Siberian State Industrial University (Novokuznetsk, Russia):

O. G. Prikhodko, Cand. Eng., Associate Prof., Dept. of Quality and Innovations Management, Vice Rector on Development of the Main Education Programs, e-mail: prihodko_og@rambler.ru

National University of Science and Technology “MISIS” (Moscow, Russia)¹ ; Vladimir State University named after A. G. and N. G. Stoletovs (Vladimir, Russia)² ; Wuhan Textile University (Wuhan, China)³:

V. B. Deev, Dr. Eng., Prof., Dept. of Metal Forming¹, Chief Scientific Researcher², Prof. of the Faculty of Mechanical Engineering and Automation³, e-mail: deev.vb@mail.ru

Siberian State Industrial University (Novokuznetsk, Russia):

A. I. Kutsenko, Cand. Eng., Associate Prof., Head of Digital Transformation Dept., e-mail: aik_mail@mail.ru

Vladimir State University named after A. G. and N. G. Stoletovs (Vladimir, Russia):

E. S. Prusov, Cand. Eng., Associate Prof., Dept. “Technology of Functional and Structural Materials”, e-mail: eprusov@mail.ru

Control of the formation of the structure and specified properties of castings in foundry production processes is inextricably linked to the thermal conditions of solidification of the castings in the mold. The nature of the thermal interaction between the casting and the mold is largely determined by the configuration of the castings as well as the properties of the cast alloy and mold material. The analysis performed in this work shows that the numerical models and empirical formulas used to calculate casting solidification parameters can be divided into three groups. The first group of models and empirical formulas gives values approaching the results of calculations by the square root law. The second group includes models and formulas, the calculation of solidified skin thickness by which exceeds the results of calculations by the square root law. The third group includes models and empirical formulas, which provide calculated data close to the theoretical curves of solidification of classical bodies. According to the results of the analysis of calculated data on the basis of the considered models, a hypothetical mechanism of the solidification process of castings has been proposed, which explains the stages of formation of their structure and the nature of the deviation of experimentally obtained values of solidification parameters from the square root law.

The research was carried out within the state assignment in the field of scientific activity of the Ministry of Science and Higher Education of the Russian Federation (theme FZUN-2020-0015, state assignment of VlSU).

1. Veinik A. I. Theory of Casting Solidification. Moscow: Mashgiz, 1960.
2. Balandin G. F. Fundamentals of the theory of formation of castings. Part 1. Moscow: Mashinostroienie, 1976.
3. Chvorinov N. Solidification of castings. Moscow: Izd. inostr. lit., 1955.
4. Gulyaev V. V. Solidification and heterogeneity of steel. Leningrad – Moscow: Metallurgizdat, 1950.
5. Veinik A. I. Thermal bases of the theory of casting. Moscow: Mashgiz, 1962.
6. Girshovich N. G., Nekhendzi Yu. A. Analytical solution of simple problems on solidification of castings of different configuration. Liteinoe proizvodstvo. 1956. No. 3. pp. 14-19; No. 4. pp. 13-17; No. 6. pp. 13-17; No. 12. pp. 13-18.
7. Stefanescu D. M. Science and Engineering of Casting Solidification, New York: Springer-Verlag, 2015. 559 p.

