ASTM E2283-03

Standard Practice for Extreme Value Analysis of Nonmetallic Inclusions in Steel and Other Microstructural Features

SIGNIFICANCE AND USE
This practice is used to assess the indigenous inclusions or second-phase constituents in metals using extreme value statistics.
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 E 45, Practice E 1122, or Practice E 1245. 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.
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.

General Information

• Status: Historical
• Publication Date: 31-Oct-2003
• ICS: 77.040.99 - Other methods of testing of metals
• Technical Committee: E04 - Metallography
• Drafting Committee: E04.09 - Inclusions

Relations

• Replaced By: ASTM E2283-07 - Standard Practice for Extreme Value Analysis of Nonmetallic Inclusions in Steel and Other Microstructural Features
• Effective Date: 15-Dec-2007
• Referred By: ASTM A1089/A1089M-14(2020) - Standard Specification for Highly Loaded Anti-Friction Bearing Steel
• Effective Date: 01-Nov-2003

Standards Content (Sample)

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:E2283–03
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 (e) indicates an editorial change since the last revision or reapproval.
1. Scope E1122 Practice for Obtaining JK Inclusion Ratings Using
Automatic Image Analysis
1.1 This practice describes a methodology to statistically
E1245 Practice for Determining the Inclusion Content or
characterize the distribution of the largest indigenous nonme-
Second-Phase Constituent of Metals by Automatic Image
tallic inclusions in steel specimens based upon quantitative
Analysis
metallographic measurements. The practice is not suitable for
assessing exogenous inclusions.
3. Terminology
1.2 Based upon the statistical analysis, the nonmetallic
3.1 Definitions—For definitions of metallographic terms
content of different lots of steels can be compared.
used in this practice, refer to Terminology, E7; for statistical
1.3 This practice deals only with the recommended test
terms, refer to Terminology E456.
methods and nothing in it should be construed as defining or
3.2 Definitions of Terms Specific to This Standard:
establishing limits of acceptability.
3.2.1 A—the area of each field of view used by the Image
f
1.4 The measured values are stated in SI units. For mea-
Analysis system in performing the measurements.
surements obtained from light microscopy, linear feature pa-
3.2.2 A —controlarea;totalareaobservedononespecimen
o
rameters shall be reported as micrometers, and feature areas
per polishing plane for the analysis. A is assumed to be 150
o
shall be reported as micrometers.
mm unless otherwise noted.
1.5 Themethodologycanbeextendedtoothermaterialsand
3.2.3 N —number of specimens used for the evaluation. N
s s
to other microstructural features.
is generally six.
1.6 This standard does not purport to address all of the
3.2.4 N —number of planes of polish used for the evalua-
p
safety concerns, if any, associated with its use. It is the
tion, generally four.
responsibility of the user of this standard to establish appro-
3.2.5 N—number of fields observed per specimen plane of
f
priate safety and health practices and determine the applica-
polish.
bility of regulatory limitations prior to use.
A
o
N 5 (1)
2. Referenced Documents f
A
f
2.1 ASTM Standards:
3.2.6 N—total number of inclusion lengths used for the
E3 Methods of Preparation of Metallographic Specimens
analysis, generally 24.
E7 Terminology Relating to Metallography
N 5 N · N (2)
s p
E45 Test Methods for Determining the Inclusion Content
3.2.7 extreme value distribution—The statistical distribu-
of Steel
tion that is created based upon only measuring the largest
E178 Practice for Dealing with Outlying Observations
feature in a given control area or volume (1,2). The continu-
E456 Terminology Relating to Quality and Statistics
ous random variable x has a two parameter (Gumbel) Extreme
E768 Practice for Preparing and Evaluating Specimens for
Value Distribution if the probability density function is given
Automatic Inclusion Assessment of Steel
by the following equation:
E883 Guide for Reflected-Light Photomicrography
1 x2l x2l
f~x! 5 exp 2 3exp 2exp 2 (3)
F S DG F S DG
d d d
This practice is under the jurisdiction of ASTM Committee E04 on Metallog-
and the cumulative distribution is given by the following
raphy and is the direct responsibility of Subcommittee E04.09 on Inclusions.
equation:
Current edition approved Nov. 1. 2003. Published December 2003.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
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.
E2283–03
F~x! 5exp~2exp~2~x2l!/ d!! (4) times larger than A .Thus, T is equal to 1000. By use of Eq 12
o
it would be found that this corresponds to a probability value
As applied to this practice, x, represents the maximum feret
of0.999,(99.9%).SimilarlybyusingEq6and7,thelengthof
diameter, Length, of the largest inclusion in each control area,
an inclusion corresponding to the 99.99% probability value
A , letting:
o
couldbecalculated.Mathematically,anotherexpressionforthe
x2l
return period is:
y 5 (5)
d
A
ref
it follows that:
T 5 (13)
A
o
F~y! 5exp~2exp~2y!! (6)
