Rate and age-dependence of shear yield stress in loose sphere packings

Frictional packings of hard spheres can be stable in loose volume fractions well below random close packing. We study the stability of these solids to shear perturbations in the little-studied regime close to the random loose packing limit [1]. We present experimental data on the shear yield stress as a function of rate and age in sedimented loose packings of frictional, non-cohesive, PMMA spheres. The yield stress is found to depend on both the rate of strain and age of the packing since last breakage, both to approximately the positive one-third power. The regime of elastic response at finite strain-rate is insensitive to the viscosity of the interstitial fluid. With this common choice of materials and preparation conditions, no rate-independent elastic regime was seen, even at the smallest strains experimentally achieved. [1] Farrell GR, Martini KM, and Menon N, \emph{Soft Matter}, \textbf{6}, 2925 (2010).