Structural aging of a cohesive and amorphous granular solid under cyclic loading

Abstract

We investigate how cyclic loading evolves the structure and deformation behaviors of a granular raft composed of particles floating at an air-oil interface. The raft has a disordered particle packing structure, and is cohesive due to capillary interactions between particles. Under uniaxial cyclic loading with a small strain amplitude, the raft's packing structure experiences an aging process characterized by logarithmically increasing packing fraction and decreasing structural heterogeneity. The observed structural change is due to particle dynamics that are organized around morphologically evolving voids in the raft. The raft is then subjected to quasi-static tension or compression tests until failure. In comparison with non-aged rafts, the rafts that experienced cyclic loading show a higher strength, higher stiffness, and lower ductility, along with qualitatively different features, such as a stress overshoot in the loading curve.

Figures (7)

• Figure 1: a) Schematic of the experimental setup with an image of the particle packing. b) A schematic demonstrating the procedure for a single loading cycle. c) Images demonstrating a tensile loading test. d) Images demonstrating a compression loading test.
• Figure 2: Snapshots of granular rafts subjected to a variety of loading amplitudes at several different loading cycle numbers.
• Figure 3: Dynamic and structural quantities during cyclic loading with amplitude $\delta_A/L_0=0.03$ over the course of $N=1000$ cycles. a) Normalized particle mean-squared displacement vs. the cycle number. The orange curve is the original MSD and the blue is the cage-relative MSD. Slope of one provided for reference. b) The system-averaged $D^2_{\mathrm{min}}$ vs. the cycle number. c) The global packing fraction vs. the cycle number. d) The system-averaged bond order parameter $\Psi_6$ vs. the cycle number. e) Distribution of $Q_k$ for $N=0$ (yellow) and $N=1000$ (blue). The solid curve is a fit to the Gaussian distribution. Inset demonstrates the Voronoi cell anisotropy vectors for a single Delaunay triangle. f) The standard deviation of $Q_k$ vs. the cycle number. In all panels, the data points and shades respectively represent the mean and the test-to-test fluctuations from 19 repetitions.
• Figure 4: Void identification and void area calculation. a) A binarized image showcasing an identified void. b) The original experimental image corresponding to a), overlaid with its Delaunay triangles highlighted in red. An example triangle $k$ is highlighted with black borders, and the associated particles are highlighted in orange. The circular sectors of the particles are highlighted in green. The insets illustrate the areas $A^k_{\mathrm{bp}}$, $A^k_{\mathrm{sc}}$, and $A_k$ that are calculated for each triangle $k$. c) Distributions of void areas based on the number of constituent particles making up the boundary of a void across all experiments taken at $N=1000$. d) A plot of the system-averaged void size across all experiments against the cycle number. The shaded region indicates standard error across repeated experiments.
• Figure 5: Dynamics of particles near voids. a) An experimental image overlaid with particle trajectories (blue) and large identified voids (red). Trajectories are from $N=0$ to $N=1000$. b) Relative displacement field around a void from $N=0$ to $N=1000$ with $N_\textrm{bp}=4$, averaged across all experiments. c) Average displacement field around a void from $N=0$ to $N=1000$ with $N_\textrm{bp}>4$ across all experiments. d) Particles colored by $D^2_{\mathrm{min},L}$ with large voids highlighted in red. e) The averaged $\bar{D}^2_{\mathrm{min},L}$ of particles as a function of their distance to the closest void, plotted for different void sizes.