Effect of Carbon-Black Loading and Crosslink Density on the Heat Build-Up in Elastomers

It has been shown that it is possible to predict the viscoelastic response of elastomers and elastomeric engineering components under both load- and position-control conditions if one assumes: a) that the modulus of the materials increases with the strain amplification factor as given by the Guth and Gold equation, b) that the occluded rubber is taken into account when using this equation, and c) that the energy loss per cycle and unit volume of material is increasing with the square of the strain-amplification factor. These calculations were applied to an assembly where one unfilled section is in series with a filled one. The overall filler loading was kept constant, and it was found that the equations derived show completely different heat-generation rates for load- and position-control conditions. While the losses are the same in both sections and equal to that of the assembly as a whole under position-control conditions, they are quite different under load-control conditions. They increase with both filler loading and values of α and abnormally high local overheating in the unfilled section occurs. These considerations indicate that a uniform mixing quality is important for compounds which will be used in dynamically deformed engineering components. Under position-control conditions, poor filler dispersion will give rise to a decrease in the dynamic modulus and the energy loss per cycle, i.e., variations in the quality of the mix will cause variability of the dynamic properties. Under load-control conditions, the situation is even worse, since the energy dissipation increases with poor mixing, and local overheating of the sections containing less than the average amount of carbon black takes place. The model is obviously too oversimplified for qualitative predictions. But it still gives good qualitative indications regarding the heat-generation rate in structures made from two elastomers having different filler loadings or for imperfectly mixed compounds.