Modelling the cyclic elasto-viscoplastic behaviour of polymers

The mechanical behaviour of polymeric materials presents some peculiarities, especially regarding the evolution of their hardening under stresses above the proportional limit. For many types of polymers (Epoxy, Polyamides, Polyvinylidene, etc.) the elastic properties are not rate-dependent, and the behaviour is elasto-viscoplastic. Also, in the case of load-unload tensile tests, preliminary studies show that the kinematic hardening of this kind of material can be much more significant than the isotropic hardening, and a negative plastic strain rate may occur even with a positive stress. Thereby, nonlinear phenomena may occur during tractive load-unload cyclic tests executed above the proportionality limit, leading to dissipation of mechanical energy. The present paper aims at the development of a general elasto-viscoplastic model for polymers, able to describe the progressive accumulation of plastic deformation for an arbitrary loading history. This model considers dissipative phenomena by the coupled effect of the internal variables with nonlinear hardening equations. Since a volume variation can be observed during plastic deformation, a modified von Mises yield criterion that accounts for the influence of the hydrostatic pressure is proposed. All parameters arisen from theory can be identified experimentally from tensile tests with different strain rates and load-unload tensile tests. The model adequacy was tested for particular types of Polyvinylidene fluoride (PVDF) and of Polyamide (PA 12), which are materials commonly used as an internal pressure sheath in offshore flexible pipes in the Brazilian pre-salt basin. One-dimensional numerical simulations were performed aiming to compare the numerical results with the experimental ones, showing a very good agreement.