A non-linear viscoelastic model developed for semi-crystalline polymer deformed at small strains with loading and unloading paths

A non-linear viscoelastic model based on rheological and molecular approaches was derived for the time- and rate-dependent responses of a semi-crystalline polymer at isothermal deformation at small strains. Particular attention was given for understanding and modelling the unloading behaviour. The crystalline phase of the polymer was considered as perfectly elastic. On the other hand, the amorphous phase was treated as an equivalent heterogeneous network of chains which is non-linearly viscoelastic. This model assumed that: (1) the non-linearity of the behaviour of the amorphous phase is not only due to the viscosity but also to microstructural phenomena occurred after the sliding of some amorphous chains; (2) to take out the influence of the crystalline phase on the amorphous one, the notion of interphase (linked amorphous phase with reduced mobility of chains) was introduced. All these microstructural considerations were integrated into the Zener model. Experimental data from mechanical tests were employed to determine the parameters of this model. Thereafter, two types of tensile test (loading-unloading and loading-relaxation-unloading) with slow and high strain rates (8 × 10−5 and 1.6 × 10−3 s−1) at room temperature were performed on an isotactic polypropylene (iPP) and the results were confronted with the model.