The viscoelastic properties of rubber under a complex loading

Abstract

This thesis aims to explore the effect of pre-strain on the viscoelastic behaviour of rubber materials. There are various conflicting theories in the literature regarding the strain dependence and resulting anisotropy of the viscoelastic behaviour. This thesis seeks to measure the behaviour and to study the possibility of using Finite Element Analysis (FEA) to predict the static behaviour of a rubber cylinder in combined torsion-tension and also the viscoelastic behaviour of rubber under various complex loadings using a Bergstrom-Boyce model1-4. To measure the induced anisotropy, a rubber test piece is subjected to a simple extension l and then it is subjected to small strain oscillations in the direction of the pre-extension or in shear. These two different deformations will allow the extent of the anisotropy in the viscoelastic behaviour induced by the pre-extension to be measured. Kuhn and Kunzle5 found that the loss factor resulting from a small oscillation decreased as a function of the static pre-strain. They and many others have interpreted this as a lowering of internal viscosity due to chain orientation. However, a simple analysis shows that this effect is due to geometric changes alone and that the essential viscoelastic behaviour expressed in terms of the deformed dimension after the application of the pre-strain as the loss modulus for an unfilled rubber is constant with strain up to an extension ratio of 2. It is also isotropic in behaviour for filled rubber compounds such as carbon black. For fumed silica filled rubber, the picture is more complex. For a moderately carbon black (25 phr) filled rubber, the loss modulus is still independent of the pre-strain for normal working strains but at highly filler contents (above 50 phr), the loss modulus increases with pre-strain at extension ratios somewhat less than 2. With silica, the coupling agent dominates the viscoelastic behaviour. For filled rubber, the change in loss modulus with strain can in part be explained by strain amplification, slippage of rubber around the filler, and shape factor effects. This approach can help to further understand the mechanism of filler reinforcement in rubber materials. Another complex loading is also used to validate these results with a static pure shear superimposed with simple shear oscillation. The results confirm the loss modulus is independent of the pre-strain for unfilled rubber and lightly filled rubber but for the most highly filled rubber, the test is unsuitable as the smallest oscillating strains were too great for linear viscoelastic behaviour. The Finite Element Analysis (FEA) shows that a rubber cylinder in combined torsion-tension test can be modelled accurately as an elastic component provided that the appropriate strain energy function (SEF) and geometry are used in the model. The correct torque and the second order effect whereby a reduction in the axial force resulting from the torsion of a pre-strained rod can both be accurately represented. The viscoelastic behaviour under various complex loadings was modelled using the Bergstrom and Boyce model1. The results show that this model can predict behaviour for uniaxial but in a complex loading the model was inappropriate.