The method of granular dynamics is used to study the quasistatic uniaxial compaction of nanopowders with a particle size from 10 nm to several hundred nanometers. The interaction of individual particles includes Hertz elastic forces, Cattaneo–Mindlin friction forces, and van der Waals dispersion forces of attraction. The influence of the model cell size on simulation results is analyzed. The curves of uniaxial compression and elastic unloading in the “axial pressure–density” coordinates are plotted. The generalization of the traditional Hertz law in the range of relatively high strains is discussed.
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M. B. Shtern, G. G. Serdyuk, L. A. Maksimenko, et al., Phenomenological Theories of Powder Compaction [in Russian], Naukova Dumka, Kiev (1982), p. 140.
G. Sh. Boltachev, N. B. Volkov, S. V. Dobrov, et al., “Modeling radial magnetic-discharge compaction of granular medium in quasistatistical approximation,” Zh. Tekh. Fiz., 77, No. 10, 58–67 (2007).
M. B. Shtern and V. D. Rud’, Mechanical and Computer Models for Consolidation of Granulated Media Based on Metal and Ceramic Powders [in Russian], Lutsk Nats. Tekh. Univ., Kiev–Lutsk (2010), p. 232.
P. A. Cundall and O. D. L. Strack, “A discrete numerical model for granular assemblies,” Geotechnique, 29, No 1, 47–65 (1979).
I. Agnolin and J.-N. Roux, “Internal states of model isotropic granular packings,” Phys. Rev. E, 76, 061302; 061303; 061304 (2007).
F. Nicot and F. A. Darve, “A multi-scale approach to granular materials,” Mech. Mat., 37, No 9, 980–1006 (2005).
A. Balakrishnan, P. Pizette, C. L. Martin, et al., “Effect of particle size in aggregated and agglomerated ceramic powders,” Acta Mat., 58, 802–812 (2010).
G. Sh. Boltachev and N. B. Volkov, “Size effect in compaction of nanopowders,” Pis’ma Zh. Tekh. Fiz., 36, Issue 17, 96–103 (2010).
H. Hertz, “Uber die Beruhrung fester elastischer Korper,” J. Reine Angew. Math., B92, 156–171 (1881).
L. D. Landau and E. M. Lifshitz, Theoretical Physics. Volume VII. Theory of Elasticity [in Russian], Nauka, Moscow (1987), p. 248.
G. Sh. Boltachev, N. B. Volkov, and K. A. Nagayev, “Effect of retardation in the dispersion forces between spherical particles,” J. Coll. Int. Sci., 355, No. 2, 421–426 (2011).
S. Luding, “Cohesive, frictional powders: contact models for tension,” Granular Mat., 10, 235–246 (2008).
A. P. Babichev, N. A. Babushkina, A. M. Bratkovskii, et al., in: I. S. Grigor’ev and E. Z. Meilikhov (eds.), Physical Quantities: Handbook [in Russian], Énergoatomizdat, Moscow (1991), p. 1232.
V. V. Ivanov, S. N. Paranin, A. N. Vikhrev, and A. A. Nozdrin, “Effectiveness of eh dynamic method of compacting nanosized powders,” Materialovedenie, No. 5, 49–55 (1997).
E. Dintwa, E. Tijskens, and H. Ramon, “On the accuracy of the Hertz model to describe the normal contact of soft elastic spheres,” Granular Mater., 10, 209–221 (2008).
R. M. McMeeking, G. Jefferson, and G. K. Haritos, “Elastic and viscoelastic response of finite particle junctions in granular materials,” in: A. Zavaliangos and A. Laptev (eds.), Recent Developments in Computer Modeling of Powder Metallurgy Processes, IOS Press, Amsterdam (2001), pp. 50–62.
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The study was supported by the Russian Fundamental Support Fund (Projects 09-08-00198 and 12-08-00298) under the “Fundamental Problems of Nonlinear Dynamics” Program (Project 09-P-2-1003), Presidium of the Russian Academy of Sciences.
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Translated from Poroshkovaya Metallurgiya, Vol. 51, No. 5–6 (485), pp. 12–21, 2012.
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Boltachev, G.S., Volkov, N.B. Compaction and elastic unloading of nanopowders under the granular dynamic method. Powder Metall Met Ceram 51, 260–266 (2012). https://doi.org/10.1007/s11106-012-9426-1
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DOI: https://doi.org/10.1007/s11106-012-9426-1