Shape effect of elongated grains on ultrasonic attenuation in polycrystalline materials

Yang, Limei; Lobkis, O. I.; Rokhlin, S. I.

doi:10.1016/j.ultras.2011.02.002

Cited by 71 publications

(44 citation statements)

References 16 publications

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“…It describes material microstructure and depends on the grain size and morphology. For ellipsoidal-shaped scatterers, 5,6,26,31,33,35 the geometrical autocorrelation function is described by generalized Poisson's statistics as an exponential distribution in terms of three effective correlation radii a X ; a Y ; a Z ,…”

Section: A Dyson Equation and Mass Operatormentioning

confidence: 99%

“…The inner products IP M!N ðp; sÞ (Ref. 35) of the covariance of the elastic modulus hdc ijkl dc abcd i are defined as…”

Section: Far-field Approximation Of the Mass Operator And Approxmentioning

confidence: 99%

“…where a ell ðpÞ ¼ a x a y a z = ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ða y a z sin s cos u s Þ 2 þ ða x a z sin s sin u s Þ 2 þ ða x a y cos sÞ 2 q is the correlation radius (the mean radius of the ellipsoidal grain) in the wave propagation direction p. 35 The stochastic limit (28) is identical to that obtained from the regular Born approximation for the nonequiaxed grains as given in Ref. 35.…”

Section: Dispersion Equations and Scattering Factors Q Mfim Q Mfmentioning

confidence: 99%

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Far-field scattering model for wave propagation in random media

Rokhlin

Guo

2015

The Journal of the Acoustical Society of America

120

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A simple approximate model is developed for ultrasonic wave propagation in a random elastic medium. The model includes second order multiple scattering and is applicable in all frequency ranges including geometric. It is based on the far field approximation of the reference medium Green's function and simplifications of the mass operator in addition to those of the first smooth approximation. In this approximation, the dispersion equation for the perturbed wave number is obtained; its solution yields the dispersive ultrasonic velocity and attenuation coefficients. The approximate solution is general and is suitable for nonequiaxed grains with arbitrary elastic symmetry. For equiaxed cubic grains, the solution is compared with the existing second order models and with the Born approximation. The comparison shows that the obtained solution has smaller error than the Born approximation and shows reasonably well the onset of multiple scattering and the applicability limit of the Born approximation at high frequency. The perturbed wave number in the developed model does not depend explicitly on the crystallite elastic properties even for arbitrary crystallographic symmetry; it depends on two nondimensional scattering elastic parameters and the macroscopic ultrasonic velocity (those are dependent on the crystallite moduli). This provides an advantage for potential schemes for inversion from attenuation to material microstructure.

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Section: A Dyson Equation and Mass Operatormentioning

confidence: 99%

“…The inner products IP M!N ðp; sÞ (Ref. 35) of the covariance of the elastic modulus hdc ijkl dc abcd i are defined as…”

Section: Far-field Approximation Of the Mass Operator And Approxmentioning

confidence: 99%

Section: Dispersion Equations and Scattering Factors Q Mfim Q Mfmentioning

confidence: 99%

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Far-field scattering model for wave propagation in random media

Rokhlin

Guo

2015

The Journal of the Acoustical Society of America

120

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“…(19) and (20). For instance, hW S p i ¼ hG pb ðq; xÞiB b ðqÞSðxÞ and hW R c i ¼Ã a ðpÞhG ac ðp; xÞi RðxÞ:…”

Section: Doubly-scattered Response (Dsr)mentioning

confidence: 99%

“…This work has been very successful for quantifying the probability that a defect is present within the base material and for quantifying grain size information. [16][17][18][19] Because most of these scattering models are based on a single-scattering ansatz, it is not possible to estimate their range of validity with any accuracy. 4,[9][10][11] Such an estimate requires information about the magnitude of the second term in a multiple scattering expansion and it must be formulated to include all aspects of the measurement system such as the transducer properties (e.g., frequency, focal length), focal depth, grain size, grain properties, etc.…”

Section: Introductionmentioning

confidence: 99%

Contribution of double scattering in diffuse ultrasonic backscatter measurements

Turner

2015

The Journal of the Acoustical Society of America

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Diffuse ultrasonic backscatter measurements are used to describe the effective grain scattering present during high frequency ultrasonic inspections. Accurate modeling of the backscatter is important for both flaw detection and microstructural characterization. Previous models have been derived under the assumption of single scattering for which the ultrasound is assumed to scatter only once in the time between excitation and detection. This assumption has been shown to be valid in many experiments for which the time scales are short or the frequency is sufficiently low. However, there are also many instances (e.g., for strongly scattering materials, unfocused beams, or long propagation paths) for which the single scattering assumption appears to break down. In this article, a model for the double scatter is developed within the previous formalism based on Wigner distribution functions. The final expression allows the effect of double scattering to be estimated for any combination of experimental parameters. The improved proposed model is anticipated to increase the capabilities of ultrasonic microstructural evaluation, especially in terms of probability of detection estimates.

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