Elastic wave propagation and scattering in heterogeneous, anisotropic media: Textured polycrystalline materials

Turner, Joseph A.

doi:10.1121/1.426168

Cited by 25 publications

(66 citation statements)

References 7 publications

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“…An additional feature observed for the qSV wave in as the SH attenuation in terms of the change with angle and damage. Analogous results have been observed in textured polycrystals by Hirsekorn [46], Ahmed and Thompson [56], and Turner [57]. In Fig.…”

Section: Example Resultssupporting

confidence: 69%

“…Outside the Rayleigh limit, simple expressions of the attenuations of the shear horizontal, quasilongitudinal, and quasishear vertical waves are derived in terms of integrations on the unit circle. Quantitative and qualitative comparisons with previous results by Zhang and Gross [26], [27], Zhang and Achenbach [25], Eriksson and Datta [30], Ahmed and Thompson [56] and Turner [57] show that the more general, direct expressions derived here are reliable and comprehensive for practical applications of detecting damage from microcracks.…”

Section: Discussionmentioning

confidence: 57%

“…This shift is thought to be the result of the induced anisotropy from the cracks as shown in the slowness plots in Fig. 4.3 as speculated elsewhere [57]. However, further investigation is necessary to determine the precise reason for this peak shift.…”

Section: Example Resultsmentioning

confidence: 94%

“…Numerical results are now presented for a specific case, in which the observed anisotropy of the cracked material is essentially due to the presence of the uniaxially aligned [56], [46], [57]. Zhang and Gross [26] comment that their attenuation results are not zero for propagation along the symmetry axis.…”

Section: Example Resultsmentioning

confidence: 99%

“…The use of an anisotropic Green's function for modeling the scattering in anisotropic media was investigated by Turner [57]. Here, this approach is employed as well to formulate the uniaxially aligned crack problem.…”

Section: Discussionmentioning

confidence: 99%

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Ultrasonic Studies of the Fundamental Mechanisms of Recrystallization and Sintering of Metals

Turner¹

2005

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ObjectivesThe purpose of this project was to develop a fundamental understanding of the interaction of an ultrasonic wave with complex media, with specific emphases on recrystallization and sintering of metals. A combined analytical, numerical, and experimental research program was implemented. Theoretical models of elastic wave propagation through these complex materials were developed using stochastic wave field techniques. The numerical simulations focused on finite element wave propagation solutions through complex media. The experimental efforts were focused on corroboration of the models developed and on the development of new experimental techniques. The analytical and numerical research allows the experimental results to be interpreted quantitatively. Alteration in Collaborative ArrangementIn fall 2002, the Ames Lab partner, Dr. James C. Foley, announced that he was leaving for another position at Los Alamos National Laboratory. Dr. R. Bruce Thompson has served as the primary contact for this collaboration since Dr. Foley departed. Accomplishments (Recrystallization)Analytical Modeling. Expressions for the ultrasonic attenuation in media with arbitrary texture have been developed using stochastic wave propagation theory. Initial attempts at deriving simple expressions for the attenuation were unsuccessful. Therefore, a modified technique was developed that relies slightly more on numerical calculations. The method is based on a generalized function of a single scalar variable σ that characterizes the state of texture. In this case the weighting function for the individual grains is given by ( ) with θ as the grain orientation angle. Thus, when σ → 0 all grains are aligned and the material is transversely isotropic at the macroscale. As σ → ∞, all grains are randomly oriented and the material is isotropic at the macroscale.In terms of attenuation, the covariance of the microstructure is the primary quantity needed for the calculation of attenuation. It is defined by in which both Eqs. (2) and (3) include the grain orientation distribution function F such that and are dependent on σ. Example results using Eq. (2) are shown in Fig. 1 for both the average elastic properties as well as quasilongitudinal slowness surfaces in terms of σ. The transition from transversely isotropy to complete isotropy is captured well using the grain orientation distribution function. Example results for attenuation are shown in Fig. 2. Again, the transition from transverse isotropy to complete isotropy is shown. Of particular note is the peak observed in the SH attenuation when σ is about 0.5. Such information may be useful for process monitoring. (a) (b)Progress was also made in the study of multiple scattering in slab geometries. These results have applications associated with heterogeneous bonding and interface layers. Two example results are shown in Fig. 3. The layer is insonified by a plane longitudinal wave. One question in the multiple scattering regime is associated with the applicability of the diffusion li...

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Section: Example Resultssupporting

confidence: 69%

Section: Discussionmentioning

confidence: 57%

Section: Example Resultsmentioning

confidence: 94%

Section: Example Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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Ultrasonic Studies of the Fundamental Mechanisms of Recrystallization and Sintering of Metals

Turner¹

2005

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Kinetic modeling of multiple scattering of elastic waves in heterogeneous anisotropic media

Baydoun¹,

Savin²,

Cottereau³

et al. 2014

Wave Motion

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Abstract. In this paper we develop a multiple scattering model for elastic waves in random anisotropic media. It relies on a kinetic approach of wave propagation phenomena pertaining to the situation whereby the wavelength is comparable to the correlation length of the weak random inhomogeneitiesthe so-called weak coupling limit. The waves are described in terms of their associated energy densities in the phase space position × wave vector. They satisfy radiative transfer equations in this scaling, characterized by collision operators depending on the correlation structure of the heterogeneities. The derivation is based on a multi-scale asymptotic analysis using spatio-temporal Wigner transforms and their interpretation in terms of semiclassical operators, along the same lines as Bal [Wave Motion 43, 132-157 (2005)]. The model accounts for all possible polarizations of waves in anisotropic elastic media and their interactions, as well as for the degeneracy directions of propagation when two phase speeds possibly coincide. Thus it embodies isotropic elasticity which was considered in several previous publications. Some particular anisotropic cases of engineering interest are derived in detail.

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Finite-element and semi-analytical study of elastic wave propagation in strongly scattering polycrystals

et al. 2022

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This work studies scattering-induced elastic wave attenuation and phase velocity variation in three-dimensional untextured cubic polycrystals with statistically equiaxed grains using the theoretical second-order approximation (SOA) and Born approximation models and the grain-scale finite-element (FE) model, pushing the boundary towards strongly scattering materials. The results for materials with Zener anisotropy indices A > 1 show a good agreement between the theoretical and FE models in the transition and stochastic regions. In the Rayleigh regime, the agreement is reasonable for common structural materials with 1 < A < 3.2 but it deteriorates as A increases. The wavefields and signals from FE modelling show the emergence of very strong scattering at low frequencies for strongly scattering materials that cannot be fully accounted for by the theoretical models. To account for such strong scattering at A > 1, a semi-analytical model is proposed by iterating the far-field Born approximation and optimizing the iterative coefficient. The proposed model agrees remarkably well with the FE model across all studied materials with greatly differing microstructures; the model validity also extends to the quasi-static velocity limit. For polycrystals with A < 1, it is found that the agreement between the SOA and FE results is excellent for all studied materials and the correction of the model is not needed.

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Elastic wave propagation and scattering in heterogeneous, anisotropic media: Textured polycrystalline materials

Cited by 25 publications

References 7 publications

Ultrasonic Studies of the Fundamental Mechanisms of Recrystallization and Sintering of Metals

Ultrasonic Studies of the Fundamental Mechanisms of Recrystallization and Sintering of Metals

Kinetic modeling of multiple scattering of elastic waves in heterogeneous anisotropic media

Finite-element and semi-analytical study of elastic wave propagation in strongly scattering polycrystals

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