Fragility and hysteretic creep in frictional granular jamming

The granular jamming transition is experimentally investigated in a two-dimensional system of frictional, bi-dispersed disks subject to quasi-static, uniaxial compression at zero granular temperature. Currently accepted results show the jamming transition occurs at a critical packing fraction $ϕ_c$. In contrast, we observe the first compression cycle exhibits {\it fragility} - metastable configuration with simultaneous jammed and un-jammed clusters - over a small interval in packing fraction ($ϕ_1 < ϕ< ϕ_2$). The fragile state separates the two conditions that define $ϕ_c$ with an exponential rise in pressure starting at $ϕ_1$ and an exponential fall in disk displacements ending at $ϕ_2$. The results are explained through a percolation mechanism of stressed contacts where cluster growth exhibits strong spatial correlation with disk displacements. Measurements with several disk materials of varying elastic moduli $E$ and friction coefficients $μ$, show friction directly controls the start of the fragile state, but indirectly controls the exponential slope. Additionally, we experimentally confirm recent predictions relating the dependence of $ϕ_c$ on $μ$. Under repetitive loading (compression), the system exhibits hysteresis in pressure, and the onset $ϕ_c$ increases slowly with repetition number. This friction induced hysteretic creep is interpreted as the granular pack's evolution from a metastable to an eventual structurally stable configuration. It is shown to depend upon the quasi-static step size $Δϕ$ which provides the only perturbative mechanism in the experimental protocol, and the friction coefficient $μ$ which acts to stabilize the pack.

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