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.

scholarly journals An Investigation Into the Accuracy of the Vector Method by Comparison With ECP Measurements

1989 ◽  
Vol 10 (2) ◽  
pp. 117-134 ◽  
Author(s):  
R. Shimizu ◽  
J. Harase ◽  
K. Ohta
Keyword(s):  
Pole Figure ◽  
Direct Measurement ◽  
Orientation Distribution ◽  
Vector Method ◽  
Inversion Result ◽  
X Ray ◽  
Pole Figures ◽  
The Mean ◽  
Actual Orientation ◽  
Good Agreement

In an attempt to investigate the accuracy of the vector method for crystal texture analysis, a comparison has been made between the inversion result of the pole figure made by X-ray studies using the VM and the inversion result of the pole figure made by ECP. A comparison has been made between the inversion by the pole figure generated by direct measurement of orientations by ECP and the actual orientation distribution (measured by ECP) displayed in the same mode. The materials studied were recrystallized Fe–3% Si and Fe–50% Ni. The main findings were:• In the mean intensities of each individual Box, the inversion results of pole figures made from orientations determined by ECP were in good agreement with the inversion from (100) pole figures made by X-ray or actual orientation distribution (made by ECP) displayed in the same mode as the vector method.• For Fe–3% Si, quite a good agreement was obtained between the results inverted from X-ray pole figure and the direct measurement by ECP for the intensity distribution of minor texture component along ζ angle. It was concluded from these investigations that the inversion of the pole figure by the vector method is accurate enough for most practical purposes.

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 An Evaluation of the Single Orientation Method for Texture Determination in Materials of Moderate Texture Strength

1990 ◽  
Vol 12 (1-3) ◽  
pp. 65-76 ◽  
Author(s):  
Stuart I. Wright ◽  
Brent L. Adams
Keyword(s):  
Pole Figure ◽  
Series Expansion ◽  
Orientation Distribution ◽  
Distribution Functions ◽  
Correlation Data ◽  
Pole Figures ◽  
Rolled Aluminum ◽  
Orientation Method ◽  
Pole Figure Data ◽  
Single Orientation

New microscopy technology has made it feasible to consider using single orientation measurements to obtain Orientation Distribution Functions (ODF). Single orientations are preferred over pole figure data in ODF calculations because the odd terms of the series expansion are not directly accessible when pole figures are used. However, the number of single orientation measurements required to calculate a statistically reliable ODF has generally been considered too large to practically obtain. This study found that the location of the major features of the ODF in rolled aluminum sheet were identifiable after only 100 measurements. However, the heights of the peaks and the secondary features required many more measurements to stabilize. Unless the orientation measurements can be automated or orientation correlation data is needed the pole figure method remains a more efficient means of obtaining the data necessary to measure texture.

Improvements in the Quantitative Evaluation of Three-Dimensional Texture. II. The Pole-Figure-Multiplying Method

1995 ◽  
Vol 28 (5) ◽  
pp. 532-533 ◽  
Author(s):  
L.-G. Yu ◽  
H. Guo ◽  
B. C. Hendrix ◽  
K.-W. Xu ◽  
J.-W. He
Keyword(s):  
Distribution Function ◽  
Texture Analysis ◽  
Pole Figure ◽  
Quantitative Evaluation ◽  
Orientation Distribution Function ◽  
Three Dimensional ◽  
Orientation Distribution ◽  
Simple Method ◽  
Pole Figures

A new simple method is proposed for determining the orientation distribution function (ODF) for three-dimensional texture analysis in a polycrystal based on the reality that the accuracy of an ODF is dependent on both the accuracy of each measured pole figure and the number of pole figures.

Improvements in the Quantitative Evaluation of Three-Dimensional Texture. I. The Nature of the Information Obtained from Pole Figures

1995 ◽  
Vol 28 (5) ◽  
pp. 527-531 ◽  
Author(s):  
L.-G. Yu ◽  
H. Guo ◽  
B. C. Hendrix ◽  
K.-W. Xu ◽  
J.-W. He
Keyword(s):  
Distribution Function ◽  
Pole Figure ◽  
Orientation Distribution Function ◽  
Angular Resolution ◽  
Three Dimensional ◽  
Orientation Distribution ◽  
High Angular Resolution ◽  
Area Theorem ◽  
Pole Figures ◽  
Experimental Resolution

The sources of indefiniteness in the orientation-distribution-function (ODF) description of crystalline texture are shown to result from the integral nature of the pole-figure measurement. An equipartition-area theorem is proved and it is shown that current methods use too few pole figures, which are measured to an unnecessarily high angular resolution. The experimental resolution is considered and the number of pole figures needed for ODF analysis is calculated as a function of the required ODF resolution.

