Abstract
Two granular systems (I and II) corresponding to oxide nanopowders having different agglomeration tendency are simulated by the granular dynamics method. The particle size is 10 nm. The interaction of particles involves the elastic forces of repulsion, the tangential forces of “friction”, the dispersion forces of attraction, and in the case of II system the opportunity of creation/destruction of hard bonds of chemical nature. The processes of the uniaxial compaction, the biaxial (radial) one, the isotropic one, the compaction combined with shear deformation as well as the pure shear deformation are studied. The effect of the positive dilatancy is revealed in the processes of shear deformation. The yield surfaces of nanopowders are constructed in the space of stress tensor invariants, i.e., the hydrostatic pressure and the deviator intensity. It is revealed that the form of the yield surfaces is similar to an ellipse, which is shifted along the hydrostatic axis to compressive pressures. The associated flow rule is analyzed. The nonorthogonality of the deformation vectors to the yield surface is established in both systems modeled.
Similar content being viewed by others
References
Siegel, R.W.: Nanostructured materials: mind over matter. Nanostruct. Mater. 4(1), 121–138 (1994)
Ivanov, V.V., Khrustov, V.R., Paranin, S.N., Medvedev, A.I., Shtol’ts, A.K., Ivanova, O.F., Nozdrin, A.A.: Stabilized zirconia nanoceramics prepared by magnetic pulsed compaction of nanosized powders. Glass Phys. Chem. 31(4), 465–470 (2005)
Ivanov, V.V., Kaygorodov, A.S., Khrustov, V.R., Paranin, S.N., Spirin, A.V.: Hard alumina-based ceramics fabricated by the use of magnetic pulsed compaction of composite nanopowders. Russ. Nanotechnol. 1(1–2), 201–207 (2006)
Khrustov, V.R., Ivanov, V.V., Kotov, Y.A., Kaygorodov, A.S., Ivanova, O.F.: Nanostructured composite ceramic materials in the ZrO\(_2\)-Al\(_2\)O\(_3\) system. Glass Phys. Chem. 33(4), 379–386 (2007)
Kaygorodov, A.S., Ivanov, V.V., Khrustov, V.R., Kotov, Y.A., Medvedev, A.I., Osipov, V.V., Ivanov, M.G., Orlov, A.N., Murzakaev, A.M.: Fabrication of Nd:Y\(_2\)O\(_3\) transparent ceramics by pulsed compaction and sintering of weakly agglomerated nanopowders. J. Eur. Ceram. Soc. 27, 1165–1169 (2007)
Shtern, M.B., Serdyuk, G.G., Maksimenko, L.A., Truhan, Y.V., Shulyakov, Y.M.: Phenomenological Theories of Powder Pressing. Naukova Dumka, Kiev (1982). (in Russian)
Boltachev, G.S., Nagayev, K.A., Paranin, S.N., Spirin, A.V., Volkov, N.B.: Magnetic Pulsed Compaction of Nanosized Powders. Nova Science Publishers Inc, NY (2010)
Tsiok, O.B., Sidorov, V.A., Bredikhin, V.V., Khvostantsev, L.G., Troitskiy, V.N., Trusov, L.I.: Relaxation effects during the densification of ultrafine powders at high hydrostatic pressure. Phys. Rev. B 51, 12127–12132 (1995)
Vassen, R., Kaiser, A., Forster, J., Buchkremer, H.P., Stover, D.: Densification of uitrafine SiC powders. J. Mater. Sci. 31, 3623–3637 (1996)
Mishra, R.S., Lesher, C.E., Mukherjee, A.K.: Nanocrystalline alumina by high pressure sintering. Mater. Sci. Forum 225–227, 617–622 (1996)
Zhao, M., Li, X., Wang, Z., Song, L., Xiao, L., Xu, B.: The effect of pressure on the specific surface area and density of nanocrystalline ceramic powders. Nanostruct. Mater. 1(5), 379–386 (1992)
Martin, C.L., Bouvard, D.: Study of the cold compaction of composite powders by the discrete element method. Acta Mater. 51(2), 373–386 (2003)
Khasanov, O.L., Dvilis, E.S., Sokolov, V.M.: Compressibility of the structural and functional ceramic nanopowders. J. Eur. Ceram. Soc. 27, 749–752 (2007)
Cha, H.R.: Densification of the nanopowder by using ultrasonic vibration compaction. Rev. Adv. Mater. Sci. 28, 90–93 (2011)
Meyers, M.A., Benson, D.J., Olevsky, E.A.: Shock consolidation: microstructurally-based analysis and computational modelling. Acta Mater. 47(7), 2089–2108 (1999)
