Multi-parameter optimization of attenuation data for characterizing grain size distributions and application to bimodal microstructures

TL;DR

This paper extends the theory of ultrasonic attenuation to complex grain size distributions, especially bimodal microstructures, and introduces an optimization method to characterize these distributions from attenuation data.

Contribution

It develops a generalized analytical model for attenuation in polycrystals with arbitrary grain size distributions and proposes a least squares optimization for bimodal microstructure characterization.

Findings

Accurately estimates volume fractions of large grains.

Provides modal equivalent diameters from attenuation data.

Validates approach with analytical and numerical data.

Abstract

In this paper, the effect on the ultrasonic attenuation of the grain size heterogeneity in polycrystals is analyzed. First, new analytical developments allowing the extension of the unified theory of Stanke and Kino to general grain size distributions are presented. It is then shown that one can additively decompose the attenuation coefficient provided that groups of grains are defined. Second, the study is specialized to a bimodal distribution of the grain size for which microstructures are numerically modeled by means of the software Neper. The additive partition of the attenuation coefficient into contributions coming from large and small grains motivates the derivation of an optimization procedure for characterizing the grain size distribution. The aforementioned approach, which is based on a least squares minimization, is at last presented and illustrated on both analytical and numerical attenuation data. It is thus shown that the method provides satisfying approximations of volume fractions of large grains and modal equivalent diameters from the frequency-dependent attenuation coefficient.