Stress upturn

Why does the above stress increase become larger and larger with increasing strain amplimde, as called the stress upturn ... 

Figure 18.1 is the typical stress-strain curves of the filled rubber (SBR filled with fine carbon black, HAF),

Mechanism of the Modulus Increase, the Stress Upturn, and the Great Tensile Strength... 

As shown in Figure 18.1, in the stress-strain curve of the real unfilled SBR vulcanizate, the stress upturn does not appear and as a result, tensile strength and strain at break are only about 2 MPa and 400%-500%, respectively. Nevertheless, the stress-strain curve of the SBR vulcanizate filled with carbon black shows the clear stress upturn and its tensile stress becomes 30 MPa. This discrepancy between both vulcanizates is actually the essential point to understand the mechanism and mechanics of the carbon black reinforcement of mbber. 

Figure 18.17 shows that the characteristics of the stress-strain curve depend mainly on the value of n the smaller the n value, the more rapid the upturn. Anyway, this non-Gaussian treatment indicates that if the rubber has the idealized molecular network strucmre in the system, the stress-strain relation will show the inverse S shape. However, the real mbber vulcanizate (SBR) that does not crystallize under extension at room temperature and other mbbers (NR, IR, and BR at high temperature) do not show the stress upturn at all, and as a result, their tensile strength and strain at break are all 2-3 MPa and 400%-500%. It means that the stress-strain relation of the real (noncrystallizing) rubber vulcanizate obeys the Gaussian rather than the non-Gaussian theory. 

Nevertheless, it is obviously shown in Figure 18.1 that the stress-strain curve of the filled mbber gives the clear stress upturn, thus its tensile strength becomes 30 MPa. Therefore, the fundamental question is what happens or what stmcture is produced in the carbon black-filled mbber under large extension, which newly generates the stress upturn. In the case of the fine carbon black-fiUed system, when carbon blacks are dispersed ideally, the carbon gel makes the continuous phase at the... 

Incidentally, as is well known, in the unvulcanized state of the filled mbber, the stress upturn does not appear even in the carbon content of = 0.2-0.25. For understanding this phenomenon, we must consider the discontinuity between the SH layers, in addition to the very low modulus of the unvulcanized mbber. Actually, as we discussed earlier, carbon blacks disperse as an aggregate of carbon particles, then the continuity of carbon gels consisting of aggregates must be much poorer than the theoretical calculation based on the perfect dispersion of carbon particles. In this case, the stress cannot be transmitted from carbon gel to carbon gel through such a very soft medium, and as a result, the stress-strain curve of the system is rather similar to the characteristics of the... 

Mechanism of Compatibility of Molecular Slippage and Stress Upturn IN Carbon Black-Filled Rubbers... 

Super-network of the strands of oriented molecules interconnected at carbon particles produced under large extension supports the increasing stress (stress upturn) and the great stress of the system at break. 

Stress upturn in the stress-strain relation of carbon black-fiUed rubbers can be reasonably revealed in terms of the non-Gaussian treatment, by regarding the distance between adjacent carbon particles as the distance between cross-links in the theory. 

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