Andrew Granato

Theory of Mechanical Damping Due to Dislocations

A quantitative theory of damping and modulus changes due to dislocations is developed. It is found that the model used by Koehler of a pinned dislocation loop oscillating under the influence of an applied stress leads to two kinds of loss, one frequency dependent and the other not. The frequency dependent loss is found to have a maximum in the high megacycle range. The second type of loss is a hysteresis loss which proves to be independent of frequency over a wide frequency range which includes the kilocycle range. This loss has a strain‐amplitude dependence of the type observed in the kilocycle range. The theory provides a quantitative interpretation of this loss.

Application of Dislocation Theory to Internal Friction Phenomena at High Frequencies

A detailed discussion of data obtained over the past 15 years concerning the damping of mechanical vibrations in the kilocycle and megacycle range is given. The dependence of the decrement and modulus change on the variables of frequency and strain‐amplitude and many other parameters is compared with predictions of the dislocation theory developed in an earlier paper. Although general agreement is obtained, and many interesting quantitative results are found, it is not possible to say that the theory agrees everywhere since not all the necessary parameters are known well enough theoretically. A number of new experiments are suggested which may permit stronger conclusions to be made. This part may be read independently of the earlier paper by the reader who does not wish to follow the development of the theory in detail.

Diffraction Effects in the Ultrasonic Field of a Piston Source and Their Importance in the Accurate Measurement of Attenuation

A study is made of the ultrasonic field produced by a circular quartz crystal transducer and the integrated response of a quartz crystal receiver with the same dimensions as the transducer. The transducer and receiver are taken to be coaxial, and it is assumed that the transducer behaves as a piston source while the integrated response is proportional to the average pressure over the receiver area. Computations are made for cases of interest in the megacycle frequency range (ka=50 to 1000; a=piston radius; λ=wavelength; k=2π/λ). The results contain features of use in identifying and correcting for diffraction errors. These features which apparently have been missed in previous investigations are compared with available experimental data. Finally correction formulas to account for diffraction effects in the accurate measurement of attenuation are discussed. It is shown that the order of magnitude of the diffraction attenuation is given by one decibel per a2/λ.

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...

Frequency Dependence of Ultrasonic Attenuation in Germanium

The attenuation of compressional waves traveling in the [100] direction in germanium has been measured in the frequency range from 5 to 300 Mc/sec. Below 20 Mc/sec, the loss was found to be mostly due to diffraction. The remaining attenuation can be described by an expression of the form α=Kfn, where α is the attenuation, f the frequency, n a constant near but somewhat less than two, and K a constant. The attenuation is attributed to the damped forced oscillation of dislocation segments. The value of the damping constant found from the data (about 1.1×10−4 g‐sec−1‐cm−1) is in agreement with the estimate of Leibfried and Nabarro.

Reaction Paths and Activation Energies for Dislocation Unpinning

For the purpose of developing a theory of thermally assisted amplitude dependent damping, the equilibrium configurations and activation energies of pinned dislocations are calculated. The model is of a dislocation pinned by an arbitrary number of equidistant pinning points of equal strength. New features not found for a simple double loop are obtained, but most of the important physical processes for the general case are already obtained for a triple loop. The more important of these features are: (i) There are intermediate energy minima between the pinned state and the broken‐away state; (ii) for a given stress more than one reaction path between the pinned state and the broken‐away state may exist; (iii) multiple‐pin breakaway can occur by a single activation; (iv) thermal breakaway can occur at smaller loop lengths or at smaller stresses than is the case for a single pin. A discussion is given of the possible reaction paths of the dislocation in the general (N‐loop) problem. It is shown which equilibri...

Ultrasonic Attenuation in Cadmium Sulphide above Room Temperature

The temperature dependence of the attenuation of 30‐Mc/sec longitudinal ultrasonic waves has been measured from room temperature to 380°C in CdS. The observed attenuation is in good agreement with the theory of Hutson and White and with the temperature dependence of the resistance measured on the same specimen.