ASTM E2283-08(2014)
(Practice)Standard Practice for Extreme Value Analysis of Nonmetallic Inclusions in Steel and Other Microstructural Features
Standard Practice for Extreme Value Analysis of Nonmetallic Inclusions in Steel and Other Microstructural Features
ABSTRACT
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.
SIGNIFICANCE AND USE
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.
5.3 This practice is not suitable for assessing the exogenous inclusions in steels and other metals because of the unpredictable nature of the distribution of exogenous inclusions. Other methods involving complete inspection such as ultrasonics must be used to locate their presence.
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.
1.3 This practice deals only with the recommended test methods and nothing in it should be construed as defining or establishing limits of acceptability.
1.4 The measured values are stated in SI units. For measurements obtained from light microscopy, linear feature parameters shall be reported as micrometers, and feature areas shall be reported as micrometers.
1.5 The methodology can be extended to other materials and to other microstructural features.
1.6 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.
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Designation: E2283 − 08 (Reapproved 2014)
Standard Practice for
Extreme Value Analysis of Nonmetallic Inclusions in Steel
and Other Microstructural Features
This standard is issued under the fixed designation E2283; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope E691Practice for Conducting an Interlaboratory Study to
Determine the Precision of a Test Method
1.1 This practice describes a methodology to statistically
E768Guide for Preparing and Evaluating Specimens for
characterize the distribution of the largest indigenous nonme-
Automatic Inclusion Assessment of Steel
tallic inclusions in steel specimens based upon quantitative
E1122Practice for Obtaining JK Inclusion Ratings Using
metallographic measurements. The practice is not suitable for
Automatic Image Analysis (Withdrawn 2006)
assessing exogenous inclusions.
E1245Practice for Determining the Inclusion or Second-
1.2 Based upon the statistical analysis, the nonmetallic
Phase Constituent Content of Metals byAutomatic Image
content of different lots of steels can be compared.
Analysis
1.3 This practice deals only with the recommended test
methods and nothing in it should be construed as defining or 3. Terminology
establishing limits of acceptability.
3.1 Definitions—For definitions of metallographic terms
1.4 The measured values are stated in SI units. For mea-
used in this practice, refer to Terminology, E7; for statistical
surements obtained from light microscopy, linear feature pa- terms, refer to Terminology E456.
rameters shall be reported as micrometers, and feature areas
3.2 Definitions of Terms Specific to This Standard:
shall be reported as micrometers.
3.2.1 A— the area of each field of view used by the Image
f
1.5 Themethodologycanbeextendedtoothermaterialsand
Analysis system in performing the measurements.
to other microstructural features.
3.2.2 A —controlarea;totalareaobservedononespecimen
o
1.6 This standard does not purport to address all of the
per polishing plane for the analysis. A is assumed to be 150
o
safety concerns, if any, associated with its use. It is the
mm unless otherwise noted.
responsibility of the user of this standard to establish appro-
3.2.3 N — number of specimens used for the evaluation. N
s s
priate safety and health practices and determine the applica-
is generally six.
bility of regulatory limitations prior to use.
3.2.4 N — number of planes of polish used for the
p
evaluation, generally four.
2. Referenced Documents
2 3.2.5 N— number of fields observed per specimen plane of
f
2.1 ASTM Standards:
polish.
E3Guide for Preparation of Metallographic Specimens
E7Terminology Relating to Metallography A
o
N 5 (1)
f
E45Test Methods for Determining the Inclusion Content of A
f
Steel
3.2.6 N—total number of inclusion lengths used for the
E178Practice for Dealing With Outlying Observations
analysis, generally 24.
E456Terminology Relating to Quality and Statistics
N 5 N ·N (2)
s p
3.2.7 extreme value distribution—Thestatisticaldistribution
thatiscreatedbasedupononlymeasuringthelargestfeaturein
This practice is under the jurisdiction of ASTM Committee E04 on Metallog-
a given control area or volume (1,2). The continuous random
raphy and is the direct responsibility of Subcommittee E04.09 on Inclusions.
Current edition approved Oct. 1, 2014. Published December 2014. Originally
approved in 2003 last previous edition approved in 2008 as E2283–08. DOI:
10.1520/E2283-08R14.
2 3
For referenced ASTM standards, visit the ASTM website, www.astm.org, or The last approved version of this historical standard is referenced on
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM www.astm.org.
