A model for the viscoelastic and viscoplastic responses of glassy polymers

A constitutive model is derived for the viscoelastic and viscoplastic behavior of amorphous glassy polymers at isothermal loading with small strains. It is assumed that an amorphous polymer is strongly heterogeneous at the microscale. It is treated as an ensemble of cooperatively rearranging regions (CRR) which relax at random times as they are thermally agitated. CRRs are bridged by links (long chains which form less cohesive space between relaxing domains and transform the macro-strain in a specimen to rearranging regions). With the growth of strain, some links break (which reflects partial disentanglement of chains and scission of bonds in the less cohesive domains). This results in nucleation and aggregation of quasi-point defects (QPD) which provide some freedom for CRRs to displace with respect to each other. At the micro-level, the viscoelastic response of a polymer is reflected by rearrangement of CRRs, whereas the viscoplastic behavior is associated with coalescence of QPDs and creation of isolated islands of CRRs. Stress-strain relations for uniaxial loading are developed using the laws of thermodynamics. The constitutive equations are verified by comparison with experimental data for polycarbonate and poly(methyl methacrylate) at ambient temperature. Fair agreement is demonstrated between results of numerical simulation and observations in relaxation tests and in tests with constant strain rates.