A model of material microstructure formation on selective laser sintering with allowance for large elastoplastic strains
V.A. Levina*, K.M. Zingermanb** , K.Yu. Krapivinc***, O.A. Ryabovab**** , A.V. Kukushkind*****
aMoscow State University, Moscow, 119991, Russia
bTver State University, Tver, 170100, Russia
cFidesys LLC, Moscow, 121205, Russia
dTula State Lev Tolstoy Pedagogical University, Tula, 300026, Russia
E-mail: *v.a.levin@mail.ru, **zingerman@rambler.ru, ***krapivin@saldlab.com, ****ryabova.oa@tversu.ru, *****kukushkinav@mail.ru
Received April 17, 2019
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DOI: 10.26907/2541-7746.2019.2.191-204
For citation: Levin V.A., Zingerman K.M., Krapivin K.Yu., Ryabova O.A., Kukushkin A.V. A model of material microstructure formation on selective laser sintering with allowance for large elastoplastic strains. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2019, vol. 161, no. 2, pp. 191–204. doi: 10.26907/2541-7746.2019.2.191-204. (In Russian)
Abstract
A mathematical model of material microstructure formation in the process of selective laser sintering was proposed. The model is based on the stress and strain analysis in a representative volume of a powder that contains some particles. The strains and stresses are caused by contact interaction of particles due to surface tension. It was assumed that the particles are made of elastoplastic material. The material properties were described by the associative Drucker–Prager model with hardening. The nonlinear efiects caused by large strains were taken into account. The model permits one to determine the shape of particles in the deformed state and the shape of pores. The numerical results were presented for the problem of contact interaction between two particles that assume the spherical shape before deformation. The displacements of centers of powder particles were specifled as input. The flnite-element method was used for computations. The flow rule was integrated using the implicit Euler backward method. The mortar method was used to solve the problem with account of contact interaction. The distribution of contact stresses over the surfaces of powder particles and the distribution of the von Mises plastic strains in the section of these particles were shown as a result of the analysis. The dependence of contact zone radius on the contact displacements of the particles' centers was investigated. It was analyzed how the radius of contact zone depends on the material parameter characterizing the pressure dependence of plastic flow.
Keywords: selective laser sintering, microstructure formation, large strains, plasticity, flnite-element method
Acknowledgments. The study was performed at Tula State Lev Tolstoy Pedagogical University and supported by the Ministry of Science and Higher Education of the Russian Federation (project no. 14.577.21.0271, project ID RFMEFI57717X0271)
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