A Mathematical Treatment of a Theory of Rubber Structure

Abstract

Abstract A brief consideration of the work that has been done on the structure of rubber convinces, one that the elasticity is wholly or at least mainly explained by a consideration of the kinetics involved. The fact that when a strip of stretched rubber, one end of which is free, contracts when it is warmed, contrary to the behavior of most bodies, and that it becomes warmed on stretching, commonly known as the Gough-Joule effect, pp. 453–461, would lead one to suspect .that there is a connection between the kinetic energy of the rubber molecule and its elasticity. Lundal, Bouasse, Hyde, Somerville and Cope, Partenheimer and Whitby and Katz have reported observations, principally stress-strain curves, which show that vulcanized rubber has a lower modulus of elasticity at higher temperatures, i. e., it becomes easier to stretch as the temperature is raised. On the other hand, Schmulewitsch, Stevens, and Williams found that the elastic modulus increases with the temperature. Williams shows that the softening of vulcanized rubber with rise of temperature is due to an increase of plasticity. In order to get rid of plastic flow, he first stretches the specimen several times to within about 50 per cent of its breaking elongation, and then obtains an autographic stress-strain curve of the rubber stretched very quickly. He finds that in this case the rubber actually becomes stiffer with rise of temperature, increasing temperatures causing the stress-strain curves to lean progressively more and more toward the stress axis. He concludes that rise of temperature has two effects, one a softening due to increase of plasticity, rendering plastic flow more easy, the other an actual stiffening of the rubber due to rise of temperature. It is not easy to explain the latter effect on any theory which does not take kinetics into account.