ASTM E2283-08(2019)
(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 values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.
1.4.1 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, health, and environmental practices and determine the applicability of regulatory limitations prior to use.
1.7 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.
General Information
Relations
Standards Content (Sample)
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.
Designation: E2283 − 08 (Reapproved 2019)
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 2. Referenced Documents
2.1 ASTM Standards:
1.1 This practice describes a methodology to statistically
E3Guide for Preparation of Metallographic Specimens
characterize the distribution of the largest indigenous nonme-
E7Terminology Relating to Metallography
tallic inclusions in steel specimens based upon quantitative
E45Test Methods for Determining the Inclusion Content of
metallographic measurements. The practice is not suitable for
Steel
assessing exogenous inclusions.
E178Practice for Dealing With Outlying Observations
1.2 Based upon the statistical analysis, the nonmetallic
E456Terminology Relating to Quality and Statistics
content of different lots of steels can be compared.
E691Practice for Conducting an Interlaboratory Study to
Determine the Precision of a Test Method
1.3 This practice deals only with the recommended test
E768Guide for Preparing and Evaluating Specimens for
methods and nothing in it should be construed as defining or
Automatic Inclusion Assessment of Steel
establishing limits of acceptability.
E1122Practice for Obtaining JK Inclusion Ratings Using
1.4 The values stated in SI units are to be regarded as 3
Automatic Image Analysis (Withdrawn 2006)
standard. No other units of measurement are included in this
E1245Practice for Determining the Inclusion or Second-
standard.
Phase Constituent Content of Metals byAutomatic Image
1.4.1 For measurements obtained from light microscopy,
Analysis
linearfeatureparametersshallbereportedasmicrometers,and
3. Terminology
feature areas shall be reported as micrometers.
3.1 Definitions—For definitions of metallographic terms
1.5 Themethodologycanbeextendedtoothermaterialsand
used in this practice, refer to Terminology, E7; for statistical
to other microstructural features.
terms, refer to Terminology E456.
1.6 This standard does not purport to address all of the
3.2 Definitions of Terms Specific to This Standard:
safety concerns, if any, associated with its use. It is the
3.2.1 A—the area of each field of view used by the Image
f
responsibility of the user of this standard to establish appro-
Analysis system in performing the measurements.
priate safety, health, and environmental practices and deter-
3.2.2 A —control area; total area observed on one specimen
mine the applicability of regulatory limitations prior to use.
o
per polishing plane for the analysis. A is assumed to be 150
o
1.7 This international standard was developed in accor-
mm unless otherwise noted.
dance with internationally recognized principles on standard-
ization established in the Decision on Principles for the 3.2.3 N —number of specimens used for the evaluation. N
s s
Development of International Standards, Guides and Recom- is generally six.
mendations issued by the World Trade Organization Technical
3.2.4 N —number of planes of polish used for the
p
Barriers to Trade (TBT) Committee.
evaluation, generally four.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
This practice is under the jurisdiction of ASTM Committee E04 on Metallog- contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
raphy and is the direct responsibility of Subcommittee E04.09 on Inclusions. Standards volume information, refer to the standard’s Document Summary page on
Current edition approved Nov. 1, 2019. Published December 2019. Originally the ASTM website.
approvedin2003.Lastpreviouseditionapprovedin2014asE2283–08(2014).DOI: The last approved version of this historical standard is referenced on
10.1520/E2283-08R19. www.astm.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E2283 − 08 (2019)
i5N
3.2.5 N—number of fields observed per specimen plane of
f
H
L 5 L (10)
( i
polish. N
i51
A 3.2.13 standard deviation of longest inclusion lengths—
o
N 5 (1)
f
Sdev is the standard deviation of the set of N maximum feret
A
f
diameters of the measured longest inclusions.
3.2.6 N—total number of inclusion lengths used for the
N 0.5
analysis, generally 24.
