scholarly journals A New Approach to Describing Three-Dimensional Orientation Distribution Functions in Textured Materials–Part I: Formation of Pole Density Distribution on Model Pole Figures

1993 ◽  
Vol 22 (2) ◽  
pp. 73-85 ◽  
Author(s):  
V. N. Dnieprenko ◽  
S. V. Divinskii
Keyword(s):  
Coordinate System ◽  
Texture Component ◽  
Three Dimensional ◽  
Orientation Distribution ◽  
Distribution Functions ◽  
Pole Density ◽  
Texture Axis ◽  
Pole Figures ◽  
Orientation Distribution Functions ◽  
Textured Materials

New method for simulation of orientation distribution functions of textured materials has been proposed. The approach is based on the concept to describe any texture class by a superposition of anisotropic partial fibre components. The texture maximum spread is described in a “local” coordinate system connected with the texture component axis. A set of Eulerian angles γ1,γ2,γ3 are introduced with this aim. To specify crystallite orientations with respect to the sample coordinate system two additional sets of Eulerian angles are introduced besides γ1,γ2,γ3. One of them, (Ψ0,θ0,ϕ0), defines the direction of the texture axis of a component with respect to the directions of the cub. The other set, (Ψ1,θ1,ϕ1), is determined by the orientation of the texture component and its texture axis in the sample coordinate system. Analytical expressions approximating real spreads of crystallites in three-dimensional orientation space have been found and their corresponding model pole figures have been derived. The proposed approach to the texture spread description permits to simulate a broad spectrum of real textures from single crystals to isotropic polycrystals with a high enough degree of correspondence.

scholarly journals A New Approach to Describing Three-Dimensional Orientation Distribution Functions in Textured Materials—Part II: Model ODF for Rolling Textures

1994 ◽  
Vol 22 (3) ◽  
pp. 169-175 ◽  
Author(s):  
V. N. Dnieprenko ◽  
S. V. Divinskii
Keyword(s):  
Three Dimensional ◽  
Rolling Texture ◽  
Orientation Distribution ◽  
Distribution Functions ◽  
Crystallite Orientation ◽  
New Approach ◽  
Texture Axis ◽  
Pole Figures ◽  
Spread Parameters ◽  
Textured Materials

Sections of a three-dimensional Orientation Distribution Function (ODF) for the α-Fe rolling texture typical for most b.c.c. metals have been constructed on the basis of the proposed new method for ODF simulation through the representation of a crystallite orientation by nine rotations, only three of which are varied for a given component. The description of texture by superposition of partial fibre components in used. A comparison of such a model ODF with an ODF reconstructed from experimental pole figures by series expansion is presented. As a result all really encountered textures can be simulated by variation of the crystallite spread parameters, texture axis positions, and predominant preferred orientations in terms of a common approach.

scholarly journals Cyclic Textures in Aluminium Wires

Texture ◽  
1972 ◽  
Vol 1 (1) ◽  
pp. 31-49 ◽  
Author(s):  
U. Schläfer ◽  
H. J. Bunge
Keyword(s):  
Neutron Diffraction ◽  
Three Dimensional ◽  
Orientation Distribution ◽  
Distribution Functions ◽  
Axially Symmetric ◽  
Fibre Texture ◽  
Pole Figures ◽  
Processing Variables ◽  
Orientation Distribution Functions ◽  
The Wire

Three-dimensional orientation distribution functions were calculated from neutron diffraction pole figures of unwound cylinders taken at different distances from the centre of cold drawn Al-wires. Their features change from the axially symmetric type at the very centre of the wire towards a texture near to the rolling type at the surface. Relations between the three-dimensional function and ordinary fibre texture pole figures were used to study the dependence of the textures on certain processing variables for cold drawn as well as recrystallized wires.

The development of the rolling texture in copper measured by neutron diffraction

1971 ◽  
Vol 4 (4) ◽  
pp. 303-310 ◽  
Author(s):  
H. J. Bunge ◽  
J. Tobisch ◽  
W. Sonntag
Keyword(s):  
Neutron Diffraction ◽  
Texture Component ◽  
Deformation Mechanism ◽  
Three Dimensional ◽  
Rolling Texture ◽  
Orientation Distribution ◽  
Distribution Functions ◽  
Anisotropic Hardening ◽  
Pole Figures ◽  
Cold Rolled

Three-dimensional orientation distribution functions of the crystallites in copper sheets, cold rolled to different degrees of reduction, have been determined using neutron diffraction pole figures. The main features of the textures may be represented by the orientation `tube' already described in prior publications. Two ranges of rolling reduction can be distinguished, a lower one (30 to 50%) and a higher one (70 to 95%) the texture changes of which correspond to those calculated after the Taylor theory. In an intermediate range (50 to 70%) a different deformation mechanism occurs which leads to an intermediate (001) [110] texture component. It is supposed that anisotropic hardening may have occurred in this range.

scholarly journals Calculation of the Normalization Factor of Incomplete Pole Figures by Cubic Extrapolation

1986 ◽  
Vol 6 (3) ◽  
pp. 167-179 ◽  
Author(s):  
M. Dahms ◽  
H.-J. Bunge
Keyword(s):  
Spline Interpolation ◽  
Orientation Distribution ◽  
Distribution Functions ◽  
Pole Density ◽  
Normalization Factor ◽  
Texture Coefficients ◽  
Cubic Materials ◽  
Pole Figures ◽  
Experimental Errors ◽  
Normalization Factors

The calculation of orientation distribution functions from incomplete pole figures can be carried out by a least squares approximation of the texture coefficients Clμν and the normalization factors Nhkl to the available experimental data. This procedure is less susceptable to instabilities due to experimental errors if the normalization factors can be calculated independently of the coefficients Clμν. In the case of cubic materials, the relationship F20 = 0 to be fulfilled by pole figure values provides an independent condition for the calculation of the normalization factor. This condition can still be improved by taking the slopes of the pole density curves at α = αmax⁡ and α = 90° into account. An economic way to consider the slope in the pole figures is to use a cubic spline interpolation.

