Model for the viscoelastic and viscoplastic responses of semicrystalline polymers

Constitutive equations are derived for the time-dependent behavior of semicrystalline polymers at isothermal loading with small strains. A semicrystalline polymer at temperatures above the glass-transition point for its amorphous phase is thought of as a network of macromolecules bridged by junctions (physical crosslinks, entanglements, and crystalline lamellae) that can slide with respect to their reference positions in the bulk material under straining. The network is assumed to be highly inhomogeneous, and it is modeled as an ensemble of mesoregions (MRs) with various strengths of interchain interaction. Two types of MRs are distinguished: passive, where these interactions prevent detachment of strands from junctions; and active, where active strands separate from junctions and dangling strands merge with the network at random times as they are thermally agitated. The viscoelastic response of a semicrystalline polymer reflects reformation of strands in active MRs, whereas its viscoplastic behavior is associated with sliding of junctions. Stress-strain relations for uniaxial deformation are developed by using the laws of thermodynamics. Adjustable parameters in the constitutive equations are found by fitting experimental data for isotactic polypropylene in a tensile test with a constant strain rate and in tensile relaxation tests at various strains. Fair agreement is demonstrated between the observations and the results of numerical simulation. It is revealed that the viscoplastic flow of junctions strongly affects the rearrangement process in active MRs, whose rate reaches a threshold value in the vicinity of the apparent yield point.