Standards volume information, refer to the standard’s Document Summary page on Theboldfacenumbersinparenthesesrefertothelistofreferencesattheendof
the ASTM website. this standard.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E2283 − 08 (2014)
variable x has a two parameter (Gumbel) Extreme Value 1
T 5 (12)
Distribution if the probability density function is given by the 1 2 P
following equation:
3.2.15 reference area, A —the arbitrarily selected area of
ref
150000 mm . A in conjunction with the parameters of the
1 x 2 λ x 2 λ
ref
f x 5 exp 2 3exp 2exp 2 (3)
~ ! F S DG F S DG
extreme value distribution is used to calculate the size of the
δ δ δ
largest inclusion reported by this standard. As applied to this
and the cumulative distribution is given by the following
analysis, the largest inclusion in each control area A is
o
equation:
measured.TheReturnPeriod, T,isusedtopredicthowlargean
F~x! 5exp~2exp~2~x 2 λ!/δ!! (4)
inclusion could be expected to be found if an area A larger
ref
than A were to be evaluated. For this standard, A is 1000
o ref
As applied to this practice, x, represents the maximum
times larger than A .Thus, T is equal to 1000. By use of Eq 12
o
feret diameter, Length, of the largest inclusion in each con-
it would be found that this corresponds to a probability value
trol area, A , letting:
o
of0.999,(99.9%).SimilarlybyusingEq6and7,thelengthof
x 2 λ
an inclusion corresponding to the 99.99% probability value
y 5 (5)
δ
couldbecalculated.Mathematically,anotherexpressionforthe
return period is:
it follows that:
A
ref
F~y! 5exp~2exp~2y!! (6)
T 5 (13)
A
o
and
3.2.16 predicted maximum inclusion length, L —the lon-
max
x 5 δ y1λ (7)
gest inclusion expected to be found in area A based upon the
ref
extreme value distribution analysis.
3.2.8 λ—the location parameter of the extreme value distri-
bution function.
4. Summary of Practice
3.2.9 δ—the scale parameter of the extreme value distribu-
4.1 This practice enables the experimenter to estimate the
tion function.
extreme value distribution of inclusions in steels.
3.2.10 reduced variate—Thevariable yiscalledthereduced
4.2 Generally, the largest oxide inclusions within the speci-
variate. As indicated in Eq 6, y is related to the probability
mens are measured. However, the practice can be used to
density function. That is y = F(P), then from Eq 6, it follows
measure other microstructural features such as graphite nod-
that:
ulesinductileiron,orcarbidesintoolsteelsandbearingsteels.
y52ln 2ln F y 52ln 2ln P (8)
~ ~ ~ !!! ~ ~ !! The practice is based upon using the specimens described in
Test Method E45. Six specimens will be required for the
3.2.11 plotting position—Each of the N measured inclusion
analysis. For inclusion analysis, an area of 150 mm should be
lengths can be represented as x, where 1 ≤ i ≤ N. The data
i
evaluated for each specimen.
points are arranged in increasing order such that:
4.3 After obtaining the specimens, it is recommended that
x # x # x # x # x .# x
1 2 3 4 5 N
they be prepared by following the procedures described in
Then the cumulative probability plotting position for data
Methods E3 and Practice E768.
point x is given by the relationship:
i
4.4 The polished specimens are then evaluated by using the
i
guidelinesforcompletingimageanalysisdescribedinPractices
P 5 (9)
i
N11
E1122 and E1245. For this analysis, feature specific measure-
The fraction ( i/(N + 1)) is the cumulative probability. ments are required. The measured inclusion lengths shall be
based on a minimum of eight feret diameter measurements.
F(y)in Eq 8 corresponds to data point x.
i i
¯
4.5 Foreachspecimen,themaximumferetdiameterofeach
3.2.12 mean longest inclusion length—L is the arithmetic
inclusion is measured. After performing the analysis for each
average of the set of N maximum feret diameters of the
specimen,thelargestmaximumferetdiameterofthemeasured
measured longest inclusions.
inclusions is recorded. This will result in six lengths. The
i5N
H
procedure is repeated three more times. This will result in a
L 5 L (10)
( i
N
i51
total of 24 inclusion lengths.