8. Dantzig J. A., Rappaz M. Solidification, Boca Raton, FL: CRS Press, 2009.
9. Fredriksson H., Akerlind U. Solidification and Crystallization Processing in Metals and Alloys. John Wiley & Sons, Ltd., 2012.
10. Flemings M. C. Solidification Processing, New York: McGraw-Hill, 1974.
11. Chvorinov N. Crystallization and heterogeneity of steels. NCSAV, Prague, Czech Republic, 1954. [in Czech].
12. Ryzhikov A. A. Technological fundamentals of foundry production. Moscow: Metallurgizdat, 1950.
13. Ruddle R. W. The Solidification of Castings. Inst. of Metals, Lnd. 1957. 116 p.
14. Ono A. Solidification: The Separation Theory and its Practical Applications, New York: Springer, 1987.
15. Temkin D.E. (ed.) Liquid metals and their solidification. Moscow: Metallurgizdat, 1962.
16. Golod V. M. Theory of foundry processes. Leningrad: Leningradskij politekhnicheskij institut, 1983.
17. Deev V. B., Prusov E. S., Shunqi M., Ri E. H., Bazlova T. A., Temlyantsev M. V., Smetanyuk S. V., Ponomareva S. V., Vdovin K. N. The influence of the melt cooling rate on shrinkage behaviour during solidification of aluminum alloys. IOP Conf. Ser.: Mater. Sci. Eng. 2019. Vol. 537. Iss. 2. 022080.
18. Cambell J. The New Metallurgy of Cast Metals, Second Edition, Butterworth Heinemann 2003.
19. Chvorinov N. Theorie der erstarrung von gussstücken. Giesserei. 1940, S. 177-186.
20. Prikhodko O. G., Deev V. B., Prusov E. S., Kutsenko A. I. Influence of Thermophysical Characteristics of Alloy and Mold Material on Casting Solidification Rate. Steel in Translation. 2020. Vol. 50. Iss. 5. pp. 296–302.
21. Souza E. N., Cheung N., Santos C. A., Garcia A. The variation of the metal/mold heat transfer coefficient along the cross section of cylindrical shaped castings. Inverse Problems in Science and Engineering. 2006. Vol. 14 (5). pp. 467–481.
22. Skocilasová B., Skocilas J. Effect of mold material on temperature distribution in alloy cast. AIP Conference Proceedings. 2016. 1768. 020017.
23. Pariona M. M., Mossi A. C. Numerical simulation of heat transfer during the solidification of pure iron in sand and mullite molds. Journal of the Brazilian Society of Mechanical Sciences and Engineering. 2005. Vol. 27 (4). pp. 399-406.
24. Zhang A., Liang S., Guo Z., Xiong S. Determination of the interfacial heat transfer coefficient at the metal-sand mold interface in low pressure sand casting. Experimental Thermal and Fluid Science. 2017. Vol. 88. pp. 472-482.
25. Zhang L., Li L. Determination of heat transfer coefficients at metal/chill interface in the casting solidification process. Heat and Mass Transfer. 2013. Vol. 49. pp. 1071-1080.
26. Dargusch M.S., Hamasaiid A., Dour G. An inverse model to determine the heat transfer coefficient and its evolution with time during solidification of light alloys. International Journal of Nonlinear Sciences and Numerical Simulation. 2008. Vol. 9 (3). pp. 275-282.
27. Vandersluis E., Ravindran C. Influence of solidification rate on the microstructure, mechanical properties, and thermal conductivity of cast A319 Al alloy. Journal of Materials Science. 2019. Vol. 54. 4325–4339.
28. Abdallah Z., Aldoumani N. Casting Processes and Modelling of Metallic Materials. London, IntechOpen, 2021.
29. Luo A. A. Advanced Metal Casting. In: Caballero F. G., ed. Encyclopedia of Materials: Metals and Alloys, Vol. 3. Oxford: Elsevier, 2022. pp. 13–26.
30. Wang T., Wei J., Wang X., Yao M. Progress and application of microstructure simulation of alloy solidification. Acta Metall. Sin. 2018. Vol. 54. No. 2. pp. 193–203.
31. Guo J., Samonds M. Modeling of alloy casting solidification. JOM. 2011. Vol. 63. pp. 19–28.
32. Stefanescu D. M., Suarez R., Kim S. B. 90 years of thermal analysis as a control tool in the melting of cast iron. China Foundry. 2020. Vol. 17. pp. 69–84.
33. Santos R. G., Garcia A. Thermal behaviour during the inward solidification of cylinders and spheres and the correlation with structural effects. International Journal Cast Metals Research. 1998. Vol. 11. pp. 187-195.
34. Havlicek F., Elbel T. Geometrical modulus of a casting and its influence on solidification process. Archives of Foundry Engineering. 2011. Vol. 11 (4). pp. 170-176.
35. Auger J.-M. Local definition for surface-based geometrical modulus and use in automated casting cooling determination. International Journal of Cast Metals Research. 2017. Vol. 30 (6). pp. 322-336.