Emmanuel P. Papadakis

Ultrasonic Phase Velocity by the Pulse‐Echo‐Overlap Method Incorporating Diffraction Phase Corrections

The pulse‐echo‐overlap method for ultrasonic time‐delay measurements is reviewed. In this method, pairs of echoes are compared by driving the x axis of a viewing oscilloscope at a frequency equal to the reciprocal of the travel time between the echoes. A method for choosing the correct cyclic overlap for the rf within the echoes is given. Utilization of the proper cyclic overlap permits the accurate measurement of ultrasonic phase velocity. When corrections for the phase advance due to ultrasonic diffraction are applied to the travel times between various pairs of echoes, the accuracy of the average round‐trip travel time is improved. Experimental verification of this is presented for longitudinal waves in isotropic materials and in the pure mode directions in cubic crystals. Delay times are accurate to 0.2 nsec or better.

Ultrasonic Diffraction Loss and Phase Change in Anisotropic Materials

The loss and phase change in progressive longitudinal waves from a finite circular piston source radiating into certain anisotropic media are calculated in this paper. Three‐dimensional calculations are presented for propagation along 3‐, 4‐, and 6‐fold symmetry axes. Relationships sufficient to permit the performance of the calculation for 2‐fold axes are derived. The anisotropy is introduced as a term in the spatial part of the phase in the integral for the pressure in the field of the piston. Geometry proper for pulse‐echo measurements was assumed in the calculation. The diffraction loss fluctuates with S = zλ/a2 (z is the distance into crystal, λ, is the wavelength, a is the transducer radius) before becoming monotonic increasing as the logarithm of S. The positions of the peaks in the loss are functions of the anisotropy of the medium. The phase change, on the other hand, increases monotonically to a limit of π/2 from S‐0 to infinity. However, the phase has plateaus where the loss has peaks. Both new...

Ultrasonic Attenuation Caused by Scattering in Polycrystalline Metals

Ultrasonic‐attenuation measurements have been made on fine‐grained specimens of several metals. The grain‐size distributions and ultrasonic velocities in these metals were also determined. The experimental attenuation is in good quantitative as well as qualitative agreement with current theory. Nickel and three iron alloys, one 30% nickel reported previously, the second 12% chromium (type 416 stainless steel), and the third 17% chromium and 1% carbon (type 440‐C stainless steel), all gave good results. Brass also gave good results, but copper showed much twinning, which as yet is unaccounted for.

Revised Grain‐Scattering Formulas and Tables

The current theory of Rayleigh and stochastic phase scattering of ultrasound in polycrystalline materials is reviewed and compared with (1) former theory and (2) experiment. It is found that, when the grain size is evaluated properly, the current theory accounts rather well for the scattering component of the ultrasonic attenuation of polycrystalline materials. A tabulation is made of the coefficients of attenuation caused by scattering for various materials. These coefficients multiplied by a factor involving the grain size and a factor involving a power of the ultrasonic frequency give the attenuation.

Ultrasonic attenuation by spectrum analysis of pulses in buffer rods: Method and diffraction corrections

A method is presented for measuring ultrasonic attenuation as a function of frequency by spectrum analysis of broad‐band echoes in a buffer/specimen system. Also presented is a new technique for diffraction corrections in this configuration. The buffer rod/spectrum analysis method with diffraction corrections is applied to three experiments to demonstrate its accuracy and versatility in measuring attenuation and defining transducer radiation/reception efficiency.

Ultrasonic Attenuation and Velocity in Hot Specimens by the Momentary Contact Method with Pressure Coupling, and Some Results on Steel to 1200°C

The momentary contact pulse‐echo method with pressure coupling has been extended to the measurement of ultrasonic attenuation in hot specimens. Previously, only velocity was measured. In the present method, the specimen is contacted momentarily by one end of a cool buffer rod about three times as long as the specimen. A piezoelectric transducer on the other end of the buffer rod transmits an ultrasonic signal and receives echoes from the buffer/specimen interface and from the free end of the specimen. The echoes are displayed on an oscilloscope and recorded by a camera. Three echoes are required to define both the attenuation coefficient in the specimen and the reflection coefficient at the buffer/specimen interface. Our results in steel show that the solution and precipitation of carbides affect the velocity drastically, while the attenuation is affected by at least one of the following: (1) magnetism, (2) recrystallization, or (3) carbon solubility, and also by grain growth at elevated temperatures.

