Geodesic
Mathematical model and algorithm for calculating pressing and sintering
Matematičeskoe modelirovanie, Tome 31 (2019) no. 2, pp. 3-17.

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On the basis of the thermodynamic approach, the constitutive relations for processes of pressing and sintering of powder composites have been obtained. A kinetic equation is been added to the system of equations of the usual theory of elastoplasticity to calculate the evolution of porosity under non-thermomechanical action by a bulk compressive stress of sintering. The modified theory is included in the computer program for calculating elastoplastic media for adaptation to sintering processes. Numerical calculations demonstrate the ability of the modified theory of elastic-plasticity to simulate the main effects of pressing and sintering, including the calculation of residual porosity, stresses and deformations in the compact, as well as its residual shape. Also on the basis of the proposed theory, the problem of "hot" sintering under the action of a mobile high-energy pulse ("laser sintering") is numerically solved. The influence of the parameters of the laser action on the sintering of powder material, as well as on the distribution of porosity and temperature, is calculated.
Keywords: pressing, sintering, porosity, sintering stress, thermo-mechanical model, finite element method, laser sintering. 
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N. G. Burago; I. S. Nikitin. Mathematical model and algorithm for calculating pressing and sintering. Matematičeskoe modelirovanie, Tome 31 (2019) no. 2, pp. 3-17. http://geodesic.mathdoc.fr/item/MM_2019_31_2_a0/

[1] R.M. German, P. Suri, S.J. Park, “Review: liquid phase sintering”, J. Mater. Sci., 44 (2009), 1–39 | DOI

[2] E.A. Olevsky, “Theory of sintering: from discrete to continuum”, Materials Science and Engineering, R23 (1998), 41–100 | DOI

[3] Iu.A. Gosteev, A.V. Fedorov, “Matematicheskoe modelirovanie spekaniia ultradispersnogo poroshka”, Fizika goreniia i vzryva, 40:2 (2004), 42–44

[4] V.V. Skorokhod, Reologicheskie osnovy teorii spekaniia, Naukova dumka, Kiev, 1972, 149 pp.

[5] V.A. Zhornik, Iu.A. Prokopenko, “Modelirovanie protsessov spekaniia poroshkovyh pokrytii pri teplovom i mekhanicheskom vozdeistviiah”, Vestnik TGTU, 16:1 (2010), 59–66

[6] J. Hermandes, J. Oliver, J.C. Cante, R. Weyler, “Numerical modeling of crack formation in powder forming processes”, Int. J. Solids and Structures, 48 (2011), 292–316. | DOI

[7] N.G. Burago, A.I. Glushko, A.N. Kovshov, “Termodinamicheskii metod polucheniia opredeliaiushchikh uravnenii dlia modelei sploshnykh sred”, Izvestiia RAN, Mekhanika tverdogo tela, 2000, no. 6, 4–15

[8] N.G. Burago, I.S. Nikitin, “Modelirovanie spekaniia s pomoshchiu teorii plastichnosti”, Inzhenernyi zhurnal: nauka i innovatsii, 2013, no. 8

[9] N.G. Burago, I.S. Nikitin, “Kontinualnaia model pressovaniia i spekaniia poroshkovykh materialov”, Materialy X Vserossiiskoi konferentsii po mekhanike deformiruemogo tverdogo tela, v 2-h tomah (18–22.09.2017, Samara, Rossiia), v. 1, SamGTU, Samara, 2017, 91–94

[10] N.G. Burago, I.S. Nikitin, V.L. Yakushev, “Hybrid numerical method for unsteady problems of continuum mechanics using arbitrary moving adaptive overlap grids”, Computational Mathematics and Mathematical Physics, 56:6 (2016), 1065–1074 | DOI | MR | Zbl

[11] M.R. Hestenes, E. Stiefel, “Method of Conjugate Gradients for Solving Linear Systems”, NBS J., 49 (1952), 409–436 | MR | Zbl

[12] V.G. Niziev, A.V. Koldoba, F.Kh. Mirzade, V.Ya. Panchenko, Yu.A. Poveschenko, M.V. Popov, “Numerical modeling of laser sintering of two-component powder mixtures”, Mathematical Models and Computer Simulations, 3:6 (2011), 723–731 | DOI | Zbl

[13] A.V. Koldoba, Yu.A. Poveschenko, M.V. Popov, G.V. Ustiugova, V.M. Chechenkin, “Matematicheskoe modelirovanie lazernogo spekaniia dvukhkomponentnykh poroshkovykh smesei”, Keldysh Institute preprints, 2009, 038, 15 pp.