Strain amplification effect

In this connection, Fig. 2 provides a qualitative illustration for interpreting modulus change of an elastomer upon filler blending 9). A hydrodynamic or strain amplification effect, the existence of filler-elastomer bonds, and the structure of carbon black 10) all play a part in this modulus increase. 

In this relation, 2C2 provides a correction for departure of the polymeric network from ideality, which results from chain entanglements and from the restricted extensibility of the elastomer strands. For filled vulcanizates, this equation can still be applied if it can be assumed that the major function of the dispersed phase is to increase the effective strain of the rubber matrix. In other words, because of the rigidity of the filler, the strain locally applied to the matrix may be larger than the measured overall strain. Various strain amplification functions have been proposed. Mullins and Tobin33), among others, suggested the use of the volume concentration factor of the Guth equation to estimate the effective strain U in the rubber matrix ... 

It follows that this strain amplification effect will be more important if a high structure carbon black is used. In this case, indeed, the real volume concentration of the filler will be significantly increased by the amount of occluded rubber trapped in the aggregates. At strains high enough, the occluded rubber, though anchored or... 

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 presence of reinforcing fiUers also increases the non-Newtonian behavior of elastomers. This effect is mainly due to the fact that the incorporation of fillers in elastomers decreases the volume of the deformable phase. As discussed in the following text, this decrease is not limited to the actual volume of the filler, but must also include the existence of occluded rubber. So, when filled mixes are submitted to shear forces, because of the lower deformable volume, the actual deformation and speed of deformation are much higher than in unfilled mixes [1,134]. This phenomenon is usually called strain amplification effect, obviously strain amplification is not specific to reinforced systems but to any filled polymer. 

The Mullins effect, which can be considered as a hysteretic mechanism related to energy dissipated by the material during deformation, corresponds to a decrease in the number of elastically effective network chains. It results from chains that reach their limit of extensibility by strain amplification effects caused by the inclusion of undeformable filler particles [24,25]. Stress-softening in filled rubbers has been associated with the rupture properties and a quantitative relationship between total hysteresis (area between the first extension and the first release curves in the first extension cycle) and the enei-gy required for rupture has been derived [26,27]. 

Within identical validity limits, Mullins and Tobin have shown that the stress-strain behavior of black-loaded rubber vulcanizates corresponds to the stress-strain response of pure gum vulcanizates multiplied by a suitable strain amplification factor X, which expresses the fact that the average strain supported by the rubber phase, is increased by the presence of filler. In other terms, the effective strain of the elastomer matrix X is given by X =X.xX, where X is the overall measured deformation of the filled material. 

As the NNRTIs are structurally diverse and yet bind to RT at a common site, the similar occurrence of resistance-conferring mutations is not surprising. As a consequence, the effectiveness of other NNRTIs may be compromised by the emergence of HIV-1 variants caused by a previous NNRTI therapy (Sardana et ah, 1992). Experiments were performed in which HIV-1 strains (JR-CSF or ME) are cultured in human lymphocytes in the presence of partially inhibitory concentrations of delavirdine (Dueweke et al., 1993b). These conditions yield mutants that are 100-fold resistant. In order to determine what mutation(s) occurs, PCR (polymerase chain reaction) amplification and DNA sequence analysis of the RT coding region were applied and indicated that mutation P236L had occurred. Mutations at amino acids 181 or 183, which have been associated with resistance to other NNRTIs, are not detected. 

So far the micro-mechanical origin of the Mullins effect is not totally understood [26, 36, 61]. Beside the action of the entropy elastic polymer network that is quite well understood on a molecular-statistical basis [24, 62], the impact of filler particles on stress-strain properties is of high importance. On the one hand the addition of hard filler particles leads to a stiffening of the rubber matrix that can be described by a hydrodynamic strain amplification factor [22, 63-65]. On the other, the constraints introduced into the system by filler-polymer bonds result in a decreased network entropy. Accordingly, the free energy that equals the negative entropy times the temperature increases linear with the effective number of network junctions [64-67]. A further effect is obtained from the formation of filler clusters or a... 

The above interpretations of the Mullins effect of stress softening ignore the important results of Haarwood et al. [73, 74], who showed that a plot of stress in second extension vs ratio between strain and pre-strain of natural rubber filled with a variety of carbon blacks yields a single master curve [60, 73]. This demonstrates that stress softening is related to hydrodynamic strain amplification due to the presence of the filler. Based on this observation a micro-mechanical model of stress softening has been developed by referring to hydrodynamic reinforcement of the rubber matrix by rigid filler... 

Fig. 47b), which impacts the slope of the stress-strain cycles. This softening effect results from the drop of the strain amplification factor Xmax with increasing pre-strain, which has been determined by an extrapolation of the adapted values, shown in the insert of Fig. 47a, with the power law approximation Eq. (53). 

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. 

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