### 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 language | English (US) |
---|---|

Pages (from-to) | 2171-2180 |

Number of pages | 10 |

Journal | Journal of the Acoustical Society of America |

Volume | 145 |

Issue number | 4 |

DOIs | |

State | Published - Apr 1 2019 |

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### ASJC Scopus subject areas

- Arts and Humanities (miscellaneous)
- Acoustics and Ultrasonics

### Cite this

**Ultrasonic wave propagation predictions for polycrystalline materials using three-dimensional synthetic microstructures : Phase velocity variations.** / Norouzian, Musa; Turner, Joseph A.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Ultrasonic wave propagation predictions for polycrystalline materials using three-dimensional synthetic microstructures

T2 - Phase velocity variations

AU - Norouzian, Musa

AU - Turner, Joseph A

PY - 2019/4/1

Y1 - 2019/4/1

N2 - 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.

AB - 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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U2 - 10.1121/1.5096644

DO - 10.1121/1.5096644

M3 - Article

VL - 145

SP - 2171

EP - 2180

JO - Journal of the Acoustical Society of America

JF - Journal of the Acoustical Society of America

SN - 0001-4966

IS - 4

ER -