Geodesic
Numerical simulation of selective laser melting by the SPH method
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 24 (2022) no. 4, pp. 419-435.

Voir la notice de l'article provenant de la source Math-Net.Ru

Currently, additive manufacturing technologies develop actively. This requires creation of computational methods to describe physical processes occurring at the time of manufacturing. One of the methods used for the production of metal powder parts is the method of selective laser melting. This paper presents an SPH-based numerical technique for modeling the process of powder sintering under the influence of a laser beam. The flow of liquid formed as a result of melting is described by the Navier-Stokes equations. Pressure forces, viscous effects and surface forces at the interface are included in the force balance. The thermal state is determined from the energy conservation law, which takes into account thermal processes, volumetric absorption of laser radiation energy, convective heat exchange with the external environment and radiation. Phase transitions between solid and liquid phases are described in the framework of the generalized formulation of the Stefan problem. The calculation method is verified on tests specific to the class of problems under consideration. A comparison is made with the analytical solution, as well as with solutions obtained by other modifications of the SPH method, and with experimental data.
Keywords: SLM, SPH, Navier-Stokes equations, thermal conductivity, Stefan problem, test problems.
Mots-clés : phase transitions 
@article{SVMO_2022_24_4_a1,
     author = {A. N. Bykov and M. N. Vishnyakova and Yu. N. Deryugin and A. B. Emelyanov and A. A. Lazarev and S. N. Polishchuk and Ch. V. Cherenkova},
     title = {Numerical simulation of selective laser melting by the {SPH} method},
     journal = {\v{Z}urnal Srednevol\v{z}skogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {419--435},
     publisher = {mathdoc},
     volume = {24},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVMO_2022_24_4_a1/}
}
TY  - JOUR
AU  - A. N. Bykov
AU  - M. N. Vishnyakova
AU  - Yu. N. Deryugin
AU  - A. B. Emelyanov
AU  - A. A. Lazarev
AU  - S. N. Polishchuk
AU  - Ch. V. Cherenkova
TI  - Numerical simulation of selective laser melting by the SPH method
JO  - Žurnal Srednevolžskogo matematičeskogo obŝestva
PY  - 2022
SP  - 419
EP  - 435
VL  - 24
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SVMO_2022_24_4_a1/
LA  - ru
ID  - SVMO_2022_24_4_a1
ER  - 
%0 Journal Article
%A A. N. Bykov
%A M. N. Vishnyakova
%A Yu. N. Deryugin
%A A. B. Emelyanov
%A A. A. Lazarev
%A S. N. Polishchuk
%A Ch. V. Cherenkova
%T Numerical simulation of selective laser melting by the SPH method
%J Žurnal Srednevolžskogo matematičeskogo obŝestva
%D 2022
%P 419-435
%V 24
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SVMO_2022_24_4_a1/
%G ru
%F SVMO_2022_24_4_a1
A. N. Bykov; M. N. Vishnyakova; Yu. N. Deryugin; A. B. Emelyanov; A. A. Lazarev; S. N. Polishchuk; Ch. V. Cherenkova. Numerical simulation of selective laser melting by the SPH method. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 24 (2022) no. 4, pp. 419-435. http://geodesic.mathdoc.fr/item/SVMO_2022_24_4_a1/

[1] I. Gibson, D. Rosen, B. Stucker, Additive Manufacturing Technologies, Springer, New York, 2015,, 498 pp.

[2] Shishkovskii I.V., Osnovy additivnykh tekhnologii vysokogo razresheniya, Piter, SPb, 2016, 348 pp. (In Russ.)

[3] M. A. Russell, A. Souto-Iglesias, T. I. Zohdi, “Numerical simulation of Laser Fusion Additive Manufacturing processes using the SPH method”, Computer Methods in Applied Mechanics and Engineering, 2018, no. 341, 163–187 | DOI | MR

[4] Savelev I.V., Kurs obschei fiziki, v. 1, Nauka, Moskva, 1970, 517 pp. (In Russ.)

[5] Samarskii A.A., Vabischevich P.N., Vychislitelnaya teploperedacha, Librokom, Moskva, 2009, 784 pp. (In Russ.)

[6] Budak B.M., Solovev E.N., Uspenskii A.B., “Raznostnyi metod so sglazhivaniem koeffitsientov dlya resheniya zadachi Stefana”, Zh. vychisl. matem. i matem. fiz., 5:5 (1965), 828-840 (In Russ.) | MR

[7] R. A. Gingold, J. J. Monaghan, “Smoothed Particle Hydrodynamics: theory and application to non-spherical stars”, Monthly Notices of the Royal Astronomical Society, 181:3 (1977), 375-389 | DOI | MR

[8] L. Lucy, “A numerical approach to the testing of the fission hypothesis”, Astronom. J., 1977, no. 82, 1013 | DOI

[9] J. J. Monaghan, “Smoothed particle hydrodynamics”, Annual Review of Astronomy and Astrophysics, 30 (1992), 543-574 | DOI

[10] M. Ordoubadi, M. Yaghoubi, F. Yeganehdoust, “Surface tension simulation of free surface using smoothed particle hydrodynamics”, Sci. Iranica B., 24:4 (2017), 2019–2033 | DOI

[11] Karslou U., Eger D., Teploprovodnost tverdykh tel, Nauka, Moskva, 1964, 488 pp. (In Russ.)

[12] Tikhonov A.N., Samarskii A.A., Uravneniya matematicheskoi fiziki, Nauka, Moskva, 1977, 742 pp. (In Russ.) | MR

[13] Y. Bao, L. Li, L. Shen, Ch. Lei, Y. Gan, A Modified Smoothed Particle Hydrodynamics Approach for Modelling Dynamic Contact Angle Hysteresis, 2018 | DOI | MR

[14] My Ha Dao, Jing Lou, “Simulations of Laser Assisted Additive Manufacturing by Smoothed Particle Hydrodynamics”, Computer Methods in Applied Mechanics and Engineering, 373 (2021) | DOI | MR

[15] X. He, P. W. Fuerschbach, T. DebRoy, “Heat transfer and fluid flow during laser spot welding of 304 stainless steel”, J. Phys. D: Appl. Phys., 36:12 (2013), 1388–1398

[16] M.Afrasiabi, C.Lüthi, M. Bambach, K. Wegener, “Multi-Resolution SPH Simulation of a Laser Powder Bed Fusion Additive Manufacturing Process”, Appl. Sci., 11:7 (2021), 2962 | DOI