Unified Description of Aging and Rate Effects in Yield of Glassy Solids

The competing effects of slow structural relaxations (aging) and deformation at constant strain rate on the shear yield stress ${\tau }^y$ of simple model glasses are examined using molecular simulations. At long times, aging leads to a logarithmic increase in density and ${\tau }^y$. The yield stress also rises logarithmically with rate but shows a sharp transition in slope at a rate that decreases with increasing age. We present a simple phenomenological model that includes both intrinsic rate dependence and the change in properties with the total age of the system at yield. As predicted by the model, all data for each temperature collapse onto a universal curve.

Figure 1

Shear yield stress as a function of waiting time. (a) Four different rates $\dot{ϵ}={10}^{-3}{t}_{\mathrm{LJ}}^{-1}$ (■), ${10}^{-4}{t}_{\mathrm{LJ}}^{-1}$ (◆), ${10}^{-5}{t}_{\mathrm{LJ}}^{-1}$ (▲), and ${10}^{-6}{t}_{\mathrm{LJ}}^{-1}$ (☆) at $T=0.2u_0/k_B$. The solid line fits to the large $t_w$ region have common slope $s_0$, and successive lines are separated by the vertical shift $s_1\ln (10)$ predicted by Eq. (2). (b) Five different temperatures $T=0.2u_0/k_B$(■), $0.15u_0/k_B$(◆), $0.1u_0/k_B$(▲), $0.05u_0/k_B$(☆), and $0.01u_0/k_B$ (□) at fixed rate $\dot{ϵ}={10}^{-4}{t}_{\mathrm{LJ}}^{-1}$. The solid lines are logarithmic fits to the data at each $T$, and their slopes $s_0$ are plotted against $T$ in the inset. The straight line in the inset is a linear fit through the origin.

Figure 2

Shear yield stress as a function of rate for 4 different waiting times $t_w=750t_{\mathrm{LJ}}$ (■), $7500t_{\mathrm{LJ}}$ (◆), $75000t_{\mathrm{LJ}}$ (▲), and $750000t_{\mathrm{LJ}}$ (☆) at $T=0.2u_0/k_B$. The solid lines indicate logarithmic fits with slopes of $s_1=0.037$ and $s^{\prime }=0.006$ for long and short waiting times, respectively. Error bars are comparable to the symbol size.

Figure 3

Plot of data for all $t_w$ and $\dot{ϵ}$ at $T=0.2u_0/k_B$ (□), $0.1u_0/k_B$ (⋄), $0.05u_0/k_B$ (△), and $0.01u_0/k_B$ (☆) and universal curves (solid lines) predicted by Eq. (2).