MODEL OF CONVECTIVE HEAT TRANSFER IN HIGH-ENTROPY ALLOYS DURING ELECTRON BEAM PROCESSING

A model of convective mixing is proposed for processing high-entropy melts of AlCoCrFeNi and CuBiSnInPb systems with low-energy high-current electron beams, taking into account evaporation from the surface of materials. The model is based on the idea that processing with concentrated energy flows leads to the appearance of vortex patterns in the molten layer. The mechanism of their formation lies in the fact that the presence of a temperature gradient in the melted layer leads to the occurrence of thermocapillary convection. The convective flow model is based on the Navier-Stokes equations, heat transfer in liquid media and boundary conditions taking into account the outflow of evaporated material. The solution of these equations by the finite element method was carried out for two cases. In the first case, the dependence of thermophysical parameters on temperature was not taken into account, and in the second, this dependence was taken into account. It showed that in the first case in the AlCoCrFeNi melt at the heating stage, the melt flow is laminar. The instability of this flow is observed at the "melt/solid" boundary. The cooling stage is characterized by the formation of vortex flows. The formation of vortices occurs both at a distance close to the radius of the irradiation spot and in the central region. In the case of the CuBiSnInPb alloy, the same pattern is observed, with the only difference that the convective flow processes proceed faster due to lower values of surface tension and liquidus temperature compared to the previous case. In the second case, electron beam processing leads to the formation of a multi-vortex pattern, which, developing at the heating stage, captures all new areas of the material. At the cooling stage, the fusion of vortices and the formation of a stationary laminar flow is observed.

1. Gao B., Hu L., Li S.-W., Hao Y., Zhang Y.-D., Tu G.-F. Study on the nanostructure for-mation mechanism of hypereutectic Al–17.5 Si alloy induced by high current pulsed elec-tron beam. Applied Surface Science. 2015;346:147‒157. http://dx.doi.org/10.1016/j.apsusc.2015.04.029

2. Lu J., Song Z., Qin H., Huang H., Sui X., Weng Y., Mo Z., Wang K., Ren X. Surface nanocrystallization and mechanical properties of mold steel induced via scanning electron beam treatment. Vacuum. 2023;218:112634. https://doi.org/10.1016/j.vacuum.2023.112634

3. Fetzer R., Mueller G., An W., Weisenburger A. Metal surface layers after pulsed electron beam treatment. Surface and Coatings Tech-nology. 2014;258:549–556. http://dx.doi.org/10.1016/j.surfcoat.2014.08.039

4. Shulov V. A., Gromov A. N., Teryaev D. A., Engel’ko V. I. Application of high-current pulsed electron beams for modifying the sur-face of gas-turbine engine blades. Russian Journal of Non-Ferrous Metals. 2016;57:256‒265. http://dx.doi.org/10.3103/S1067821216030147

5. Markov A.B., Meisner L.L., Yakovlev E.V., Meisner S.N., Gudimova E.Y., Petrov V.I. Surface cratering on the surface of stainless steel and TiNi irradiated by a low-energy, high-current electron beam: morphology and topography. Izvestiya Vuzov. Fizika. 2015;58(9/3):173‒177. (In Russ.).

6. Lyu P., Chen Y., Liu Z., Cai J., Zhang C., Jin Y., Guan Q., Zhao N. Surface modification of CrFeCoNiMo high entropy alloy induced by high-current pulsed electron beam. Applied Surface Science. 2020;504:144453.

7. https://doi.org/10.1016/j.apsusc.2019.144453

8. Lyu P., Peng T., Miao Y., Liu Z., Gao Q., Zhang C., Jin Y., Guan Q., Cai J. Microstruc-ture and properties of CoCrFeNiMo0.2 high-entropy alloy enhanced by high-current pulsed electron beam. Surface and Coatings Technol-ogy. 2021;410:126911.

