scholarly journals A New Composite-Sample Method for Orientation-Distribution Analysis

1992 ◽  
Vol 19 (1-2) ◽  
pp. 1-8 ◽  
Author(s):  
P. R. Morris ◽  
R. E. Hook ◽  
G. W. Whelan
Keyword(s):  
Sheet Steel ◽  
Rolling Direction ◽  
Orientation Distribution ◽  
Composite Sample ◽  
Distribution Analysis ◽  
Crystallite Orientation ◽  
Pole Figures ◽  
Permit Application ◽  
Sample Method ◽  
Adjacent Sheet

A new composite-sample method is suggested for crystallite orientation distribution analysis. The proposed method entails preparation of composites such that the surface to be examined is perpendicular to the rolling direction. The suggested reference frame is (—ND, TD, RD) for Roe's method. This choice simplifies expression of the results with respect to the conventional (RD, TD, ND) frame. A novel technique employing laser welding on three surfaces is used to bond adjacent sheet layers. The proposed composite-sample can be more easily and accurately constructed. It requires only about 12 percent of the material needed for Lopata and Kula's method. Existing programs for incomplete pole-figures have been modified to permit application of the new method. The method is expected to be statistically advantageous where materials develop “pancake”- or acicular-shaped grains. The method is illustrated for a deep-drawing aluminum-killed sheet steel, and results are compared with those obtained with a conventional sheet-sample.

scholarly journals The Development of Rolling Textures in Low-Carbon Steels

Texture ◽  
1972 ◽  
Vol 1 (2) ◽  
pp. 129-140 ◽  
Author(s):  
H. Inagaki ◽  
T. Suda
Keyword(s):  
Rolling Direction ◽  
Orientation Distribution ◽  
Fiber Texture ◽  
Carbon Steels ◽  
Normal Direction ◽  
Distribution Analysis ◽  
Low Carbon ◽  
Crystallite Orientation ◽  
Low Carbon Steels ◽  
Polycrystalline Iron

The crystallite orientation distribution analysis was applied to the study of the development of the rolling textures in low-carbon steels. It was found that the constraining effect of the grain boundary remarkably influences the rolling textures of polycrystalline iron. This enhances the crystal rotations, which would not be expected to occur in single crystals; and grains having the {110}〈112〉 orientations are forced to rotate about the 〈111〉axes lying in the sheet normal direction toward the {110}〈110〉 orientations. This is the origin of the 〈111〉 fiber texture normally found in the rolling textures of low-carbon steels. The presence of the partial fiber texture having the 〈111〉 axes inclined 30 deg from the sheet normal toward the rolling direction could not be confirmed.

scholarly journals A Test of the Refinement Procedure for Determining the Crystallite Orientation Distribution: Polyethylene Terephthalate

Texture ◽  
1972 ◽  
Vol 1 (1) ◽  
pp. 9-16 ◽  
Author(s):  
W. R. Krigbaum ◽  
Anna Marie Harkins Vasek
Keyword(s):  
Distribution Function ◽  
Polyethylene Terephthalate ◽  
Orientation Distribution Function ◽  
Orientation Distribution ◽  
Fiber Texture ◽  
Fiber Axis ◽  
Crystallite Orientation ◽  
Plane Normal ◽  
Pole Figures ◽  
Refinement Procedure

A test of the refinement procedure for improving the crystallite orientation distribution function is presented for a fiber texture sample of polyethylene terephthalate. This is a particularly difficult example because the triclinic unit cell offers no simplification due to symmetry, and the pole figures are sharply peaked. The analysis employed 17 observed pole figures and an additional 29 unobserved pole figures reconstructed from the crystallite orientation distribution function. After three cycles of refinement, in which the maximum value of the coefficient was increased from 6 to 16, the standard deviations, σq and σw, of the plane-normal and crystallite orientation distributions were reduced by about a factor of 3. The refined crystallite orientation distribution function indicates that the c-axis tends to align along the fiber axis for this polyethylene terephthalate sample.

scholarly journals Comparison of Incomplete Pole-Figure Methods for Surfaces Perpendicular to Rolling, Transverse and Normal Directions

1992 ◽  
Vol 19 (1-2) ◽  
pp. 75-80 ◽  
Author(s):  
P. R. Morris ◽  
R. E. Hook
Keyword(s):  
Pole Figure ◽  
Reference Frame ◽  
Reference Frames ◽  
Spherical Surface ◽  
Sheet Steel ◽  
Case Series ◽  
Orientation Distribution ◽  
Steel Sample ◽  
Pole Figures ◽  
Surface Harmonic

Coefficients for a generalized-spherical-harmonic expansion of the crystallite orientation distribution function (ODF) through L=16 were obtained by an incomplete pole-figure method from a deep-drawing aluminum-killed sheet steel sample with surface perpendicular to the sheet-normal direction (ND). These coefficients were subsequently transformed from the RD, TD, ND reference frame to –ND, TD, RD and ND, RD, TD reference frames. Spherical-surface-harmonic expansions of incomplete {110}, {100}, and {112} pole-figures were calculated for each reference frame and used as input data to calculate ODF coefficients for each frame. The thus-calculated coefficients were transformed to the RD, TD, ND frame in each case. Series expansions of pole-figures and ODF for each frame are compared with the initial data.

