Estimates of Nonlinear Elastic Constants and Acoustic Nonlinearity Parameters for Textured Polycrystals

Christopher M. Kube, Joseph A. Turner

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

In this article, expressions are derived for the Voigt, Reuss, and Hill estimates of the third-order elastic constants for polycrystals with either cubic or hexagonal crystal symmetry and orthorhombic physical symmetry. General forms of the fourth- and sixth-rank elastic stiffness and compliance tensors for crystal and physical symmetries are given. Explicit expressions are reduced from these tensors for the case of polycrystals exhibiting orthorhombic sample symmetry with either cubic or hexagonal crystallites. The estimated third-order elastic constants of the textured polycrystal are obtained in terms of second- and third-order single-crystal elastic constants and orientation distribution coefficients (ODCs), which are used to account for anisotropic physical symmetry. The acoustic nonlinearity parameter, (Formula presented.), is defined through combinations of the second- and third-order Voigt, Reuss, and Hill estimates of the elastic constants for a textured polycrystal. The model predicts that (Formula presented.) is dependent on the type of averaging scheme used and the texture-defining ODCs. The model is quantitatively evaluated for polycrystalline iron, aluminum, and titanium using second- and third-order single-crystal elastic constants and experimentally measured ODCs. The interrelation between (Formula presented.) and polycrystalline anisotropy offers potential for techniques associated with quantitative texture analysis.

Original languageEnglish (US)
Pages (from-to)157-177
Number of pages21
JournalJournal of Elasticity
Volume122
Issue number2
DOIs
StatePublished - Feb 1 2016

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Polycrystals
Elastic constants
Crystal symmetry
Acoustics
Crystal orientation
Tensors
Textures
Single crystals
Titanium
Aluminum
Crystallites
Anisotropy
Iron
Stiffness
Crystals

Keywords

  • Acoustoelasticity
  • Crystallographic texture
  • Harmonic generation
  • Micromechanics
  • Nonlinear elasticity
  • Nonlinearity parameter
  • Polycrystal elasticity
  • Third-order elastic constants

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

Estimates of Nonlinear Elastic Constants and Acoustic Nonlinearity Parameters for Textured Polycrystals. / Kube, Christopher M.; Turner, Joseph A.

In: Journal of Elasticity, Vol. 122, No. 2, 01.02.2016, p. 157-177.

Research output: Contribution to journalArticle

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AB - In this article, expressions are derived for the Voigt, Reuss, and Hill estimates of the third-order elastic constants for polycrystals with either cubic or hexagonal crystal symmetry and orthorhombic physical symmetry. General forms of the fourth- and sixth-rank elastic stiffness and compliance tensors for crystal and physical symmetries are given. Explicit expressions are reduced from these tensors for the case of polycrystals exhibiting orthorhombic sample symmetry with either cubic or hexagonal crystallites. The estimated third-order elastic constants of the textured polycrystal are obtained in terms of second- and third-order single-crystal elastic constants and orientation distribution coefficients (ODCs), which are used to account for anisotropic physical symmetry. The acoustic nonlinearity parameter, (Formula presented.), is defined through combinations of the second- and third-order Voigt, Reuss, and Hill estimates of the elastic constants for a textured polycrystal. The model predicts that (Formula presented.) is dependent on the type of averaging scheme used and the texture-defining ODCs. The model is quantitatively evaluated for polycrystalline iron, aluminum, and titanium using second- and third-order single-crystal elastic constants and experimentally measured ODCs. The interrelation between (Formula presented.) and polycrystalline anisotropy offers potential for techniques associated with quantitative texture analysis.

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