Institute of Metals Division - Ultrasonic Attenuation Study of Dislocation Motion Part I. Theoretical

Formulae are given for calculating the modes of wave propagation in a single-crystdl specimen possessing a given crystallographic orientation. Such calculations lead to determination of the orientation factor appearing in the Granato-Lucke theory for the attenuation of these waves due to dislocation damping. A detailed treatment is given for the case of an aluminum crystal possessing the orientation having a maximum Schmid fac -tor of 0.5. FOR a number of years the attenuation of ultrasonic waves propagating in metals has been used to investigate various phenomena causing internal friction.Most of the experiments were performed on polycrystalline test specimens and the waves were assumed to be propagating in an isotopic medium. However Alers 6 in 1955 and more recently Hikata et at. Chiao and Gordon,8 and Swanson and Green 10 have used measurements of attenuation of ultrasonic waves to study internal-friction changes in single crystals. These authors were concerned with the energy losses experienced by the ultrasonic waves due to dislocation motion induced by plastic deformation of the crystals. Alers measured the attenuation of 7 mc per sec ultrasonic pulses propagating in zinc single crystals before, during, and after plastic deformation. Simultaneously he measured the time-dependent plastic strain at constant stress in order to study the correlation between this strain and attenuation. The crystals were oriented in such a way that the applied stress provided a direct shear on the slip plane, thus causing the deformation to proceed by slip on this plane. At the same time the high-frequency sound pulses were sent through the crystal perpendicular to the slip plane. He found that the attenuation of transverse waves, the stress vectors of which lie in the slip plane, was very sensitive to the deformation. The polarization of the particle displacements, associated with these waves, relative to the applied static shear stress, and hence the direction of slip, had no obvious effect on the results. The attenuation of longitudinal waves was affected by the deformation only when the slip plane was not perpendicular to the propagation direction. This indicated that the attenuation was caused by dislocations introduced by the deformation and moving only in the slip plane. Hikata et al. made simultaneous measurements of attenuation, velocity changes, and stress-strain relations on aluminum single crystals deformed in tension. Both longitudinal and shear waves were used, at frequencies of 10 and 13 mc per sec. They placed emphasis on the choice of propagation modes and polarization of the ultrasonic waves, such that interactions between these waves and dislocations on selected slip systems could be investigated. They also selected specimens possessing specific crys-tallographic orientations, which allowed investigation as a function of the number of equally favored slip systems under the applied stress. They found that, for symmetrical orientations, the change of attenuation decreases with the increasing number of equally favored slip systems, i.e., in the order