Abstract
Via cyclic loading and unloading tests of natural/styrene-butadiene rubber (NSBR) blends at room temperature, the effects of the stretching, rate, temperature, and volume fraction of carbon black in the filled rubber on a permanent set (residual strain) were studied. The results showed that increasing the stretching, rate, and volume fraction of carbon black and reducing the temperature yielded greater residual strain. The uniaxial tensile behaviors of composites with the Mullins effect and residual strain were simulated using the ABAQUS software according to the aforementioned data. An Ogden-type constitutive model was derived, and the theory of pseudo-elasticity proposed by Ogden and Roxburgh was used in the model. It was found that the theory of pseudo-elasticity and the Ogden constitutive model are applicable to this composite, and if combined with plastic deformation, the models are more accurate for calculating the residual strain after unloading.
Highlights
Carbon black-filled rubber on the virgin loading shows significant hysteresis during the load–unload–reload–unload cycle, which is called the Mullins effect
The Mullins effect is negligible in unfilled rubber but becomes obvious in rubber filled with a high carbon black content
Uniaxial tensile experiments involving different stretching ratios of natural/styrene-butadiene blends with different carbon black contents were performed, and the influences of different factors on the residual strain were investigated according to these experiments
Summary
Carbon black-filled rubber on the virgin loading shows significant hysteresis during the load–unload–reload–unload cycle, which is called the Mullins effect. Ogden and Roxburgh (1999) [5, 6] used a single softening damage variable to model the idealized Mullins effect in filled rubber, which experiences uniaxial tension and biaxial and multiaxial tension, while ignoring the residual strain. Uniaxial tensile experiments involving different stretching ratios of natural/styrene-butadiene blends with different carbon black contents were performed, and the influences of different factors on the residual strain were investigated according to these experiments. A combination of the Mullins effect and plastic deformation theory was introduced using the Ogden–Roxburgh pseudo-elastic model, and the Mullins effect with the residual strain of the Advances in Polymer Technology nominal stress (MPa) virgin loading curve. 2.5 blends was simulated and verified using the finite-element software ABAQUS
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