Theoretical Model for the Elastic Behavior of Filler-Reinforced Vulcanized Rubbers

One of the more important advances in rubber science during the past twenty years has been the development of quantitative theories describing the elastic properties of pure-gum vulcanized rubbers. As a result it is now possible to account for their equilibrium stress-strain behavior with considerable success. There is, however, no adequate theory to describe the elastic properties of filler-reinforced rubber vulcanizates and the work described herein is an attempt to provide a basis for such a theory. When a reinforcing filler is added to rubber it produces a large increase in the stiffness of the vulcanizate. This increase is reduced and may be substantially destroyed by deformation. Numerous attempts have been made to describe the increase of stiffness resulting from the introduction of fillers and relationships describing the dependence of the modulus on the concentration and particle shape of the filler have been developed. However, these do not take into account the softening which results from previous deformation and thus have limited applicability. Recently Blanchard and Parkinson have attempted to develop empirical relationships to describe the elastic properties in simple extension of reinforced rubber vulcanizates after they have been previously deformed. They started with the appropriate stress-strain relationships from the classical kinetic theory and introduced two curve-fitting parameters to describe stress-strain data obtained in conventional tensile tests on a Goodbrand machine. In this way they were able to fit the course of the stress-strain data obtained after previous extension at extensions less than those previously applied and to describe the dependence of the parameters on previous deformation. Unfortunately, the significance of the parameters is obscure.