Ultrasonic Scattering and Attenuation in Polycrystalline Copper and α-Brass

Abstract

The ultrasonic pulse-echo technique has been employed to study scattering and attenuation in polycrystalline copper and α-brass. Specimens in the form of cylindrical rods were annealed to various grain sizes and tested at frequencies between 100 kc and 18 Mc, corresponding to scatterer circumference to wavelength ratios (πD/Λ) from 10−3 to 1.6. The primary objectives of this investigation were to study the scattering process by direct observation of the scattered radiation, and to study the associated attenuation under conditions not previously amenable to measurement; these included cases where pulse patterns were complicated by excessive scattering, and by mode dispersion. A preliminary investigation of the complications attending the propagation of acoustic pulses was performed for steel rods over a range of specimen radius to wavelength ratios (a/Λ) similar to that to be covered in the later work. Pulse patterns were found to be relatively free from complication far a/Λ<0.1, and >10, approximately. In the intermediate range, the distribution of the input energy among the various vibration types was found to vary with a/Λ, and with the details of the excitation. At low a/Λ, (<0.2), where solutions of the Pochhammer frequency equation predict only one mode of vibration for the rod, an additional mode was observed. This made corresponded in timing to a shear mode generated upon reflection of the predicted made, and can be accounted for by considering those roots of the frequency equation corresponding to Bessel functions of imaginary argument. To avoid the complications due to mode dispersion, the scattering experiments were designed to measure critically backscattered radiation, i.e., the scattered sound that arrived at the detector before any of the modes could effect a round trip. The observed scattering levels were in reasonable agreement with theoretical expectations (based on Bhatia's theory for scattering in the long wavelength region), except at low πD/Λ where the backscattering was seen to decrease with increasing frequency. The reason for this discrepancy is not yet definitely established, but it is believed to be a manifestation of propagation phenomena associated with the presence of attenuated vibrations in lossless media. Attenuation measurements were performed with pulses of duration comparable to the length of the specimen. This, combined with the high scattering ability of the medium, results in a pulse pattern whose envelope masks the details of the mode pattern. The rate of decay of this envelope corresponds to the attenuation of scattered sound and hence characterizes the intrinsic absorption properties of the metal. At πD/Λ≈10−1 the energy attenuations were approximately 3×10−3 db/grain for copper and approximately 3×10−4 db/grain for α-brass. Comparison of the experimental data with the principal attenuation mechanisms operative at these frequencies showed the observed attenuation to vary over most of the range in the manner expected for elastic hysteresis damping.