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 w τ 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 w τ 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 λ w in the strain hardening regime, and we let the sample age for a waiting time t w , 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 t w . 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.

We extend a theory for the deformation of glassy polymers based on the heterogeneous nature of the dynamics up to the strain-hardening regime. We attribute the latter to the increase of free-energy barriers for α-relaxation as a consequence of local orientation of monomers. The free-energy barriers are set on a scale ξ ≈ 5 nm or of about N c ∼ 1000 monomers which are involved in the α-relaxation mechanism. The variation of the local free-energy barriers is given by the expression , where ΔF 0 is the free-energy barrier per monomer in the glassy state, typically ∼40–45k B T g for an aged polymer, is the local order parameter (nematic in nature) whose distribution is computed during the course of deformation, is the local stress, and G 0′ is the bulk glassy modulus. is an energy scale of the typical order of 0.2–0.3k B T g. The second term is negative and is responsible for yielding and the onset of plastic flow. The third one is positive and becomes important after a large deformation has significantly oriented the chains on the scale of the monomers. It may overcompensate the decrease of the free-energy barriers due to the increasing stress and is responsible for strain hardening. Since the contribution of the stress to the reduction of the free-energy barrier between stress softening and the deformation λ ∼ 2 is of the order of −5k B T g, the contribution which leads to strain hardening, , is found to be of the order of 10 k B T g, which corresponds to an increase of the order of 0.01k B T g per monomer. This order of magnitude is compatible with the calculated values of the order parameter q ∼ 0.3 in the direction of tension during our simulations as well as that measured by Vogt et al. (1990) by NMR. We calculate the evolution dynamics of the order parameter . Its dynamics is controlled by a driving force due to the local stress and a relaxation process due to rotational diffusion. The latter is entropic in nature and may be very slow in glassy polymers. We compare the predictions of our model to recent experimental results regarding the evolution of both the dominant relaxation time under applied strain and the width of the relaxation times distribution up to a large deformation amplitude, and more specifically their non-monotonic behavior.