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ASTM E81-96(2007)

(Test Method)

Standard Test Method for Preparing Quantitative Pole Figures

Standard Test Method for Preparing Quantitative Pole Figures

SIGNIFICANCE AND USE
Pole figures are two-dimensional graphic representations, on polar coordinate paper, of the average distribution of crystallite orientations in three dimensions. Data for constructing pole figures are obtained with X-ray diffractometers, using reflection and transmission techniques.
Several alternative procedures may be used. Some produce complete pole figures. Others yield partial pole figures, which may be combined to produce a complete figure.
SCOPE
1.1 This test method covers the use of the X-ray diffractometer to prepare quantitative pole figures.
1.2 The test method consists of several experimental procedures. Some of the procedures (1-5) permit preparation of a complete pole figure. Others must be used in combination to produce a complete pole figure.
1.3 Pole figures (6) and inverse pole figures (7-10) are two-dimensional averages of the three-dimensional crystallite orientation distribution. Pole figures may be used to construct either inverse pole figures (11-13) or the crystallite orientation distribution (14-21). Development of series expansions of the crystallite orientation distribution from reflection pole figures (22, 23) makes it possible to obtain a series expansion of a complete pole figure from several incomplete pole figures. Pole figures or inverse pole figures derived by such methods shall be termed calculated. These techniques will not be described herein.
1.4 Provided the orientation is homogeneous through the thickness of the sheet, certain procedures (1-3) may be used to obtain a complete pole figure.
1.5 Provided the orientation has mirror symmetry with respect to planes perpendicular to the rolling, transverse, and normal directions, certain procedures (4, 5, 24) may be used to obtain a complete pole figure.
1.6 The test method emphasizes the Schulz reflection technique (25). Other techniques (3, 4, 5, 24) may be considered variants of the Schulz technique and are cited as options, but not described herein.
1.7 The test method also includes a description of the transmission technique of Decker, et al (26), which may be used in conjunction with the Schulz reflection technique to obtain a complete pole figure.
1.8 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.

General Information

Status
Historical
Publication Date
30-Apr-2007
ICS
77.040.99 - Other methods of testing of metals
Technical Committee
E04 - Metallography
Drafting Committee
E04.11 - X-Ray and Electron Metallography
Current Stage
Ref Project

Relations

Replaces
ASTM E81-96(2001) - Standard Test Method for Preparing Quantitative Pole Figures
Effective Date
01-May-2007
Replaced By
ASTM E81-96(2011) - Standard Test Method for Preparing Quantitative Pole Figures
Effective Date
01-Oct-2011

