Calculation of the elastic anisotropy of Ti:6Al-4V alloy sheet from pole figure data

1973 ◽  
Vol 4 (3) ◽  
pp. 701-705 ◽  
Author(s):  
R. H. Olsen ◽  
H. A. Moreen
Keyword(s):  
Pole Figure ◽  
Elastic Anisotropy ◽  
Alloy Sheet ◽  
Pole Figure Data

scholarly journals An Analysis of Elastic Anisotropy and Microyielding in Polycrystalline Molybdenum TZM

1979 ◽  
Vol 3 (4) ◽  
pp. 231-243 ◽  
Author(s):  
A. Kumar ◽  
W. B. Hutchinson
Keyword(s):  
Grain Size ◽  
Pole Figure ◽  
Elastic Moduli ◽  
Elastic Anisotropy ◽  
Major Influence ◽  
Orientation Data ◽  
Grain Sizes ◽  
Orientation Distributions ◽  
Pole Figure Data ◽  
Polycrystalline Molybdenum

Samples of molybdenum TZM alloy in sheet form have been investigated in the warm-worked condition and after recrystallisation heat treatments to produce a range of different grain sizes. Orientation distributions were calculated from measured pole figure data and specimens were cut at various angles around the sheet to determine the planar variations in Young's modulus and microyield stress. Elastic moduli have been calculated for the materials on the basis of several different models using the preferred orientation data. Excellent agreement is found between the measured moduli and those calculated according to the Eshelby-Kröner-Kneer model. Variations in stress level from grain to grain were also calculated according to this model and used to predict the initiation of plastic flow, i.e. the microyield point. These predictions also agree closely with measured values. Variation of grain size did not have a major influence on elasticity or microyielding.

scholarly journals The Elastic Constants of the Single Crystal of the Mg-Zn-Zr-REM Alloy from the Data of the Elastic Anisotropy and the Texture of the Polycrystalline Sheet

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
S. V. San’kova ◽  
N. M. Shkatulyak ◽  
V. V. Usov ◽  
N. A. Volchok
Keyword(s):  
Single Crystals ◽  
Young’S Modulus ◽  
Elastic Constants ◽  
Elastic Anisotropy ◽  
Young's Modulus ◽  
Rare Earth Metals ◽  
Alloy Sheet ◽  
Pole Figures ◽  
Integral Characteristics ◽  
Experimental Values

The measuring of the constants of single-crystals requires the availability of crystals of relatively big size. In this paper the elastic constants of the single crystals of magnesium alloy with zinc, zirconium, and rare earth metals (REM) were determined by means of the experimental anisotropy of Young’s modulus and integral characteristics of texture (ICT), which were found from pole figures. Using these constants the anisotropy of Young’s modulus of alloy sheet ZE10 was calculated. Deviation of calculated values from experimental values did not exceed 2%.

scholarly journals A Method for the Generation of Various Ghost Correction Algorithms—the Example of the Positivity Method and the Exponential Method

1991 ◽  
Vol 13 (4) ◽  
pp. 199-212 ◽  
Author(s):  
P. Van Houtte
Keyword(s):  
Pole Figure ◽  
Taylor Series ◽  
The Other ◽  
New Method ◽  
Series Expansions ◽  
Theoretical Scheme ◽  
Taylor Series Expansions ◽  
Exponential Method ◽  
Pole Figure Data

A theoretical strategy is presented that can derive the algorithms of several existing ghost correction methods. The examples of the positivity method and the “GHOST” method are elaborated. A new method is derived as well: the “exponential” method. It can successfully replace the quadratic method as a method that yields an exactly non-negative complete C.O.D.F. from pole figure data. The theoretical scheme that can generate all these algorithms makes use of the fact, that several parameter sets can be defined in order to describe a C.O.D.F. The parameters of one set are then functions of those of the other. The algorithms are derived from Taylor series expansions of these functions.

Elaboration on the hexagonal grid and spiral trace schemes for pole figure data collection

2008 ◽  
Vol 23 (2) ◽  
pp. 87-91 ◽  
Author(s):  
Anthony C. Rizzie ◽  
Thomas R. Watkins ◽  
E. Andrew Payzant
Keyword(s):  
Data Collection ◽  
Pole Figure ◽  
Aluminum Foil ◽  
Hexagonal Grid ◽  
Equal Area ◽  
X Ray ◽  
Pole Figures ◽  
Area Sampling ◽  
Data Points ◽  
Pole Figure Data

A practical description of the mathematics required to implement the hexagonal grid and spiral trace pole figure data collection schemes is presented. Applying the concepts of stereographic and equal area projections with geometry, spreadsheets were created to calculate the angular settings of the goniometer. Using the generated settings, the hexagonal grid and spiral trace schemes were programmed into the existing X-ray software and employed to collect data for a sample of aluminum foil. The resulting (111) pole figures were similar to those collected with the conventional 5°χ×5°ϕ grid. The hexagonal grid has been shown by others to reduce the number of data points and time needed to complete a pole figure, while providing equal area sampling. Although not optimized, the spiral method was also investigated as another alternative to the 5°χ×5°ϕ grid.

scholarly journals Multi-scale phase analyses of strain-induced martensite in austempered ductile iron (ADI) using neutron diffraction and transmission techniques

2020 ◽  
Vol 56 (8) ◽  
pp. 5296-5306
Author(s):  
Xiaohu Li ◽  
Sergio Soria ◽  
Weimin Gan ◽  
Michael Hofmann ◽  
Michael Schulz ◽  
...  
Keyword(s):  
Neutron Diffraction ◽  
Pole Figure ◽  
Ductile Iron ◽  
Imaging Techniques ◽  
Austempered Ductile Iron ◽  
Quantitative Phase Analysis ◽  
Strain Induced Martensite ◽  
Phase Quantification ◽  
Pole Figure Data ◽  
Multi Phase

AbstractThe content of strain-induced martensite in austempered ductile iron has been quantitatively determined using three different kinds of neutron methods: (1) high-resolution powder diffraction with subsequent standard Rietveld refinement, (2) phase quantification using pole figure measurements and (3) Bragg edge neutron transmission. The accuracy and scope of applications of these neutron diffraction and imaging techniques for phase quantification have been compared and discussed in detail. Combination of these methods has been confirmed as effective for dealing with problems like peak overlap in multi-phase materials and texture formation after plastic deformation. Further, the results highlight the potential of using single peak pole figure data for quantitative phase analysis with high accuracy.

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.

A new method for texture measurements using a general area detector diffraction system

2003 ◽  
Vol 18 (2) ◽  
pp. 99-102 ◽  
Author(s):  
Kurt Helming ◽  
Mike Lyubchenko ◽  
Bob He ◽  
Uwe Preckwinkel
Keyword(s):  
Data Collection ◽  
Data Quality ◽  
Pole Figure ◽  
New Method ◽  
General Area ◽  
X Ray ◽  
Area Detector ◽  
New Methods ◽  
Analysis Process ◽  
Pole Figure Data

Advances in X-ray texture solutions require new methods and descriptions for the texture analysis process, e.g., when using general area detector diffraction systems. A new method is presented that defines a general pole figure resolution and provides the possibility to optimize strategies for efficient pole figure data collection. Application of the new method improves resolution and (!) speed. New software enables simultaneous monitoring of pole and detector space. This allows a fundamentally better understanding of the collected information, e.g., in situations where peaks overlap or high backgrounds compromise data quality.

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.

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