Three‐Dimensional Orientation Distribution Function of Crystals in Cold‐Rolled Copper

1968 ◽  
Vol 39 (12) ◽  
pp. 5503-5514 ◽  
Author(s):  
Hans‐Joachim Bunge ◽  
Frank Haessner
Keyword(s):  
Distribution Function ◽  
Orientation Distribution Function ◽  
Three Dimensional ◽  
Orientation Distribution ◽  
Cold Rolled

Orientation Distribution of Fiber Suspensions in Extensional Flow

2013 ◽  
Vol 785-786 ◽  
pp. 981-984 ◽  
Author(s):  
Zan Huang ◽  
Jin Ping Qu ◽  
Ji Wei Geng ◽  
Shu Feng Zhai ◽  
Shi Kui Jia
Keyword(s):  
Differential Equation ◽  
Distribution Function ◽  
Orientation Distribution Function ◽  
Fiber Orientation ◽  
Extensional Flow ◽  
Three Dimensional ◽  
Orientation Distribution ◽  
Fiber Suspensions ◽  
Short Fibers ◽  
Fiber Orientation Distribution

An orientation distribution function is adopted to describe three-dimensional orientation distribution of short fibers suspensions in extensional flow. A mathematical model of evolution process on fiber orientation distribution function is established by analytical method. Numerical simulation is also used to describe two and three dimensional orientation distribution of fibers. Therefore, analytical solution of differential equation on forecast fiber orientation distribution is deduced.

Calculation of the crystal orientation distribution function from synchrotron radiation experimental data

1989 ◽  
Vol 22 (6) ◽  
pp. 559-561 ◽  
Author(s):  
J. A. Szpunar ◽  
P. Blandford ◽  
D. C. Hinz
Keyword(s):  
Experimental Data ◽  
Distribution Function ◽  
Synchrotron Radiation ◽  
Orientation Distribution Function ◽  
Crystal Orientation ◽  
Orientation Distribution ◽  
Pole Figures ◽  
Cold Rolled ◽  
Expansion Coefficients ◽  
Crystal Orientation Distribution Function

Series-expansion coefficients for an orientation distribution function (ODF) of cold-rolled aluminium sheet were calculated from the intensity of Debye–Scherrer rings obtained in an experiment using synchrotron radiation. Calculated and observed pole figures demonstrate that a sufficiently good approximation to the ODF is obtained from coefficients calculated to l = 8.

scholarly journals The Misorientation Distribution Function

1986 ◽  
Vol 6 (3) ◽  
pp. 201-215 ◽  
Author(s):  
J. Pospiech ◽  
K. Sztwiertnia ◽  
F. Haessner
Keyword(s):  
Distribution Function ◽  
Orientation Distribution Function ◽  
Three Dimensional ◽  
Orientation Distribution ◽  
Two Dimensional ◽  
Misorientation Distribution ◽  
Rotation Axes

The analysis of misorientations has up to now usually be carried out by comparing the values obtained experimentally using two dimensional distributions of rotation axes or rotation angles with the distribution calculated by Mackenzie for the statistically random case. In this paper the presentation of the distribution of the misorientations is based on the three dimensional orientation distribution function (ODF) (as described by Bunge). The new function is termed the misorientation distribution function (MDF) to differentiate it from the ODF. The advantages in using this function are presented and illustrated by three MDF's derived from the work of Haessner, Pospiech and Sztwiertnia.