Boltachev, G.S., Volkov, N.B., Ivanov, V.V., Kaygorodov, A.S.: Shock-wave compaction of the granular medium initiated by magnetically pulsed accelerated striker. Acta Mech. 204, 37–50 (2009)
Ning, J.L., Jiang, D.M., Shim, K.B.: Preparation of textured zinc oxide ceramics by extrusion and spark plasma sintering. Adv. Appl. Ceram. 105(6), 265–269 (2006)
Filonenko, V.P., Khvostantsev, L.G., Bagramov, R.K., Trusov, L.I., Novikov, V.I.: Compacting tungsten powders with varying particle size using hydrostatic pressure up to 5 GPa. Powder Metall. Met. Ceram. 31, 296–299 (1992)
Vassen, R., Stoever, D.: Compaction mechanisms of ultrafine SiC powders. Powder Technol. 72, 223–226 (1992)
Saha, B.P., Kumar, V., Joshi, S.V., Balakrishnan, A., Martin, C.L.: Investigation of compaction behavior of alumina nano powder. Powder Technol. 224, 90–95 (2012)
Balakrishnan, A., Pizette, P., Martin, C.L., Joshi, S.V., Saha, B.P.: Effect of particle size in aggregated and agglomerated ceramic powders. Acta Mater. 58, 802–812 (2010)
Boltachev, G.S., Volkov, N.B.: Simulation of nanopowder compaction in terms of granular dynamics. Tech. Phys. 56, 919–930 (2011)
Boltachev, G.S., Volkov, N.B., Kaygorodov, A.S., Loznukho, V.P.: The peculiarities of uniaxial quasistatic compaction of oxide nanopowders. Nanotechnol. Russ. 6, 639–646 (2011)
Boltachev, G.S., Lukyashin, K.E., Shitov, V.A., Volkov, N.B.: Three-dimensional simulations of nanopowder compaction processes by granular dynamics method. Phys. Rev. E 88, 012209 (2013)
Olevsky, E.A., Bokov, A.A., Boltachev, G.S., Volkov, N.B., Zayats, S.V., Ilyina, A.M., Nozdrin, A.A., Paranin, S.N.: Modeling and optimization of uniaxial magnetic pulse compaction of nanopowders. Acta Mech. 224(12), 3177–3195 (2013)
Dobrov, S.V., Ivanov, V.V.: Simulation of pulsed magnetic molding of long powdered products. Tech. Phys. 49(4), 413–419 (2004)
Cooper, A.R., Eaton, L.E.: Compaction behavior of several ceramic powders. J. Am. Ceram. Soc. 45(3), 97–101 (1962)
Denny, P.J.: Compaction equations: a comparison of the Heckel and Kawakita equations. Powder Technol. 127, 162–172 (2002)
Drucker, D.C., Prager, W.: Soil mechanics and plastic analysis or limit design. Q. Appl. Math. 10(2), 157–165 (1952)
Schwedes, J.: Shearing behaviour of slightly compressed cohesive granular materials. Powder Technol. 11(1), 59–67 (1975)
Maximenko, A.L., Olevsky, E.A., Shtern, M.B.: Plastic behavior of agglomerated powder. Comput. Mater. Sci. 43, 704–709 (2008)
Nott, P.R.: Classical and cosserat plasticity and viscoplasticity models for slow granular flow. Acta Mech. 205, 151–160 (2009)
Heyliger, P.R., McMeeking, R.M.: Cold plastic compaction of powders by a network model. J. Mech. Phys. Solids 49(9), 2031–2054 (2001)
Pizette, P., Martin, C.L., Delette, G., Sornay, P., Sans, F.: Compaction of aggregated ceramic powders: from contact laws to fracture and yield surfaces. Powder Technol. 198, 240–250 (2010)
Procopio, A.T., Zavaliangos, A.: Simulation of multi-axial compaction of granular media from loose to high relative densities. J. Mech. Phys. Solids 53(7), 1523–1551 (2005)
Skorokhod, V.V.: Rheological Principles of Sintering Theory. Naukova Dumka, Kiev (1972). (in Russian)
Olevskii, E.A., Shtern, M.B.: Rheological foundations of powder consolidation processes and the “mean-square” concept. Powder Metall. Met. Ceram. 43, 355–363 (2004)
Gryaznov, V.G., Kaprelov, A.M., Romanov, A.E.: Critical instability of dislocations in microcrystals. Pis’ma Zh. Tekh. Fiz. (Sov. Tech. Phys. Lett.) 15(2), 39–44 (1989)
Cundall, P.A., Strack, O.D.L.: A discrete numerical model for granular assemblies. Geotechnique 29, 47–65 (1979)
Agnolin, I., Roux, J.N.: Internal states of model isotropic granular packings. I. Assembling process, geometry, and contact networks. Phys. Rev. E 76, 061302 (2007)