3.2.13 standard deviation of longest inclusion lengths—
4.6 The 24 measurements are used to estimate the values of
Sdev is the standard deviation of the set of N maximum feret
δ and λ for the extreme value distribution for the particular
diameters of the measured longest inclusions.
material being evaluated. The largest inclusion L expected
max
N 0.5
2 to be in the reference area A is calculated, and a graphical
ref
H
Sdev 5 ~L 2 L! /~N 21! (11)
F G
( i
representation of the data and test report are then prepared.
i51
3.2.14 return period—the number of areas that must be 4.7 The reference area used for this standard is 150000
observed in order to find an inclusion equal to or larger than a mm . Based upon specific producer, purchaser requirements,
specified maximum inclusion length. Statistically, the return other reference areas may be used in conjunction with this
period is defined as: standard.
E2283 − 08 (2014)
4.8 When required, the procedure can be repeated to evalu- ofeachdetectedoxideinclusion.Themeasuredferetdiameters
atemorethanonetypeofinclusionpopulationinagivensetof are stored in the computer’s memory for further analysis. This
specimens. For example, oxides and sulfides or titanium- procedure is repeated until an area of 150 mm is analyzed.
carbonitrides could be evaluated from the same set of speci-
6.5.3 In situations where only a very few inclusions are
mens.
contained within the inspected area, the specimen can first be
observed at low magnification, and the location of the inclu-
5. Significance and Use
sionsnoted.Theobservedinclusionscanthenberemeasuredat
high magnification.
5.1 This practice is used to assess the indigenous inclusions
6.5.4 Afterthespecimenisanalyzed,usingtheaccumulated
or second-phase constituents in metals using extreme value
data, the maximum feret diameter of the largest measured
statistics.
inclusion in the 150 mm area is recorded. This procedure is
5.2 Itiswellknownthatfailuresofmechanicalcomponents,
repeated for each of the other five specimens.
suchasgearsandbearings,areoftencausedbythepresenceof
6.5.5 The specimens are then repolished and the procedure
largenonmetallicoxideinclusions.Failureofacomponentcan
is repeated until each specimen has been evaluated four times.
oftenbetracedtothepresenceofalargeinclusion.Predictions
This will result in a set of 24 maximum feret diameters. For
related to component fatigue life are not possible with the
each repolishing step, it is recommended that at least 0.3 mm
evaluations provided by standards such as Test Methods E45,
of material be removed in order to create a new plane of
Practice E1122, or Practice E1245. The use of extreme value
observation.
statistics has been related to component life and inclusion size
¯
6.5.6 The mean length, L, is then calculated using Eq 10.
distributions by several different investigators (3-8). The pur-
pose of this practice is to create a standardized method of 6.5.7 The standard deviation, Sdev, is calculated using Eq
performing this analysis. 11.
5.3 This practice is not suitable for assessing the exogenous
6.6 The24measuredinclusionlengthsaresortedinascend-
inclusions in steels and other metals because of the unpredict-
ing order. An example of the calculations is contained in
able nature of the distribution of exogenous inclusions. Other
Appendix X1. The inclusions are then given a ranking. The
methods involving complete inspection such as ultrasonics
smallest inclusion is ranked number 1, the second smallest is
must be used to locate their presence.
ranked number 2 etc.
6.7 The probability plotting position for each inclusion is
6. Procedure
basedupontherank.TheprobabilitiesaredeterminedusingEq
6.1 Testspecimensareobtainedandpreparedinaccordance
9: P = i/(N + 1). Where 1 ≤ i ≤ 24, and N = 24.
i
with E3, E45 and E768.
6.8 A graph is created to represent the data. Plotting
6.2 The microstructural analysis is to be performed using
positions for the ordinate are calculated from Eq 8: y =
i
the types of equipment and image analysis procedures de-
−ln(−ln(P)).Thevariable yinthisanalysisisreferredtoasthe
i
scribed in E1122 and E1245.
Reduced Variate (Red. Var.). Typically the ordinate scale
6.3 Determine the appropriate magnification to use for the ranges from −2 through +7. This corresponds to a probability
analysis. For accurate measurements, the largest inclusion
range of inclusion lengths from 0.87 through 99.9%. The
measured should be a minimum of 20 pixels in length. For ordinate axis is labeled as Red. Var. It is also possible to
specimenscontainingrelativelylargeinclusions,objectivelens
include the Probability values on the ordinate. In this case, the
having magnifications ranging from 10 to 20× will be ad- ordinatecanbelabeledProbability(%).Theabscissaislabeled
equate. Generally, for specimens with small inclusions, an
asInclusionLength(mm);theunitsofinclusionlengthshallbe
objective lens of 32 to 80× will be required. The same
micrometers.
