Structure of plastically compacting granular packings

Abstract

In this paper we present results of structural studies of compacting experimental systems of ductile grains in two and three dimensions. The high precision of our two-dimensional experiments enables a detailed study of the evolution of coordination numbers and local crystalline arrangements as a function of the packing fraction. The structure in both dimensions deviates considerably from that of hard disks and spheres, although geometrically, crystalline arrangements dominate on a local scale ͑in two dimensions͒. In three dimensions, the evolution of the coordination number is compared to experimental packings of hard and ductile grains from the literature. This comparison shows that the evolution of coordination number with packing fraction is not unique for ductile systems in general, but must depend on rheology and grain size.

Coordination measurements in compacted NaCl irregular powders using X-ray microtomography

“…Coordination: Table 2 shows that the average coordination number Z of the initial packing for both kinds of particles (Z = 10 and Z = 11) is significantly larger than for spherical particles (typically Z = 6 for random close packed spheres 1,[12][13][14]23,24 ). This observation is not likely to be caused by the spread in particle size.…”

“…[1][2][3][4][5][6][7] In the theory of densification processes, powder particles are generally assimilated to spheres, most often of a single size. For monomodal spherical powders, the coordination number Z and contact area A have been measured using quantitative metallography, 8 and their evolution with the packing density was predicted by Arzt 1,9 whose model was later simplified by Helle et al 10 Since that time, several other authors have also * used micromechanical analysis (e.g., 11 ) and experiment (e.g., 12 ) to characterize these structural parameters.…”

“…Evolution of the mean coordination number Z with packing density: experimental data from the present study 75 ( ) and 400 m salt ( ) and linear fit ( ), compared with experimental data of isostatic compaction of sphere packings from Fischmeister et al8 (᭹) and Uri et al12 ( ), predictions from the discrete element simulations of this work without friction ( ) and with friction μ = 0.2 + no particle rotation ( ), and analytical sphere packing model of Arzt for cold-compaction ( ) 1 .…”

Oscillatory ductile compaction dynamics in a cylinder

“…New contacts would preferentially form in the vertical direction, because of the anisotropic compaction, and thus would tend to redirect stresses toward the bottom. The number of new contacts in the ensemble is limited, and the average number of contacts per grain increased from 6.5 to 7 [20] during a typical experiment. 50-100 new contacts were expected to form during an experiment, which is roughly twice the typical number of oscillations.…”

“…The average contact diameter, d c , was found by first taking the average value of each contact diameter over the series of time steps in t ∈ [20,60], and then find the average of this set, d c = 2.66 ± 0.02 mm.…”