Stress Softening of Filled Rubber and Its Internal Morphologies

Filled rubbers are important materials in various industrial applications such as tire. The mechanical reinforcement, strong nonlinearity and large hysteretic behavior under large deformation are specific features of these materials. Regardless these phenomena have been investigated in both experimentally and theoretically for many years, there still remain many fundamental problems to be solved. These features are recognized relating to the structure of filler networks in the polymer matrices, therefore it is important to characterize these networks in detail. Klüppel et al. have carried out the experimental and theoretical investigations to the large hysteretic behavior when such materials are repeatedly extend (called Mullins effect). In their model, the effect of filler is taken into account via hydrodynamic interactions of rigid self-similar filler networks in polymer matrices, and the large hysteresis of filled rubber is referred to successive breaks-down of filler networks along with the elongation.

 In this presentation, we will report the results of Mullins effects and its relationships to the filler networks based on Klüppel’s techniques for various samples. In our analysis, we introduced new empirical parameters to Klüppel’s original model, which represents the mechanical stiffness between the filler particles originated from filler-filler or filler-polymer interactions. We will present (1) the parameter related to the mechanical stiffness of filler networks can be changed depending on types of filler-polymer interactions, and (2) mass fractal dimensions of filler networks can be investigated for various samples which have various types of mass fractal dimensions.