In a previous theory expounded by one of the authors on the mechanical and optical analysis of the filler reinforced rubber vulcanizates, the degree of adhesion (1-ζ) was treated as a fixed parameter. When the specimens containing the filler of higher concentration are extended, the degree of adhesion (1-ζ) decreases and the remarkable relaxation (softening) appears in the specimens as shown in Fig. 1.Under the rate theory explained in the paper preceding this report, the hysteresis loops in extension cycles for filler-reinforced vulcanized rubbers are analysed as follows.The present specimens are natural rubber vulcanizates corporated alternately with one of the three species of carbon black, i.e. ISAF (Intermediate Super-Abrasion Furnace), HAF (High Abrasion Furnace), or SRF (semi-reinforcing furnace) and of the two species of non-black, i.e. Hi-Sil (silica) or CaCO3 (calcium carbonate), all these five sorts with various concentrations of X=0 (pure vulcanizate), 0.05, 0.1, 0.15, 0.2, 0.25, (here X denotes the volume ratio of filler to rubber examined). Each specimen was extended to the maximum extension ratio αm=2 for the 1st cycle; for the 2nd, αm=3 and so on. The experimental curves of tension in each extension course, namely αm=2, 3, 4 and 5, are shown in Figs. 2-11. Moreover, the experimental and, theoretical hysteresis curves for αm=3 (48sec) and αm=4 (72sec) in the case of X=0.1 or X=0.2 are shown in Figs. 12-17. Most of the curves for various αm and X are omitted here.It has been proved that according to the above analysis, the hysteresis loops containing the Mullins effect in the filled specimen can be analysed by means of the present theory based on the rate processes, but the details in the phenomena must be expected in future studies. Especially precise examinations of the elementary process in rheology, for instance, about stress relaxation, creep and the rate of recovery and so on, must be made quantitatively and these experiments are now being prepared.
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