Gilabert, F.A., Roux, J.N., Castellanos, A.: Computer simulation of model cohesive powders: influence of assembling procedure and contact laws on low consolidation states. Phys. Rev. E 75, 011303 (2007)
Gilabert, F.A., Roux, J.N., Castellanos, A.: Computer simulation of model cohesive powders: plastic consolidation, structural changes, and elasticity under isotropic loads. Phys. Rev. E 78, 031305 (2008)
Zhu, H.P., Zhou, Z.Y., Yang, R.Y., Yu, A.B.: Discrete particle simulation of particulate systems: a review of major applications and findings. Chem. Eng. Sci. 63, 5728–5770 (2008)
Luding, S.: Cohesive, frictional powders: contact models for tension. Granul. Matter 10, 235–246 (2008)
Salot, C., Gotteland, P., Villard, P.: Influence of relative density on granular materials behavior: DEM simulations of triaxial tests. Granul. Matter 11, 221–236 (2009)
Teufelsbauer, H., Wang, Y., Chiou, M.C., Wu, W.: Flow-obstacle interaction in rapid granular avalanches: DEM simulation and comparison with experiment. Granul. Matter 11, 209–220 (2009)
Yang, J., Wu, C.Y., Adams, M.: DEM analysis of particle adhesion during powder mixing for dry powder inhaler formulation development. Granul. Matter 15, 417–426 (2013)
Boltachev, G.S., Volkov, N.B., Dobrov, S.V., Ivanov, V.V., Nozdrin, A.A., Paranin, S.N.: Simulation of radial pulsed magnetic compaction of a granulated medium in a quasi-static approximation. Tech. Phys. 52, 1306–1315 (2007)
Paranin, S., Ivanov, V., Nikonov, A., Spirin, A., Khrustov, V., Ivin, S., Kaygorodov, A., Korolev, P.: Densification of nano-sized alumina powders under radial magnetic pulsed compaction. Adv. Sci. Technol. 45, 899–904 (2006)
Reissner, E., Sagoci, H.F.: Forced torsional oscillations of an elastic half-space. I. J. Appl. Phys. 15, 652–654 (1944)
Lur’e, A.I.: Three-Dimensional Problems of the Theory of Elasticity. Interscience Publishers, NY (1964)
Sun, W., Zeng, Q., Yu, A., Kendall, K.: Calculation of normal contact forces between silica nanospheres. Langmuir 29(25), 7825–7837 (2013)
Bartels, G., Unger, T., Kadau, D., Wolf, D.E., Kertesz, J.: The effect of contact torques on porosity of cohesive powders. Granul. Matter 7, 139–143 (2005)
Greenwood, J.A., Minshall, H., Tabor, D.: Hysteresis losses in rolling and sliding friction. Proc. R. Soc. A 259, 480–507 (1961)
Brilliantov, N.V., Pöschel, T.: Rolling friction of a viscous sphere on a hard plane. Europhys. Lett. 42(5), 511–516 (1998)
Castellanos, A.: The relationship between attractive interparticle forces and bulk behaviour in dry and uncharged fine powders. Adv. Phys. 54, 263–376 (2005)
Valverde, J.M., Castellanos, A.: Compaction of fine powders: from fluidized agglomerates to primary particles. Granul. Matter 9, 19–24 (2007)
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)
Povarennykh, A.S.: Mineral Hardness. Izdat. AN Ukrainian SSR, Kiev (1963). (in Russian)
Herrmann, H.J.: Granular matter. Physica A 313(1–2), 188–210 (2002)
Rudnicki, J.W., Rice, J.R.: Conditions for the localization of deformation in pressure-sensitive dilatant materials. J. Mech. Phys. Solids 23, 371–394 (1975)
Garagash, I.A., Nikolayevskii, V.N.: Non-associated rules of flow and plastic deformation localization. Usp. Mekh. 12, 131–183 (1989)
Holcomb, D.J., Rudnicki, J.W.: Inelastic constitutive properties and shear localization in tennessee marble. Int. J. Numer. Anal. Methods Geomech. 25, 109–129 (2001)
Acknowledgments
The reported study was fulfilled within State programme (No. 0389-2014-0006, 2015–2017 years) and was partially supported by RFBR, research project No. 14-08-90404 Ukr_a and NASU (project No. 25-08-14).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Boltachev, G.S., Volkov, N.B., Kochurin, E.A. et al. Simulation of the macromechanical behavior of oxide nanopowders during compaction processes. Granular Matter 17, 345–358 (2015). https://doi.org/10.1007/s10035-015-0561-5
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10035-015-0561-5