Viscoelastoplasticity of amorphous glassy polymers

Constitutive equations are derived for the viscoelastoplastic response of glassy polymers at isothermal loading with small strains. An amorphous polymer is treated as an ensemble of plastic flow units (at the meso-level), each of which consists of a number of cooperatively rearranging regions (at the micro-level). In the phase space, a rearranging region is modeled as a point trapped in a cage (potential well), where it hops to higher energy levels. Rearrangement occurs when the relaxing region reaches (in a hop) some liquid-like energy level, whose position with respect to the energy landscape is determined by the intensity of plastic strains in the flow unit. Stress-strain relations for a solid polymer are derived using the laws of thermodynamics. Adjustable parameters in the model are found by fitting observations for three kinds of epoxy glasses and high-density polyethylene. A fair agreement is demonstrated between the experimental data and the results of numerical simulation.