  Polymer composite materials are widely used for their exceptional mechanical
properties, notably their ability to resist large deformations. Here we examine
the failure stress and strain of rubbers reinforced by varying amounts of
nano-sized silica particles. We find that small amounts of silica increase the
fracture stress and strain, but too much filler makes the material become
brittle and consequently fracture happens at small deformations. We thus find
that as a function of the amount of filler there is an optimum in the breaking
resistance at intermediate filler concentrations. We use a modified Griffith
theory to establish a direct relation between the material properties and the
fracture behavior that agrees with the experiment.
