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 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.

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 Development of Rolling Textures in an Austenitic Stainless Steel

1992 ◽  
Vol 19 (1-2) ◽  
pp. 101-121 ◽  
Author(s):  
C. D. Singh ◽  
V. Ramaswamy ◽  
C. Suryanarayana
Keyword(s):  
Stainless Steel ◽  
Austenitic Stainless Steel ◽  
Shear Bands ◽  
Three Dimensional ◽  
Rolling Texture ◽  
Orientation Distribution ◽  
Distribution Functions ◽  
Texture Development ◽  
Slip Planes ◽  
Heterogeneous Deformation

Three dimensional texture analysis by means of orientation distribution functions (ODF) was used to examine the texture development during rolling at 473 K in an austenitic stainless steel. With the help of ODFs results, the different stages of texture development could be assigned to the existing theories of heterogeneous deformation mechanisms of low SFE face-centred cubic metals. The texture at very low degree of rolling consists of two limited orientation tubes with their fibre axes 〈110〉//ND and 〈110〉60∘ND and agrees with the predictions made by Taylor model. With further deformation, twinning causes the reduction of ≈{112}〈111〉 component and leads to the formation of twin {552}〈115〉. Abnormal slip on slip planes parallel to the twin boundaries rotates the twins into the {332}〈113〉 and {111}〈110〉 positions. The shear bands formation in the rotated twin-matrix lamellae changes their orientations near to {011}〈100〉 and {011}〈112〉 positions. Finally, normal slip again continues and sharpens the brass-type rolling texture.

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.

scholarly journals Texture and Lamellae Distribution Functions in Lamellar Eutectics

1986 ◽  
Vol 6 (4) ◽  
pp. 265-287 ◽  
Author(s):  
H. J. Bunge
Keyword(s):  
Three Dimensional ◽  
Orientation Distribution ◽  
Distribution Functions ◽  
X Rays ◽  
Two Dimensional ◽  
Absorption Factor ◽  
X Ray Diffraction ◽  
Diffraction Vector ◽  
X Ray ◽  
Pole Figures

The crystallographic orientation distribution and the geometrical lamellae orientation distribution in lamellar eutectics are, in general, not independent of each other. The combined orientation-lamellae distribution function depends on five angular parameters. X-ray diffraction in such eutectics may exhibit an anisotropic macroscopic absorption factor if the penetration depth of the X-rays is large compared with their planar size. As a consequence, the reflected X-ray intensity may depend on a third angle γ, i.e. a rotation of the sample about the diffraction vector s additionally to the usual pole figure angles α, β which describe the orientation of the diffraction vector s with respect to the sample coordinate system. It is thus necessary to measure three-dimensional generalized pole figures instead of conventional two-dimensional ones.

scholarly journals The Development of Rolling Texture in α-Brass Determined by Neutron Diffraction

Texture ◽  
1974 ◽  
Vol 1 (4) ◽  
pp. 211-231 ◽  
Author(s):  
J. Tobisch ◽  
A. Mücklichf
Keyword(s):  
Neutron Diffraction ◽  
Three Dimensional ◽  
Rolling Texture ◽  
Orientation Distribution ◽  
Zinc Alloy ◽  
Tube Axis ◽  
Pole Figures ◽  
Cold Rolled

The three-dimensional orientation distribution was calculated from neutron diffraction pole figures for a copper 27.2% zinc alloy cold rolled to different degrees of deformation. The results agree qualitatively with those of other authors. There are however differences in the quantitative respect which influence the conclusions to be drawn. For rolling degrees lower than about 70% the texture exhibits an orientation tube similar to that of the copper type, but with a significantly different distribution along the tube axis. For rolling degrees larger than 70% the texture can be described by the orientation {110}〈112〉. The deformation is assumed to occur according to the Wassermann model and the Hu model respectively in these two ranges.

scholarly journals The Development of the Rolling Texture of Iron Determined by Neutron-Diffraction

Texture ◽  
1974 ◽  
Vol 1 (3) ◽  
pp. 157-171 ◽  
Author(s):  
D. Schläfer ◽  
H. J. Bunge
Keyword(s):  
Carbon Steel ◽  
Neutron Diffraction ◽  
Three Dimensional ◽  
Low Carbon Steel ◽  
Rolling Texture ◽  
Orientation Distribution ◽  
Distribution Functions ◽  
Fibre Axis ◽  
Low Carbon ◽  
Angle Of Rotation