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ASTM E81-96(2007) - Standard Test Method for Preparing Quantitative Pole Figures
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NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation: E81 – 96 (Reapproved 2007)
Standard Test Method for
1
Preparing Quantitative Pole Figures
ThisstandardisissuedunderthefixeddesignationE81;thenumberimmediatelyfollowingthedesignationindicatestheyearoforiginal
adoptionor,inthecaseofrevision,theyearoflastrevision.Anumberinparenthesesindicatestheyearoflastreapproval.Asuperscript
epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope 1.8 This standard does not purport to address all of the
safety concerns, if any, associated with its use. It is the
1.1 This test method covers the use of the X-ray diffracto-
responsibility of the user of this standard to establish appro-
meter to prepare quantitative pole figures.
priate safety and health practices and determine the applica-
1.2 The test method consists of several experimental proce-
2
bility of regulatory limitations prior to use.
dures. Some of the procedures (1-5) permit preparation of a
complete pole figure. Others must be used in combination to
2. Summary of Test Method
produce a complete pole figure.
2.1 The test method consists of characterizing the distribu-
1.3 Pole figures (6) and inverse pole figures (7-10) are two
tion of orientations of selected lattice planes with respect to
dimensional averages of the three-dimensional crystallite ori-
sample-fixed coordinates (6). The distribution will usually be
entation distribution. Pole figures may be used to construct
obtained by measurement of the intensity of X rays diffracted
either inverse pole figures (11-13) or the crystallite orientation
by the sample. In such measurements the detector and associ-
distribution (14-21). Development of series expansions of the
ated limiting slits are fixed at twice the appropriate Bragg
crystallite orientation distribution from reflection pole figures
angle,andthediffractedintensityisrecordedastheorientation
(22, 23) makes it possible to obtain a series expansion of a
of the sample is changed (1-6, 25, 26, 27).After the measured
completepolefigurefromseveralincompletepolefigures.Pole
data have been corrected, as necessary, for background, defo-
figuresorinversepolefiguresderivedbysuchmethodsshallbe
cusing, and absorption, and normalized to have an average
termed calculated. These techniques will not be described
value of unity, the results may be plotted in stereographic or
herein.
equal-area projection.
1.4 Provided the orientation is homogeneous through the
2.2 The geometry of the Schulz (25) reflection method is
thickness of the sheet, certain procedures (1-3) may be used to
illustrated in Fig. 1. Goniometers employing this geometry are
obtain a complete pole figure.
commerciallyavailable.ThesourceofXraysisindicatedby L.
1.5 Provided the orientation has mirror symmetry with
Slit S1 limits divergence of the incident beam in the plane of
respect to planes perpendicular to the rolling, transverse, and
projection. Slit S2 limits divergence perpendicular to the plane
normal directions, certain procedures (4, 5, 24) may be used to
of projection. The sample, indicated by crosshatching, may be
obtain a complete pole figure.
tilted about the axis FF8, which is perpendicular to the
1.6 The test method emphasizes the Schulz reflection tech-
diffractometer axis and lies in the plane of the sample. The tilt
nique (25). Other techniques (3, 4, 5, 24) may be considered
angle was denoted f by Schulz (25). The sample position
variants of the Schulz technique and are cited as options, but
shown in Fig. 1 corresponds to f=0 deg, for which approxi-
not described herein.
mateparafocusingconditionsexistatthedetectorslit,S3.With
1.7 The test method also includes a description of the
theapplicationofadefocusingcorrection,thismethodisuseful
transmission technique of Decker, et al (26), which may be
over a range of colatitude f from 0 deg to approximately 75
used in conjunction with the Schulz reflection technique to
deg.
obtain a complete pole figure.
2.2.1 Tilting the sample about FF8, so as to reduce the
distance between L and points in the sample surface above the
plane of projection, causes X rays diffracted from these points
1
This test method is under the jurisdiction of ASTM Committee E04 on
to be displaced to the left of the center of S3, while X rays
Metallography and is the direct responsibility of Subcommittee E04.11 on X-Ray
diffractedfrompointsinthesamplesurfacebelowtheplaneof
and Electron Metallography.
Current edition approved May 1, 2007. Published May 2007. Originally
projection are displaced to the right of the center of S3. The
approvedin1949.Lastpreviouseditionapprovedin2001asE81–96(2001).DOI:
displacement is equal to 2D tan f cos u, where D is the
10.1520/E0081-96R07.
2
distance above or below the plane of projection. The inte-
Theboldfacenumbersinparenthesesrefertothelistofreferencesattheendof
this test method. grated, or total, diffra
...

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This practice describes a methodology to statistically characterize the distribution of the largest indigenous non-metallic inclusions in steel specimens based upon quantitative metallographic measurements. This practice enables the experimenter to estimate the extreme value distribution of inclusions in steels. The procedures in determining non-metallic inclusions in steel are presented and discussed in details.
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5.1 This practice is used to assess the indigenous inclusions or second-phase constituents in metals using extreme value statistics.  
5.2 It is well known that failures of mechanical components, such as gears and bearings, are often caused by the presence of large nonmetallic oxide inclusions. Failure of a component can often be traced to the presence of a large inclusion. Predictions related to component fatigue life are not possible with the evaluations provided by standards such as Test Methods E45, Practice E1122, or Practice E1245. The use of extreme value statistics has been related to component life and inclusion size distributions by several different investigators (3-8). The purpose of this practice is to create a standardized method of performing this analysis.  
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SCOPE
1.1 This practice describes a methodology to statistically characterize the distribution of the largest indigenous nonmetallic inclusions in steel specimens based upon quantitative metallographic measurements. The practice is not suitable for assessing exogenous inclusions.  
1.2 Based upon the statistical analysis, the nonmetallic content of different lots of steels can be compared.  
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4.4 If the grains in a polycrystalline material are large enough, this test method can also be used to determine their orientations and differences in orientation can be documented or mapped or both.
SCOPE
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1.3 Units—The values stated in either SI units or inch-pound units are to be regarded separately as standard. The values stated in each system may not be exact equivalents; therefore, each system shall be used independently of the other. Combining values from the two systems may result in non-conformance with the standard.  
1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.5 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

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