Dendritic growth at the solidification interface in selective laser melting of 316L steel
DOI:
https://doi.org/10.7242/1999-6691/2023.16.2.15Keywords:
dendritic growth, interface, selective laser melting, stainless steel, mathematical modeling of microstructure formationAbstract
Metal powder-based additive manufacturing is a rapidly developing area of mechanical engineering mainly related to the active utilization of 3D printers in the industry. One of the important characteristics of the products obtained using this technology is the strength which depends on the initial microstructure of the material. The morphology of the products manufactured by selective laser melting (SLM) is of dendritic-cellular type. In this paper, the problem of determining the characteristic size of dendrites formed during high-speed solidification at the boundary of the molten pool by selective laser melting of a 316L stainless steel powder layer is considered. Input parameters are defined as the macro parameters of the system under study, such as the thermodynamic properties of a stainless steel melt, the speed of a laser beam, as well as the orientation angle of the tail of the molten pool, where the main section of the crystallization front is located. The mathematical model is based on the Ivantsov approximation of parabolic-shaped crystals, which is found as an approximate solution of the axisymmetric problem of heat and mass transfer. A numerical simulation is performed using a two-dimensional dendritic growth model by Alexandrov and Galenko. The model describes the steady growth of a dendrite in a two-component system in the presence of convection in a solidifying melt. Using this model, the authors propose a method for calculating the solidification velocity and the tip diameter of dendrites, depending on the macroscopic parameters, which in turn can be the control parameters for obtaining the specified properties of the manufactured product. The calculated values are compared to the results of the experimental investigation by transmission electron microscopy of 316L steel samples manufactured by selective laser melting.
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Novikov S.V., Ramazanov K.N. Additivnyye tekhnologii: sostoyaniye i perspektivy [Additive technologies: state and prospects]. Ufa, UGATU, 2022. 75 р.
Lad’yanov V.I., Styazhkina I.V., Kamayeva L.V. Vliyaniye temperatury rasplava na kristallizatsiyu i svoystva splava
Fe – 10 at.% Si [Influence of the melt temperature on the crystallization and properties of the alloy Fe – 10 at.% Si]. Perspektivnyye materialy, 2010, no. 9, pp. 251-254.
Kamaeva L.V., Sterkhova I.V., Lad’yanov V.I. Viscosity and supercooling of Fe-Cr (≤40 at % Cr) melts. Inorg. Mater., 2012, vol. 48, pp. 318-324. https://doi.org/10.1134/S0020168512030089
Kalinichenko A.S., Krivosheyev Yu.K. Opredeleniye glubiny pereokhlazhdeniya rasplava i kharaktera strukturoobrazovaniya pri zakalke iz zhidkogo sostoyaniya [Determination of the depth of melt supercooling and the nature of structure formation during quenching from a liquid state]. Lit’ye i metallurgiya – Foundry production and metallurgy, 2001, no. 3, pp. 60-65.
Yap C.Y., Chua C.K., Dong Z.L., Liu Z.H., Zhang D.Q., Loh L.E., Sing S.L. Review of selective laser melting: Materials and Applications. Appl. Phys. Rev., 2015, vol. 2, 041101. https://doi.org/10.1063/1.4935926
Ivanov I.A., Dub V.S., Karabutov A.A., Cherepetskaya E.B., Bychkov A.S., Kudinov I.A., Gapeev A.A., Krivilyov M.D., Simakov N.N., Gruzd S.A., Lomaev S.L., Dremov V.V., Chirkov P.V., Kichigin R.M., Karavaev A.V., Anufriev M.Yu., Kuper K.E. Effect of laser induced ultrasound treatment on material structure in laser surface treatment for selective laser melting applications. Sci. Rep., 2021, vol. 11, 23501. https://doi.org/10.1038/s41598-021-02895-8
Ivantsov G.P. Temperaturnoye pole vokrug sharoobraznogo, tsilindricheskogo i igloobraznogo kristalla, rastushchego v pereokhlazhdennom rasplave [Temperature field around spherical, cylindrical and needle-shaped dendrite growing in supercooled melt]. DAN SSSR, 1947, vol. 58, no. 4, pp. 567-569.
Nestler B., Danilov D., Galenko P. Crystal growth of pure substances: Phase-field simulations in comparison with analytical and experimental results. J. Comput. Phys., 2005, vol. 207, pp. 221-239. https://doi.org/10.1016/j.jcp.2005.01.018
Alexandrov D.V., Galenko P.K. Selection criterion of stable dendritic growth at arbitrary Peclet numbers with convection. Phys. Rev. E, 2013, vol. 87, 062403. https://doi.org/10.1103/PhysRevE.87.062403
Toropova L.V. Matematicheskoye modelirovaniye ustoychivoy mody dendritnogo rosta pri razlichnykh usloviyakh kristallizatsii [Mathematical modeling of a stable mode of dendritic growth under various crystallization conditions]. PhD dissertation, Ural Federal University, Ekaterinburg, 2020. 124 p.
Aleksandrov D.V., Galenko P.K. Dendrite growth under forced convection: analysis methods and experimental tests. Phys. Usp., 2014, vol. 57, pp. 771-786. https://doi.org/10.3367/UFNe.0184.201408b.0833
Porsching T.A. Jacobi and Gauss–Seidel methods for nonlinear network problems. SIAM J. Numer. Anal., 1969, vol. 6, pp. 437-449. https://doi.org/10.1137/0706039
Khairallah S.A., Anderson A. Mesoscopic simulation model of selective laser melting of stainless steel powder. J. Mater. Process. Tech., 2014, vol. 214, pp. 2627-2636. http://dx.doi.org/10.1016/j.jmatprotec.2014.06.001
Gordeev G.A., Ankudinov V., Kharanzhevskiy E.V., Krivilyov M.D. Numerical simulation of selective laser melting with local powder shrinkage using FEM with the refined mesh. Eur. Phys. J. Spec. Top., 2020, vol. 229, pp. 205-216. https://doi.org/10.1140/epjst/e2019-900100-6
Gordeev G.A., Krivilyov M.D., Ankudinov V.E. Computer simulation of selective laser melting of fine-grained metallic powders. Vychisl. mekh. splosh. sred – Computational Continuum Mechanics, 2017, vol. 10, no. 3, pp. 293-312. https://doi.org/10.7242/1999-6691/2017.10.3.23
Pinomaa T., Lindroos M., Walbrühl M., Provatas N., Laukkanen A. The significance of spatial length scales and solute segregation in strengthening rapid solidification microstructures of 316L stainless steel. Acta Mater., 2020, vol. 184, pp. 1 16. https://doi.org/10.1016/j.actamat.2019.10.044
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