10.1016/j.vacuum.2012.03.026.
  15. Moskalioviene T., Galdikas A., Rivière J.P., Pichon L. Modeling of nitrogen penetration in polycrystalline AISI 316L austenitic stainless steel during plasma nitriding. Surface & Coatings Technology, 2011, vol. 205, iss. 10, pp. 3301–3306. DOI: 10.1016/j.surfcoat.2010.11.060.
  16. Christiansen T.L., Somers M.A.J. Stress and Composition of Carbon Stabilized Expanded Austenite on Stainless Steel. Metallurgical and Materials Transactions A, 2009, vol. 40, iss. 8, pp. 1791–1798. DOI: 10.1007/s11661-008-9717-9.
  17. Christiansen T.L., Somers M.A.J. The Influence of Stress on Interstitial Diffusion-Carbon Diffusion Data in Austenite Revisited. Defect and Diffusion Forum, 2010, vol. 297–301, pp. 1408–1413. DOI: 10.4028/www.scientific.net/DDF.297-301.1408.
  18. Fedorov A.A. Diffuziya azota v nerzhaveyushchei stali. Tekhnicheskie nauki v Rossii i za rubezhom. In: Technical Sciences in Russia and Abroad. Proceedings of the Third International Scientific Conference. Moscow, Buki-Vedi Publ., 2014, pp. 85–88. (In Russian).
  19. Einstein A. Sobranie nauchnykh trudov v chetyrekh tomakh. T. III. I.E. Tamm, Ya.A. Smorodinsky, B.G. Kuznetsov, ed. Raboty po kineticheskoy teorii, teorii izlucheniya i osnovam kvantovoi mekhaniki 1901-1955 [A Collection of Scientific Studies. Vol. III. I.E. Tamm, Ya.A. Smorodinsky, B.G. Kuznetsov, ed. Works on Kinetic Theory, Radiation Theory and Foundations of Quantum Mechanics]. M., Nauka Publ., 1966, pp. 108–117. (In Russian).
  20. Kazakov A.L., Spevak L.F. The boundary element method and the power series method in one-dimensional problems of nonlinear filtering. Izv. Irkutskogo gos. un-ta. Ser. Matematika, 2012, vol. 5, no. 2, pp. 2–17. (In Russian).
  21. Kazakov A.L., Spevak L.F. Numerical and analytical studies of a nonlinear parabolic equation with boundary conditions of a special form. Applied Mathematical Modelling, 2013, vol. 37, iss. 10–11, pp. 6918–6928. DOI: 10.1016/j.apm.2013.02.026.


Article reference

Mathematical Modelling of Plasma Nitriding of Austenitic Stainless Steel / L. F. Spevak, O. A. Nefedova, A. V. Makarov, G. V. Samoilova // Diagnostics, Resource and Mechanics of materials and structures. - 2015. - Iss. 6. - P. 68-79. -
DOI: 10.17804/2410-9908.2015.6.068-079. -
URL: http://eng.dream-journal.org/issues/2015-6/2015-6_65.html
(accessed: 06/22/2024).


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