Numerical evaluation of micro- to macroscopic mechanical behavior of carbon-black-filled rubber

We investigate the characteristic deformation behavior of rubber with carbon black (CB) filler. The deformation behaviors of a plane strain rubber unit cell containing CB fillers under monotonic and cyclic strain are investigated by computational simulation with a nonaffine molecular-chain network model. The results reveal the substantial enhancement of the resistance of the rubber to macroscopic deformation, which is caused by the marked orientation hardening due to the highly localized deformation in the rubber. The disentanglement of the molecular chain during the deformation of rubber results in the magnification of the hysteresis loss, i.e., the Mullins effect, occurring in stress–stretch curves under cyclic deformation processes. The increase in volume fraction and in aggregation of the distribution of CB substantially raises the resistance of the rubber to deformation and hysteresis loss. The effect of the heterogeneous distribution of the initial average number of segments of molecular chains on the hysteresis loss has been clarified.