Ultrasonic Measurement of Some Mineral Filled Plastics

Abstract

Absrroct-Several composite systems such as vinyl-tungsten, polymethylmethacrylatecrystabolite, and epoxycrystabolite have been examined for the variation of the longitudinal velocity as a function of volume fraction of the hard constituent. When the Voigt and Reuss velocity bounds rather than elastic bounds are plotted for these composite systems, the bounds are widely divergent and the V-bound is concave downward, while the R-bound is concave upward and has a well-defined minimum velocity. The experimental data for all the systems conform to the R-bounds indicating that the composite systems are families of true Reuss solids. The velocity minimum occurs because the density increases more rapidly than the elastic modulus. C OMPOSITE materials, where the matrix is soft and the filler is hard, are encountered in many situations. Our experience includes backing materials for ultrasonic transducers, dental restorative materials, and hard biological tissues like bone and teeth. Composites are materials made of two or more constituents in intimate contact. The composite is homogeneous and isotropic when the filler is a powder uniformly distributed throughout the matrix. When the filler is fibrous, the composite can exhibit anisotropic behavior and hard tissues are fibrous and anisotropic. In this paper only homogeneous isotropic composites will be discussed and only with respect to the performance of the longitudinal sonic velocity as it is affected by the amount of the hard filler included in the solid. The ultrasonic transducers employed in the measurements emitted well-damped pulses. For the vinyl-tungsten composite system listed in Table 11, the pulse duration was about one microsecond, but for the other materials it was 100 nanoseconds. Hence in all instances, the use of ultrasonics ensured that the measurements were made at high strain rates with very little displacement, so that only the elastic properties affected the measurements and plastic deformation was negligible. The samples could be retested since there was no deformation or destruction. Moreover, the ultrasonic tests could be repeated with little variation on the same sample and the results were repeatable for similar samples. What is desired is a technique for predicting the velocity characteristics of the composite system as a function of the volume fraction of the hard filler constituent. In a 1973 paper [l] it was shown that the longitudinal sonic velocity of the tungsten-vinyl composite decreased markedly to a