Recasting Classical Expansion of Orientation Distribution Function as Tensorial Fourier Expansion

Article Engineering, Multidisciplinary

Crystallographic Texture and Group Representations

Chi-Sing Man

Summary: This article introduces the basic concepts and mathematical foundations of classical texture analysis, focusing on the harmonic method and the approach initiated by Roe. The orientation distribution function (ODF) is defined on the rotation group SO(3), and the Wigner D-functions are used instead of generalized spherical harmonics. The article also discusses tensorial Fourier expansion of the ODF and tensorial texture coefficients.

JOURNAL OF ELASTICITY (2022)

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Article Materials Science, Multidisciplinary

Bayesian inference of elastic constants and texture coefficients in additively manufactured cobalt-nickel superalloys using resonant ultrasound spectroscopy

Jeff Rossin et al.

Summary: Bayesian inference with sequential Monte Carlo is used to quantify orientation distribution function coefficients and calculate fully anisotropic elastic constants of additively manufactured specimens based on experimentally measured resonant frequencies. The method also considers residual stress-induced shifts on resonant frequencies, allowing for accurate estimation without stress-relief heat treatment. Through this approach, the accurate determination of all 21 possible independent elastic constants is achieved.

ACTA MATERIALIA (2021)

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Article Engineering, Multidisciplinary