Material Tensors and Pseudotensors of Weakly-Textured Polycrystals with Orientation Distribution Function Defined on the Orthogonal Group

Du, Wei; Man, Chi‐Sing

doi:10.1007/s10659-016-9610-5

Cited by 9 publications

(16 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Under this assumption crystallite symmetries are described by subgroups of SO (3), which would nominally exclude the common structural metals (e.g., aluminum, copper, iron, titanium) from consideration. On the other hand, as far as the present study is concerned, the classical theory and a more general theory [7] with the ODF defined on the orthogonal group O(3) lead effectively to the same constitutive formulas (2.12) and (2.13).…”

Section: Constitutive Equationmentioning

confidence: 85%

See 1 more Smart Citation

Monitoring near-surface depth profile of residual stress in weakly anisotropic media by Rayleigh-wave dispersion

et al. 2018

Self Cite

View full text Add to dashboard Cite

Herein we study the inverse problem on inferring depth profile of near-surface residual stress in a weakly anisotropic medium by boundary measurement of Rayleigh-wave dispersion if all other relevant material parameters of the elastic medium are known. Our solution of this inverse problem is based on a recently developed algorithm by which each term of a highfrequency asymptotic formula for dispersion relations can be computed for Rayleigh waves that propagate in various directions along the free surface of a vertically-inhomogeneous, prestressed, and weakly anisotropic half-space. As a prime example of possible applications we focus on a thick-plate sample of AA 7075-T651 aluminum alloy, which has one face treated by low plasticity burnishing (LPB) that induced a depth-dependent prestress at and immediately beneath the treated surface. We model the sample as a prestressed, weakly-textured orthorhombic aggregate of cubic crystallites and assume that by nondestructive and/or destructive measurements we have ascertained everything about the sample, including the LPB-induced prestress, before it is put into service. Under the supposition that the prestress be partially relaxed but other material parameters remain unchanged after the sample undergoes a period of service, we examine the possibility of inferring the depth profile of the partially relaxed stress by boundary measurement of Rayleigh-wave dispersion.

show abstract

Section: Constitutive Equationmentioning

confidence: 85%

“…, ·] are concerned, we may use classical texture analysis and treat [7] the aluminum crystallites as if their point group were O, the proper point group in the same Laue class as O h .…”

Section: )mentioning

confidence: 99%

Monitoring near-surface depth profile of residual stress in weakly anisotropic media by Rayleigh-wave dispersion

et al. 2018

Self Cite

View full text Add to dashboard Cite

show abstract

“…For the case of orthorhombic texture, there exist three orthogonal 2-fold axes of symmetry that are parallel to the axes x 1 , x 2 , and x 3 . For this case, W lmn = 0 when m is odd, while W lmn = W lmn = (−1) n W * lmn when m is even where * denotes complex conjugate [51,53].…”

Section: Resultsmentioning

confidence: 99%

Estimates of Nonlinear Elastic Constants and Acoustic Nonlinearity Parameters for Textured Polycrystals

Kube

Turner

2015

J Elast

View full text Add to dashboard Cite

In this article, expressions are derived for the Voigt, Reuss, and Hill estimates of the third-order elastic constants for polycrystals with either cubic or hexagonal crystal symmetry and orthorhombic physical symmetry. General forms of the fourth-and sixthrank elastic stiffness and compliance tensors for crystal and physical symmetries are given. Explicit expressions are reduced from these tensors for the case of polycrystals exhibiting orthorhombic sample symmetry with either cubic or hexagonal crystallites. The estimated third-order elastic constants of the textured polycrystal are obtained in terms of second-and third-order single-crystal elastic constants and orientation distribution coefficients (ODCs), which are used to account for anisotropic physical symmetry. The acoustic nonlinearity parameter,β, is defined through combinations of the second-and third-order Voigt, Reuss, and Hill estimates of the elastic constants for a textured polycrystal. The model predicts thatβ is dependent on the type of averaging scheme used and the texture-defining ODCs. The model is quantitatively evaluated for polycrystalline iron, aluminum, and titanium using second-and third-order single-crystal elastic constants and experimentally measured ODCs. The interrelation betweenβ and polycrystalline anisotropy offers potential for techniques associated with quantitative texture analysis.

show abstract

“…For more detailed discussions on the preliminaries presented in §2a, see [6, Chap. 17], [16] and the references therein; for those in §2b, see [4].…”

Section: Preliminariesmentioning

confidence: 99%

“…A more natural approach is to let the ODF be defined on the orthogonal group O(3) [4,5]. Then Gnormalcr is allowed to be the proper or improper crystallographic point group that characterizes the crystal class of the crystallites in question.…”

Section: Introductionmentioning

confidence: 99%

Tensorial Fourier expansion of orientation distribution function defined on the orthogonal group O(3)

Du,

Man

2023

Phil. Trans. R. Soc. A.

View full text Add to dashboard Cite

Recently, Man and Du, in the context of classical texture analysis where the orientation distribution function (ODF) is defined on the rotation group SO(3), presented a systematic procedure by which the classical expansion of an ODF truncated at the order l = L can be directly rewritten as a tensorial Fourier expansion truncated at the same order. In classical texture analysis, the groups of crystallite and texture symmetries are assumed to be subgroups of SO(3), which is unreasonable, say, for aggregates of crystallites in a crystal class defined by an improper point group. In this paper, we consider ODFs defined on the orthogonal group O(3) and extend the aforementioned procedure to write down tensorial Fourier expansions for polycrystals with crystallite symmetry defined by any of the 21 improper point groups. Examples that illustrate the general procedure are given. This article is part of the theme issue ‘Foundational issues, analysis and geometry in continuum mechanics’.

show abstract

Material Tensors and Pseudotensors of Weakly-Textured Polycrystals with Orientation Distribution Function Defined on the Orthogonal Group

Cited by 9 publications

References 22 publications

Monitoring near-surface depth profile of residual stress in weakly anisotropic media by Rayleigh-wave dispersion

Monitoring near-surface depth profile of residual stress in weakly anisotropic media by Rayleigh-wave dispersion

Estimates of Nonlinear Elastic Constants and Acoustic Nonlinearity Parameters for Textured Polycrystals

Tensorial Fourier expansion of orientation distribution function defined on the orthogonal group O(3)

Contact Info

Product

Resources

About