H
Sdev 5 ~L 2 L! /~N 21! (11)
F G
( i
i51
N 5 N ·N (2)
s p
3.2.14 return period—the number of areas that must be
3.2.7 extreme value distribution—Thestatisticaldistribution
observed in order to find an inclusion equal to or larger than a
thatiscreatedbasedupononlymeasuringthelargestfeaturein
specified maximum inclusion length. Statistically, the return
a given control area or volume (1,2). The continuous random
period is defined as:
variable x has a two parameter (Gumbel) Extreme Value
Distribution if the probability density function is given by the
T 5 (12)
following equation:
1 2 P
1 x 2 λ x 2 λ
3.2.15 reference area, A —the arbitrarily selected area of
ref
f x 5 exp 2 3exp 2exp 2 (3)
~ ! F S DG F S DG
δ δ δ
150000 mm . A in conjunction with the parameters of the
ref
extreme value distribution is used to calculate the size of the
and the cumulative distribution is given by the following
largest inclusion reported by this standard. As applied to this
equation:
analysis, the largest inclusion in each control area A is
o
F~x! 5exp~2exp~2~x 2 λ!/δ!! (4)
measured.TheReturnPeriod,T,isusedtopredicthowlargean
inclusion could be expected to be found if an area A larger
As applied to this practice, x, represents the maximum ref
than A were to be evaluated. For this standard, A is 1000
feret diameter, Length, of the largest inclusion in each con- o ref
times larger than A .Thus, T is equal to 1000. By use of Eq 12
o
trol area, A , letting:
o
it would be found that this corresponds to a probability value
x 2 λ
of0.999,(99.9%).SimilarlybyusingEq6and7,thelengthof
y 5 (5)
δ
an inclusion corresponding to the 99.99% probability value
it follows that: couldbecalculated.Mathematically,anotherexpressionforthe
return period is:
F~y! 5exp~2exp~2y!! (6)
A
ref
and T 5 (13)
A
o
x 5 δ y1λ (7)
3.2.16 predicted maximum inclusion length, L —the lon-
max
3.2.8 λ—the location parameter of the extreme value distri-
gest inclusion expected to be found in area A based upon the
ref
bution function.
extreme value distribution analysis.
3.2.9 δ—the scale parameter of the extreme value distribu-
tion function. 4. Summary of Practice
3.2.10 reduced variate—Thevariable yiscalledthereduced
4.1 This practice enables the experimenter to estimate the
variate. As indicated in Eq 6, y is related to the probability
extreme value distribution of inclusions in steels.
density function. That is y = F(P), then from Eq 6, it follows
4.2 Generally, the largest oxide inclusions within the speci-
that:
mens are measured. However, the practice can be used to
y52ln 2ln F y 52ln 2ln P (8)
~ ~ ~ !!! ~ ~ !!
measure other microstructural features such as graphite nod-
3.2.11 plotting position—Each of the N measured inclusion ulesinductileiron,orcarbidesintoolsteelsandbearingsteels.
lengths can be represented as x, where 1 ≤ i ≤ N. The data The practice is based upon using the specimens described in
i
points are arranged in increasing order such that: Test Method E45. Six specimens will be required for the
analysis. For inclusion analysis, an area of 150 mm should be
x # x # x # x # x .# x
1 2 3 4 5 N
evaluated for each specimen.
Then the cumulative probability plotting position for data
point x is given by the relationship:
4.3 After obtaining the specimens, it is recommended that
i
they be prepared by following the procedures described in
i
P 5 (9)
i Methods E3 and Practice E768.
N11
4.4 The polished specimens are then evaluated by using the
The fraction ( i/(N + 1)) is the cumulative probability.
guidelinesforcompletingimageanalysisdescribedinPractices
F(y)in Eq 8 corresponds to data point x.
i i
E1122 and E1245. For this analysis, feature specific measure-
¯
3.2.12 mean longest inclusion length—L is the arithmetic
ments are required. The measured inclusion lengths shall be
average of the set of N maximum feret diameters of the
based on a minimum of eight feret diameter measurements.
measured longest inclusions.
4.5 Foreachspecimen,themaximumferetdiameterofeach
inclusion is measured. After performing the analysis for each
Theboldfacenumbersinparenthesesrefertothelistofreferencesattheendof
this standard. specimen,thelargestmaximumferetdiameterofthemeasured
E2283 − 08 (2019)
inclusions is recorded. This will result in six lengths. The system, A. For each specimen, an area of 150 mm shall be
f
procedure is repeated three more times. This will result in a evaluated.UsingEq1,thenumberoffieldsofviewrequiredto
total of 24 inclusion lengths. perform the analysis is N = A / A = 150 / A. N should be
f o f f f
rounded up to the next highest integer value; that is, if N is
f
4.6 The 24 measurements are used to estimate the values of
calculated to be 632.31, then 633 fields of view shall be
δ and λ for the extreme value distribution for the particular
examined.