Application of ODF to the Rietveld Profile Refinement of Polycrystalline Solid

1993 ◽  
Vol 37 ◽  
pp. 49-57
Author(s):  
C. S. Choi ◽  
E. F. Baker ◽  
J. Orosz
Keyword(s):  
Three Dimensional ◽  
Inverse Pole Figure ◽  
Orientation Distribution ◽  
Pole Density ◽  
Diffraction Profile ◽  
Refinement Method ◽  
Pole Figures ◽  
Diffraction Patterns ◽  
Characterization Of Materials ◽  
Profile Refinement

The Rietveld profile refinement method is probably the most popular technique used for the crystallographic characterization of materials including crystal structures and phase analysis, but it has been used mostly with ideal powder sample, not with textured polycrystals, because effects of strong and complex textures. Most technological materials are fabricated by using thermo-mechanical forming processes, which inevitably produce strong and complex preferential orientations of the crystallites. Consequently, the diffraction patterns of a given technological material are not unique but vary considerably with the measuring direction, with intensity variations as large as factors of hundreds, depending on the degree of texture. The texture effect on the diffraction pattern of a certain sample direction is directly proportional to the pole density of the corresponding inverse pole figure, which can be obtained from the three-dimensional orientation distribution function (ODF) of the material. The ODFs of materials with high crystal symmetry, such as cubic, hexagonal, tetragonal, and orthorhombic, can be determined quite precisely, using modern texture analysis techniques (for example, Bungel, Wenk, and Kallend et al.). The pole density distributions of the inverse pole figures can be used in the diffraction profile calculation of a highly textured sample.

Texture Evolution in Rolled Mg-13wt%Li-X Alloy

2007 ◽  
Vol 546-549 ◽  
pp. 347-350 ◽  
Author(s):  
Li Li ◽  
Tie Tao Zhou ◽  
Huan Xi Li ◽  
Chang Qi Chen ◽  
Qiu Lin Wu ◽  
...  
Keyword(s):  
Texture Evolution ◽  
Orientation Distribution ◽  
Fiber Texture ◽  
Distribution Functions ◽  
Thickness Reduction ◽  
Rolled Sheet ◽  
Pole Figures ◽  
Cold Rolled ◽  
Orientation Distribution Functions

Texture evolution in Mg-13wt%Li-X alloy cold-rolled from 1.35 mm to 0.34 mm thickness was investigated, by obtaining pole figures and orientation distribution functions (ODFs). Punching tests were conducted to reveal the effect of texture nature on formability. It was found that: (1) the textures of the as-received sheet are characterized by α fiber texture, a γ fiber texture and a cubic texture in both cold-rolled and annealed conditions; (2) with thickness reduction though rolling, the intensity of the γ fiber texture continuously increases and finally the γ fiber texture connects into {111} tube texture, the texture of <11 0> orientation flows towards {223}<11 0> along α fiber, the cubic texture of {001}<100> turns into {035}<100>, while some grains concentrate at {011}<41 1> orientation; (3) good punching behavior of the cold-rolled sheet corresponds to the appearance of a well-developed γ fiber texture.

scholarly journals Pole Figure Inversion Using Finite Elements Over Rodrigues Space

2002 ◽  
Vol 35 (2) ◽  
pp. 113-144 ◽  
Author(s):  
Nathan R. Barton ◽  
Donald E. Boyce ◽  
Paul R. Dawson
Keyword(s):  
Finite Elements ◽  
Pole Figure ◽  
Orientation Distribution ◽  
Distribution Functions ◽  
Pole Figures ◽  
Orientation Distribution Functions ◽  
Pole Figure Data ◽  
Straight Lines ◽  
And Inversion

Using finite elements over Rodrigues space, methods are developed for the formation and inversion of pole figures. The methods take advantage of the properties of Rodrigues space, particularly the fact that geodesics corresponding to pole figure projection paths are straight lines. Both discrete and continuous pole figure data may be inverted to obtain orientation distribution functions (ODFs) in Rodrigues space, and we include sample applications for both types of data.

scholarly journals ODF Calculation by Series Expansion from Incompletely Measured Pole Figures Using the Positivity Condition Part I—Cubic Crystal Symmetry

1987 ◽  
Vol 7 (3) ◽  
pp. 171-185 ◽  
Author(s):  
M. Dahms ◽  
H. J. Bunge
Keyword(s):  
Series Expansion ◽  
Iterative Procedure ◽  
Orientation Distribution ◽  
Distribution Functions ◽  
Crystal Symmetry ◽  
Cubic Crystal ◽  
Positivity Condition ◽  
Pole Figures ◽  
Orientation Distribution Functions

The calculation of orientation distribution functions (ODF) from incomplete pole figures can be carried out by an iterative procedure taking into account the positivity condition for all pole figures. This method strongly reduces instabilities which may occasionally occur in other methods.

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