Modelling the viscoplastic response of polyethylene in uniaxial loading-unloading tests

Two series of uniaxial cyclic tests are performed on low-density polyethylene at room temperature. In the first series of experiments, injection-molded specimens are stretched to several maximal strains ε_max in the region of sub-yield deformations with a constant cross-head speed, ε̇ = 10 mm/min, and retracted down to the zero stress with the same strain rate. In the other series, loading-unloading tests are carried out with the maximal strain ε_max = 0.10 and cross-head speeds ranging from 5 to 200 mm/min. A constitutive model is derived for the viscoplastic behavior of a semi-crystalline polymer at small strains. A polymer is modelled as an equivalent network of chains bridged by permanent junctions (entanglements, physical cross-links on the surfaces of crystallites and lamellar blocks). The network is treated as an ensemble of meso-regions connected by links (crystalline lamellae). Deformation of a specimen induces sliding of junctions with respect to their reference positions both at active loading and unloading (this process reflects sliding of junctions in amorphous regions and fine slip of crystalline lamellae). At retraction, sliding of junctions is accompanied by mutual displacements of meso-domains (that reflects coarse slip and fragmentation of lamellar blocks). The constitutive equations are determined by 5 adjustable parameters that are found by matching the experimental stress-strain curves.