Single Scattering and Diffusive Limits of the Ultrasonic Radiative Transfer Equation

Turner, Joseph A.; Weaver, Richard L.

doi:10.1007/978-1-4615-1987-4_6

Cited by 5 publications

(3 citation statements)

References 7 publications

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“…Additionally, they introduced the Wigner transform techniques to describe the beam effects of a piston transducer. Turner and Weaver [77][78] also developed the radiative transfer theory to describe the diffusion of ultrasonic energy when the propagation distance is large and the ultrasound loss coherence. From the fundamental assumptions (ISA, the Born approximation, the weak anisotropy assumption, etc.)…”

Section: Discussionmentioning

confidence: 99%

Multiple Scattering Theory for Polycrystalline Materials with Strong Grain Anisotropy: Theoretical Fundamentals and Applications

He¹

2019

Preprint

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This work is a natural extension of the author's previous work: "Multiple scattering theory for heterogeneous elastic continua with strong property fluctuation: theoretical fundamentals and applications" (arXiv:1706.09137 [physics.geo-ph]), which established the foundation for developing multiple scattering model for heterogeneous elastic continua with either weak or strong fluctuations in mass density and elastic stiffness. Polycrystalline material is another type of heterogeneous materials that widely exists in nature and extensively used in industry. In this work, the corresponding multiple scattering theory for polycrystalline materials with randomly oriented anisotropic crystallites is developed. To validate the theory, the theoretical results for a series of materials such as OFHC copper, 304 stainless steel, and Inconel 600 are compared to experimental measurements and the numerical results obtained using finite element simulations. Detailed analysis shows that the new theory is capable of predicting the dispersion and attenuation of polycrystals with satisfactory accuracy. The results also show the new model can give an estimate on the average grain size with a relative error equal to or less than ten percent. As applications in ultrasonic nondestructive evaluation, we calculated the dispersion and attenuation coefficient of one of the most important polycrystalline materials in aeronautics engineering: high-temperature titanium alloys. The effects of grain symmetry, grain size, and alloying elements on the dispersion and attenuation behaviors are examined. Key information is obtained which has significant implications for quantitatively evaluating the average grain size, monitoring the phase transition, and even estimating gradual change in chemical composition of titanium components in gas turbine engines. For applications in seismology, the velocities and Q-factors for both hexagonal and cubic polycrystalline iron models for the Earth's uppermost inner core are obtained in the whole frequency range. Using the realistic material parameters of iron under the high temperature and high-pressure conditions calculated from ab initio simulations, the numerical results show that the Q-factors range from 0.001 to 0.05, which shows good agreement with that inferred from real seismic data. The new model predicts the velocity of longitudinal waves varies between ± 1% to ± 5 % relative to the Voight average velocity, while the velocity of transverse waves varies from ± 10% to ± 20%, which gives promising explanation to the abnormally slow transverse velocity observed in practical measurements. The numerical results support the conjecture that the Earth's uppermost inner core is a solid polycrystalline medium. The comprehensive numerical examples show the new model is capable of capturing the most important scattering features of both ultrasonic and seismic waves with satisfactory accuracy. This work provides a universal, quantitative model for characterization of a large variety of polycrystalline materials. It als...

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Section: Discussionmentioning

confidence: 99%

Multiple Scattering Theory for Polycrystalline Materials with Strong Grain Anisotropy: Theoretical Fundamentals and Applications

He¹

2019

Preprint

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“…In various backscattering experiments line transducers are often applied for inspection of heterogeneous materials. The work of Margetan et al, Rose, and Turner and Weaver found that the single scattering process provides valuable microstructural information about the complex materials studied [1][2][3]. The independent scatter model (ISM) was developed as a first-order model for grain noise from scattering in polycrystals [1].…”

Section: Introductionmentioning

confidence: 99%

Ultrasonic backscatter in two-phase media and its dependency on the correlation function

Liu

Turner²

2013

Proceedings of Meetings on Acoustics

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“…He also employed a Born approximation which limited the validity of the results to frequencies below the geometrical optics regime, and obtained the exact diffusivity for randomly distributed orientation of all crystallites. Turner and Weaver [51], [52], [53], [54], [55] proposed to model ultrasonic multiple scattering effects in a medium containing randomly located discrete scatterers using radiative transfer theory and applied that theory to polycrystalline media as well. They demonstrated that the scattered intensity is angularly dependent as expected.…”

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confidence: 99%

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

Turner¹

2005

Self Cite

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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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Single Scattering and Diffusive Limits of the Ultrasonic Radiative Transfer Equation

Cited by 5 publications

References 7 publications

Multiple Scattering Theory for Polycrystalline Materials with Strong Grain Anisotropy: Theoretical Fundamentals and Applications

Multiple Scattering Theory for Polycrystalline Materials with Strong Grain Anisotropy: Theoretical Fundamentals and Applications

Ultrasonic backscatter in two-phase media and its dependency on the correlation function

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

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