Application Of Fractional Differential Rheological Model To Dynamic Mechanical Properties Of Vulcanized Rubber

Filled rubber is a typical viscoelastic material, which has the high damping ability and is widely used in high-speed train, automotive, aerospace and machinery, etc. Therefore, it is crucial for selecting a suitable model to describe the dynamic viscoelasticity of the filled rubber. The dynamic viscoelasticity of the filled rubber is not only affected by their molecular chain characteristics, but also influenced by many external factors. Base on the experiments, the influence factors of the dynamic viscoelasticity of the filler rubber were first analyzed in this article, which included the temperature, frequency and strain amplitude and so on. Then some suitable fractional differential viscoelastic models were selected to fit the experimental data under different conditions. The main work can be summarized as follows:1. The temperature sweep measurements were conducted under various frequencies using a Gabo Eplexor 500N dynamic mechanical analyzer (DMA) to investigate the frequency-dependent glass transition temperature, T_g. Then, the isothermal frequency sweep measurements under various temperatures ranging from T_g to T_g+50℃were accomplished. These results reveal that the storage modulus, the loss modulus and the loss factor decrease with the temperature; and higher frequency results in higher storage and loss moduli. The fractional differential Kelvin model was used to fit the frequency sweep measurement data of the dynamic viscoelasticity. There was a good agreement with tests. It is demonstrated that the fractional differential Kelvin model is capable of modeling the frequency dependent of the rubber material under various temperatures.2. The frequency sweep test data were analyzed by the frequency-temperature superposition principle. The dynamic modulus master curve for -40℃was constructed by horizontal shifts only along the logarithmic frequency axis, which establish the dynamic mechanical behavior over a frequency range of 16 decades (from -7 to 9). Then the fractional differential Zener model was used to analyze the master curves. There was a good agreement with the master curve when the logarithmic frequency axis is from–2 to 7. It is demonstrated that the fractional differential Zener model is capable of modeling the dynamic viscoelastic behavior of the material in a broad frequency range when the material is near its T_g.3. The internal variable theory and the intrinsic time scale were brief introduced. The fractional differential Kelvin model and Zener model with intrinsic time scale were derived based on the internal variable theory.4. The frequency sweep measurements under various strain amplitudes were accomplished at room temperature. Both the fractional differential Kelvin model and the intrinsic time based fractional differential Kelvin model were used to fit the test data. The results reveal that the fractional differential Kelvin model is capable of modeling the frequency dependent effects of the material only under small strain amplitude, while the intrinsic time based fractional differential Kelvin model is more powerful for modeling the frequency dependent effects of the material within greater strain amplitudes.5. The strain amplitude sweep measurements under various frequencies or temperatures were accomplished. The results reveal that the Payne effect exists when the temperature range is from -15℃to 23℃, but when the temperature is -30℃or -35℃, the storage and the loss moduli decreases with the increasing strain amplitude only. Then the intrinsic time based fractional differential Zener model was used to analyze the tests. It is also known that the intrinsic time based fractional differential Zener model is capable of modeling the Payne effect of vulcanized rubber near T_g and can qualitative describe dynamic modulus with strain amplitude trends when the temperature gets higher.