Thorough ultrasonic rheology of soft, visco-elastic materials: Example of crosslinked Polyurethane elastomer

We present a thorough procedure for measuring the rheological properties of soft, highly attenuating, visco-elastic materials at ultrasonic frequencies. The material chosen for this illustration is a crosslinked Polyurethane (PU) elastomer (Sika UR3440 type), which is widely used in the field of underwater acoustics. We determine its complex longitudinal modulus M and shear modulus G as function of frequency in the range 1-5 MHz and of temperature in the range 5-40 °C. M is determined from the measurement of the transmission of longitudinal, plane waves by a slab of PU immersed in water. G is determined by contact measurements from the transmission and reflection of transverse, plane waves by a slab of PU. This determination of G for such a soft and viscous material as PU is made possible by the use of thin slabs and the implementation of an original signal analysis. M, G and bulk modulus K are found to obey the time-temperature superposition principle and to be accurately described by a fractional derivative rheological model. This allows us to propose analytic formulas for the frequency and temperature dependence of M, G and K valid above PU glass transition temperature.