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 λ for a wide range of the strain ratė γ, by an original dielectric spectroscopy set up. The mechanical stress modies the shape of the dielectric spectra mainly because it aects the dominant polymer relaxation time τ , which depends on λ and is a decreasing function ofγ. 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 τ. A small inuence ofγ and λ on the dielectric strength cannot be excluded. Mechanical and dynamical properties of polymers are intensively studied, due to their fundamental and technological importance [1]. When strained at a given strain rate, beyond the elastic regime in which the stress is proportional to strain, glassy polymers exhibit a maximum in the stress-strain curves (yield point) at a strain of a few percents [2] and the deformation becomes irreversible (see Fig.1). At larger strains, depending on the history of the sample [3], the stress drops (strain-softening regime) before reaching a plateau corresponding to plastic ow. Strain-hardening may then occur at even larger strains, depending on the molecular weight and on the cross-linking of the polymer [4]. The key new insights obtained either by numerical simulations [57] or experiments [8 11] are that strain hardening appears to be controlled by the same mechanisms that control plastic ow [1215]. However the microscopic mechanisms leading to such a mechanical behavior are not fully understood [16, 17]. For example it is unclear to what extent the relaxation dynamics in polymer glasses is modied when the sample is stretched into the plastic region (see for example refs.[1821]). The purpose of this letter is to bring new insight into this problem by presenting the results of experiments in which we performed dielectric spectroscopy of polymer samples stretched till the strain hardening regime. Di-electric spectroscopy, allows the investigation of the dynamics of relaxation processes by means of the polarization of molecular dipoles. It is directly sensitive to polymer mobility and probes directly the segmental motion. It can be used to quantify the mobile fraction of polymers. Measuring the dielectric response of polymers in situ had been pioneered by Venkataswamy et al. [22]. It is complementary to other techniques, such as Nuclear Magnetic Resonance [23] and the diusion of probe molecules [2426], used to study the molecular dynamics of polymers under stress. The dielectric spectroscopy has already been used in combination with mechanical deformation to study the dynamics in the amorphous phase of polymer under stress [27, 28]. The results of these experiments were limited to the yield point whereas the experimental studies of the microscopic behavior and processes FIG. 1. Stress evolution over a wide range of λ at several constant strain rates : 2.5 × 10 −3 s −1 (black), 2.5 × 10 −4 s −1 (red), 2.5 × 10 −5 s −1 (green) and 2.5 × 10 −6 s −1 (blue). 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 lm (D) and electrodes (E) connected to the dielectric spectrometer (not sketched). during strain hardening are more scarce. In this letter we present the results obtained by our original experimental apparatus which can measure with high accuracy the evolution of the Dielectric Spec-trum(DS) of a sample stretched, till the strain hardening regime, at dierent strain rates. Thus we can precisely compare the DS s obtained as a function of stress at room temperature with those (named DS T) obtained as a function of temperature in an unstressed sample. This comparison allows us to extract useful informations on the relaxation dynamics under stress at various strain rates. Our experimental results bring new important informa-tions because they clearly show an acceleration of the dynamics which reaches a maximum in the softening regions. Instead the molecular mobility slows down again during the strain hardening regimes