A. Hikata

Dislocation Contribution to the Second Harmonic Generation of Ultrasonic Waves

The experimental evidence and the associated theory are presented for the dislocation contribution to the generation of the second harmonic of an ultrasonic wave in solids. The contribution is measured through the changes, as a function of static bias stress, in the amplitude of the second harmonic of a fundamental wave (10 Mc/sec compressional wave) propagating in the specimen.In aluminum single crystals the amplitude of the second harmonic, for a given amplitude of the fundamental, changes markedly with static bias stresses ranging from 0 to 106 dyn/cm2. In alloys, there are essentially no changes of the amplitude of the second harmonic even for bias stresses up to 107 dyn/cm2. These observations are consistent with the predicted dependence of the amplitude on dislocation loop length and on the static stress. The effects of small amounts of plastic deformation were consistent with the proposed model.

Recovery of damping and modulus changes following plastic deformation

Abstract A theory is developed which assumes that changes with time in the decrement and modulus of a crystalline material following plastic deformation are a result of dislocation pinning by deformation—induced point defects. This time dependence is based upon the Cottrell-Bilby t 2 3 law for strain-aging. Comparison of the results of the theory with available data shows that the measured time law is that predicted by the theory for specimens which have been deformed between about 0.4 and 4.0 per cent. For smaller and larger deformations, deviations are obtained. Although measurements so far available permit only a qualitative check of the predictions of the theory with regard to the dependence of the recovery rate on purity and deformation, a check of the temperature dependence is afforded by recovery measurements of Youngs modulus for copper. From these an activation energy for the migration of vacancies in copper is determined to be 1.0 eV. A number of experiments needed for checking the theory further are proposed.

Sensitivity of Ultrasonic Attenuation and Velocity Changes to Plastic Deformation and Recovery in Aluminum

Measurements of changes in ultrasonic attenuation together with changes in ultrasonic velocity have been made concurrently with load strain measurements in tensile tests on the same specimen of aluminum. The results of such measurements taken during loading of the specimen, during relaxation or recovery at constant strain, and during unloading show a number of interesting effects. These observed effects are interpreted in terms of dislocation behavior for the various stages of the experiment. The experimental results for attenuation α and velocity change Δv/v permit the calculation of changes in dislocation density and loop length based on a dislocation damping theory developed in this laboratory to include both megacycle and kilocycle frequencies. The strain due to dislocation motion was calculated with a simple model and with dislocation loop lengths and densities obtained from the data and the theory just mentioned. The comparison of the calculated strain and the measured strain lends support to the us...

Anharmonicity Due to Glide Motion of Dislocations

The generation, due to glide motion of dislocations, of the second harmonic of an ultrasonic stress or strain wave propagating in a crystal is studied by using the string model of dislocations in the presence of a static bias stress. The calculated results agree semiquantitatively with the experiment by Hikata, Chick, and Elbaum. The dependence of the amplitude of the second harmonic on bias stress, when this stress is sufficient to cause dislocation unpinning, can be accounted for by the dislocation damping effect that is associated with the anomalous velocity change due to unpinning.

Ultrasonic attenuation and velocity data on aluminum single crystals as a function of deformation and orientation

Abstract Aluminum single crystals oriented for single slip and for “polyslip” were deformed in tension, at room temperature. These tests were limited to a total tensile strain of up to 1 per cent. Simultaneous measurements of attenuation and velocity changes were made continuously during the tensile deformation. Both longitudinal and shear waves were used, at frequencies of 10 Mc/s and 13 Mc/s. The observed changes in attenuation in the polyslip orientations were consistent with an explanation based on the number of equally favored slip systems in each case. The results on crystals oriented for single slip indicate that in the easy glide range of strain hardening, dislocation multiplication is confined to the primary slip system only. The end of easy glide is associated with dislocations multiplying in other slip systems. An increase in attenuation is also observed prior to the onset of the macroscopic yield. This increase is presently attributed to an increase in dislocation loop length, caused by a breakaway mechanism. In the early stages of deformation, for all orientations, an increase of ultrasonic velocity, relative to the unstrained condition, is observed. The changes of attenuation and of velocity reported here, are consistent with theoretical results derived from the treatment of dislocation damping given by Granato and Lucke.

Electrical‐Charge Study in Sodium Chloride during Plastic Deformation

Electrical charges developed during plastic deformation of sodium chloride were investigated. Experiments are chosen (orientation and shape of the crystals; direction of applied stress) to enable the edge and screw components of dislocation loops to emerge separately on two different pairs of the external surfaces of the specimen. The experimental results indicate that an electrical charge is associated only with the edge components of dislocation loops. It is also found that in tensile experiments of a bent specimen (accidentally or intentionally) negative charge appears on the concave side and positive charge appears on the convex side, and the negative charge is larger, in absolute value, than the positive charge, in the early stages of deformation. A model is proposed to explain these results.

Frequency Dependence of Ultrasonic Attenuation and Velocity on Plastic Deformation

The dependence of ultrasonic attenuation and velocity on plastic deformation in 2S aluminum is compared at two frequencies, five and ten megacycles, and the comparison shows agreement as regards frequency dependence with what one can expect from dislocation damping theory.

Ultrasonic study of mechanically alloyed Co40Sn60

Ultrasonic velocity changes of mechanically alloyed Co40Sn60 are investigated as a function of temperature at low temperatures. It is found that the velocity increases logarithmically with temperature below ∼1 K, indicating the existence of features characteristic of the glassy state. With the two level tunneling system (TLS) model developed for amorphous materials, factors nM2 and K are determined, where n is the density of states of TLS, M and K are TLS coupling constants for phonons and electrons, respectively.

Ultrasonic attenuation and velocity studies of amorphous PdSiCu

Abstract Measurements of ultrasonic attenuation and velocity changes have been carried out on the metallic glass Pd0.775Si0.665Cu0.06 as a function of amplitude, in the frequency range 10 to 90 MHz, for 0.3 ≤ T ≤ 10 K. The amplitude dependent attenuation changes observed in these studies are larger by a factor of 100 to 1000 than the values obtained from current two level system tunneling theory, with the use of parameters determined experimentally at higher frequencies by other workers. These attenuation changes have a linear (rather than quadratic) dependence on frequency and very weak T dependence (rather than 1/T). These results are compared with data on vitreous silica obtained in the same range of frequencies and temperature.

Ultrasonic studies of the amorphous binary alloy Pd0.82Si0.18 at low temperatures

Abstract Ultrasonic attenuation and velocity changes are measured in an amorphous Pd 0.82 Si 0.18 binarys alloy at frequencies from 10 MHz to 200 MHz (transverse) and temperatures down to 0.27 K. The attenuation is found to contain an amplitude dependent (saturable) component. These observations, as well as the temperature dependence of the velocity changes, are consistent with the predictions of the two level tunnelling systems (TLS) theory. Contrary to the predictions of this theory, however, linear frequency dependence and essentially no temperature dependence of saturable attenuation changes were observed at very low temperatures.