# The Inverse Problem in Materials Characterization through Ultrasonic Attenuation and Velocity Measurements

## Abstract

The inverse problem in materials characterization is most often skipped over in favor of a correlation because the inverse problem is so difficult and the correlation is only tedious, not hard. In this talk the basic difficulty in the inverse problem field will be illustrated by two examples: finding grain size in metals when ultrasonic attenuation is measured, and finding graphite shape in cast iron when ultrasonic velocity is measured.

The basic difficulty arises because the measured quantity, attenuation or velocity, is a function of several variables. Thus, any single variable among the latter cannot be written as a single-valued function of the measured quantity.

For instance, attenuation α, caused by grain scattering, is a function of frequency f, grain diameter D, grain substructure μ, grain size distribution “GSD”, and the ratio of the grain diameter to the ultrasonic wavelength D/λ. The total attenuation “ATT” is also a function of geometrical beam spreading “BS” (which depends on sample anisotropy) as well as on physical absorption mechanisms “ABS” which in turn are functions of frequency and other parameters.

^{2}. The result is

The talk will present further clarifications of these challenging research opportunities using ultrasonic attenuation and velocity.

## Keywords

Inverse Problem Grain Size Distribution Physical Acoustics Ultrasonic Velocity Ductile Iron## Preview

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