Voigt, Reuss, Hill, and self-consistent techniques for modeling ultrasonic scattering

Christopher M. Kube, Joseph A. Turner

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Scopus citations

Abstract

An elastic wave propagating in a metal loses a portion of its energy from scattering caused by acoustic impedance differences existing at the boundaries of anisotropic grains. Theoretical scattering models capture this phenomena by assuming the incoming wave is described by an average elastic moduli tensor Cijkl0(x) that is perturbed by a grain with elasticity Cijkl(x′) where the scattering event occurs when x = x′. Previous models have assumed that Cijkl0(x) is the Voigt average of the single-crystal elastic moduli tensor. However, this assumption may be incorrect because the Voigt average overestimates the wave's phase velocity. Thus, the use of alternate definitions of Cijkl0(x) to describe the incoming wave is posed. Voigt, Reuss, Hill, and self-consistent definitions of Cijkl0(x) are derived in the context of ultrasonic scattering models. The scattering-based models describing ultrasonic backscatter, attenuation, and diffusion are shown to be highly dependent on the definition of Cijkl0(x).

Original languageEnglish (US)
Title of host publication41st Annual Review of Progress in Quantitative Nondestructive Evaluation, Volume 34
EditorsDale E. Chimenti, Leonard J. Bond
PublisherAmerican Institute of Physics Inc.
Pages926-934
Number of pages9
ISBN (Electronic)9780735412927
DOIs
Publication statusPublished - Jan 1 2015
Event41st Annual Review of Progress in Quantitative Nondestructive Evaluation, QNDE 2014 - Boise, United States
Duration: Jul 20 2014Jul 25 2014

Publication series

NameAIP Conference Proceedings
Volume1650
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference41st Annual Review of Progress in Quantitative Nondestructive Evaluation, QNDE 2014
CountryUnited States
CityBoise
Period7/20/147/25/14

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Keywords

  • Hill
  • Reuss
  • Self-consistent
  • Ultrasonic scattering
  • Voigt
  • attenuation
  • diffusivity
  • grain noise
  • polycrystal elasticity

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Kube, C. M., & Turner, J. A. (2015). Voigt, Reuss, Hill, and self-consistent techniques for modeling ultrasonic scattering. In D. E. Chimenti, & L. J. Bond (Eds.), 41st Annual Review of Progress in Quantitative Nondestructive Evaluation, Volume 34 (pp. 926-934). (AIP Conference Proceedings; Vol. 1650). American Institute of Physics Inc.. https://doi.org/10.1063/1.4914698