Explicit Backscattering Coefficient for Ultrasonic Wave Propagating in Hexagonal Polycrystals with Fiber Texture

Guo, Sha

doi:10.1007/s10921-018-0500-6

Cited by 4 publications

(10 citation statements)

References 45 publications

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“…When two of them go to infinity, the ODF would be equivalent to fiber (axisymmetric) texture like Refs. [39,53]. Note that ODFs in different notations are related to each other, for example, the relation between Bunge's ODF and Roe's ODF has been investigated in Ref.…”

Section: Gaussian Form Odfmentioning

confidence: 99%

“…The elastic constants rotation matrix and details about elastic constants covariance calculation can be found in Refs. [39,40,50,53,59]. It is worthy to mention that Voigt effective elastic constants (or called Voigt reference media) are used in this whole paper because it is more suitable for wave scattering modeling [23,60], although different homogenization methods like self-consistent reference medium are available for polycrystalline media [58,61].…”

Section: Two-point Statistics For Textured Polycrystalsmentioning

confidence: 99%

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Attenuation and Phase Velocity of Elastic Wave in Textured Polycrystals with Ellipsoidal Grains of Arbitrary Crystal Symmetry

Guo

2020

Acoustics

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This study extends the second-order attenuation (SOA) model for elastic waves in texture-free inhomogeneous cubic polycrystalline materials with equiaxed grains to textured polycrystals with ellipsoidal grains of arbitrary crystal symmetry. In term of this work, one can predict both the scattering-induced attenuation and phase velocity from Rayleigh region (wavelength >> scatter size) to geometric region (wavelength << scatter size) for an arbitrary incident wave mode (quasi-longitudinal, quasi-transverse fast or quasi-transverse slow mode) in a textured polycrystal and examine the impact of crystallographic texture on attenuation and phase velocity dispersion in the whole frequency range. The predicted attenuation results of this work also agree well with the literature on a textured stainless steel polycrystal. Furthermore, an analytical expression for quasi-static phase velocity at an arbitrary wave propagation direction in a textured polycrystal is derived from the SOA model, which can provide an alternative homogenization method for textured polycrystals based on scattering theory. Computational results using triclinic titanium polycrystals with Gaussian orientation distribution function (ODF) are also presented to demonstrate the texture effect on attenuation and phase velocity behaviors and evaluate the applicability and limitation of an existing analytical model based on the Born approximation for textured polycrystals. Finally, quasi-static phase velocities predicted by this work for a textured polycrystalline copper with generalized spherical harmonics form ODF are compared to available velocity bounds in the literature including Hashin–Shtrikman bounds, and a reasonable agreement is found between this work and the literature.

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Section: Gaussian Form Odfmentioning

confidence: 99%

Section: Two-point Statistics For Textured Polycrystalsmentioning

confidence: 99%

Attenuation and Phase Velocity of Elastic Wave in Textured Polycrystals with Ellipsoidal Grains of Arbitrary Crystal Symmetry

Guo

2020

Acoustics

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“… θ , ϕ , ζ are three Euler angles in Bunge’s convention. When two of the three texture parameters go to infinity, namely σ ϕ → ∞ and σ ζ → ∞ , the ODF would correspond to a fiber texture [41, 42]. For a fiber texture case, the texture parameter σ θ is related to the texture full-width at half-maximum (FWHM) by 4 arcsin ( σ θ ln 2 ) [37,42] and a larger σ θ corresponds to a weaker texture.…”

Section: The Full-wave Second-order Attenuation Model In Textured mentioning

confidence: 99%

“…The Gaussian ODF is favorable for wave scattering modeling, especially for the illustration of texture impact on wave scattering [26, 35]. However, most experimental texture analyses, such as X ray diffraction, neutron diffraction, and orientation imaging microscopy (OIM), adopt generalized spherical harmonics [30, 43, 44]; one may convert the generalized spherical harmonics ODF to the Gaussian ODF when the texture component is simple, for example, a fiber texture [34, 42].…”

Section: The Full-wave Second-order Attenuation Model In Textured mentioning

confidence: 99%

A far-field scattering model in textured polycrystals with ellipsoidal grains of arbitrary crystal symmetry

Guo

2020

Mathematics and Mechanics of Solids

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Modeling the scattering-induced attenuation of elastic waves in heterogeneous polycrystals has practical applications in seismology and non-destructive evaluation. However, attenuation modeling for polycrystals with preferred crystallographic orientation (statistically anisotropic or textured polycrystals) has not been well studied. The far-field approximation (FFA) model, which is applicable for arbitrary crystal (triclinic) symmetry and valid for the whole frequency range (Rayleigh region, stochastic regime, and geometric region), has been reported for texture-free polycrystalline materials. This paper extends the FFA model to textured polycrystals with ellipsoidal grains of arbitrary crystal symmetry. This FFA model for textured polycrystals encompasses two advantages: a simple form of dispersion equation and high computational efficiency. Furthermore, this FFA model can predict both the attenuation and phase velocity of elastic waves in textured polycrystals. The FFA model in this study has also been validated by comparison with the full-wave second-order attenuation model on textured polycrystals of triclinic grains. This work provides a simple and efficient tool to predict the elastic wave behavior in heterogeneous polycrystalline materials.

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“…Others extended to texture and lower crystal symmetries. [19][20][21][22][23] Ghoshal et al 24 established a mathematical formalism within a multiple scattering framework that included transducer modeling. The scattered response was given as a convolution of the displacement fields' Wigner transforms with an intensity operator defined by the Bethe-Salpeter equation.…”

Section: Introductionmentioning

confidence: 99%

Generalized ultrasonic scattering model for arbitrary transducer configurations

Argüelles

Turner

2019

The Journal of the Acoustical Society of America

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Ultrasonic scattering in polycrystalline media is directly tied to microstructural features. As a result, modeling efforts of scattering from microstructure have been abundant. The inclusion of beam modeling for the ultrasonic transducers greatly simplified the ability to perform quantitative, fully calibrated experiments. In this article, a theoretical scattering model is generalized to allow for arbitrary source and receiver configurations, while accounting for beam behavior through the total propagation path. This extension elucidates the importance and potential of out-of-plane scattering modes in the context of microstructure characterization. The scattering coefficient is explicitly written for the case of statistical isotropy and ellipsoidal grain elongation, with a direct path toward expansion for increased microstructural complexity. Materials with crystallites of any symmetry can be studied with the present model; the numerical results focus on aluminum, titanium, and iron. The amplitude of the scattering response is seen to vary across materials, and to have varying sensitivity to grain elongation and orientation depending on the transducer configuration selected. The model provides a pathway to experimental characterization of microstructure with optimized sensitivity to parameters of interest. V

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Explicit Backscattering Coefficient for Ultrasonic Wave Propagating in Hexagonal Polycrystals with Fiber Texture

Cited by 4 publications

References 45 publications

Attenuation and Phase Velocity of Elastic Wave in Textured Polycrystals with Ellipsoidal Grains of Arbitrary Crystal Symmetry

Attenuation and Phase Velocity of Elastic Wave in Textured Polycrystals with Ellipsoidal Grains of Arbitrary Crystal Symmetry

A far-field scattering model in textured polycrystals with ellipsoidal grains of arbitrary crystal symmetry

Generalized ultrasonic scattering model for arbitrary transducer configurations

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