Strain Dependence of Dynamic Mechanical Properties of Carbon Black-Filled Rubber Compounds

The strain dependencies of dynamic mechanical properties of carbon black-filled rubber compounds have been modeled by Kraus. Evaluation of the Kraus model with carbon black loadings up to 110 phr shows that it provides a fairly good overall description of elastic modulus, G′, as a function of strain, γ. The model description of G′ strain dependence improves with decreased carbon black loading, and is very good with carbon black loadings of 50 phr and less. The model description of viscous modulus strain dependence, G″(γ), is less successful than the G′(γ) description. Several empirical modifications of the viscous modulus model are examined. The most improved model is a very good approximation to viscous modulus over a wide experimental strain-range. Its utility, and that of the Kraus G′(γ) model, are illustrated through calculation of simple shear dynamic properties from torsion property measurements on a solid cylinder, where the strain amplitude varies across the specimen radius. The models allow transformation of the apparent moduli, reported as functions of strain amplitude at the cylinder's outer edge, to their true counterparts, G′(γ) and G″(γ), as functions of uniform strain amplitude. Although the G′(γ) and modified G″(γ) models apply to a wide range of experimental strains, some uncertainties associated with each model's accuracy remain, and there are inconsistencies in the relation of one model to the other. Reservations associated with the models might be resolved through refined treatments of the test specimen geometries.