Microscopic Dynamics in the Strain Hardening Regime of Glassy Polymers

Abstract

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.

Theory of Plasticity and Strain Hardening of Glassy Polymers

“…This increase of β corresponds to a decrease of the width of the DRT. Then, β decreases up to the end of the tensile test, which corresponds to an increase of the width of the DRT during strain hardening, as observed experimentally by Lee et al − and by Hem et al , …”

“…The evolution of τ c is very similar to that of τ d or τ α at the same temperatures. The evolution of β (Figure b) is non-monotonic, as has been observed experimentally by the groups of Ediger − and of Ciliberto. − In the same way as in simulations without strain hardening, β first increases up to a temperature-dependent strain value of about 30 to 45%, which corresponds to the onset of strain hardening. This increase of β corresponds to a decrease of the width of the DRT.…”

“…For large deformation amplitudes, Hem et al have argued that, for polymers which experience strain hardening, monomer orientation contributes to increasing free-energy barriers, which become normalΔ F ( σ ∼ , T , ρ ) = normalΔ F 0 ( T , ρ ) − ξ 3 σ ∼ : σ ∼ 2 G 0 ′ + N normalc κ ( ε ) where ε is the strain. This is of course a short-hand notation since the orientation depends on the whole deformation history and relaxes, at least partially, during the applied deformation.…”

“…The dynamics is accelerated even before yield up to the stress-softening regime and the onset of plastic flow. Conversely, the dominant relaxation time τ α increases in the strain-hardening regime. − ,− It was also observed that the evolution of the width of the DRT is non-monotonic. The width first decreases, then reaches a minimum at the end of the stress softening regime, and increases again in the strain-hardening regime.…”

“…Indeed, the measured increase of the stress in the strain-hardening regime is consistent with the increase of the monomer relaxation time τ α . It was argued by Hem et al , that this increase of the relaxation time may account for an additional contribution to the flow stress of the order of σ normalh normala normalr normald ( ε ) = G 0 ′ ( τ α false( ε false) − τ s o f t ) ε̇ , where ε (resp. ε̇ ) is the strain (resp.…”