Ultrasonic wave propagation predictions for polycrystalline materials using three-dimensional synthetic microstructures

Phase velocity variations

Musa Norouzian, Joseph A Turner

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In most theoretical work related to effective properties of polycrystals, the media are assumed to be infinite with randomly oriented grains. Therefore, the bulk material has absolute isotropy because each direction includes an infinite number of grains with infinite possibilities for grain orientation. However, real samples will always include a finite number of grains such that the inspection volume will have some associated anisotropy. Thus, bounds on the bulk properties are expected for a given measurement. Here, the effect of the number of grains on the variations of elastic anisotropy is studied using synthetic polycrystals comprised of equiaxed cubic grains (17 volumes with 100 realizations each). Voigt, Reuss, and self-consistent techniques are used to derive the effective elastic modulus tensor. The standard deviation of the average elastic modulus is then quantified for several materials with varying degrees of single-crystal anisotropy and is shown to be inversely proportional to the square root of the number of grains. Finally, the Christoffel equation is used to study the relevant phase velocities. With appropriate normalization, a master curve is derived with respect to the finite sample size, which shows the expected variations of phase velocity for the longitudinal, fast shear, and slow shear modes.

Original languageEnglish (US)
Pages (from-to)2171-2180
Number of pages10
JournalJournal of the Acoustical Society of America
Volume145
Issue number4
DOIs
StatePublished - Apr 1 2019

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ultrasonic radiation
phase velocity
wave propagation
microstructure
predictions
polycrystals
modulus of elasticity
shear
elastic anisotropy
anisotropy
isotropy
Waves
Prediction
Three-dimensional
Microstructure
inspection
standard deviation
tensors
single crystals
curves

ASJC Scopus subject areas

  • Arts and Humanities (miscellaneous)
  • Acoustics and Ultrasonics

Cite this

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abstract = "In most theoretical work related to effective properties of polycrystals, the media are assumed to be infinite with randomly oriented grains. Therefore, the bulk material has absolute isotropy because each direction includes an infinite number of grains with infinite possibilities for grain orientation. However, real samples will always include a finite number of grains such that the inspection volume will have some associated anisotropy. Thus, bounds on the bulk properties are expected for a given measurement. Here, the effect of the number of grains on the variations of elastic anisotropy is studied using synthetic polycrystals comprised of equiaxed cubic grains (17 volumes with 100 realizations each). Voigt, Reuss, and self-consistent techniques are used to derive the effective elastic modulus tensor. The standard deviation of the average elastic modulus is then quantified for several materials with varying degrees of single-crystal anisotropy and is shown to be inversely proportional to the square root of the number of grains. Finally, the Christoffel equation is used to study the relevant phase velocities. With appropriate normalization, a master curve is derived with respect to the finite sample size, which shows the expected variations of phase velocity for the longitudinal, fast shear, and slow shear modes.",
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