Elastic properties of rubber particles in toughened PMMA: ultrasonic and micromechanical evaluation

Ultrasonic measurements and micromechanical models are used to evaluate elastic properties of rubber particles dispersed in toughened polymers. Ultrasonic phase velocities and attenuation spectra of rubber-toughened poly(methyl methacrylate) (PMMA) with different rubber particle fractions are measured for longitudinal as well as transverse waves. The ultrasonic properties of rubber-toughened PMMA are found to depend markedly on the rubber particle fraction. The bulk and shear moduli determined from the measured velocities are in turn used to estimate those moduli of the particles based on existing micromechanics models, namely the three-phase model and the Hashin–Shtrikman upper and lower bounds. The bulk modulus of the particle estimated by the three-phase model is found to be in close agreement with the result of previous investigators. Implications of the Hashin–Shtrikman bounds for the particle moduli are also examined.