Simulation of Metal Surface Layer Modification by Nano-Particles upon Pulsed Induction Heating

The purpose of the study was to consider the applicability of high-frequency electromagnetic field for metal heating and melting with a view to its subsequent modification. Two-dimensional numerical simulation of the processes during the modification of the substrate surface metal layer was carried out. The substrate surface was covered with a layer of specially prepared nano-size refractory particles, which become active crystallization centers after the penetration into the melt. The proposed mathematical model is used to consider the processes including heating, phase transition and heat transfer in the molten metal, the nucleation and growth of the solid phase in the presence of a modifier material in the melt. The distribution of the electromagnetic energy in the metal is described by empirical formulae. The melting of the metal is considered at the Stephan's approximation, and during solidification all nano-size particles are assumed to be centers of volume-consecutive crystallization. The flow in the liquid is described by Navier — Stokes equations in Boussinesq approximation. Distribution of nanoparticles in the melt is simulated by moving markers. According to the results of numerical experiments, the flow structure in the melt was evaluated depending upon the amount of surface-active impurities in the metal. The modes of the induction-pulse action are detected: they promote creating the flows for the homogeneous distribution of modifying particles in the melt. Findings of the research show that application of pulses of high frequency electromagnetic field for heating and melting of metals allows modifying the metal deeper in comparison with the use of a laser. Characteristics of the volume and successive crystallization are considered, as well as the growth characteristics of the solid phase. The dimensions of the two-phase zone and the zone of the metastable state are estimated when the proportion of the crystalline phase increases very slowly and is practically close to zero

References

[1] Saburov V.P., Cherepanov A.N., Zhukov M.F., et al. Plazmokhimicheskiy sintez ultradispersnykh poroshkov i ikh primenenie dlya modifitsirovaniya metallov i splavov [Plasma chemical synthesis of ultradisperse powder and its application for metals and alloys modification]. Novosibirsk, Nauka Publ., 1995. 339 p.

[2] Cherepanov A.N., Popov V.N. Analysis of modification of the heat resistant alloy by nano-size refractory particles. Vestnik NGU. Seriya: Fizika [Vestnik NSU. Series: Physics], 2015, vol. 10, no. 3, pp. 97–102 (in Russ.).

[3] Montealegre M.A., Castro G., Rey P., Arias J.L., Vazquez P., Gonzalez M. Surface treatments by laser technology. Contemporary Materials, 2001, no. 1, pp. 19–30.

[4] Marusin M.V., Shchukin V.G., Marusin V.V. Surface alloying of carbon steel with Cu under high energy induction treatment. Fizika i khimiya obrabotki materialov [Physics and Chemistry of Materials Treatment], 2010, no. 5, pp. 67–70 (in Russ.).

[5] Marusin V.V. HF impulse hardening of parts. Obrabotka metallov, 2004, no. 2, pp. 14–15 (in Russ.).

[6] Solonenko O.P., Cherepanov A.N., Marusin V.V., Poluboyarov V.A. Combined technologies of emerging powder materials, coating and layer hardening with controlled nano- and micro-structure. Tyazheloe mashinostroenie, 2007, no. 10, pp. 10–13 (in Russ.).

[7] Vedenov A.A., Gladush G.G. Fizicheskie protsessy pri lazernoy obrabotke materialov [Physical processes in process of laser materials treatment]. Moscow, Energoatomizdat Publ., 1985. 208 p.

[8] He X., Fuerschbach P.W., DebRoy T. Heat transfer and fluid flow during laser spot welding of 304 stainless steel. Journal of Physics D: Applied Physics, 2003, vol. 36, no. 12, pp. 1388–1398. DOI: 10.1088/0022-3727/36/12/306

[9] Seyhan I., Egry I. The surface tension of undercooled binary iron and nickel alloys and the effect of oxygen on the surface tension of Fe and Ni. International Journal of Thermophysics, 1999, vol. 20, iss. 4, pp. 1017–1028. DOI: 10.1023/A:1022638400507

[10] Ribic B., Tsukamoto S., Rai R., DebRoy T. Role of surface active elements during keyhole mode laser welding. Journal of Physics D: Applied Physics, 2011, vol. 44, no. 48, pp. 5753–5766. DOI: 10.1088/0022-3727/44/48/485203

[11] Cherepanov A.N., Popov V.N. Numerical analysis of the influence of surface-active substance in the melt on the distribution of modifying particles and crystallization at the treatment of metal surface by a laser pulse. Thermophysics and Aeromechanics, 2014, vol. 21, iss. 3, pp. 355–363. DOI: 10.1134/S0869864314030093

[12] Donghua Dai, Dongdong Gu. Influence of thermodynamics within molten pool on migration and distribution state of reinforcement during selective laser melting of AlN/AlSi10Mg composites. International Journal of Machine Tools & Manufacture, 2016, vol. 100, pp. 14–24. DOI: 10.1016/j.ijmachtools.2015.10.004

[13] Sahoo P., DebRoy T., McNallan M.J. Surface tension of binary metal–surface active solute systems under conditions relevant to welding metallurgy. Metallurgical Transactions B, 1988, vol. 19, iss. 3, pp. 483–491. DOI: 10.1007/BF02657748

[14] Ehlen G., Ludwig A., Sahm P.R. Simulation of time-dependent pool shape during laser spot welding: Transient effects. Metallurgical and Materials Transactions A, 2003, vol. 34, iss. 12, pp. 2947–2961. DOI: 10.1007/s11661-003-0194-x

[15] Pavlov N.A. Inzhenernye teplovye raschety induktsionnykh nagrevateley [Engineering thermal calculation of induction heaters]. Moscow, Energiya Publ., 1978. 120 p.

[16] Budak B.M., Soboleva E.N., Uspenskii A.B. A difference method with coefficient smoothing for the solution of Stefan problems. USSR Computational Mathematics and Mathematical Physics, 1965, vol. 5, no. 5, pp. 59–76. DOI: 10.1016/0041-5553(65)90005-4

[17] Hoche D., Muller S., Rapin G., et al. Marangoni convection during free electron laser nitriding of titanium. Metallurgical and Materials Transactions B, 2009, vol. 40, iss. 4, pp. 497–507. DOI: 10.1007/s11663-009-9243-1

[18] Balandin G.F. Osnovy teorii formirovaniya otlivki. Ch. 1. Teplovye osnovy teorii. Zatverdevanie i okhlazhdenie otlivki [Fundamentals of cast forming theory. Vol. 1. Cast hardening and cooldown]. Moscow, Mashinostroenie Publ., 1979. 335 p.

[19] Harlow F.H., Welch J.E. Numerical calculation of time-depend viscous incompressible flow of fluid with free surface. Physics of Fluids, 1965, vol. 8, iss. 12, pp. 2182–2189. DOI: 10.1063/1.1761178

[20] Patankar S.V., Spalding D.B. A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. International Journal of Heat and Mass Transfer, 1972, vol. 15, iss. 10, pp. 1787–1806. DOI: 10.1016/0017-9310(72)90054-3

[21] Chorin A.J. A numerical method for solving incompressible viscous flow problems. Journal of Computational Physics, 1997, vol. 135, iss. 2, pp. 118–125. DOI: 10.1006/jcph.1997.5716