### 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 language | English (US) |
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Title of host publication | 41st Annual Review of Progress in Quantitative Nondestructive Evaluation, Volume 34 |

Editors | Dale E. Chimenti, Leonard J. Bond |

Publisher | American Institute of Physics Inc. |

Pages | 926-934 |

Number of pages | 9 |

ISBN (Electronic) | 9780735412927 |

DOIs | |

State | Published - Jan 1 2015 |

Event | 41st Annual Review of Progress in Quantitative Nondestructive Evaluation, QNDE 2014 - Boise, United States Duration: Jul 20 2014 → Jul 25 2014 |

### Publication series

Name | AIP Conference Proceedings |
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Volume | 1650 |

ISSN (Print) | 0094-243X |

ISSN (Electronic) | 1551-7616 |

### Conference

Conference | 41st Annual Review of Progress in Quantitative Nondestructive Evaluation, QNDE 2014 |
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Country | United States |

City | Boise |

Period | 7/20/14 → 7/25/14 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*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

**Voigt, Reuss, Hill, and self-consistent techniques for modeling ultrasonic scattering.** / Kube, Christopher M.; Turner, Joseph A.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*41st Annual Review of Progress in Quantitative Nondestructive Evaluation, Volume 34.*AIP Conference Proceedings, vol. 1650, American Institute of Physics Inc., pp. 926-934, 41st Annual Review of Progress in Quantitative Nondestructive Evaluation, QNDE 2014, Boise, United States, 7/20/14. https://doi.org/10.1063/1.4914698

}

TY - GEN

T1 - Voigt, Reuss, Hill, and self-consistent techniques for modeling ultrasonic scattering

AU - Kube, Christopher M.

AU - Turner, Joseph A.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - 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).

AB - 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).

KW - Hill

KW - Reuss

KW - Self-consistent

KW - Ultrasonic scattering

KW - Voigt

KW - attenuation

KW - diffusivity

KW - grain noise

KW - polycrystal elasticity

UR - http://www.scopus.com/inward/record.url?scp=85031777146&partnerID=8YFLogxK

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U2 - 10.1063/1.4914698

DO - 10.1063/1.4914698

M3 - Conference contribution

AN - SCOPUS:85031777146

T3 - AIP Conference Proceedings

SP - 926

EP - 934

BT - 41st Annual Review of Progress in Quantitative Nondestructive Evaluation, Volume 34

A2 - Chimenti, Dale E.

A2 - Bond, Leonard J.

PB - American Institute of Physics Inc.

ER -