9. https://doi.org/10.1016/j.surfcoat.2021.126911

10. Shu C., Yao Z., Li X., Du W., Tao X., Yang H. Microstructure and wear mechanism of CoCrCuFeNiVx high entropy alloy by sinter-ing and electron beam remelting. Physica B: Condensed Matter. 2022;638:413834. https://doi.org/10.1016/j.physb.2022.413834

11. Popov V.V., Katz-Demyanetz A., Koptyug A. Selective electron beam melting of Al0.5CrMoNbTa0.5 high entropy alloys using elemental powder blend. Heliyon. 2019;5(2):e01188. https://doi.org/10.1016/j.heliyon.2019.e01188

12. Kuwabara K., Shiratori H., Fujieda T., Yama-naka K., Koizumi Y., A. Chiba. Mechanical and corrosion properties of AlCoCrFeNi high-entropy alloy fabricated with selective electron beam melting. Additive Manufacturing. 2018;23:264‒271. https://doi.org/10.1016/j.addma.2018.06.006

13. Zhang M., Zhou X., Wang D., He L., Ye X., Zhang W. Additive manufacturing of in-situ strengthened dual-phase AlCoCuFeNi high-entropy alloy by selective electron beam melt-ing. Journal of Alloys and Compounds. 2022;893:162259. https://doi.org/10.1016/j.jallcom.2021.162259

14. Yu T., Wang H., Han K., Zhang B. Micro-structure and wear behavior of AlCrTiNbMo high-entropy alloy coating prepared by elec-tron beam cladding on Ti600 substrate. Vacu-um. 2022;199:110928. http://dx.doi.org/10.1016/j.vacuum.2022.110928

15. Cai J., Yao Y., Wei J., Guan Q., Lyu P., Ye Y., Li Y. Microstructure and transient oxida-tion behavior of NiCoCrAlYSiHf coating modified via high-current pulsed electron beam. Surface and Coatings Technology. 2021;422:127499. http://dx.doi.org/10.1016/j.surfcoat.2021.127499

16. Leivi A.Ya., Talala K.A., Krasnikov V.S., Yalovets A.P. Modification of the properties of structural materials by intense flows of charged particles and plasma. Bulletin of the South Ural State University. Skeria "Mechani-cal Engineering". 2016;16(1):28‒55. (In Russ.). http://dx.doi.org/10.14529/engin160103

17. Leivi A.Ya., Yalovets A.P. Modeling of the ef-fect of intense plasma flows on matter. Chelya-binsk: IP Myakotin I.V., 2016:111. (In Russ.).

18. Kuznetsov P.M., Feodorov V.A. Surface to-pology of Fe-Si alloy in the laser radiation ex-posure. Materials Physics and Mechanics. 2014;20:56‒61.

19. Lambert P. Surface Tension in Microsystems Engineering Below the Capillary Length. Hei-delberg: Springer.2013;327..

20. V'yukhin V.V., Chikova O.A., Tsepelev V.S. Surface tension of liquid high-entropy equiatomic alloys of a Cu–Sn–Bi–In–Pb sys-tem. Russian Journal of Physical Chemistry A. 2017;91(4):613–616.

21. Chikova O.A., Il'in V.Y., Tsepelev V.S., V'yukhin V.V. Viscosity of high-entropy melts in the Cu-Bi-Sn-In-Pb system. Inorgan-ic Materials. 2016;52(5):517–522.

22. Uporov S., Bykov V., Pryanichnikov S., Shubin A., Uporova N. Effect of synthesis route on structure and properties of AlCo-CrFeNi high-entropy alloy. Intermetallics. 2017;83:1‒8. https://doi.org/10.1016/j.intermet.2016.12.003

23. Rohila S., Mane R.B., Ummethala G., Panigrahi B.B. Nearly full-density pressureless sintering of AlCoCrFeNi-based high-entropy alloy powders. Journal of Materials Research. 2019;34:777–786. https://doi.org/10.1557/jmr.2019.9

24. Samokhin A.A., Il’ichev N.N., Pivovarov P.A., Si-dorin A.V. Laser vaporisation of absorbing liquid un-der transparent cover. Bulletin of the Lebedev Physics Institute. 2016;43(5):156‒159. http://dx.doi.org/10.3103/S106833561605002X

25. Akhmanov S.A. Emel’yanov V.I., Koroteev N.I., Seminogov V.N. Interaction of powerful laser radiation with the surfaces of semicon-ductors and metals: nonlinear optical effects and nonlinear optical diagnostics. Soviet Phys-ics Uspekhi. 1985;28:1084‒1124. https://doi.org/10.1070/PU1985v028n12ABEH003986

26. Sarychev V.D., Granovskii A.Yu., Nevskii S.A., Konovalov S.V., Gromov V.E. Model of convection mass transfer in titanium alloy at low energy high current electron beam action. IOP Conference Series: Materials Science and Engineering. 2017;168(1):012031. http://dx.doi.org/10.1088/1757-899X/168/1/012031

27. Debroy T. Welding in Digital Age. Welding Journal. 2015;94(4):58–64.