Kurt Lücke

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.

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.

Theory of the Thermal Breakaway of a Pinned Dislocation Line with Application to Damping Phenomena

Although the mechanical theory of Granato and Lucke for the strain‐amplitude‐dependent internal friction and modulus changes of solids containing dislocations gives a fair account of many of the observed effects, simple theoretical considerations show that the effect of thermal fluctuations should be very important. To extend the theory to finite temperatures, a detailed study of the possible static equilibrium configurations of a pinned dislocation line as a function of external stress is required. This is done here for the two specific examples of a dislocation with a single pinning point and a dislocation with a continuous pinning agent. It is shown in a general way how the damping and modulus change can be computed from these results, and a qualitative discussion of expected behavior is given. For high concentrations of pinning points, the theory is also applicable in the field of yield point phenomena, and the results found here are compared with previous calculations.

Temperature dependence of amplitude‐dependent dislocation damping

A theory of the damping due to the break‐away of dislocations from pinning points given by the authors for low temperatures has been extended into the high‐temperature range by taking into account thermal activation during break‐away. It has been found that in the high‐temperature range the amplitude dependence is described by the same formula as in the low‐temperature range (Granato‐Lucke formula) but the parameters have a different meaning.

Ultrasonic Attenuation Caused by Thermoelastic Heat Flow

Expressions for the attenuation of sound waves in a standard linear viscoelastic body have been derived and have been applied to the attenuation due to the thermoelastic effect.The thermoelastic attenuation for sound waves has been computed for single crystals and polycrystalline materials under application of the high‐frequency approximation of sound propagation. For single crystals the attenuation in the main propagation directions have been computed explicitly for cubic and hexagonal crystals taking into account the anisotropy of the elastic properties and thermal expansion.Comparison with experiments in the megacycle region shows that the attenuation caused by heat flow between the grains of a polycrystalline specimen is usually overpowered by scattering at the grain structure. Also the computed attenuation caused by heat flow between the regions of compressions and rarefaction of the wave is for many materials much smaller than the measured values.For single crystals of certain metals, however, the c...

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...

Orientation of recrystallized grains in strained aluminum single crystals

Abstract Artificially nucleated crystals were grown in strained aluminum single crystals by cutting them at one end with pliers and then subjecting them to recrystallization heating. An overwhelming majority of the new crystals showed an orientation characterized by a 40° rotation around the [111] axis relative to the old matrix. Recrystallization always started at the cut end with many fine grains. After further heating most of these fine grains disappeared and only a few large crystals were left. They grew further into the deformed matrix and one of them finally occupied the full diameter of the wire. Laue and Debye-Scherrer X-ray photographs showed that in the early stage of recrystallization the orientation of the many fine grains were distributed at random, while the crystal finally obtained usually was characterized by a 40° [111] rotation. This indicates that the preferred orientation of the final crystals originates in growth selection. The preference for [111] rather than the other 〈111〉 axes may be caused either by the plastic deformation of the old matrix, or by the fact that the boundary between the two crystals is a pure tilt boundary if both have a common [111] axis.

Quantitative investigation of ultrasonic attenuation in copper single crystals

The dislocation contribution to the ultrasonic attenuation of high‐purity copper single crystals has been quantitatively determined by forming the difference between the measured attenuation and the nondislocation part of attenuation as measured after heavy irradiation. In this way mainly, the influence of temperature, deformation, γ irradiation, and heat treatment on the dislocation damping has been studied. The measurements were evaluated according to the Granato‐Lucke theory of dislocation resonance. One of the main objectives of the work was to test the applicability of various experimental and theoretical methods for gaining quantitative information on dislocations from ultrasonic attenuation measurements.