Texturescope: An automatic TEM technique for the imaging of preferred orientations

1991 ◽  
Vol 49 ◽  
pp. 792-793
Author(s):  
H. Weiland
Keyword(s):  
Electron Microscope ◽  
Large Range ◽  
Structural Parameters ◽  
Rolling Direction ◽  
Orientation Distribution ◽  
X Rays ◽  
Area Of Interest ◽  
Pole Figures ◽  
Sheet Products ◽  
Individual Grains

The distribution of crystallographic orientations, the texture, is one of the basic structural parameters. Knowledge of the texture on a very local scale is necessary to study aspects of processes such as recrystallization and deformation. With an electron microscope, the texture can be determined1 either by measuring the orientations of individual grains or by measuring local pole figures and obtaining in this way the orientation distribution of hundreds of grains. The latter method, however, does not preserve the spatial distribution of the orientations.The measurement of pole figures in the TEM is based on the same principles used for conventional pole figure determination by X-rays in transmission. The electron microscope has the additional capability that the area of interest can be imaged. For the measurement of local pole figures, the intensity distribution along a selected hkl-diffraction ring is measured, while the specimen is tilted around a specified axis over a large range (e.g. sheet products are usually tilted around the rolling direction). The measured diffracted intensities must be corrected for absorption of the primary and diffracted beams as well as for the change in diffracting volume. Using selected area diffraction, pole figures of specimen areas between 300 μm and 1 μm in diameter can be analyzed quantitatively.

Crystallite Orientation Analysis from Incomplete Pole Figures

1974 ◽  
Vol 18 ◽  
pp. 514-534 ◽  
Author(s):  
Peter R. Morris
Keyword(s):  
Orientation Distribution ◽  
Manganese Steel ◽  
Legendre Functions ◽  
Crystallite Orientation ◽  
Associated Legendre Functions ◽  
Sheet Surface ◽  
Pole Figures ◽  
Orthogonality Relations ◽  
Crystallographic Symmetry ◽  
Physical Symmetry

AbstractThe use of incomplete pole figures results in the loss of orthogonality relations among the associated Legendre functions, and necessitates explicitly evaluating integrals of products of these functions. The required indefinite integrals of associated Legendre functions and their products have been evaluated for cubic crystallographic symmetry and orthotropic physical symmetry through sixteenth order.The solution has been particularized for {200}, {222}, and {110} back-reflection pole figures, where data are confined to the region not exceeding 60 degrees from the sheet normal direction.Data obtained from a sample of low—manganese steel sheet are used to illustrate the method, and results are compared to those obtained using complete pole figures obtained with a composite sample of the same material.The method described makes it possible to study crystallite orientation distribution as a function of distance from the sheet surface, by a series of pole figure measurements on the surface after successive material removals by polishing and etching.

scholarly journals Texture analysis with a time-of-flight neutron strain scanner

2014 ◽  
Vol 47 (4) ◽  
pp. 1337-1354 ◽  
Author(s):  
Florencia Malamud ◽  
Javier R. Santisteban ◽  
Miguel Angel Vicente Alvarez ◽  
Raúl Bolmaro ◽  
Joe Kelleher ◽  
...  
Keyword(s):  
Nuclear Power ◽  
Rolling Direction ◽  
Time Of Flight ◽  
Orientation Distribution ◽  
Al Alloy ◽  
X Ray ◽  
Pole Figures ◽  
Transmission Measurements ◽  
The Uk ◽  
Zr Alloys

A time-of-flight (TOF) neutron strain scanner is a white-beam instrument optimized to measure diffractograms at precise locations within bulky specimens, typically along two perpendicular sample orientations. Here, a method is proposed that exploits the spatial resolution (∼1 mm) provided by such an instrument to determine in a nondestructive manner the crystallographic texture at selected locations within a macroscopic object. The method is based on defining the orientation distribution function (ODF) of the crystallites from several incomplete pole figures, and it has been implemented on ENGIN-X, a neutron strain scanner at the ISIS facility in the UK. This method has been applied to determine the texture at different locations of Al alloy plates welded along the rolling direction and to study a Zr2.5%Nb pressure tube produced for a CANDU nuclear power plant. For benchmarking, the results obtained with this instrument for samples of ferritic steel, copper, Al alloys and Zr alloys have been compared with measurements performed using conventional X-ray diffractometers and more established neutron techniques. For cases where pole figure coverage is incomplete, the use of TOF neutron transmission measurements simultaneously performed on the specimens is proposed as a simple and powerful test to validate the resulting ODF.

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.

MISORIENTATION DISTRIBUTION FUNCTION FOR CUBIC CRYSTALS

2019 ◽  
Vol 85 (5) ◽  
pp. 28-32
Author(s):  
A. S. Kolyanova ◽  
Y. N. Yaltsev
Keyword(s):  
Distribution Function ◽  
Grain Boundaries ◽  
Orientation Distribution ◽  
Recrystallization Annealing ◽  
Misorientation Distribution ◽  
Cubic Crystals ◽  
Special Boundaries ◽  
Pole Figures ◽  
Two Samples ◽  
Euler Space

A calculation method for obtaining the misorientation distribution function (MDF) for cubic crystals which can be used to estimate the presence or absence of special boundaries in the materials is presented. The calculation was carried out for two samples of Al-Mg-Si alloy subjected to various mechanical and thermal treatments: the first sample is subjected to rolling; the second sample is subjected to recrystallization annealing. MDF is calculated for each sample; the results are presented in the Euler space and in the angle-axis space. The novelty of the method consists in the possibility of gaining data on the grain boundaries from X-ray texture analysis without using electron microscopy. A calculation involving only mathematical operations on matrices was performed on the basis of the orientation distribution function restored from incomplete pole figures. It is shown that no special boundaries are observed in the deformed sample, whereas in the recrystallized alloy, special boundaries are detected at Ʃ = 23, 13, and 17. The shortcoming of the proposed method can be attributed to the lack of accurate data on grain boundaries, since all possible orientation in the polycrystal should be taken into account in MDF calculation.

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