Structural Relaxation Time of a Polymer Glass during Deformation

In order to determine the structural relaxation time of a polymer glass during deformation, a strain rate switching experiment is performed in the steady-state plastic flow regime. A lightly cross-linked poly(methylmethacrylate) glass was utilized and, simultaneously, the segmental motion in the glass was quantified using an optical probe reorientation method. After the strain rate switch, a nonmonotonic stress response is observed, consistent with previous work. The correlation time for segmental motion, in contrast, monotonically evolves toward a new steady state, providing an unambiguous measurement of the structural relaxation time during deformation, which is found to be approximately equal to the segmental correlation time. The Chen-Schweizer model qualitatively predicts the changes in the segmental correlation time and the observed nonmonotonic stress response. In addition, our experiments are reasonably consistent with the material time assumption used in polymer deformation modeling; in this approach, the response of a polymer glass to a large deformation is described by combining a linear-response model with a time-dependent segmental correlation time.

Figure 1

High-to-low strain rate switching experiment (switching from $6\times {10}^{-5}$ to $6\times {10}^{-6}{\mathrm{s}}^{-1}$ at $t=3075\mathrm{s}$). (a) Time dependence of measured stress $\sigma$; along with the functional fit $Y=Y_s+(Y_i-Y_s)\exp [-(t-t_0)/{\tau }_Y]$ starting after the minimum at 4000 s, shown in red. The fitted transition time is ${\tau }_{\sigma }=3760\pm 160\mathrm{s}$. (b) Measured local strain rate; ${\dot{\gamma }}_{\mathrm{locl}}$ is plotted with $t$. (c) A subset of the normalized anisotropy decay curves $r(t^{\prime })/r(0)$, measured at various times $t$ after the start of deformation, are shown as examples. Solid lines are KWW fits. (d) The segmental correlation time ${\tau }_{\mathrm{seg}}$ extracted from the KWW fits are plotted vs time $t$. Error bars show fitting errors. Solid curves are similar functional fits as in (a) with ${\tau }_{\tau \text{−}\mathrm{seg}}=165\pm 10$ for the green curve and ${\tau }_{\tau \text{−}\mathrm{seg}}=1330\pm 110$ for the magenta curve.

Figure 2

Low-to-high strain rate switching experiment (switching from $6\times {10}^{-6}$ to $6\times {10}^{-5}{\mathrm{s}}^{-1}$ at $t=17114\mathrm{s}$). Variations of $\sigma$, ${\dot{\gamma }}_{\mathrm{locl}}$, a few $r(t^{\prime })/r(0)$, and ${\tau }_{\mathrm{seg}}$ are shown in (a)–(d) respectively. Error bars are fitting errors. Solid curves in (d) are the functional fits $Y=Y_s+(Y_i-Y_s)\exp [-(t-t_0)/{\tau }_Y]$ with timescales ${\tau }_{\tau \text{−}\mathrm{seg}}=2365\pm 85\mathrm{s}$ for the green curve and ${\tau }_{\tau \text{−}\mathrm{seg}}=200\pm 45$ for the magenta curve.

Figure 3

Experimental time vs material time: (a),(c) The variation of ${\tau }_{\mathrm{seg}}$ vs $t$ during the full span of the experiments [fitted data from Figs. 1 and 2] is shown along with the calculated material time. (b),(d) Normalized anisotropy decay curves for the two types of experiments are replotted. In material time, ${\xi }^{\prime }$ is used to denote elapsed material time since the beginning of an anisotropy measurement.

Figure 4

Chen-Schweizer model predictions for strain rate switching experiments on PMMA glass, using the global strain rates $6\times {10}^{-5}$ and $6\times {10}^{-6}{\mathrm{s}}^{-1}$ as inputs. Model outputs are the time variation of (a) the stress $\sigma$, (b) the segmental correlation time ${\tau }_{\mathrm{seg}}$, and (c) the structural state variable $S_0$. Black curves are for high-to-low strain rate switching, and dotted red lines are for low-to-high strain rate switching.