Abstract
An algorithm for modeling the evolution of a monodispersed ensemble of precipitates of a variable composition during heat treatment has been developed. In this algorithm, we for the first time have simultaneously taken into consideration the effect of diffusion processes in particles on their evolution kinetics, as well as the multicomponent nature of the alloy, and diffusion interaction between the components. The proposed method is based on the simultaneous solution of a set of diffusion equations and the balance and thermodynamic equations. A qualitative comparison of the results of calculations of the variation of the carbonitride-precipitate composition over the depth of precipitates upon heat treatment with available experimental data has been performed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. V. Popov and I. I. Gorbachev, “Simulation of the Evolution of Precipitates in Multicomponent Alloys,” Fiz. Met. Metalloved. 95(5), 16–25 (2003) [Phys. Met. Metallogr. 95, 417–426 (2003)].
V. V. Popov, I. I. Gorbachev, and J. A. Alyabieva, “Simulation of VC Precipitate Evolution in Steels with Consideration for the Formation of New Nuclei,” Philos. Mag. 85(22), 2449–2467 (2005).
L. Meyer, H. E. Buhler, and F. Heisterkamp, “Metallkundliche Untersuchungen zur Wirkungsweise von Titan in unlegierten Baustahlen,” Arch. Eisenhuttehw. 43(11), 823–832 (1972).
M. Hillert and L.-I. Staffonsson, “The Regular Solution Model for Stoichiometric Phases and Ionic Melts,” Acta Chem. Scand. 24(10), 3618–3626 (1970).
B. Sundman and J. Agren, “A Regular Solution Model for Phase with Several Components and Sublattices, Suitable for Computer Applications,” J. Phys. Chem. Solids 42(4), 297–301 (1981).
V. V. Popov, “Simulation of Dissolution of Carbide and Nitride Precipitates in Austenite,” Fiz. Met. Metalloved. 84(4), 39–52 (1997) [Phys. Met. Metallogr. 84, 349–358 (1997)].
V. V. Popov, “Numerical Simulation of Diffusion Interaction between Precipitates and the Matrix in Multicomponent Systems,” Izv. Ross. Akad. Nauk, Met., No. 2, 129–138 (1997).
V. F. Shatinskii and A. N. Nesterenko, Protective Diffusion Coatings (Naukova Dumka, Kiev, 1988) [in Russian].
T. G. Vozmishcheva and I. A. Murtazin, “Numerical Solution of Thermoduffusion Problem with Various Boundary Conditions,” Fiz. Met. Metalloved., No. 6, 105–109 (1988).
Ya. D. Kogan and A. A. Bulgach, “Computer Simulation of the Kinetics of Diffusion Saturation upon Gas Nitriding,” Metalloved. Term. Obrab. Met., No. 1, 10–20 (1974).
W. D. Murray and F. Landis, “Numerical and Machine Solution of Transient Heat Conduction Problems Involving Melting or Freezing,” Trans. ASME, Ser. C: J. Heat Transfer 2(2), 106–112 (1959).
E. N. Akimova, I. I. Gorbachev, and V. V. Popov, “Solving Multicomponent Diffusion Problems Using Parallel Algorithm of the Matrix “Progonka” Method. Mathematical Modeling,” Mat. Model. 17(9), 85–92 (2005).
V. V. Popov, Simulation of Transformations in Carbonitrides upon Heat Treatment of Steels (Ural. Otd. Ross. Akad. Nauk, Ekaterinburg, 2003) [in Russian].
M. Y. Wey, T. Sakuma, and T. Nishizawa, “Growth of Alloy Carbide Particles in Austenite,” Trans. JIM 22(10), 733–742 (1981).
M. I. Gol’dshtein and V. V. Popov, Solubility of Interstitial Phases in Steels upon Heat Treatment (Metallurgiya, Moscow, 1989) [in Russian].
V. V. Popov, M. L. Lobanov, and A. O. Khomenko, “Diffusion Interaction between Titanium Carbonitrides and Iron,” Fiz. Khim. Obrab. Mater. 76(5), 156–162 (1993).
J. H. Swisher, “Sulfur Solubility and Internal Sulfidation of Iron-Titanium Alloys,” Trans. AIME 242(12), 2433–2439 (1968).
L. S. Lyakhovich, L. G. Voroshkin, and B. M. Khusid, “Study of Diffusion Mass Transfer in Multicomponent Solutions,” Izv. Akad. Nauk BSSR, Ser. Fiz. Energ. Nauk, No. 4, 116–122 (1976).
J. Agren, “A Revised Expression for the Diffusivity of Carbon in Binary Fe-C Austenite,” Scr. Metall. 20(11), 1507–1510 (1986).
P. Grieveson and E. T. Turkdogan, “Kinetics of Reaction of Gaseous Nitrogen with Iron: I. Kinetics of Nitrogen Solution in γ-Iron,” Trans. Metall. Soc. AIME 230(3), 407–414 (1964).
J.-O. Anderson and J. Agren, “Models for Numerical Treatment of Multicomponent Diffusion in Simple Phases,” J. Appl. Phys. 72(4), 1350–1355 (1992).
F. J. J. Van Loo and G. F. Bastin, “On the Diffusion of Carbon in Titanium Carbide,” Metall. Trans. A 20A(3), 403–411 (1989).
Yu. F. Levinskii, Yu. D. Stroganov, S. E. Salibekov, et al., “Diffusion of Nitrogen in Titanium,” Izv. Akad. Nauk SSSR, Neorg. Mater. 4(12), 2068–2073 (1968).
Author information
Authors and Affiliations
Additional information
Original Russian Text © I.I. Gorbachev, V.V. Popov, E.N. Akimova, 2006, published in Fizika Metallov i Metallovedenie, 2006, Vol. 102, No. 1, pp. 694–704.
Rights and permissions
About this article
Cite this article
Gorbachev, I.I., Popov, V.V. & Akimova, E.N. Computer simulation of the diffusion interaction between carbonitride precipitates and austenitic matrix with allowance for the possibility of variation of their composition. Phys. Metals Metallogr. 102, 18–28 (2006). https://doi.org/10.1134/S0031918X06070039
Received:
Issue Date:
DOI: https://doi.org/10.1134/S0031918X06070039