Microscopic Dynamics in the Strain Hardening Regime of Glassy Polymers

We study by dielectric spectroscopy the molecular dynamics of relaxation processes during plastic flow of glassy polymers up to the strain hardening regime for three different protocols of deformation. The measured dielectric spectra cover 4 decades in frequencies and allow us to measure the evolution as a function of the applied strain of the dominant relaxation time τα and of the width wτ of the distribution of relaxation times. The first protocol is performed at constant strain rate λ̇. We confirm that for increasing strain both τα and wτ first decrease, reaching a minimum in the stress softening regime before increasing in the strain hardening regime. In the second protocol we stop the deformation at some point λw in the strain hardening regime, and we let the sample age for a waiting time tw, during which the applied stress remains high. Upon resuming the deformation at constant λ̇, stress–strain displays a yield stress and a stress softening regime comparable in magnitude to that of the reference protocol before rejoining the reference curve. In contrast, the dielectric spectrum measured during the second protocol recovers the one measured during the reference curve much later than strain–stress. In the third protocol the stress is canceled during tw. In this case, after recovering the constant λ̇ the dielectric spectrum and the stress–strain curve rejoin almost immediately the reference curve. We interpret these different behaviors as the consequence of changes in the free energy barriers for α-relaxation induced by the stress applied to the sample. These changes are the sum of two contributions: (a) The first one, which allows for plastic flow, is due to the applied stress σ and, according to a recently published theory, scales as −σ2. (b) The second contribution κ(λ), which is a function of the chain orientation at the monomer level, is positive and is responsible for the stress hardening regime. The first one evolves immediately upon varying the stress, whereas the second relaxes very slowly upon cessation of the applied stress. Our interpretation for the results of the third protocol is that aging dynamics is frozen when the stress is removed, as it is known for polycarbonate at room temperature. Our experiments set precise conditions for a theory of strain hardening.