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.

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.

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.

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.

scholarly journals Application of Anisotropic Texture Components

1997 ◽  
Vol 28 (3-4) ◽  
pp. 181-195 ◽  
Author(s):  
Th. Eschner ◽  
J.-J. Fundenberger
Keyword(s):  
Aluminum Alloy ◽  
Texture Analysis ◽  
Series Expansion ◽  
Texture Component ◽  
Tensile Testing ◽  
Texture Evolution ◽  
Orientation Distribution ◽  
Distribution Functions ◽  
Weighted Sum ◽  
Recent Developments

The description of textures in terms of texture components is an established conception in quantitative texture analysis. Recent developments lead to the representation of orientation distribution functions as a weighted sum of model functions, each corresponding to one anisotropic texture component. As was shown previously, an adequate texture description is possible with only a very small number of anisotropic texture components. As a result, textures and texture changes can be described by a small number of vivid parameters and their variations, namely by volume parts, half widths and ideal orientations.The texture of a tensile tested commercial aluminum alloy was investigated by decomposition into anisotropic components. The texture evolution during tensile testing is represented by the corresponding changes of the component parameters and compared with results from an iterative series expansion analysis.

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.

scholarly journals {111} Orientation Induced Anisotropy of Shape Memory Effect in NiTiNb Pipe Joints

Metals ◽  
2020 ◽  
Vol 10 (6) ◽  
pp. 776
Author(s):  
Mingyan Sun ◽  
Qichao Fan ◽  
Yingying Wang ◽  
Qin Yang ◽  
Jie Chen ◽  
...  
Keyword(s):  
Shape Memory ◽  
Shape Memory Effect ◽  
Memory Effect ◽  
Electron Backscatter Diffraction ◽  
Orientation Distribution ◽  
Distribution Functions ◽  
Induced Anisotropy ◽  
Texture Intensity ◽  
Pole Figures ◽  
Pipe Joints

This work aims to clarify the influence of texture type and intensity on the shape memory effect (SME) in NiTiNb shape memory alloy (SMA) pipe joints, especially revealing the causes for the anisotropy of SME via texture changes. Three NiTiNb rods with different intensities of the {111}<110> texture were fabricated, and their microstructures, crystalline orientation distribution functions and inverse pole figures were obtained by X-ray diffraction and electron backscatter diffraction measurements. Simultaneously, the SME was characterized by inner-diameter recoverability of the corresponding pipe joints. For a given intensity of the {111}<110> texture, the SME of the NiTiNb pipe joints strongly depended on the expansion direction due to {111}<110> orientation-induced anisotropy of SME. In addition, both the SME and anisotropy of NiTiNb pipe joints increased with the increased intensity of the {111}<110> texture. Therefore, a suitable expansion direction and strong texture intensity should be considered for high SME in NiTiNb pipe joints.

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 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.

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