Strain-rate amplification

Viscoelastic methods for the characterisation of gum rubbers are extended to rubber compounds, and the ways in which the viscoelastic properties of gum rubbers are manifested in the properties of the corresponding compounds are examined. The development of a method for evaluating strain amplification and strain rate amplification is described. Examples are presented of the characterisation of compounds with respect to variations in gum rubbers and carbon black grades, and consideration is given to the unique characteristics of compounds which are not observed in gum rubbers. Quality control tests for gum rubbers and compounds based on viscoelasticity are reviewed. 32 refs. 

When is found by this procedure, it may be presented as a function of time (Equation 7.14). From this relationship, the strain rate of the matrix rubber, , may be estimated. It follows that the strain-rate amplification, x, is... 

Figure 7.12 shows the strain-rate amplification calculated from the data of Figure 7.11 [20]. 

Figure 7.12 Strain-rate amplification of ACM compound ENB, containing 50 phr of carbon black - NllO, N330 and N550.

The strain-rate amplification decreases with increasing elongation in two stages. After the initial decrease, the amplification remains constant or increases slightly and then decreases again. At the last point, which is near the yield point, the amplification becomes 1 or even less than 1 with N330 and N550. The strain rate of the matrix is either the... 

Figures 7.13 and 7.14 are the strain-amplification and the strain-rate amplification, respectively, of the compounds made with sample EP of ACM. The effect of the particle size of carbon black is the same as that with sample ENB, but the magnitude and the patterns of the amplifications are different between the two gum rubbers.

In section 7.3 a quantitative relationship between a gum rubber and its compound in the elongational behaviour is described in terms of strain- and strain-rate amplification. The... 

It is certain that the relaxation behavior of filled rubbers at large strains involves numerous complications beyond the phenomena of linear viscoelasticity in unfilled amorphous polymers. Breakdown of filler structure, strain amplification, failure of the polymer-filler bond, scission of highly extended network chains and changes in network chain configuration probably all play important roles in certain ranges of time, strain rate, and temperature. A clear understanding of the interplay of these effects is not yet at hand. 

The strain amplification proposed here is very different from that given by Mullins and Tobin. Uncrosslinked rubbers are used and therefore they are not in equilibrium deformation. The material behaviour is time dependent, i.e., viscoelastic. Therefore, the modulus ( e) is a function of strain and strain rate, e. If the stress is uniform throughout the specimen. Equation (7.5) may be adopted for the dynamic situation. If the matrix is a glass, a stress concentration may occur in the vicinity of fillers. When the matrix is a rubber, the stress concentration dissipates quickly. If the rate of dissipation is much faster than the deformation rate, the stress may be regarded as uniform, and this is the approximation used. At large deformations close to failure, stress concentration may occur and the approximation may not be valid. In such a case the amplification defined by Equation (7.5) includes the effect of the non-uniform stress. The equation is rewritten for the dynamic behaviour as... 

The effects of HAF black on the stress relaxation of natural rubber vulcanizates was studied by Gent (178). In unfilled networks the relaxation rate was independent of strain up to 200% extension and then increased with the development of strain induced crystallinity. In the filled rubber the relaxation rate was greatly increased, corresponding to rates attained in the gum at much higher extensions. The results can be explained qualitatively in terms of the strain amplification effect In SBR, which does not crystallize under strain and in cis-polybutadiene, vulcanizates of which crystallize only at very high strains, the large increase in relaxation rate due to carbon black is not found (150). 

The influence of filler is not limited to this enhancement of the non-Newtonian behavior of elastomers. At very small shear rates, filled green compounds also exhibit an additional increase of viscosity that cannot be explained by strain amplification. This effect is usually attributed to the existence of the filler network the direct bonding of reinforcing objects by adsorbed chains implies a increased force to be broken. Obviously this influence can be observed only at very low strain, because a very small increase of interaggregate distances immediately implies a desorption of the bridging elastomeric chains. 

The viscosity of a liquid is a parameter that measures the resistance of that liquid to flow. For example, water has a very low viscosity, while honey has a much larger or thicker viscosity. Newtonian fluids have constant values of viscosity, which means that the stress in a flowing liquid is proportional to the rate of strain of the flow. Non-Newtonian liquids do not have constant viscosity, but rather have viscosities that can be functions of the rate of strain, the total amount of strain, and other flow characteristics. Huids are usually non-Newtonian as a result of microscopic additives such as polymers or particles. These additives alter the viscosity of a liquid and impart nonlinear flow behavior, such as viscoelasticity. The non-Newtonian behavior of many complex liquids is described thoroughly in several texts, for example [1]. In this entry we focus on behavior and applications of polymer solutions in microfluidic devices. For example, DNA is a biopolymer that is common in microfluidics applications such as gene sequencing and amplification. 

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