Propagation of Ultrasonic Bulk Waves in High Polymers

Abstract

The propagation of supersonic waves in bulk rubbers has been studied from 40 kc/sec. to 10 Mc/sec. and from −60°C to 60°C. The wave velocity was found to increase with decreasing temperature, leveling off both at high and low temperatures, and was found to increase slightly with frequency. Peaks in attenuation as a function of either temperature or frequency were observed, the peaks occurring at lower temperatures for lower frequencies. The peaks for butyl, a high loss rubber, are broader and higher than those for GR‐S and Hevea, which are lower loss rubbers. The results are in qualitative agreement with data obtained by strip methods at audiofrequencies. However, for bulk waves the real and imaginary parts of two elastic constants, the bulk and shear moduli, determine wave velocity and attenuation; hence, independent measurements of shear wave properties are necessary to evaluate these constants. A three constant theory is discussed, assuming a shear viscosity only, so that an effective modulus K+4μ/3 is obtained, where K and μ are the bulk and shear moduli. Relaxation times of the order 10⁻⁶ to 10⁻⁸ second are indicated. Approximate values of the dynamic Young's modulus are obtained from the effective modulus by assuming that the high frequency dispersion is due to the appearance of a ``crystalline'' shear elasticity. These results are correlated with low frequency data, and the dynamic Young's modulus and the loss factor are plotted. The loss factor exhibits a maximum in the dispersion region. Results are plotted in the range from 1 c.p.s. to 10⁷ c.p.s., which covers a wider range of frequency than earlier investigations. The necessary distribution of relaxation times is discussed.