A model for the non-linear viscoelastic response and physical aging in glassy polymers

Abstract

Constitutive relations are derived for the non-linear viscoelastic behavior of amorphous polymers subjected to physical aging. The model is based on the concept of temporary networks, where a viscoelastic medium is treated as a network of active chains that break and reform due to micro-Brownian motion. With reference to the Adam–Gibbs theory of cooperative relaxation, the breakage and reformation rates are assumed to depend on the current temperature and the configurational entropy, which is determined as a difference between the specific entropies of the equilibrium liquid and glass. Unlike previous studies, the model accounts for the compressibility of polymers below the glass transition temperature. Constitutive equations for viscoelastic media at finite strains are developed using the laws of thermodynamics. For small values of strains, these relationships are simplified and reduced to linear integral equations with some internal time driven by the fictive temperature and the hydrostatic stress (an extension of the KAHR model to non-linear materials). To verify the constitutive model, we determine the adjustable parameters using the data obtained in short-term creep tests and comparing the results of numerical simulation with the observations in long-term tests. Fair agreement is demonstrated for the experimental data of high-density polyethylene and poly(vinyl chloride) with the numerical predictions.