Modelling the microstructure and the viscoelastic behaviour of carbon black filled rubber materials from 3D simulations

Volume fraction and spatial repartition of fillers impact the physical properties of rubber. Extended percolating networks of nano-sized fillers significantly modify the macroscopic mechanical properties of rubbers. Random models that describe the multiscale microstructure of rubber and efficient Fourier-based numerical algorithms are combined to predict the material’s mechanical properties. From TEM image analysis, various types of multiscale models were proposed and validated, accounting for the non-homogeneous distribution of fillers: in the present work, aggregates are located outside of an exclusion polymer simulated by two families of random models. The first model generates the exclusion polymer by a Boolean model of spheres. In the second model, the exclusion polymer is a mosaic model built from a Johnson-Mehl tessellation. Here the exclusion polymer and the polymer containing the filler show a similar morphology, contrary to the Boolean model. Aggregates are then described as the intersection of a Boolean model of spheres and of the complementary of the exclusion polymer. Carbon black particles are simulated by a Cox model of spheres in the aggregates. The models rely on a limited number of parameters fitted from experimental covariance and cumulative granulometry. The influence of the model parameters on percolation properties of the models is studied numerically from 3D simulations. Finally, a novel Fourier-based algorithm is proposed to estimate the viscoelastic properties of linear heterogeneous media, in the harmonic regime. The method is compared to analytical results and to a different, time-discretized FFT scheme. As shown in this work, the proposed numerical method is efficient for computing the viscoelastic response of microstructures containing rubbers and fillers.