Effect of the microstructure parameters on the mullins softening in carbon-black filled styrene-butadiene rubbers

A quantitative estimate of the Mullins softening is proposed and tested on various carbon-black filled styrene-butadiene rubbers. To model the behavior of elastomeric materials, some constitutive equations reported in the literature are based on the account of a strain amplification factor, which evolves with the maximum strain history. The amplification factor is grounded on the representation of filled rubbers as heterogeneous materials made of hard rigid domains and soft deformable domains. In this work, this factor is split into two parts with opposite effects that account for the Mullins softening and for the filler reinforcement, respectively. Evolutions of both parts are obtained through a direct analysis of cyclic uniaxial tensile tests performed on a series of materials. The Mullins softening part is shown to linearly depend on the filler volume fraction and on the maximum strain applied, when defined as the first invariant of the Hencky tensor. Its changes with the gum cross-link density parameter are insignificant. The reinforcement part of the amplification factor shows quadratic dependence on the filler volume fraction.