A spherical harmonic approach for the determination of HCP texture from ultrasound: A solution to the inverse problem

Lan, Bo; Lowe, M. J. S.; Dunne, Fionn P.E.

doi:10.1016/j.jmps.2015.06.014

Cited by 11 publications

(28 citation statements)

References 42 publications

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“…Substituting equation 23 back into 22 makes the latter into the spherical convolution theorem for HCP materials in [1], which proves the compatibility of the generalised theorem with HCP materials and that the HCP theorem is indeed a special case of the generalised one.…”

Section: Using the Theorem For Inverse Studies On Hcp Materialsmentioning

confidence: 71%

“…Similar ideas to those presented in [1] are employed, but now with full consideration of all three Euler angles.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

“…expands out approximately as a sphere, with some distortions introduced by the anisotropy within the polycrystal; and if only the wave propagation in a certain direction is of interest, the problem can be simplified to be a wave going through an array of crystals in a straight line [1]. Consider the case shown in Figure 3 where the wave goes through a cubic polycrystalline aggregate in the direction of r, with the mini-cubes on each crystal in the figure representing its crystallographic orientation.…”

Section: Refinement Of the Grain Average Modelmentioning

confidence: 99%

“…The inverse study on HCP materials was fully analysed in our previous paper [1], and it can be proved that the spherical convolution theorem obtained specifically for HCP materials is actually a special case of the generalised convolution theorem described by equations 18 and 19.…”

Section: Using the Theorem For Inverse Studies On Hcp Materialsmentioning

confidence: 99%

“…In [1] it was argued that the spherical convolution approach for HCP materials had the flexibility to change the convolution kernel from ultrasonic phase velocities to slowness, group velocity, or Young's modulus, etc, and it is the same for the generalised spherical convolution approach in this paper. So despite that ultrasonic wave phase velocities have been used as the kernel during the deduction of the theorem equation 19, slowness, which is a commonly used concept to evaluate ultrasonic wave phase and group velocities in the non-destructive testing world, can also be used as the kernel to calculate the phase velocity variations in polycrystals; and single crystal group velocity and Young's modulus can be used as the kernel to calculate their respective resulting properties in polycrystals.…”

Section: The Flexibility To Change the Kernel In The Theoremmentioning

confidence: 99%

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A generalized spherical harmonic deconvolution to obtain texture of cubic materials from ultrasonic wave speed

Lan

Lowe

Dunne

2015

Journal of the Mechanics and Physics of Solids

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In this paper, the spherical harmonic convolution approach for HCP materials [1] is extended into a generalised form for the principal purpose of bulk texture determination in cubic polycrystals from ultrasonic wave speed measurements. It is demonstrated that the wave speed function of a general single crystal convolves with the polycrystal Orientation Distribution Function (ODF) to make the resultant polycrystal wave speed function such that when the three functions are expressed in harmonic expansions, the coefficients of any one function may be determined from the coefficients of the other two. All three Euler angles are taken in account in the description of the ODF such that the theorem applies for all general crystal systems.The forward problem of predicting polycrystal wave speed with knowledge of single crystal properties and the ODF is solved for all general cases, with validation carried out on cubic textures showing strong sensitivity to texture and excellent quantitative accuracy in predicted wave speed amplitudes. Importantly, it is also revealed by the theorem that the cubic structure is one of only two crystal systems (the other being HCP) whose orientation distributions can be inversely determined from polycrystal wave velocities by virtue of their respective crystal symmetries. Proof of principle is then established by recovering the ODFs of representative cubic textures solely from the wave velocities generated from a computational model using these texture inputs, and excellent accuracies are achieved in the recovered ODF coefficients as well as the resultant pole figures. Hence the methodology is argued to provide a powerful technique for wave propagation studies and bulk texture measurement in cubic polycrystals and beyond.

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Section: Using the Theorem For Inverse Studies On Hcp Materialsmentioning

confidence: 71%

“…Similar ideas to those presented in [1] are employed, but now with full consideration of all three Euler angles.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

Section: Refinement Of the Grain Average Modelmentioning

confidence: 99%

Section: Using the Theorem For Inverse Studies On Hcp Materialsmentioning

confidence: 99%

Section: The Flexibility To Change the Kernel In The Theoremmentioning

confidence: 99%

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A generalized spherical harmonic deconvolution to obtain texture of cubic materials from ultrasonic wave speed

Lan

Lowe

Dunne

2015

Journal of the Mechanics and Physics of Solids

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Determining elastic anisotropy of textured polycrystals using resonant ultrasound spectroscopy

et al. 2021

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Polycrystalline materials can have complex anisotropic properties depending on their crystallographic texture and crystal structure. In this study, we use resonant ultrasound spectroscopy (RUS) to nondestructively quantify the elastic anisotropy in extruded aluminum alloy 1100-O, an inherently low-anisotropy material. Further, we show that RUS can be used to indirectly provide a description of the material’s texture, which in the present case is found to be transversely isotropic. By determining the entire elastic tensor, we can identify the level and orientation of the anisotropy originated during extrusion. The relative anisotropy of the compressive (c11/c33) and shear (c44/c66) elastic constants is 1.5% ± 0.5% and 5.7% ± 0.5%, respectively, where the elastic constants (five independent elastic constants for transversely isotropic) are those associated with the extrusion axis that defines the symmetry of the texture. These results indicate that the texture is expected to have transversely isotropic symmetry. This finding is confirmed by two additional approaches. First, we confirm elastic constants and the degree of elastic anisotropy by direct sound velocity measurements using ultrasonic pulse echo. Second, neutron diffraction (ND) data confirm the symmetry of the bulk texture consistent with extrusion-induced anisotropy, and polycrystal elasticity simulations using the elastic self-consistent model with input from ND textures and aluminum single-crystal elastic constants render similar levels of polycrystal elastic anisotropy to those measured by RUS. We demonstrate the ability of RUS to detect texture-induced anisotropy in inherently low-anisotropy materials. Therefore, as many other common materials have intrinsically higher elastic anisotropy, this technique should be applicable for similar levels of texture, providing an efficient general diagnostic and characterization tool.

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Direct volumetric measurement of crystallographic texture using acoustic waves

et al. 2018

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A spherical harmonic approach for the determination of HCP texture from ultrasound: A solution to the inverse problem

Cited by 11 publications

References 42 publications

A generalized spherical harmonic deconvolution to obtain texture of cubic materials from ultrasonic wave speed

A generalized spherical harmonic deconvolution to obtain texture of cubic materials from ultrasonic wave speed

Determining elastic anisotropy of textured polycrystals using resonant ultrasound spectroscopy

Direct volumetric measurement of crystallographic texture using acoustic waves

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