Surface Energy Effects for Small Holes or Particles in Elastomers

Expansion of a small spherical hole in a highly elastic solid is treated theoretically. Both elastic and surface energy terms are considered; the corresponding surface forces are assumed to be additive. The surface energy of the elastomer is assumed to be similar to that of simple liquids. Pressures or triaxial tensions required to inflate pre-existing holes to an indefinitely large size are calculated. Small holes require extremely large pressures, of the order of 1000 atm for holes of 10 A˚ radius. These results suggest a means of determining the distribution of hole sizes in elastomers and account, in principle, for experimental observations of cavitation processes. Detachment of the elastomer from a small rigid inclusion is treated in a similar way. The general absence of dilation or cavitation on stretching carbon black filled elastomers is thus accounted for solely in terms of the small size of these filler particles.