Yielding in an amorphous solid subject to constant stress at finite temperatures

Understanding the nature of the yield transition is a long-standing problem in the physics of amorphous solids. Here we use molecular dynamics simulations to study the response of amorphous solids to constant stresses at finite temperatures. We compare amorphous solids that are prepared using fast and slow quenches and show that for thermal systems, the steady-state velocity exhibits a continuous transition from very slow creep to a finite strain rate as a function of the stress. This behavior is observed for both well-annealed and poorly annealed systems. However, the transient dynamics is different in the latter and involves overcoming an energy barrier. Due to the different simulation protocol, the strain rate as a function of stress and temperature follows a scaling relation that is different from the ones that are shown for systems where the strain is controlled. Collapsing the data using this scaling relation allows us to calculate critical exponents for the dynamics close to yield, including an exponent for thermal rounding. We also demonstrate that strain slips due to avalanche events above yield follow standard scaling relations and we extract critical exponents that are comparable to the ones obtained in previous studies that performed simulations of both molecular dynamics and elastoplastic models using strain-rate control.

Figure 1

Strain rate as a function of the applied stress $\mathrm{\Sigma }$, at the steady state, for a poorly annealed system at different temperatures. The inset shows the same plot in semilogarithmic scale.

Figure 2

Data collapse of the part of the data close to ${\mathrm{\Sigma }}_c$ from Fig. 1 onto a single master curve using the scaling relation (1).

Figure 3

Data collapse of the data from Fig. 1 onto a single master curve using the scaling relation (3). The solid line is a fit to the function $a{f}^{\beta }$. The inset shows the same plot in semilogarithmic scale.

Figure 4

Effect of the cooling rate on the steady-state strain rate at $T={10}^{-4}$. We can see that even for a very slow quench the transition from creep to a flowing phase is continuous. The inset shows the same plot in semilogarithmic scale.

Figure 5

Strain rate as a function of time for simulations of a binary mixture. Different colors correspond to different stresses. The stress changes (from bottom to top) from $\mathrm{\Sigma }=0.02$ (cold) to $\mathrm{\Sigma }=0.48$ (warm) in steps of 0.02. The black line represents the transient strain rate at approximately ${\mathrm{\Sigma }}_c$. (a) Results for a sample prepared using the slowest quench protocol. One can see that for the slow quench, the system becomes arrested for higher stress values and exhibits a transient decrease in the strain rate followed by an increase towards the steady state. (b) Results for samples prepared using the fastest quench protocol.

Figure 6

Avalanche sizes obtained from the thermostated simulations. The red horizontal line represents the average strain rate $\langle \dot{\gamma }\rangle$ and the colored parts of the curve represent avalanches. An avalanche duration is the time that the strain rate spends above the average value.

Figure 7

Avalanche size distribution at $\mathrm{\Sigma }=0.5$ for $N=9216$ at $T={10}^{-4}$.

Figure 8

(a) Avalanche size distributions for different system sizes $L$ ($L=\sqrt{N}$ is the linear system size). (b) Finite-size scaling of the avalanche size distribution exhibiting data collapse.