Effect of Shape on the Static and Dynamic Stress–Strain Relationship of Bonded Rubber in Compression

Abstract

THE stress–strain relationship of rubber under unidirectional compression with free expansions in the other two directions has been derived from the kinetic theory of rubber-like elasticity by Treloar¹ and others. These conditions can be simulated by compressing the rubber between parallel plates at which friction is eliminated by lubrication. The static compressive stress σ_s (lb./in.²) is given by where G _s is the static shear modulus and λ the ratio of compressed to initial height. This relationship holds true provided the lubrication is adequate. Where free lateral expansion is prevented by friction or bonding at the confining surfaces, the shape of the rubber influences the stress–strain relationships in a way that has hitherto defied systematic analysis. Kimmich² showed that most of the difficulty in correlating published results may be explained by the nature of the surface of the compressing plates and of the rubber, the manner of applying the stress, the thixotropic behaviour of some rubbers, and because the stress–strain relationship is not linear. As the industrial uses of rubber in compression (usually with the faces bonded to metal) are very numerous, a mathematical relation between stress and strain is essential for design purposes. It is the purpose of this communication to point out a general relationship obtained from experimental results for rubber specimens of various sizes bonded to metal plates.