C. G'Sell et al., The influence of the amorphous matrix on the plastic hardening at large strain of semicrystalline polymers, MODEL SIM M, 7(5), 1999, pp. 817-828
The stress-strain behaviour of polyethylene, determined from mechanical tes
ts at constant true strain rate, is characterized by high strain hardening
in uniaxial tension and strain softening in simple shear. The strong influe
nce of the deformation path is correlated with the different crystalline te
xtures developed. This behaviour is analysed on a theoretical basis in term
s of the specific response of a polycrystalline viscoplastic aggregate and
of a rubber-like hyperelastic network. For the 100% crystalline model (by C
anova), the tensile hardening is overestimated with respect to experiment,
but the shear softening is correctly predicted. In contrast, for the 100% a
morphous model (by van der Giessen), the tensile hardening is smaller, but
the shear response cannot reproduce the softening. Therefore, the discussio
n is focused on a composite model which mixes the constitutive equations of
the crystalline phase and of the amorphous phase through the self-consiste
nt scheme of Herve and Zaoui. Originally established for elastic multiphase
materials, this model is applied here to the nonlinear case of polyethylen
e by means of an incremental tangent computation. The stress-strain curves
predicted by this approach can be fitted with very good precision to the ex
perimental curves in tension and shear with reasonable values of the micros
tructural parameters.