Computer simulation of model cohesive powders: Plastic consolidation, structural changes, and elasticity under isotropic loads

Abstract

The quasistatic behavior of a simple two-dimensional model of a cohesive powder under isotropic loads is investigated by discrete element simulations. We ignore contact plasticity and focus on the effect of geometry and collective rearrangements on the material behavior. The loose packing states, as assembled and characterized in a previous numerical study [Gilabert, Roux, and Castellanos, Phys. Rev. E 75, 011303 (2007)], are observed, under growing confining pressure P , to undergo important structural changes, while solid fraction Phi irreversibly increases (typically, from 0.4-0.5 to 0.75-0.8). The system state goes through three stages, with different forms of the plastic consolidation curve, i.e., Phi as a function of the growing reduced pressure P;{*}=PaF_{0} , defined with adhesion force F0 and grain diameter a . In the low-confinement regime (I), the system undergoes negligible plastic compaction, and its structure is influenced by the assembling process. In regime II the material state is independent of initial conditions, and the void ratio varies linearly with lnP [i.e., Delta(1Phi)=lambdaDelta(lnP;{*}) ], as described in the engineering literature. Plasticity index lambda is reduced in the presence of a small rolling resistance (RR). In the last stage of compaction (III), Phi approaches an asymptotic, maximum solid fraction Phi_{max} , as a power law Phi_{max}-Phi proportional, variant(P;{*});{-alpha} , with alpha approximately 1 , and properties of cohesionless granular packs are gradually retrieved. Under consolidation, while the range xi of fractal density correlations decreases, force patterns reorganize from self-balanced clusters to force chains, with correlative evolutions of force distributions, and elastic moduli increase by a large amount. Plastic deformation events correspond to very small changes in the network topology, while the denser regions tend to move like rigid bodies. Elastic properties are dominated by the bending of thin junctions in loose systems. For growing RR those tend to form particle chains, the folding of which, rather than tensile ruptures, controls plastic compaction.

Discrete simulation of model, loose cohesive powders: plastic consolidation, fractal microstructure and tensile strength

“…On reducing P * at any stage (as shown on Fig. 3 for P * = 13.3), Φ remains constant, apart from small, nearly elastic [11] changes. Subsequently, plastic compaction is resumed only if the highest value P * c applied in the past, the preconsolidation pressure, is exceeded.…”

“…10 −4 F 1 a -with F 1 = Max{F 0 , aP}, with a similar tolerance on controlled internal stresses. The stability of such equilibrium states can also be checked with stiffness matrcies [11]. Considerable structural changes are witnessed under growing P * , as the initial loose structure (Fig.…”

“…[10,11], which might be consulted for more details on the model, we consider 2D assemblies of N disks, with diameters uniformly distributed in the interval [a/2, a]. The disks interact with their contacting or very close neighbors, with forces that combine normal and tangential elasticity (involving spring constants K N , K T ), Coulomb friction (with friction coefficient µ), some viscous damping (the values of which are irrelevant in quasistatic conditions), and some simplified form of van der Waals attraction.…”

“…Such a situation, with loose systems, has hardly been addressed by numerical means, as the recent literature rather explored dynamic compaction [4,5], gravity deposition [6], steady flows [7], or denser materials [8,9]. We introduce a simple model material and report on its consolidation properties, in relation to its microstructure, thus presenting a brief account of studies published in two recent papers [10,11], to which a section with new results on the resistance to tension is added. The paper ends with a short discussion.…”

Simulation of the macromechanical behavior of oxide nanopowders during compaction processes

“…The granular dynamics method (or discrete element method) suggested for the first time by Cundall and Strack [21] and being developed strongly at present time [12,13,14,15,22,23,24,25,26,27,28,29,30] is a convenient alternative to real and laborious experiments and is a very promising approach, which allows finding the detailed information on powder systems. Due to a great extent of the sphericity and the nondeformability (strength) of individual particles of oxide nanopowders being studied, the granular dynamics method is particularly attractive and promising tool of the theoretical analysis.…”