Nonlinear stress relaxation is far more difficult to model than creep. The present work shows that in the case of a polymer, focusing on the material's nonaffine local strains and stresses provides a sound basis for modeling stress relaxation in a physically realistic way. This new, though still simplified, model (1) describes a clearly nonlinear (strain‐dependent) behavior that only becomes linear at very low strains, (2) has the potential to predict faster stress relaxation than creep, (3) is the first to account for the effect of reduced differences between the initial and the final plateau modulus, as in the case of semicrystalline materials, which increase the longest relaxation times, (4) explicitly quantifies the effect of temperature, when one considers the whole distribution of relaxation times, (5) may be extended to also account for the effect of changes in free volume, and (6) ensure very fast computation of relevant physical parameters and extrapolated long time behavior at any temperature, from experiments near room temperature spanning only a few hours. All predicted features generally agree with known experimental behavior, and initial comparisons with experimental stress‐relaxation modulus data for a poly(methylmethacrylate) validate the formulation to within relative errors of 1.34%. The model may nevertheless still be upgraded beyond the much simplified physical picture adopted here by relaxing most the present assumptions (e.g., by upgrading the two‐level process description) and, eventually, by also taking into account the effect of the fast initial strain ramp up to its nominal value. The work also discusses in detail the values and physical meaning of the model parameters. POLYM. ENG. SCI., 54:404–416, 2014. © 2013 Society of Plastics Engineers

The stress‐ and temperature‐dependent non‐linear creep behaviour of polymers and other materials is quantitatively modelled as a superposition of a wide range of activated motions at the molecular scale, covering wide but well‐defined space and time scales. The resulting time, temperature and stress dependences are coupled (not fully separable) except at low stress values, where linear viscoelastic behaviour is directly obtained, improving on previous (approximate or questionable) time‐temperature and time‐stress superposition or equivalence relationships. The behaviour has been shown to have a strong cooperative nature, which may be interpreted in terms of varying clusters of identifiable structural elements within the material. Reasonably good descriptions of the experimental creep behaviour of both amorphous and semicrystalline polymers have already been achieved, but this work concentrates on the behaviour of an amorphous polycarbonate (PC), including the physical characterization and modelling of its retardation time spectrum.

We expand our analytical modeling strategy for polymer non-linear stress relaxation (A) to specify the remaining steps to accurately deal with the nonaffine nature of the materials' local strains and stresses relative to their average overall values, and (B) to make it consistent with a new cooperative theory of amorphous materials dynamics, providing a model of tunable fragility that sheds light to most aspects of the behavior, including the glass transition. The stress relaxation models (1) describe a nonlinear (straindependent) behavior that becomes linear at very low strains, (2) quantify the effect of temperature, (3) may quantify the effects of changes in free volume, and (4) ensure very fast computations of the materials' response irrespective of the experimental time scale. The models are sensitive to the influence of different initial states of the material, as may result from varying degrees of molecular orientation and aging levels, and are able to predict from experimental stress relaxation moduli (for a poly (methylmethacrylate)-PMMA and a bis-phenol-A polycarbonate-PC) the values of the crossover frequency, m c , crossover temperature, T c , and the minimum activation energy, in addition to the initial and long-time plateau moduli, in agreement with independently measured values. POLYM.ENG. SCI., 56:348-360,

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Non-linear creep is described by a non-simulative, analytical, dynamic molecular modelling approach. Elementary, molecular-scale, process-relevant frequencies are derived by adequate kinetic formulation. They follow almost exactly an Arrhenius-like behaviour with a range of activation enthalpies. Their relative contribution to the overall macroscopic behaviour of the materials is quantified to account for the materials’ retardation time spectra and final non-Arrhenius behaviour. A new creep compliance equation is derived, yielding a fully coupled timetemperature- stress formulation, with long-term predictive capability. Experimental data for poly(methyl methacrylate) are analysed to identify the extent to which timetemperature and time-stress correspondence relationships may be valid, and it is shown that they are approximations (especially the latter), limited to narrow ranges of experimental variables, in contrast to the proposed model, which more reasonably fits the experimental behaviour.