Scattering of Ultrasound in Damaged Media

Liyong Yang
Department of Engineering Mechanics
University of Nebraska - Lincoln
Advisor:  Dr. Joseph Turner

Date: Tuesday, October 9, 2001
Time: 3:30 p.m.
Place: W183 Nebraska Hall


The influence of damage from microcracking on the scattering of ultrasound is discussed with specific application to concrete. The influence of damage from penny-shaped microcracks within a homogeneous medium is first considered. The microcracks are assumed to be randomly oriented and uniformly distributed. Explicit expressions are derived for the attenuation of longitudinal and shear waves in terms of the statistics of the damage and the effective elastic moduli of the medium. The derivation is based on diagrammatic methods. The problem is formulated in terms of the Dyson equation, which is solved for the mean field response within the limits of the first-order smoothing approximation. The attenuation results are given here in a direct way. The longitudinal and shear attenuations are discussed in terms of their frequency dependence and damage dependence. The effective elastic moduli of the statistical distribution of microcracks and the most appropriate damage parameter are discussed. Comparisons with ultrasonic attenuation estimates for undamaged concrete are used to assess the ability of ultrasound to detect damage in concrete. These comparisons are made in terms of the ultrasonic inspection frequency and depth of damage.