Mechanical rejuvenation and overaging in the soft glassy rheology model

Mechanical rejuvenation and overaging of glasses is investigated through stochastic simulations of the soft glassy rheology (SGR) model. Strain- and stress-controlled deformation cycles for a wide range of loading conditions are analyzed and compared to molecular dynamics simulations of a model polymer glass. Results indicate that deformation causes predominantly rejuvenation, whereas overaging occurs only at very low temperatures, small strains, and for high initial energy states. Although the creep compliance in the SGR model exhibits full aging independent of applied load, large stresses in the nonlinear creep regime cause configurational changes leading to rejuvenation of the relaxation time spectrum probed after a stress cycle. During recovery, however, the rejuvenated state rapidly returns to the original aging trajectory due to collective relaxations of the internal strain.

Figure 1

(a) Stress vs strain and (b) energy vs strain at zero noise temperature. Curves are obtained from an ensemble average of 10,000 particles with initial liquid temperatures of $x_l=2$ (solid) and $x_l=1.5$ (dashed).

Figure 2

(Color online) Relative difference in energy versus maximum strain after a single strain cycle of amplitude ${\gamma }_{\max }$. (a) Noise temperature $x=0.1$, 0.2, 0.3, 0.5, and 0.8 from bottom to top, $x_l=2$ and $\dot{\gamma }=0.25$ for each sample. (b) $x_l=1.25$, 1.5, 2.5, and 5 from top to bottom, $x=0.001$ and $\dot{\gamma }=0.25$ for each sample. (c) $\dot{\gamma }=1$ (circle), 0.5 (square), 0.25 (triangle), 0.1 (diamond), and 0.01 (cross), $x=0.5$ and $x_l=2$.

Figure 3

(Color online) Distribution of energy barriers after a zero temperature strain cycle. ${\gamma }_{\max }=1.5$ (circle), 2 (square), and 2.5 (triangle). The initial energy distribution $P_0\left(E\right)$ and the landscape density of states $\rho \left(E\right)$ are shown as dashed lines.

Figure 4

(Color online) Molecular dynamics results for the relative difference in energy versus strain after a single strain cycle. (a) $T=0.01$ (circle), 0.1 (square), and $0.2u_0∕k_B$ (triangle). The quench time is $t_{\mathrm{qu}}=750{\tau }_{\mathrm{LJ}}$ and $\dot{\gamma }=5.3\times {10}^{-5}{\tau }_{\mathrm{LJ}}^{-1}$ for each sample. (b) $t_{\mathrm{qu}}=750{\tau }_{\mathrm{LJ}}$ (square) and $7500{\tau }_{\mathrm{LJ}}$ (circle). $T=0.01u_0∕k_B$ and $\dot{\gamma }=5.3\times {10}^{-5}{\tau }_{\mathrm{LJ}}^{-1}$. (c) $\dot{\gamma }=5.3\times {10}^{-6}{\tau }_{\mathrm{LJ}}^{-1}$ (circle), $5.3\times {10}^{-5}{\tau }_{\mathrm{LJ}}^{-1}$ (square), and $5.3\times {10}^{-4}{\tau }_{\mathrm{LJ}}^{-1}$ (triangle). $T=0.2u_0∕k_B$ and $t_{\mathrm{qu}}=750{\tau }_{\mathrm{LJ}}$.

Figure 5

(Color online) Relative energy change due to a stress cycle applied for $t=10$. In (a) the energy difference is plotted versus the stress, and in (b) the same data is plotted versus the maximum strain in the stress cycle. $x=0.1$ (circles), 0.2 (squares), 0.4 (triangles), and 0.6 (diamonds). $x_l=2$ for each sample. The dashed line in (b) is the energy versus strain for an equivalent strain-controlled protocol at $x=0.1$.

Figure 6

(Color online) Creep compliance of the SGR model quenched from $x_l=\infty$ (see text) and aged for $t_w=100$ (circles), 316 (squares), 1000 (triangles), 3162 (diamonds), and 10 000 (×’s) at $x=0.5$ and $\sigma =0.75$ (within the nonlinear regime).

Figure 7

(Color online) (a) Energy as a function of wait time after a stress cycle of duration $t=t_w$. $\sigma =0.05$ (circles), 0.6 (squares), 0.7 (triangles), 0.75 (diamonds). $x=0.5$ and $x_l=\infty$ for each sample. (b) Scaled correlation functions for $t_w=100$, 316, 1000, 3162, and 10 000 (all overlapping) for $\sigma =0.75$. Data collapse is obtained for $\mu =0.68$.

Figure 8

(Color online) (a) Aging exponent versus the stress in the SGR model, as determined from the correlation functions (4) after a stress cycle of duration $t=t_w$. $x=0.5$ and $x_l=\infty$. (b) Aging exponent versus stress from molecular dynamics simulations of a model polymer glass using (circles) the creep compliance and (squares) the mean-squared displacement after stress release at $10t_w$. $T=0.2u_0∕k_B$.

Figure 9

(Color online) (a) Energy during a stress cycle and the subsequent recovery (solid line) compared to an unstressed glass (dashed). Samples are quenched from $x_l=\infty$ and aged for $t_w=100$ at $x=0.5$ before measurement. Stressed sample is loaded at $\sigma =0.7$ for $t=t_w$. (b), (c) The distribution of energy barriers of the unstressed sample (circles) and the stressed sample (+) at $t=125$ (b) and $t=800$ (c).