Density scaling and quasiuniversality of flow-event statistics for athermal plastic flows

Athermal steady-state plastic flows were simulated for the Kob-Andersen binary Lennard-Jones system and its repulsive version in which the sign of the attractive terms is changed to a plus. Properties evaluated include the distributions of energy drops, stress drops, and strain intervals between the flow events. We show that simulations at a single density in conjunction with an equilibrium-liquid simulation at the same density allow one to predict the plastic flow-event statistics at other densities. This is done by applying the recently established “hidden scale invariance” of simple liquids to the glass phase. The resulting scaling of flow-event properties reveals quasiuniversality, i.e., that the probability distributions of energy drops, stress drops, and strain intervals in properly reduced units are virtually independent of the microscopic pair potentials.

Figure 1

(a) Typical stress-strain signal for a glass that is shear deformed under athermal quasistatic conditions. The horizontal dashed line indicates the steady-state average flow stress $\langle \sigma \rangle$. (b), (c) Illustration of the key observables measured in this work: the (shear) stress drops $\Delta \sigma$, the strain intervals between drops $\Delta \gamma$, and the energy drops $\Delta U$. (d) The Lennard-Jones pair potential of the Kob-Andersen binary Lennard-Jones (KABLJ) model and its repulsive counterpart with a plus in front of the $r^{-6}$ term (RKABLJ) as functions of the distance between particles $i$ and $j,r_{ij}$.

Figure 2

Distributions of potential-energy drops $P\left(\Delta U\right)$ for (a) the KABLJ and (c) the RKABLJ systems at different densities, and distributions of stress drops $P\left(\Delta \sigma \right)$ for (b) the KABLJ and (d) the RKABLJ systems. At the reference densities, which are $1.5$ for the KABLJ system and $1.0$ for the RKABLJ system, each distribution was fitted with a smooth function (green dashed curves). For each system the scaling function $h\left(\rho \right)=A{\rho }^4\pm B{\rho }^2$ was found by simulations of the equilibrium liquid at the reference density (see the main text for details). Based on these inputs and a dimensional analysis, the distributions at other densities are uniquely predicted (purple full curves).

Figure 3

Mean steady-flow observables as functions of density for the KABLJ (top panels) and RKABLJ (bottom panels) systems. The continuous curves are proportional to $h\left(\rho \right)$ or $\rho h\left(\rho \right)$ for quantities having units of energy or stress, respectively. The purple dashed lines in two of the subfigures give examples of the predictions of asymptotic power-law scaling functions $h\left(\rho \right)\propto {\rho }^{\gamma }$. Previous effective scaling theories [44] predicted power laws corresponding to density-independent scaling exponents, which would imply the purple dashed lines to coincide. The deviations from simple power-law scaling are most pronounced for the RKABLJ system.

Figure 4

Distributions of dimensionless energy drops $\Delta U/h\left(\rho \right)$, stress drops $\Delta \sigma /\left[\rho h\left(\rho \right)\right]$, and strain intervals $\Delta \gamma$ for the KABLJ, RKABLJ, and $n=10$ inverse power law (IPL) systems. This figure demonstrates quasiuniversality of the plastic flow-event properties. Note that this is not an empirical collapse; no adjustable parameters were involved.