material being evaluated. The largest inclusion L expected
max
to be in the reference area A is calculated, and a graphical 6.5 Image Analysis Measurements:
ref
representation of the data and test report are then prepared. 6.5.1 In this practice, feature specific parameters are mea-
sured for each individual inclusion. The measured inclusion
4.7 The reference area used for this standard is 150000
lengths shall be based on a minimum of eight feret diameters.
mm . Based upon specific producer, purchaser requirements,
6.5.2 For each field of view, focus the image either manu-
other reference areas may be used in conjunction with this
allyorautomatically,andmeasurethemaximumferetdiameter
standard.
ofeachdetectedoxideinclusion.Themeasuredferetdiameters
4.8 When required, the procedure can be repeated to evalu-
are stored in the computer’s memory for further analysis. This
atemorethanonetypeofinclusionpopulationinagivensetof 2
procedure is repeated until an area of 150 mm is analyzed.
specimens. For example, oxides and sulfides or titanium-
6.5.3 In situations where only a very few inclusions are
carbonitrides could be evaluated from the same set of speci-
contained within the inspected area, the specimen can first be
mens.
observed at low magnification, and the location of the inclu-
sionsnoted.Theobservedinclusionscanthenberemeasuredat
5. Significance and Use
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.
6.5.5 The specimens are then repolished and the procedure
suchasgearsandbearings,areoftencausedbythepresenceof
largenonmetallicoxideinclusions.Failureofacomponentcan is repeated until each specimen has been evaluated four times.
This will result in a set of 24 maximum feret diameters. For
oftenbetracedtothepresenceofalargeinclusion.Predictions
related to component fatigue life are not possible with the each repolishing step, it is recommended that at least 0.3 mm
of material be removed in order to create a new plane of
evaluations provided by standards such as Test Methods E45,
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- 6.5.7 The standard deviation, Sdev, is calculated using Eq
pose of this practice is to create a standardized method of 11.
performing this analysis.
6.6 The24measuredinclusionlengthsaresortedinascend-
5.3 This practice is not suitable for assessing the exogenous ing order. An example of the calculations is contained in
inclusions in steels and other metals because of the unpredict- Appendix X1. The inclusions are then given a ranking. The
able nature of the distribution of exogenous inclusions. Other smallest inclusion is ranked number 1, the second smallest is
methods involving complete inspection such as ultrasonics ranked number 2 etc.
must be used to locate their presence.
6.7 The probability plotting position for each inclusion is
basedupontherank.TheprobabilitiesaredeterminedusingEq
6. Procedure
9: P = i/(N + 1). Where 1 ≤ i ≤ 24, and N = 24.
i
6.1 Testspecimensareobtainedandpreparedinaccordance
6.8 A graph is created to represent the data. Plotting
with E3, E45 and E768.
positions for the ordinate are calculated from Eq 8: y =
i
6.2 The microstructural analysis is to be performed using
−ln(−ln(P)).Thevariable yinthisanalysisisreferredtoasthe
i
the types of equipment and image analysis procedures de-
Reduced Variate (Red. Var.). Typically the ordinate scale
scribed in E1122 and E1245.
ranges from −2 through +7. This corresponds to a probability
6.3 Determine the appropriate magnification to use for the range of inclusion lengths from 0.87 through 99.9%. The
analysis. For accurate measurements, the largest inclusion ordinate axis is labeled as Red. Var. It is also possible to
measured should be a minimum of 20 pixels in length. For include the Probability values on the ordinate. In this case, the
specimenscontainingrelativelylargeinclusions,objectivelens ordinatecanbelabeledProbability(%).Theabscissaislabeled
having magnifications ranging from 10 to 20× will be ad- asInclusionLength(mm);theunitsofinclusionlengthshallbe
equate. Generally, for specimens with small inclusions, an micrometers.
objective lens of 32 to 80× will be required. The same
6.9 Estimation of the Extreme Value Distribution Param-
magnification shall be used for all the specimens to be
eters:
analyzed.
6.9.1 Several methods can be used to estimate the param-
6.4 Using the appropriate calibration factors, calculate the eters of the extreme value distribution. Using linear regression
area of the field of view observed by the image analysis to fit a straight line to the plot of the Reduced Variate as a
...
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