Single and double-step stress relaxation and constitutive modeling of viscoelastic behavior of swelled and un-swelled natural rubber loaded with carbon black

A phenomenological one-dimensional constitutive model, characterizing the mechanical behavior of viscoelastic natural rubber filled with the percolation concentration of HAF carbon black is developed in this investigation. This simple differential form model is based on a combination of linear and non-linear springs with dashpots, incorporating typical polymeric behavior such as shear thinning, thermal softening and non-linear dependence on deformation. The material parameters for this model are determined for the investigated vulcanizates. The model was also developed on same samples after immersion in kerosene for different intervals of times. One step mechanism of relaxation was appeared for straining the samples to different strain levels with constant strain rate. On the other hand, two step mechanisms of relaxation were appeared on straining specimens to same strain level but with different strain rates.