The scale behavior of fillers in elastomers by means of indentation tests

Indentation tests were carried out on a carbon black filled rubber sample on different length scales. The experiments covered the range from aggregation of particles on the submicron scale up to structures which represent the bulk properties of the sample on the millimeter scale. The local stiffness was used to visualize the areas investigated; therefore, mechanical images were obtained for all length scales. So-called "mechanical units" were defined for every scale. The size distribution curves for the mechanical units were analyzed and they were found to be non-Gaussian-shaped for every scale. Moreover, the distribution curves of the mechanical units are similar to the distribution curves of particles and aggregates obtained by electron microscopy reported in the literature. Evaluation by means of fractal analysis led to fractal dimensions for the mechanical units. It could be shown in the present case that the fractal dimension Dapproximate to1.24 of the mechanical units in the range of submicrons up to several hundred microns is in good agreement with that of the filler aggregates proposed in the literature. Furthermore, D is constant over a wide range of about 6 decades in area scale starting from aggregates up to the size of agglomerates. This leads to the conclusion that the local arrangement of the filler ensembles seems to be self-similar from the smallest scale of aggregation of particles up to the largest formation observed by indentation testing on the millimeter scale.