magnification shall be used for all the specimens to be
6.9 Estimation of the Extreme Value Distribution Param-
analyzed.
eters:
6.4 Using the appropriate calibration factors, calculate the
6.9.1 Several methods can be used to estimate the param-
area of the field of view observed by the image analysis
eters of the extreme value distribution. Using linear regression
system, A. For each specimen, an area of 150 mm shall be
f
to fit a straight line to the plot of the Reduced Variate as a
evaluated.UsingEq1,thenumberoffieldsofviewrequiredto
function of inclusion length is the easiest method; however, it
perform the analysis is N = A / A = 150 / A. N should be
f o f f f
is the least precise. This is because the larger values of the
rounded up to the next highest integer value; that is, if N is
f
inclusion lengths are more heavily weighted than the smaller
calculated to be 632.31, then 633 fields of view shall be
inclusion lengths. Two other methods for estimating the
examined.
parametersarethemethodofmoments(mom),andthemethod
6.5 Image Analysis Measurements: of maximum likelihood (ML).The method of moments is very
6.5.1 In this practice, feature specific parameters are mea- easytocalculate,butthemethodofmaximumlikelihoodgives
sured for each individual inclusion. The measured inclusion estimates that are more precise. While both methods will be
lengths shall be based on a minimum of eight feret diameters. described, the maximum likelihood method shall be used to
6.5.2 For each field of view, focus the image either manu- calculatethereportedvaluesofδandλforthisstandard.(Since
allyorautomatically,andmeasurethemaximumferetdiameter the ML solution is obtained by numerical a
...
This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: E2283 − 08 E2283 − 08 (Reapproved 2014)
Standard Practice for
Extreme Value Analysis of Nonmetallic Inclusions in Steel
and Other Microstructural Features
This standard is issued under the fixed designation E2283; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. 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.
1.3 This practice deals only with the recommended test methods and nothing in it should be construed as defining or establishing
limits of acceptability.
1.4 The measured values are stated in SI units. For measurements obtained from light microscopy, linear feature parameters
shall be reported as micrometers, and feature areas shall be reported as micrometers.
1.5 The methodology can be extended to other materials and to other microstructural features.
1.6 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.
2. Referenced Documents
2.1 ASTM Standards:
E3 Guide for Preparation of Metallographic Specimens
E7 Terminology Relating to Metallography
E45 Test Methods for Determining the Inclusion Content of Steel
E178 Practice for Dealing With Outlying Observations
E456 Terminology Relating to Quality and Statistics
E691 Practice for Conducting an Interlaboratory Study to Determine the Precision of a Test Method
E768 Guide for Preparing and Evaluating Specimens for Automatic Inclusion Assessment of Steel
E1122 Practice for Obtaining JK Inclusion Ratings Using Automatic Image Analysis (Withdrawn 2006)
E1245 Practice for Determining the Inclusion or Second-Phase Constituent Content of Metals by Automatic Image Analysis
3. Terminology
3.1 Definitions—For definitions of metallographic terms used in this practice, refer to Terminology, E7; for statistical terms,
refer to Terminology E456.
3.2 Definitions of Terms Specific to This Standard:
3.2.1 A — the area of each field of view used by the Image Analysis system in performing the measurements.
f
3.2.2 A — control area; total area observed on one specimen per polishing plane for the analysis. A is assumed to be 150 mm
o o
unless otherwise noted.
3.2.3 N — number of specimens used for the evaluation. N is generally six.
s s
This practice is under the jurisdiction of ASTM Committee E04 on Metallography and is the direct responsibility of Subcommittee E04.09 on Inclusions.