Buffer‐Rod System for Ultrasonic Attenuation Measurements

A method has been developed for making ultrasonic attenuation measurements in a large sample by means of a solid buffer rod temporarily bonded to the sample. A piezoelectric transducer is permanently bonded to the other end of the buffer rod. The ratios of the amplitudes of certain echoes are used to find the ultrasonic attenuation in the sample and the reflection coefficient at the buffer‐sample interface at various frequencies across the band of the transducer. The echo‐amplitude ratios are not affected by operating the transducer away from its resonant frequency, because none of the echoes considered arise from reflections at the buffer‐transducer interface. A numerical analysis of the echo amplitudes is presented in which the reflection coefficient is assumed constant and the ultrasonic attenuation is taken as a power of the frequency. Experimental data are given on shear waves in a glass buffer rod on a fused‐silica sample. The reflection coefficient varies little while the ultrasonic attenuation inc...

Grain‐Size Distribution in Metals and Its Influence on Ultrasonic Attenuation Measurements

A transformation has been derived relating the number of spheres of a certain radius R per unit volume (the “volume distribution of spheres”) to the number of circles smaller than a certain radius r per unit area (the “area distribution of circles”) appearing on a plane cutting through the volume. The transformation was applied to several hypothetical grain‐size distributions for polycrystalline metals to find the resulting hypothetical area distribution of grain images on photomicrographs. Comparison of the hypothetical area distributions to experimentally found area distributions gave the following conditions that the true volume distribution of grains must meet: (1) It must be finite at R=0, and (2) it must have a nonzero decreasing tail for large values of R. The common assumption of a single grain diameter is insufficient to explain the experimental area distribution of grain images. The functions NV(R) = Rn exp(−kR) and NV(R) = exp[−(lnR/R0)2/2σV2] were judged plausible for the volume distribution f...

Diffraction of Ultrasound Radiating into an Elastically Anisotropic Medium

The diffraction loss‐distance characteristics in crystals have been computed for the single‐slit transducer geometry in ultrasonic pulse‐echo measurements. The characteristics are functions of elastic anisotropy and show several local maxima and minima before becoming monotonic at large distances from the transducer. By applying scale factors to the ordinates and abscissas of the characteristics, they were made applicable to the case of a circular transducer. The scale factors were chosen to bring the computed single‐slit characteristic for isotropic materials into coincidence with the well‐known isotropic‐diffraction characteristic for circular‐piston sources. The scaled crystal characteristics served to predict the positions of the local loss maxima to 15% and their amplitudes to 25% or better in four experiments. Certain crystals produce less diffraction loss per unit length than others because of the dependence of diffraction on anisotropy. The scaled diffraction loss‐distance characteristics can be u...

Correction for Diffraction Losses in the Ultrasonic Field of a Piston Source

In ultrasonic attenuation experiments carried on by the pulse method, it is important to know the part of the measured attenuation contributed by diffraction in the ultrasonic field. In certain cases, particularly at the lower megacycle frequencies, the diffraction loss can be much greater then the attenuation intrinsic to the specimen. The diffraction loss in decibels has been computed elsewhere as a function of the distance the ultrasonic pulse travels back and forth in the sample. Here an expression for the increment to the attenuation is derived taking into consideration which echoes the decibel drop is measured. It is shown that the first echo has suffered a considerable loss at the lower frequencies and that one must consider that loss in computing the increment to the attenuation caused by diffraction if he has used that echo as one at which the decibel loss is measured. If that loss is not considered, the incremental attenuation will be excessive.