Stress-dependent second-order grain statistics of polycrystals

Kube, Christopher M.; Turner, Joseph A.

doi:10.1121/1.4932026

Cited by 9 publications

(8 citation statements)

References 58 publications

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“…The introduction of the stress-dependence into X I!S was achieved by utilizing the stress-dependent elastic moduli of the polycrystal. 22 As was shown in Kube et al, 42 the same stress-dependent elastic moduli can be used to model acoustoelasticity or the phase velocity dependence on the stress state of the polycrystalline material. Thus, the same physical mechanism that leads to stressdependent phase velocities causes the scattering from grain boundaries to be influenced by material stresses.…”

Section: Discussionmentioning

confidence: 99%

“…Analytical forms of the 44 independent components of N for polycrystalline materials with a uniaxial stress r 33 was given in Kube and Turner. 22 As an example, the analytical form of the component N …”

Section: Discussionmentioning

confidence: 99%

“…The procedure for calculating these independent components is given elsewhere. 22 Once all of the components of N are known, a differential scattering coefficient X can then be formed from inner products of N with the propagation and displacement vectors of the incident and scattered waves. X defines the differential scattering cross-section of the scattered wave field from an ensemble of grains contained within the ultrasonic beam.…”

Section: Theorymentioning

confidence: 99%

“…19 Kube et al experimentally demonstrated the influence of applied loads on ultrasonic backscatter. 20,21 More recently, Kube and Turner 22 reformulated the stressdependent elastic properties of the polycrystal to allow for residual stresses and provided a correction to Turner and Ghoshal 19 (see Appendix A of Kube and Turner 22 ). In this article, the stress-dependent elastic moduli 22 of the individual grains composing the polycrystal are used to model the influence of material stress on ultrasonic (bulk wave) scattering from grain boundaries.…”

Section: Introductionmentioning

confidence: 99%

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Stress-dependent ultrasonic scattering in polycrystalline materials

Kube

Turner

2016

The Journal of the Acoustical Society of America

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Stress-dependent elastic moduli of polycrystalline materials are used in a statistically based model for the scattering of ultrasonic waves from randomly oriented grains that are members of a stressed polycrystal. The stress is assumed to be homogeneous and can be either residual or generated from external loads. The stress-dependent elastic properties are incorporated into the definition of the differential scattering cross-section, which defines how strongly an incident wave is scattered into various directions. Nine stress-dependent differential scattering cross-sections or scattering coefficients are defined to include all possibilities of incident and scattered waves, which can be either longitudinal or (two) transverse wave types. The evaluation of the scattering coefficients considers polycrystalline aluminum that is uniaxially stressed. An analysis of the influence of incident wave propagation direction, scattering direction, frequency, and grain size on the stress-dependency of the scattering coefficients follows. Scattering coefficients for aluminum indicate that ultrasonic scattering is much more sensitive to a uniaxial stress than ultrasonic phase velocities. By developing the stress-dependent scattering properties of polycrystals, the influence of acoustoelasticity on the amplitudes of waves propagating in stressed polycrystalline materials can be better understood. This work supports the ongoing development of a technique for monitoring and measuring stresses in metallic materials.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stress-dependent ultrasonic scattering in polycrystalline materials

Kube

Turner

2016

The Journal of the Acoustical Society of America

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“…However, FEM is a numerical method and it has limited practical application to the ultrasonic characterization of grain microstructures. Due to the industrial needs of ultrasonic characterization of microstructure characteristics from ultrasound measurements, many studies have strived to develop analytical attenuation models for polycrystalline materials with a variety of complexities such as the low symmetry constituents [7,[24][25][26][27], the duplex microstructure [10] and the columnar grains [28].…”

Section: Introductionmentioning

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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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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Dependence of diffuse ultrasonic backscatter on residual stress in 1080 steel

Turner¹

2016

Ultrasonics

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Stress-dependent second-order grain statistics of polycrystals

Cited by 9 publications

References 58 publications

Stress-dependent ultrasonic scattering in polycrystalline materials

Stress-dependent ultrasonic scattering in polycrystalline materials

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

Dependence of diffuse ultrasonic backscatter on residual stress in 1080 steel

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