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Transparent Al2O3 ceramics have attracted considerable interest for use in a wide range of optical, electronic and structural applications. The fabrication of these ceramics using powder metallurgy processes requires the development of theoretical approaches to the compaction of nanopowders. In this work, we investigate the compaction processes of two model granular systems imitating Al2O3 nanosized powders. System I is a loosely aggregated powder, and system II is a powder strongly inclined to agglomeration (for instance, calcined powder). The processes of isostatical (uniform), biaxial, and uniaxial compaction as well as uniaxial compaction with simultaneous shear deformation are studied. The energy parameters of compaction such as the energy change of elastic interparticle interactions and dispersion interactions, dissipative energy losses related to the processes of interparticle friction, and the total work of compaction are calculated for all the processes. The nonapplicability of the associated flow rule to the description of deformation processes of oxide nanopowders is shown and an alternative plastic flow rule is suggested. A complete system of determining the relationship of the flow including analytical approximations of yield surfaces is obtained.
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Two granular systems (I and II) corresponding oxide nanopowders having different agglomeration tendency are simulated by the granular dynamics method. The particle size is 10 nanometer. 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 simple shear deformation are studied. The effect of the positive dilatancy is found out in the processes of shear deformation. The loading 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 loading 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 loading surface is established in the both systems modeled.
The paper concerns the nanopowder high-speed, $10^4$ - $10^9$ s${}^{-1}$, compaction processes modeling by a two-dimensional granular dynamics method. Nanoparticles interaction, in addition to known contact laws, included dispersive attraction, formation of a strong interparticle bonding (powder agglomeration) as well as the forces caused by viscous stresses in the contact region. For different densification rates, the pressure vs. density curves (densification curves) were calculated. Relaxation of the stresses after the compression stage was analyzed as well. The densification curves analysis allowed us to suggest the dependence of compaction pressure as a function of strain rate. It was found that in contrast to the plastic flow of metals, where the yield strength is proportional to the logarithm of the strain rate, the power-law dependence of applied pressure on the strain rate as $ppropto v^{1/4}$ was established for the modeled nanosized powders.
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