The development of the rolling texture of a low carbon steel was investigated by neutron diffraction calculating three-dimensional orientation distribution functions. The textures consist of two limited fibre axis components A and B centered about (1¯1¯1)[1¯21]+5∘ and (001)[1¯10] respectively with an angle of rotation of about 70∘. For rolling degrees larger than 50% the intensity of the fibre axis component A is being modulated so as to favour the orientation (1¯1¯2)[1¯10]. The texture may be considered as inverse to the low concentration brass texture in the sense of interchanging rolling and normal directions. It may be understood in terms of {110}〈111〉—glide and {112}〈111〉—twinning.

scholarly journals Approximation of the Orientation Distribution of Grains in Polycrystalline Samples by Means of Gaussians

1992 ◽  
Vol 19 (1-2) ◽  
pp. 9-27 ◽  
Author(s):  
D. I. Nikolayev ◽  
T. I. Savyolova ◽  
K. Feldmann
Keyword(s):  
Rolling Texture ◽  
Expansion Method ◽  
Operating Mode ◽  
Orientation Distribution ◽  
New Method ◽  
Gaussian Distributions ◽  
Positivity Condition ◽  
The Central Limit Theorem ◽  
Pole Figures ◽  
Series Expansion Method

The orientation distribution function (ODF) obtained by classical spherical harmonics analysis may be falsified by ghost influences as well as series truncation effects. The ghosts are a consequence of the inversion symmetry of experimental pole figures which leads to the loss of information on the “odd” part of ODF.In the present paper a new method for ODF reproduction is proposed. It is based on the superposition of Gaussian distributions satisfying the central limit theorem in the SO(3)-space as well as the ODF positivity condition. The kind of ODF determination offered here is restricted to the fit of Gaussian parameters and weights with respect to the experimental pole figures. The operating mode of the new method is demonstrated for a rolling texture of copper. The results are compared with the corresponding ones obtained by the series expansion method.

A software for diffraction stress factor calculations for textured materials

2012 ◽  
Vol 27 (2) ◽  
pp. 114-116 ◽  
Author(s):  
Thomas Gnäupel-Herold
Keyword(s):  
Distribution Function ◽  
Pole Figure ◽  
Elastic Constants ◽  
Orientation Distribution Function ◽  
Lattice Strain ◽  
Orientation Distribution ◽  
Crystallite Orientation ◽  
Interaction Models ◽  
Grain Interaction ◽  
Textured Materials

A software for the calculation of diffraction elastic constants (DEC) for materials both with and without preferred orientation was developed. All grain-interaction models that can use the crystallite orientation distribution function (ODF) are incorporated, including Kröner, Hill, inverse Kröner, and Reuss. The functions of the software include: reading the ODF in common textual formats, pole figure calculation, calculation of DEC for different (hkl,φ,ψ), calculation of anisotropic bulk constants from the ODF, calculation of macro-stress from lattice strain and vice versa, as well as mixture ratios of (hkl) of overlapped reflections in textured materials.

Textures Applied to Mechanical Processing Technology Assessment in Ancient Bronze

2005 ◽  
Vol 495-497 ◽  
pp. 719-724
Author(s):  
R.E. Bolmaro ◽  
B. Molinas ◽  
E. Sentimenti ◽  
A.L. Fourty
Keyword(s):  
Orientation Distribution ◽  
Distribution Functions ◽  
Archaeological Sites ◽  
Mechanical Processing ◽  
Post Processing ◽  
X Ray Diffraction ◽  
Mechanical Process ◽  
X Ray ◽  
Pole Figures ◽  
Microscopic Inspection

Some ancient metallic art craft, utensils, silverware and weapons are externally undistinguishable from modern ones. Not only the general aspect and shape but also some uses have not changed through the ages. Moreover, when just some small pieces can be recovered from archaeological sites, the samples can not easily be ascribed to any known use and consequently identified. It is clear that mechanical processing has changed along history but frequently only a "microscopic" inspection can distinguish among different techniques. Some bronze samples have been collected from the Quarto d’Altino (Veneto) archaeological area in Italy (paleovenetian culture) and some model samples have been prepared by a modern artisan. The sample textures have been measured by X-ray Diffraction techniques. (111), (200) and (220) pole figures were used to calculate Orientation Distribution Functions and further recalculate pole figures and inverse pole figures. The results were compared with modern forging technology results. Textures are able to discern between hammering ancient techniques for sheet production and modern industrial rolling procedures. However, as it is demonstrated in the present work, forgery becomes difficult to detect if the goldsmith, properly warned, proceeds to erase the texture history with some hammering post-processing. The results of this contribution can offer to the archaeologists the opportunity to take into consideration the texture techniques in order to discuss the origin (culture) of the pieces and the characteristic mechanical process developed by the ancient artisan. Texture can also help the experts when discussing the originality of a certain piece keeping however in mind the cautions indicated in this publication.

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