Analysis of ultrasonic attenuation in particle-reinforced plastics by a differential scheme

Attenuation of ultrasonic longitudinal waves in some particle-reinforced polymer composites is studied theoretically by a micromechanical model based on a differential (incremental) scheme. A set of differential equations is established by which the attenuation spectrum of the composite can be computed from the known properties of viscoelastic matrix and elastic particles. For a composite reinforced with glass particles with radius 0.15 mm, the proposed scheme is shown to predict the attenuation in better agreement with the foregoing experimental results than the previous simplistic independent scattering model. Based on this scheme, the dependence of the longitudinal attenuation spectrum of a particulate polymer composite on the wavelength-to-particle radius ratio and the particle volume fraction is examined in detail. It is then shown theoretically that the attenuation of the composite decreases monotonically with the particle volume fraction when the particle radius is sufficiently small compared to the incident wavelength, while it shows non-monotonic particle-fraction dependence when the ratio of the particle radius to the wavelength is larger. To examine this theoretical finding from an experimental point of view, the longitudinal attenuation in a glass-particle-reinforced polyester composite with particle radius 0.0225 mm is measured for different particle volume fractions. The measured attenuation characteristics are shown to support the qualitative features of the theoretical prediction.