Description of the tensile stress–strain behavior of filler-reinforced rubber-like networks using a Langevin-theory-based approach. Part I

Abstract

A combination of the Langevin-theory-based James–Guth equation with the phenomenological C2 term of the Mooney–Rivlin equation (modified by introducing an additional empirical parameter) is shown to represent the tensile stress–strain dependencies obtained on retraction of a number of carbon-black- and silica-reinforced butadiene–styrene networks. The stress–strain behavior at increasing strain of both pre-strained and virgin specimens is more complex but it can be satisfactorily described using the concept of a strain-dependent finite extensibility parameter (introduced previously for unfilled networks). The accuracy of data description is better than ca. 4%. Similarly to unfilled networks, the increase in the finite extensibility parameter with increasing strain is ascribed to strain-induced changes in network topology (increase in network mesh size). On retraction, such changes probably take place to a much lesser degree if at all.