Relaxation time of a polymer glass stretched at very large strains

The polymer relaxation dynamic of a sample, stretched up to the stress hardening regime is measured at room temperature as a function of the strain $\lambda$ for a wide range of the strain rate $\dot{\gamma }$ using an original dielectric spectroscopy set up. The mechanical stress modifies the shape of the dielectric spectra mainly because it affects the dominant polymer relaxation time $\tau$, which depends on $\lambda$ and is a decreasing function of $\dot{\gamma }$. The fastest dynamics is not reached at yield but in the softening regime. The dynamics slows down during the hardening, with a progressive increase of $\tau$. A small influence of $\dot{\gamma }$ and $\lambda$ on the relative dielectric strength cannot be excluded.

Figure 1

Stress evolution over a wide range of $\lambda$ at several constant strain rates: $2.5\times {10}^{-3}{\mathrm{s}}^{-1}$ (black), $2.5\times {10}^{-4}{\mathrm{s}}^{-1}$ (red), $2.5\times {10}^{-5}{\mathrm{s}}^{-1}$ (green), and $2.5\times {10}^{-6}{\mathrm{s}}^{-1}$ (blue) (from top to bottom). Several identical specimens have been measured for each strain rate. Inset: Tensile machine for dielectric measurements under stress: motor (A), load cell (B), linear transducer (C), sample fastening cylinders with the stretched polymer film (D), and electrodes (E) connected to the dielectric spectrometer (not sketched).

Figure 2

Dependence on $\lambda$ of ${\varepsilon }_n^{\prime }$ (a) and $\text{tn}\delta$ (b) measured at several frequencies during the stretching experiment at $\dot{\gamma }=2.5\times {10}^{-4}{\mathrm{s}}^{-1}$. In both panels the solid lines (left ordinate) represent ${\varepsilon }_n^{\prime }$ (a) and $\text{tn}\delta$ (b) as a function of $\lambda$, whereas the dashed line (right ordinate) show the corresponding evolution of the stress, which reveals that the low-frequency components of ${\text{DS}}_s$ have a maximum in the softening regime of the polymer film.

Figure 3

Normalized real part ${\varepsilon }_n^{\prime }$ (a) and $\text{tn}\delta$ (b) as a function of $\lambda$ measured at 7 Hz for different strain rates: $2.5\times {10}^{-3}{\mathrm{s}}^{-1}$ (black triangles), $2.5\times {10}^{-4}{\mathrm{s}}^{-1}$ (red circles), $2.5\times {10}^{-5}{\mathrm{s}}^{-1}$ (green squares), and $2.5\times {10}^{-6}{\mathrm{s}}^{-1}$ (blue diamonds).

Figure 4

The normalized real part ${\varepsilon }_n^{\prime }$ (a) and $\text{tn}\delta$ (b) as a function of frequency measured, at $T=25{}^{\circ }\mathrm{C}$, during a stretching experiment at $2.5\times {10}^{-4}{\mathrm{s}}^{-1}$ at different values of the strain: $\lambda =1.00$ (equilibrium), $\lambda =1.08$ (plastic yield), $\lambda =1.17$ (softening regime), and $\lambda =1.70$ (hardening regime). In the background, continuous orange lines represent ${\varepsilon }_n^{\prime }$ (a) and $\text{tn}\delta$ (b) measured at $\lambda =1$ in the temperature range between $137{}^{\circ }\mathrm{C}$ (bottom orange curve) and $152{}^{\circ }\mathrm{C}$ (top orange curve) at $1{}^{\circ }\mathrm{C}$ increment [28].

Figure 5

(a) Dependence on frequency of $\text{tn}\delta$, measured in the softening regime $\lambda =1.17$, at different $\dot{\gamma }$: $2.5\times {10}^{-3}{\mathrm{s}}^{-1}$ (black triangles), $2.5\times {10}^{-4}{\mathrm{s}}^{-1}$ (red circles), $2.5\times {10}^{-5}{\mathrm{s}}^{-1}$ (green squares), and $2.5\times {10}^{-6}{\mathrm{s}}^{-1}$ (blue diamonds). The low-frequency parts of each curve are fitted by a power law (straight lines) $\text{tn}\delta =1/{\left(\omega {\tau }_{\mathrm{eff}}\right)}^{\beta }$. The timescale ${\tau }_{\mathrm{eff}}$ depends on $\dot{\gamma }$ but the scaling power $\beta =0.50\pm 0.05$ is found to be constant within experimental errors. (b) The fitted timescale ${\tau }_{\mathrm{eff}}$ as a function of the strain rate $\dot{\gamma }$ measured at several strains: $\lambda =1.17$ (softening regime), $\lambda =1.30$, and $\lambda =1.70$ (hardening regime). The relaxation time follows the law ${\tau }_{\mathrm{eff}}=a\left(\lambda \right)/\dot{\gamma }$ (dashed lines) with the coefficient $a\left(\lambda \right)$ plotted in the inset.