Description of orientation coherence in polycrystalline materials

Adams, Brent L.; Morris, Peter R.; Wang, T.T.; Willden, K.S.; Wright, Stuart I.

doi:10.1016/0001-6160(87)90293-8

Cited by 80 publications

(43 citation statements)

References 25 publications

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“…(Note: the relations in (61) are not used in this paper because s 1 , s 2 , and s 3 are directly taken as unspecified material constants) and The shape coefficients s 2 00 , s 2 20 , s 4 00 , s 4 20 , and s 4 40 in (62)-(65) are all real numbers for an orthorhombic aggregate of crystallites due to (27).…”

Section: Constitutive Relation Taking Account Of the Crystalline Meanmentioning

confidence: 99%

Constitutive relation of an orthorhombic polycrystal with the shape coefficients

2005

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An orthorhombic polycrystal is an orthorhombic aggregate of tiny crystallites. In this paper, we study the effect of the crystalline mean shape on the constitutive relation of the orthorhombic polycrystal. The crystalline mean shape and the crystalline orientation arrangement are described by the crystalline shape function (CSF) and the orientation distribution function (ODF), respectively. The CSF and the ODF are expanded as an infinite series in terms of the Wigner D-functions. The expanded coefficients of the CSF and the ODF are called the shape coefficients s l m0 and the texture coefficients c l mn , respectively. Assuming that C eff in the constitutive relation depends on the shape coefficients s l m0 and the texture coefficients c l mn , by the principle of material frame-indifference we derive an analytical expression for C eff up to terms linear in s l m0 and c l mn , and the expression would be applicable to the polycrystal whose texture is weak and whose crystalline mean shape has weak anisotropy. C eff contains six unspecified material constants (λ, µ, c, s 1 , s 2 , s 3 ), five shape coefficients (s 2 00 , s 2 20 , s 4 00 , s 4 20 , s 4 40 ), and three texture coefficients (c 4 00 , c 4 20 , c 4 40 ). The results based on the perturbation approach are used to determine the five material constants approximately. We also find that the shape coefficients s 2 m0 and s 4 m0 are all zero if the crystalline mean shape is a cuboid. Some examples are given to compare our computational results.

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Section: Constitutive Relation Taking Account Of the Crystalline Meanmentioning

confidence: 99%

Constitutive relation of an orthorhombic polycrystal with the shape coefficients

2005

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“…Fortunately, a framework of hierarchical spatial statistics of the microstructure is available in the literature in the form of n-point correlation functions [20][21][22][23][24][25]. Local state distributions, f (h), are often termed one-point statistics, as they reflect the probability density of finding a specific local state at a randomly selected point in the microstructure.…”

Section: Statistics Of the Microstructurementioning

confidence: 99%

Novel microstructure quantification framework for databasing, visualization, and analysis of microstructure data

Niezgoda

Kanjarla

Kalidindi

2013

Integr Mater Manuf Innov

115

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The study of microstructure and its relation to properties and performance is the defining concept in the field of materials science and engineering. Despite the paramount importance of microstructure to the field, a rigorous systematic framework for the quantitative comparison of microstructures from different material classes has yet to be adopted. In this paper, the authors develop and present a novel microstructure quantification framework that facilitates the visualization of complex microstructure relationships, both within a material class and across multiple material classes. This framework, based on the stochastic process representation of microstructure, serves as a natural environment for developing relational statistical analyses, for establishing quantitative microstructure descriptors. In addition, it will be shown that this new framework can be used to link microstructure visualizations with properties to develop reduced-order microstructure-property linkages and performance models.

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“…4,5) Suppose that two material points that are identified by vectorsã a 1 (¼ ðx 1 ; y 1 Þ) andã a 2 (¼ ðx 2 ; y 2 Þ) and connected by a vectorr r (¼ã a 2 {ã a 1 ) have crystallographic orientations of g 1 and g 2 , respectively, as shown in Fig. 1.…”

Section: Two-point Orientation Auto-correlation Function (Tp-oacf)mentioning

confidence: 99%

“…Then a TP-OCF was defined to be a two-point joint density function quantifying ''the probability of finding a pair of grains (or material points) having specified crystallographic orientations at the tail and the head of a vectorr r''. For a given orientation pair ðg 1 ; g 2 Þ, the probability of finding an orientation pair ðg 1 ; g 2 Þ connected byr r, in which g 1 2 Å 1 and g 2 2 Å 2 , can be expressed by 2,4,5) …”

Section: Two-point Orientation Auto-correlation Function (Tp-oacf)mentioning

confidence: 99%

Application of Two-Point Orientation Auto-Correlation Fucntion (TP-OACF)

Choi¹,

Rollett

Piehler

2006

Mater. Trans.

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A two-point orientation auto-correlation function (TP-OACF) was developed in order to quantify the spatial distribution of targeted texture components. An example of a TP-OACF was demonstrated using an idealized orientation map. Characteristics of the spatial distribution of major texture components in 6022-T4 Al sheets deformed in plane-strain tension were also quantified using a TP-OACF. The results showed that f110gh1 " 1 12i and f123gh63 " 4 4i orientations (in fNDghPDi notation, where PD is the pulling direction) tend to form localized diagonal and horizontal bands through the thickness, respectively, after the plane-strain deformation. The cube orientation on the surface initially showed a relatively strong texture band along the RD, but this banding behavior was less significant after the plane-strain deformation.

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Description of orientation coherence in polycrystalline materials

Cited by 80 publications

References 25 publications

Constitutive relation of an orthorhombic polycrystal with the shape coefficients

Constitutive relation of an orthorhombic polycrystal with the shape coefficients

Novel microstructure quantification framework for databasing, visualization, and analysis of microstructure data

Application of Two-Point Orientation Auto-Correlation Fucntion (TP-OACF)

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