The influence of the amorphous matrix on the plastic hardening at large strain of semicrystalline polymers

The stress-strain behaviour of polyethylene, determined from mechanical tests at constant true strain rate, is characterized by high strain hardening in uniaxial tension and strain softening in simple shear. The strong influence of the deformation path is correlated with the different crystalline textures developed. This behaviour is analysed on a theoretical basis in terms of the specific response of a polycrystalline viscoplastic aggregate and of a rubber-like hyperelastic network. For the 100% crystalline model (by Canova), the tensile hardening is overestimated with respect to experiment, but the shear softening is correctly predicted. In contrast, for the 100% amorphous model (by van der Giessen), the tensile hardening is smaller, but the shear response cannot reproduce the softening. Therefore, the discussion is focused on a composite model which mixes the constitutive equations of the crystalline phase and of the amorphous phase through the self-consistent scheme of Herve and Zaoui. Originally established for elastic multiphase materials, this model is applied here to the nonlinear case of polyethylene by means of an incremental tangent computation. The stress-strain curves predicted by this approach can be fitted with very good precision to the experimental curves in tension and shear with reasonable values of the microstructural parameters.