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.

scholarly journals Coordinate Free Tensorial Representation of the Orientation Distribution Function With Harmonic Polynomials

1993 ◽  
Vol 21 (4) ◽  
pp. 233-250 ◽  
Author(s):  
David D. Sam ◽  
E. Turan Onat ◽  
Pavel I. Etingof ◽  
Brent L. Adams
Keyword(s):  
Distribution Function ◽  
Orientation Distribution Function ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Measurement Data ◽  
Orientation Distribution ◽  
Harmonic Polynomials ◽  
Crystallite Orientation ◽  
Orientation Measurement ◽  
Three Dimensional Space

The crystallite orientation distribution function (CODF) is reviewed in terms of classical spherical function representation and more recent coordinate free tensorial representation (CFTR). A CFTR is a Fourier expansion wherein the coefficients are tensors in the three-dimensional space. The equivalence between homogeneous harmonic polynomials of degree k and symmetric and traceless tensors of rank k allows a realization of these tensors by the method of harmonic polynomials. Such a method provides for the rapid assembly of a tensorial representation from microstructural orientation measurement data. The coefficients are determined to twenty-first order and expanded in the form of a crystallite orientation distribution function, and compared with previous calculations.

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 Correlations Between the Rolling Textures in FCC Ni–Co Alloys and the BCC Transformation Textures in Controlled Rolled Steels

1990 ◽  
Vol 12 (1-3) ◽  
pp. 141-153 ◽  
Author(s):  
R. K. Ray ◽  
Ph. Chapellier ◽  
J. J. Jonas
Keyword(s):  
Distribution Function ◽  
Orientation Distribution Function ◽  
Rolling Texture ◽  
Orientation Distribution ◽  
Variant Selection ◽  
Rolled Steel ◽  
Orientation Relationships ◽  
Cold Rolled ◽  
Co Alloys ◽  
Stacking Fault Energies

Three fcc Ni–Co alloys with different stacking fault energies (SFE's) were cold rolled 95% and their textures were characterized by the orientation distribution function (ODF) method. BCC transformation textures were calculated from these experimental textures using three different orientation relationships for the γ→α transformation. The transformed ODF's derived from the Bain relationship were much sharper than the ones deduced from the Kurdjumov–Sachs (K–S) or the Nishiyama–Wassermann (N–W) relations. The ferrite texture determined on a controlled rolled steel, heavily deformed in the unrecrystallized γ region, agrees reasonably well with the bcc texture calculated using the K–S relation from the rolled Ni–Co alloy with similar SFE. The major texture components of the ferrite, namely {332}〈113〉 and {311}〈011〉, are found to originate from the two major rolling texture components of the austenite, i.e. the {110}〈112〉(Bs) and {112}〈111〉(Cu), respectively. Such ferrite transformation from heavily deformed austenite seems to follow the K–S relationship without any variant selection. By contrast, the texture of the martensite produced from deformed austenite appears to involve significant amounts of variant selection.

scholarly journals The Influence of Molybdenum on the Texture and Magnetic Anisotropy of Fe–xMo–5Ni–0.05C Alloys

1999 ◽  
Vol 31 (4) ◽  
pp. 231-238 ◽  
Author(s):  
H. Abreu ◽  
J. R. Teodósio ◽  
J. Neto ◽  
M. Silva ◽  
C. S. Da Costa Viana
Keyword(s):  
Distribution Function ◽  
Magnetic Anisotropy ◽  
Orientation Distribution Function ◽  
Texture Component ◽  
Texture Evolution ◽  
Rolling Direction ◽  
Orientation Distribution ◽  
Easy Magnetization ◽  
Saturation Induction ◽  
Cold Rolled

Diagrams of remanent induction, Br, versus saturation induction, Bs, for Fe–5Ni–xMo–0.05C alloys, where x is equal to 11%, 15% or 19%, were determined for samples 60%, 80%, 90% and 97% cold rolled and magnetically age-annealed at 610°C for 1h. The texture evolution in those alloys was analysed as a function of rolling reduction, by means of the orientation distribution function (ODF). The results show that a sharp {100} 〈110〉 texture component develops in the 11%-Mo alloy for rolling reductions in excess of 90%. This leads to the highest values of the remanent induction, Br, and of the Br/Bs ratio for this alloy as a result of 〈100〉 directions, the easy magnetization directions, lying at 45° to the rolling direction.

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