Dynamic Stress Softening Effect

Dynamic Stress Softening Effect 5.1.10.1 Physical Considerations... 

The Payne effect of carbon black reinforced rubbers has also been investigated intensively by a number of different researchers [36-39]. In most cases, standard diene rubbers widely used in the tire industry, bke SBR, NR, and BR, have been appbed, but also carbon black filled bromobutyl rubbers [40-42] or functional rubbers containing tin end-modified polymers [43] were used. The Payne effect was described in the framework of various experimental procedures, including pre-conditioning-, recovery- and dynamic stress-softening studies [44]. The typically almost reversible, non-linear response found for carbon black composites has also been observed for silica filled rubbers [44-46]. 

It is observed that the values do not reach its initial position within the relaxation time of the experiment, but a recovery of the E values have been attained (Fig. 18). This behaviour of a rubber can be explained by the stress softening effect during the dynamic strain. Nevertheless, a high extent of recovery in the reverse amplitude sweep indicates that a good filler-filler network has been re-established at a low loading of tubes in the S-SBR-BR matrix. So, at least it can be said that rather than damage or permanent break of the tubes, the amplitude sweep disrupted the filler-filler network in the rubber matrix. It is noted that the absolute values of E at small amplitudes are somewhat differed from each other as compared with the value obtained from the phr CNT-filled compound. The difference may be developed from ageing of the samples. 

Effect of mixing duration on the magnitude of dynamic stress softening. 

Modeling Dynamic Stress Softening as a Filler Network" Effect... 

The effects of secondary aggregation of small particle carbon blacks on the elastic modulus at small strains are large. They have been studied primarily in dynamic oscillatory loading experiments and are discussed in Section VII, dealing with viscoelastic behavior. The effects of prior deformation on stress-strain relationships (stress softening) are also time-dependent phenomena, consideration of which is postponed to a later point in this review. 

Other factors affecting the signals in the dynamic mode are adsorption-induced effects, such as surface stress and position dependence, which can either stiffen or soften the cantilever, thereby varying the spring constant. The relationship between the surface stress and stiffness of a cantilever has been intensively discussed [20-22]. Lee et al. visually demonstrated the dependence of resonance frequency on a pattern of a gold layer on the surface of a cantilever [23]. In any case, we have to be careful about these effects when we analyze the signals obtained with the dynamic mode. 

Another softening phenomenon which manifests the dependence of the stress upon the entire history of deformation is the so-called Payne effect. Like the Mullins effect, this is a softening phenomena but it concerns the behavior of carbon blackfilled rubber subjected to oscillatory displacement. Strain dependence of the storage and loss moduli (Payne effect) at 70 °C and 10 Hz for a rubber compotmd with different concentration of carbon black filler [7] (Fig. 26). Indeed, the dynamic part of the stress response presents a rather strong nonlinear amplitude dependence, which is actually the Payne effect [8, 16, 43]. 

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