Storage and Loss Moduli of Low-Impedance Materials at kHz Frequencies

Abstract

Standard Dynamic Mechanical Analysis (DMA) is generally used to measure the mechanical properties of polymers at frequencies around and below 100 Hz. Ultrasonic (US) techniques measure wave speeds and impedances at higher frequencies. However, both approaches run into issues between the two regimes. DMA systems become less reliable due to the dynamic response of the frames and load path as one tries increasing the frequency. On the other hand, the internal multiple reflections in the wave propagation techniques introduce challenges in clean measurements and require careful analysis. In this presentation, we introduce a robust procedure for determining the storage and loss moduli of low-impedance materials, where a cylindrical sample is placed between two long metal bars, similar to SHPB technique. However, unlike SHPB, the incidence signal is created by a very light impact, to ensure that the sample does not experience permanent or large deformation. Furthermore, due to the length of the specimen, dynamic equilibrium is neither guaranteed nor intended. The reflected and transmitted pulses are measured using semi-conductor strain gages. The wave speed may be determined using a phase spectral analysis of the time-resolved signals. Determination of the material loss requires a more thorough transfer matrix analysis. The method was applied to a soft polyurea elastomer that was tested in a temperature-control chamber and results were compared with DMA and US data using time-temperature superposition (TTS). While the predictions of the storage modulus using DMA and TTS matched very well with the direct measurements, the DMA/TTS predictions generally underestimate the material loss at higher frequencies. We expect that this method may be applied successfully to other low impedance materials including foams and metamaterials.