A method to predict the dynamical behaviors of carbon black filled natural rubber at different temperatures

In the tire industry, the Payne effect and hysteresis loss of carbon black (CB) filled rubber under cyclic loading are two kinds of most concerned issues. In this paper, effects of temperature ranging from -30 °C to 50 °C on the Payne effect and hysteresis loss of the CB filled natural rubber are investigated. Experimental results show that the amplitudes of the Payne effect are improved with the decreasing of temperature, especially, at -30 °C, an enhanced Payne effect is observed. The hysteresis loss of the material shows a decreasing tendency with the increasing of temperature. Moreover, the logarithmic storage modulus and loss modulus vs. logarithmic strain amplitude curves at different temperatures can be shifted vertically along the ordinate to get a single smooth one, and the temperature shift factor satisfies the Williams-Landel-Ferry (WLF) equation. This can provide an accelerated method to evaluate the Payne effect at any temperature based on just fewer test data. According to the Kraus model and Payne effect test data, a method to predict the hysteresis loss of the material under different temperatures is developed and validated. The method proposed in the paper can provide an accelerated method to evaluate the Payne effect at arbitrary temperature based on fewer test data, and then accurate estimation of the hysteresis loss of CB filled rubber under cyclic loadings with various temperatures.