Rohn Truell

Scattering of a Plane Longitudinal Wave by a Spherical Obstacle in an Isotropically Elastic Solid

Scattering by a spherical obstacle of a plane longitudinal wave propagating in an isotropically elastic solid is computed. Expressions for the scattered wave and the total scattered energy are given. Three special types of obstacle—an isotropically elastic sphere, a spherical cavity, and a rigid sphere—are discussed in detail, especially for Rayleigh scattering. The result for the isotropically elastic sphere is compared with the well‐known result of scattering of a plane wave propagating in an ideal fluid by a sphere of another ideal fluid.

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.

Scattering of a Plane Transverse Wave by a Spherical Obstacle in an Elastic Medium

An analysis of the scattering of transverse elastic waves by spherical obstacles is presented. The scatterer is taken to be (a) a cavity, (b) a rigid sphere, (c) a fluid‐filled cavity, and (d) to consist of an elastic material with properties different from those of the surrounding material. The problems are carried as far as possible analytically without approximations and are reported as matrix equations. The solution of these equations yields the expansion coefficients that describe the waves which are scattered outward from the obstacle and which are excited within the scatterer. A general expression for the scattering cross section offered to a transverse wave has been derived. The Rayleigh approximation is then considered in detail for three of the cases.

The Measurement of Ultrasonic Attenuation in Solids by the Pulse Technique and Some Results in Steel

Pulse techniques for the measurement of attenuation in solids have been extended and refined sufficiently to obtain dependable measurements over a frequency range from 5 to 50 megacycles. Understanding of the relative importance of beam spreading, geometrical boundaries, and method of coupling has been improved. Coupling by means of water buffer and direct mounting is discussed in detail.Attenuation measurements in the frequency range from 5 to 50 megacycles have been made on chrome molybdenum steel specimens, and these measurements have shown large differences in ultrasonic attenuation for samples of the same chemical composition but different heat treatment. The resulting differences are connected with anisotropy which appears in the photomicrographs. The attenuation measurements are quite sensitive to heat treatment and other factors. The application of the methods to metallurgical problems and the physics of solids is suggested.

Ultrasonic Attenuation Unit and Its Use in Measuring Attenuation in Alkali Halides

An instrument for measurement of ultrasonic attenuation and velocity in the frequency range from 5–200 mc/sec is described. The unit incorporates pulsed rf oscillator, superheterodyne receiver, exponential wave‐form generator, precision time delay generator (useful in velocity measurements), CRT display circuits, and appropriate synchronization circuits. Ultrasonic attenuation measurements made in single crystals of NaCl and KCl during deformation and recovery at several temperatures are reported here.An instrument for measurement of ultrasonic attenuation and velocity in the frequency range from 5–200 mc/sec is described. The unit incorporates pulsed rf oscillator, superheterodyne receiver, exponential wave‐form generator, precision time delay generator (useful in velocity measurements), CRT display circuits, and appropriate synchronization circuits. Ultrasonic attenuation measurements made in single crystals of NaCl and KCl during deformation and recovery at several temperatures are reported here.

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...

Scattering of a Plane Longitudinal Wave by a Spherical Fluid Obstacle in an Elastic Medium

The method of Ying and Truell for studying the scattering of longitudinal elastic waves by spherical obstacles is applied to the particular case of scattering by a fluid‐filled cavity that is embedded in an isotropic elastic solid. Exact solutions for the expansion coefficients which describe the scattered elastic wave are obtained. The limiting case of ka≪1 (Rayleigh scattering) is considered in detail. A general expression for the scattering cross section is derived.

Effect of Lack of Parallelism of Sample Faces on the Measurement of Ultrasonic Attenuation

The measurement of ultrasonic attenuation and velocity at megacycle frequencies demands that the sample faces be parallel within limits that require extreme care. The importance of maintaining the tolerances in question is shown in terms of the echo patterns for various cases in which the tolerances are held and in which they are not. In order to measure attenuation of crystalline quartz to within about 10% at 1000 Mc/sec, the required wedge angle θ should be about 5×10−8 rad or less. This turns out to be just barely possible. under rather special conditions. At the highest frequencies attained thus far (i.e., about 25 000 Mc/sec) with ultrasonic stress waves, the limits on parallelism are so severe that there are at present no instruments capable of making the necessary measurements to control the sample parallelism.

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.

Operating Characteristics of a High Yield Rf Ion Source

An rf ion source has been constructed, which yields up to 15 ma of hydrogen ion current consisting of 80–90 percent protons. The ion current yield has been studied as a function of rf power and frequency, gas pressure, and dc (extracting) voltage. These relationships are correlated with internal phenomena of the gas discharge and of ion extraction therefrom.