The scale behavior of fillers in elastomers by means of indentation tests |
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Authors: | Volker Herrmann Klaus Unseld Hans-Bernd Fuchs |
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Institution: | (1) Dunlop GmbH, Chemical Technology Dunlopstrasse 2, 63450 Hanau Germany e-mail: volker.herrmann@dunlop.de Tel.: +49-6181-681987 Fax: +49-6181-685987, DE |
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Abstract: | 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 D≈1.24 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.
Received: 15 May 2001 Accepted: 18 August 2001 |
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Keywords: | Atomic force microscopy Dynamic indentation Mechanical imaging Fractal dimension Carbon black morphology |
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