Abstract Rubber materials under cyclic mechanical loading show special properties compared to other materials. This research aims to quantitatively clarify the relationship between cyclic deformation and temperature variation of carbon black filled styrene-butadiene rubber (SBR) under steady state condition after the rubber is accommodated enough both mechanically and thermally. A dumbbell specimen was subjected to uniaxial cyclic tension at various loading conditions. Temperature variation on the gauge zone surface of the specimen was measured by infrared thermography. In addition to the experiment, the temperature variation of the specimen was also predicted theoretically. The prediction is composed of three parts. The first part shows a three-elements model to reproduce the mechanical behavior with considering residual strain and stress softening. The material parameters are determined to match the experimental data at each loading condition. The second part predicts the temperature variation under adiabatic condition by considering three factors: isentropic elastic, entropic elastic and viscous dissipation effects. Third, a correction scheme is proposed to consider the heat transfer between the specimen and the surrounding air or others. As a result, the temperature amplitude and phase difference between temperature and strain are predicted. The predicted results were compared with the experimental data. It is confirmed that the predicted results are in good agreement with ones obtained by the infrared thermography. Furthermore, the phase difference between temperature and strain is about 180∘ at the small deformation area (isentropic elastic effect dominated) while it is almost about 0∘ at large deformation area (entropic elastic effect dominated). In addition to this, there exists a phase transition area between these two areas. It is concluded that the proposed method is a good way to provide quantitative information of the temperature variation of rubber materials subjected to uniaxial cyclic loading under steady state.

中文翻译：

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n 稳态单轴拉伸循环载荷下橡胶温度变化的定量研究

摘要 橡胶材料在循环机械载荷下表现出与其他材料相比的特殊性能。本研究旨在定量阐明填充炭黑的丁苯橡胶 (SBR) 在稳定状态下，在橡胶在机械和热方面得到足够的适应后，循环变形与温度变化之间的关系。哑铃试样在各种载荷条件下承受单轴循环张力。通过红外热成像测量试样的测量区表面的温度变化。除了实验之外，还从理论上预测了试件的温度变化。预测由三部分组成。第一部分显示了一个三元素模型，用于在考虑残余应变和应力软化的情况下重现机​​械行为。确定材料参数以匹配每个加载条件下的实验数据。第二部分通过考虑等熵弹性、熵弹性和粘性耗散效应三个因素来预测绝热条件下的温度变化。第三，提出修正方案以考虑试样与周围空气或其他之间的热传递。结果，预测了温度和应变之间的温度幅度和相位差。将预测结果与实验数据进行了比较。经证实，预测结果与红外热成像得到的结果吻合良好。此外，温度和应变之间的相位差在小变形区（等熵弹性效应主导）约为180∘，而在大变形区（熵弹性效应主导）几乎约为0∘。除此之外，在这两个区域之间还存在相变区域。得出的结论是，所提出的方法是提供稳态下承受单轴循环载荷的橡胶材料温度变化的定量信息的好方法。