An investigation of the visco-elastic properties of rubber

Abstract

The object of the present investigation is to examine the dynamical properties of rubber in the light of the theory of visco-elasticity . This theory, which attempts to describe the dynamical behaviour of deformable solids, has been deduced from the thermodynamics of a solid with the help of certain physical assumptions. Certain mathematical approximations are also necessary to obtain the stress-strain relations in simple form. In this form they express each stress component as the sum of two groups of terms, the first being the usual Hooke's Law expression, linear in the strain components, while the second is a similar expression in terms of the rate of strain components. Now, according to the theoretical deduction of these stress-strain relations, it is not to be expected that they will be of universal applicability, least of all of be expected that they will be of universal applicability, least of all of a substance which has so many queer elastic properties as rubber. But the theory suggest that, between suitably defined upper and lower visco-elastic limits of the rate of strain, these stress-strain relations may still be capable of describing approximately the dynamical behaviour of a substance such a rubber. The damping of vibrations in solids has been a subject of frequent investigation, and certain visco-elastic constants for metals at various temperatures have already been determined. But investigators, who have noticed deviations from theoretically predicted results, have either attributed these deviations to experimental errors,§ or else pointed out simply that the visco-elastic hypothesis fails and must be modified in some way. Often this latter point is clear from theoretical consideration alone—for instance, rubber shows a residual creep after being strained, which is contrary to the assumptions of the theory of visco-elasticity. But, just as in the statics of deformable solids our first interest is in the behaviour within the elastic limits, in the dynamics of deformable solids our first interest is in the behaviour within the visco-elastic limits. In the present investigation we attempt to discover within what limits, if any, the theory of visco-elastic is applicable; and then to determine the values of the "normal visco-elastic constant" and the "coefficient of normal viscosity" within those limits.