Parameters estimation of generalized Maxwell model for SBR and carbonfilled SBR using a direct high-frequency DMA measurement system

Due to their desired physical properties as viscoelastic materials, polymers have attracted the attention of various industrial engineering systems. Accurate examination and measurement of physical properties of polymers is a key step required for their full-scale adoption and integration in industrial settings. Simulation studies, provide a relatively inexpensive and valuable analytical framework for analyzing the physical properties of such systems. Generalized Maxwell Model (GMM) is the standard analytical model used for analyzing viscoelastic materials. The viscoelastic constitutive parameters of the GMM are usually inferred by fitting the model to the master curve obtained from Dynamic Mechanical Analysis (DMA) tests. However, since conventional DMA tests are limited to low-frequency measurements, Williams, Landel and Ferry (WLF) relation is used to predict the high-frequency properties from the tests done at low frequencies. Known limitations and imprecisions of this indirect measurement method result in inaccurate inference of viscoelastic constitutive parameters in the GMM fitting procedure. In the current study, data obtained from a new high-frequency DMA (HFDMA), capable of performing tests at frequencies between 100-7000 Hz, is used to fit GMM equations through numerical optimization techniques. The new HFDMA operates the simple shear test for a double-sandwich specimen, directly at high-frequencies and therefor doesn't suffer from inaccuracies caused by the indirect measurements. The storage moduli, loss moduli and damping factor of Styrene-Butadiene Rubber (SBR) and carbon-black filled SBR (SBR-CB) at the frequency range of 100Hz - 5 kHz are measured using the new HFDMA, and compared with the results of a conventional DMA to demonstrate the difference between the direct and indirect measurement methods. It is shown that the direct measurement method is 5% - 7% more accurate than the indirect measurement method, at least for the SBR and SBR-CB. Finally, new GMM viscoelastic constitutive parameters for SBR and SBR-CB are presented.