Effect of nonparallelism on the measurement of ultrasonic attenuation in solids

Evaluation of attenuation of ultrasonic waves in solids from pulse echo trains can be complicated by a number of factors. In this thesis one considers the effect of nonparallelism of the sample surfaces. A mathematical model for correcting the echo height for the effect of a wedge-shaped sample is constructed. By using a unique coordinate system, the path of a multiply-reflected ultrasonic wave is transformed into an equivalent unidirectional path. A diffraction correction then is applied by numerically integrating an improved version of the farfield solution to the diffraction integral. This model is used to interpret data taken on a steel plate which has different facets ground over a range of angles between 0 and 0.01175 radians. Plots are given of corrected attenuation measurements made with circular piezoelectric transucers having resonance frequencies between 3 and 7 MHz.

A comparison is made between the present model and that of Truell and Oates [J. Acoust. Soc. Am. 35,1382 (1963)], which was intended as an indicator of the necessity for applying a correction for nonparallelism. The present model corrects the first four echoes for _3 frequencies f < 6 MHz and angles γ < 4 x 10^-3 radians.