Current edition approved Feb. 1, 2008Oct. 1, 2014. Published February 2008 December 2014. Originally approved in 2003 last previous edition approved in 20072008
as E2283–07.–08. DOI: 10.1520/E2283-08.10.1520/E2283-08R14.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
The last approved version of this historical standard is referenced on www.astm.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E2283 − 08 (2014)
3.2.4 N — number of planes of polish used for the evaluation, generally four.
p
3.2.5 N — number of fields observed per specimen plane of polish.
f
A
o
N 5 (1)
f
A
f
3.2.6 N—total number of inclusion lengths used for the analysis, generally 24.
N 5 N ·N (2)
s p
3.2.7 extreme value distribution—The statistical distribution that is created based upon only measuring the largest feature in a
given control area or volume (1,2). The continuous random variable x has a two parameter (Gumbel) Extreme Value Distribution
if the probability density function is given by the following equation:
1 x 2 λ x 2 λ
f~x! 5 exp 2 3exp 2exp 2 (3)
F S DG F S DG
δ δ δ
and the cumulative distribution is given by the following equation:
F~x! 5 exp~2exp~2~x 2 λ!/δ!! (4)
As applied to this practice, x, represents the maximum feret diameter, Length, of the largest inclusion in each control area,
A , letting:
o
x 2 λ
y 5 (5)
δ
it follows that:
F y 5exp 2exp 2y (6)
~ ! ~ ~ !!
and
x 5 δ y1λ (7)
3.2.8 λ—the location parameter of the extreme value distribution function.
3.2.9 δ—the scale parameter of the extreme value distribution function.
3.2.10 reduced variate—The variable y is called the reduced variate. As indicated in Eq 6, y is related to the probability density
function. That is y = F(P), then from Eq 6, it follows that:
y 52ln 2ln F y 52ln 2ln P (8)
~ ~ ~ !!! ~ ~ !!
3.2.11 plotting position—Each of the N measured inclusion lengths can be represented as x , where 1 ≤ i ≤ N. The data points
i
are arranged in increasing order such that:
x # x # x # x # x . . . # x
1 2 3 4 5 N
Then the cumulative probability plotting position for data point x is given by the relationship:
i
i
P 5 (9)
i
N11
The fraction ( i / (N + 1)) is the cumulative probability. F(y ) in Eq 8 corresponds to data point x .
i i
3.2.12 mean longest inclusion length—L¯ is the arithmetic average of the set of N maximum feret diameters of the measured
longest inclusions.
i5N
H
L 5 L (10)
( i
N
i51
3.2.13 standard deviation of longest inclusion lengths—Sdev is the standard deviation of the set of N maximum feret diameters
of the measured longest inclusions.
N 0.5
H
Sdev 5 ~L 2 L! / N 2 1 (11)
~ !
F G
( i
i51
3.2.14 return period—the number of areas that must be observed in order to find an inclusion equal to or larger than a specified
maximum inclusion length. Statistically, the return period is defined as:
T 5 (12)
12 P
3.2.15 reference area, A —the arbitrarily selected area of 150 000 mm . A in conjunction with the parameters of the extreme
ref ref
value distribution is used to calculate the size of the largest inclusion reported by this standard. As applied to this analysis, the
The boldface numbers in parentheses refer to the list of references at the end of this standard.
E2283 − 08 (2014)
largest inclusion in each control area A is measured. The Return Period, T, is used to predict how large an inclusion could be
o
expected to be found if an area A larger than A were to be evaluated. For this standard, A is 1000 times larger than A . Thus,
ref o ref o
T is equal to 1000. By use of Eq 12 it would be found that this corresponds to a probability value of 0.999, (99.9 %). Similarly
by using Eq 6 and 7, the length of an inclusion corresponding to the 99.99 % probability value could be calculated. Mathematically,
another expression for the return period is:
A
ref
T 5 (13)
A
o
3.2.16 predicted maximum inclusion length, L —the longest inclusion expected to be found in area A based upon the
max ref
extreme value distribution analysis.
4. Summary of Practice
4.1 This practice enables the experimenter to estimate the extreme value distribution of inclusions in steels.
4.2 Generally, the largest oxide inclusions within the specimens are measured. However, the practice can be used to measure
other microstructural features such as graphite nodules in ductile iron, or carbides in tool steels and bearing steels. The practice
is based upon using the specimens described in Test Method E45. Six specimens will be required for the analysis. For inclusion
analysis, an area of 150 mm should be evaluated for each specimen.
4.3 After obtaining the specimens, it is recommended that they be prepared by following the procedures described in Methods
E3 and Practice E768.
4.4 The polished specimens are then evaluated by using the guidelines for completing image analysis described in Practices
E1122 and E1245. For this analysis, feature specific measurements are required. The measured inclusion lengths shall be based
on a minimum of eight feret diameter measurements.
4.5 For each specimen, the maximum feret diameter of each inclusion is measured. After performing the analysis for each
specimen, the largest maximum feret diameter of the measured inclusions is recorded. This will result in six lengths. The procedure
is repeated three more times. This will result in a total of 24 inclusion lengths.
