Estimation of Single-Crystal Elastic Constants from Ultrasonic Measurements on Polycrystalline Specimens

Abstract

In past work we reported on measurements of ultrasonic velocity, attenuation and backscattering in nickel‐alloy materials used in the fabrication of rotating jet‐engine components. Attenuation and backscattering were shown to be correlated to the average grain diameter, which varied with position in the billet specimens studied. The ultrasonic measurements and associated metallographic studies found the local microstructures to be approximately equiaxed and free of texture in these cubic‐phase metals. In this paper we explore a method for deducing the single‐crystal elastic constants of a metal using the combined ultrasonic and metallographic data for a polycrystalline specimen. We specifically consider the case seen in the jet‐engine alloys: polycrystalline cubic microstructures having equiaxed, randomly oriented grains. We demonstrate how the three independent elastic constants {C11, C12, C44} can be deduced from the density, the mean grain diameter, the ultrasonic attenuation at one or more frequencies, and the longitudinal and shear wave speeds. The method makes use of the attenuation theory of Stanke and Kino, and the Hill averaging procedure for estimating the sonic velocity through a polycrystalline material. Elastic constant inputs to the velocity and attenuation models are adjusted to optimize the agreement with experiment. The method is demonstrated using several specimens of Inconel 718 and Waspaloy, and further tested using four specimens of pure Nickel.