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.

Optimization of X-Ray Pole Figure Measurement

2004 ◽  
Vol 443-444 ◽  
pp. 137-140 ◽  
Author(s):  
Leszek Tarkowski ◽  
L. Laskosz ◽  
Jan T. Bonarski
Keyword(s):  
Pole Figure ◽  
Orientation Distribution ◽  
Measurement Procedure ◽  
Registration Method ◽  
Pole Figures ◽  
Applied Optimization ◽  
Measurement Results ◽  
Traditional Mode ◽  
Reference Sphere ◽  
Comparison Of The Results

The traditionally applied registration method of the back-reflection pole figure is based on the equiangular measurement lattice. It determines also the equiangular character of presentation of measurement results in form of stereographic projection, termed as the pole figure. The mentioned registration mode is characterized by an unequal density of the measurement points on the pole figure. It is the evident disadvantage of the traditional registration mode. In order to eliminate the drawback, and to increase the efficiency of the measurement procedure, an optimization of the registration method was made. The optimization consists in dividing a reference sphere of the stereographical projection into uniform regions, so called equal solid angles (ESA). As a result of the applied optimization, over 40% reduction in number of the measurement points and in the registration time at preserved pole figure quality was obtained. For verification of the new solution, a set of experimental pole figures of cold rolled copper by the traditional mode as well as the introduced ESA one was recorded. Comparison of the results of texture analysis based on the orientation distribution function was carried out. The results of measurements performed by the ESA method confirm the efficiency of the introduced optimization.

scholarly journals Non-Random Orientation Distribution Functions With Random Pole Figures

1979 ◽  
Vol 3 (3) ◽  
pp. 169-190 ◽  
Author(s):  
H. J. Bunge ◽  
C. Esling
Keyword(s):  
Distribution Function ◽  
Pole Figure ◽  
Orientation Distribution Function ◽  
Orientation Distribution ◽  
Distribution Functions ◽  
Random Orientation ◽  
Numerical Examples ◽  
Pole Figures ◽  
Orientation Distribution Functions

It is shown, theoretically and with numerical examples, that the orientation distribution function may vary between zero and two or even more times random while a corresponding pole figure is completely random.

scholarly journals Determination of the Complete Orientation Distribution Function by the Zero-Range Method

1986 ◽  
Vol 6 (4) ◽  
pp. 289-313 ◽  
Author(s):  
H. P. Lee ◽  
H. J. Bunge ◽  
C. Esling
Keyword(s):  
Distribution Function ◽  
Pole Figure ◽  
Orientation Distribution Function ◽  
Statistical Error ◽  
Orientation Distribution ◽  
Positivity Condition ◽  
Additional Information ◽  
Pole Figures ◽  
Zero Range

Because of the superposition of pole figures corresponding to symmetrically equivalent crystal directions, only the reduced orientation distribution function f∼(g) can be obtained directly by pole figure inversion. The additional information contained in the positivity condition of the ODF allows, however, the determination of an approximation to the “indeterminable” part and hence of the complete ODF f(g), if the texture has sufficiently large zero-ranges. The application of the method and the accuracy of the results was tested using two theoretical and one experimental textures. The accuracy of the complete ODF depends on the size of the zero-range, the errors in its determination, and on the errors, experimental and truncational, of the reduced ODF. The “physical zero” used in order to determine the zero-range is defined according to the statistical error of the pole figure measurement.

scholarly journals Energy Dispersive Diffractometry for Quantitative Texture Studies

1990 ◽  
Vol 12 (4) ◽  
pp. 243-247 ◽  
Author(s):  
J. A. Szpunar
Keyword(s):  
Distribution Function ◽  
Neutron Diffraction ◽  
Pole Figure ◽  
Orientation Distribution ◽  
Energy Dispersive ◽  
Rolled Steel ◽  
Pole Figures ◽  
Cold Rolled ◽  
Expansion Coefficients

Energy dispersive diffractometry is becoming a useful tool for texture measurements. In this work we demonstrated that the intensity measured at points in four inverse pole figures for cold-rolled steel can be used to calculate the orientation distribution function (ODF) with an accuracy sufficient for the determination of about 12 series expansion coefficients. A pole figure generated from such a selective experiment agrees with the pole figure measured by neutron diffraction.

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