4.6 The 24 measurements are used to estimate the values of δ and λ for the extreme value distribution for the particular material
being evaluated. The largest inclusion L expected to be in the reference area A is calculated, and a graphical representation
max ref
of the data and test report are then prepared.
4.7 The reference area used for this standard is 150 000 mm . Based upon specific producer, purchaser requirements, other
reference areas may be used in conjunction with this standard.
4.8 When required, the procedure can be repeated to evaluate more than one type of inclusion population in a given set of
specimens. For example, oxides and sulfides or titanium-carbonitrides could be evaluated from the same set of specimens.
5. Significance and Use
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.
5.3 This practice is not suitable for assessing the exogenous inclusions in steels and other metals because of the unpredictable
nature of the distribution of exogenous inclusions. Other methods involving complete inspection such as ultrasonics must be used
to locate their presence.
6. Procedure
6.1 Test specimens are obtained and prepared in accordance with E3, E45 and E768.
6.2 The microstructural analysis is to be performed using the types of equipment and image analysis procedures described in
E1122 and E1245.
6.3 Determine the appropriate magnification to use for the analysis. For accurate measurements, the largest inclusion measured
should be a minimum of 20 pixels in length. For specimens containing relatively large inclusions, objective lens having
magnifications ranging from 10 to 20× will be adequate. Generally, for specimens with small inclusions, an objective lens of 32
to 80× will be required. The same magnification shall be used for all the specimens to be analyzed.
E2283 − 08 (2014)
6.4 Using the appropriate calibration factors, calculate the area of the field of view observed by the image analysis system, A .
f
For each specimen, an area of 150 mm shall be evaluated. Using Eq 1, the number of fields of view required to perform the
analysis is N = A / A = 150 / A .N should be rounded up to the next highest integer value; that is, if N is calculated to be 632.31,
f o f f f f
then 633 fields of view shall be examined.
6.5 Image Analysis Measurements:
6.5.1 In this practice, feature specific parameters are measured for each individual inclusion. The measured inclusion lengths
shall be based on a minimum of eight feret diameters.
6.5.2 For each field of view, focus the image either manually or automatically, and measure the maximum feret diameter of each
detected oxide inclusion. The measured feret diameters are stored in the computer’s memory for further analysis. This procedure
is repeated until an area of 150 mm is analyzed.
6.5.3 In situations where only a very few inclusions are contained within the inspected area, the specimen can first be observed
at low magnification, and the location of the inclusions noted. The observed inclusions can then be remeasured at high
magnification.
6.5.4 After the specimen is analyzed, using the accumulated data, the maximum feret diameter of the largest measured inclusion
in the 150 mm area is recorded. This procedure is repeated for each of the other five specimens.
6.5.5 The specimens are then repolished and the procedure is repeated until each specimen has been evaluated four times. This
will result in a set of 24 maximum feret diameters. For each repolishing step, it is recommended that at least 0.3 mm of material
be removed in order to create a new plane of observation.
6.5.6 The mean length, L¯, is then calculated using Eq 10.
6.5.7 The standard deviation, Sdev, is calculated using Eq 11.
6.6 The 24 measured inclusion lengths are sorted in ascending order. An example of the calculations is contained in Appendix
X1. The inclusions are then given a ranking. The smallest inclusion is ranked number 1, the second smallest is ranked number 2
etc.
6.7 The probability plotting position for each inclusion is based upon the rank. The probabilities are determined using Eq 9: P
i
= i / (N + 1). Where 1 ≤ i ≤ 24, and N = 24.
6.8 A graph is created to represent the data. Plotting positions for the ordinate are calculated from Eq 8: y = −ln(−ln(P )). The
i i
variable y in this analysis is referred to as the Reduced Variate (Red. Var.). Typically the ordinate scale ranges from −2 through
+7. This corresponds to a probability range of inclusion lengths from 0.87 through 99.9 %. The ordinate axis is labeled as Red.
Var. It is also possible to include the Probability values on the ordinate. In this case, the ordinate can be labeled Probability (%).
The abscissa is labeled as Inclusion Length (mm); the units of inclusion length shall be micrometers.
6.9 Estimation of the Extreme Value Distribution Parameters:
6.9.1 Several methods can be used to estimate the parameters of the extreme value distribution. Using linear regression to fit
a strai
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