Physical aging and nonlinear viscoelasticity of amorphous glassy polymers

Constitutive equations are developed for the nonlinear viscoelastic response of polymeric glasses subjected to physical aging. An amorphous polymer is treated as an ensemble of cooperatively rearranged regions (CRRs) connected by links. A CRR is modeled as a point trapped in its potential well on the energy landscape. At random times, CRRs hop to higher energy levels as they are thermally agitated. In the stress-free state, all CRRs are located at the bottom levels of their potential wells. Under loading, they ascend to higher energy levels, the ascent energy being proportional to the mechanical energy of the relaxing region. In the sub-yield region, some links between CRRs break, providing additional degrees of freedom for relaxing regions (which results in an increase in the rate of rearrangement). Stress–strain relations are derived and verified by comparison with experimental data in relaxation tests for polycarbonate and poly(methyl methacrylate) [PMMA]. Fair agreement is demonstrated between observations and results of numerical simulation. The effect of annealing temperature, waiting time and the strain level on adjustable parameters in the constitutive equations is studied in detail. It is demonstrated that the time–aging time superposition principle is not necessary for the description of physical aging. Analysis of experimental data in the framework of the coarsening concept reveals that mechanical loading does not induce rejuvenation of glassy polymers, but results in an increase in the relaxation rate in accordance with the theory of thermomechanically activated processes.