The Strain Dependence of Rubber Viscoelasticity. III. Natural and Butyl Rubber at High Extensions

Abstract

Abstract In previous papers in this series the linear viscoelastic behavior of gum and filled rubbers has been studied at mean extensions up to 100%. Linearity was assured by allowing each specimen to relax at the required extension to its equilibrium state and then measuring the complex Young's modulus for very small strains superimposed upon this equilibrium extension. Analysis of the data was made either in terms of a Mooney strain-energy function or, more generally, by relation to the experimentally determined equilibrium stress-strain curve of the material. At much higher strains, however, the use of a strain-energy function is invalidated by the hysteretic behavior of the rubber, and the determination of a stress-strain curve at anything resembling equilibrium becomes increasingly difficult. Consequently, in the region of high strain it is preferable to examine the strain dependence of the viscoelasticity without involving a direct comparison with the equilibrium behavior. In principle, the most significant analysis would be obtained from a study of the strain dependence of the relaxation or retardation spectrum. The long-time end of the spectrum could perhaps be measured using a refined creep or stress relaxation technique, although considerable care would be required to separate the effects from the residual behavior resulting from the initial large elongation. In the rubber-glass transition region, with which this work is primarily concerned, the difficulty lies in making measurements over a sufficiently wide frequency range. Normally the Williams—Landel—Ferry (WLF) equation would be used to transform constant-frequency data from a wide temperature range to the equivalent isothermal spectrum over a wide frequency range; however, the validity of this equation has been confirmed only for amorphous polymers, and its application to highly stretched, anisotropic rubber involves several untested assumptions as discussed further below. The main object of the present paper is to describe the observed variations in the viscoelasticity of natural and butyl rubber over a wide range of extension and temperature, although, of necessity, over a limited range of frequency. In addition, a tentative indication of the influence of strain upon the relaxation spectra is given, and the implications of this are examined.