Constitutive model for physical ageing in amorphous glassy polymers

Constitutive equations are derived for the linear viscoelastic behaviour of amorphous glassy polymers subjected to physical ageing. A polymer is treated as an ensemble of cages where relaxing regions are trapped. At random times flow units hop to higher energy levels in their potential wells as they are thermally activated. Rearrangement occurs when a relaxing region reaches some liquid-like state in a hop. Our main hypothesis is that the energy landscape of a glassy polymer in phase space is independent of temperature, whereas the energy level of the liquid-like state is not, its position being determined by the current and fictive temperatures. In the vicinity of some thermal equilibrium, the fictive temperature obeys an analogue of the Tool equation, where the characteristic time is proportional to the characteristic time of rearrangement in the ensemble of relaxing regions. The governing equations for the fictive temperature and constitutive equations for the viscoelastic response of amorphous polymers are developed and verified by comparison with experimental data for polycarbonate and two epoxy glasses. Fair agreement is demonstrated between observations and results of numerical simulations.