3.2.16 predicted maximum inclusion length, L —the
max
and
longest inclusion expected to be found in area A based upon
ref
the extreme value distribution analysis.
x5d y1l (7)
3.2.8 l—the location parameter of the extreme value distri-
4. Summary of Practice
bution function.
4.1 This practice enables the experimenter to estimate the
3.2.9 d—the scale parameter of the extreme value distribu-
extreme value distribution of inclusions in steels.
tion function.
4.2 Generally, the largest oxide inclusions within the speci-
3.2.10 reduced variate—Thevariable yiscalledthereduced
mens are measured. However, the practice can be used to
variate. As indicated in Eq 6, y is related to the probability
measure other microstructural features such as graphite nod-
density function. That is y = F (P), then from Eq 6, it follows
ulesinductileiron,orcarbidesintoolsteelsandbearingsteels.
that:
The practice is based upon using the specimens described in
y52ln~2ln~F~y!!!52ln~2ln~P!! (8)
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
evaluated for each specimen.
i
points are arranged in increasing order such that:
4.3 After obtaining the specimens, it is recommended that
x # x # x # x # x .# x they be prepared by following the procedures described in
1 2 3 4 5 N
Methods E3 and Practice E768.
Then the cumulative probability plotting position for data
4.4 The polished specimens are then evaluated by using the
point x is given by the relationship:
i
guidelinesforcompletingimageanalysisdescribedinPractices
i
E1122andE1245.Forthisanalysis,featurespecificmeasure-
P 5 (9)
i
N 11
ments are required. The measured inclusion lengths shall be
Thefraction( i/(N+1))isthecumulativeprobability. F(y)
based on a minimum of eight feret diameter measurements.
i
in Eq 8 corresponds to data point x.
4.5 Foreachspecimen,themaximumferetdiameterofeach
i
–
inclusion is measured. After performing the analysis for each
3.2.12 mean longest inclusion length—L is the arithmetic
specimen,thelargestmaximumferetdiameterofthemeasured
average of the set of N maximum feret diameters of the
inclusions is recorded. This will result in six lengths. The
measured longest inclusions.
procedure is repeated three more times. This will result in a
i5N
–
total of 24 inclusion lengths.
L 5 L (10)
( i
N
i51
4.6 The 24 measurements are used to estimate the values of
3.2.13 standard deviation of longest inclusion lengths— d and l for the extreme value distribution for the particular
Sdev is the standard deviation of the set of N maximum feret
material being evaluated. The largest inclusion L expected
max
diameters of the measured longest inclusions. to be in the reference area A is calculated, and a graphical
ref
representation of the data and test report are then prepared.
N
–
2 0.5
Sdev 5 @ ~L 2 L! / ~N 21!# (11)
( 4.7 The reference area used for this standard is 150000
i
i51
mm . Based upon specific producer, purchaser requirements,
3.2.14 return period—the number of areas that must be
other reference areas may be used in conjunction with this
observed in order to find an inclusion equal to or larger than a
standard.
specified maximum inclusion length. Statistically, the return
4.8 When required, the procedure can be repeated to evalu-
period is defined as:
atemorethanonetypeofinclusionpopulationinagivensetof
specimens. For example, oxides and sulfides or titanium-
T 5 (12)
1 2 P
carbonitrides could be evaluated from the same set of speci-
mens.
3.2.15 reference area, A —the arbitrarily selected area of
ref
150000 mm . A in conjunction with the parameters of the
ref
5. Significance and Use
extreme value distribution is used to calculate the size of the
largest inclusion reported by this standard. As applied to this 5.1 This practice is used to assess the indigenous inclusions
analysis, the largest inclusion in each control area A is or second-phase constituents in metals using extreme value
o
measured.TheReturnPeriod, T,isusedtopredicthowlargean statistics.
inclusion could be expected to be found if an area A larger 5.2 Itiswellknownthatfailuresofmechanicalcomponents,
ref
than A were to be evaluated. For this standard, A is 1000 suchasgearsandbearings,areoftencausedbythepresenceof
o ref
E2283–03
largenonmetallicoxideinclusions.Failureofacomponentcan each repolishing step, it is recommended that at least 0.3 mm
oftenbetracedtothepresenceofalargeinclusion.Predictions of material be removed in order to create a new plane of
related to component fatigue life are not possible with the observation.
–
evaluations provided by standards such as Test Methods E45,
6.5.6 The mean length, L, is then calculated using Eq 10.
Practice E1122, or Practice E1245. The use of extreme value
6.5.7 The standard deviation, Sdev, is calculated using Eq
statistics has been related to component life and inclusion size
11.
distributions by several different investigators (3-8). The pur-
6.6 The24measuredinclusionlengthsaresortedinascend-
pose of this practice is to create a standardized method of
ing order. An example of the calculations is contained in
performing this analysis.
Appendix X1. The inclusions are then given a ranking. The
5.3 This practice is not suitable for assessing the exogenous
smallest inclusion is ranked number 1, the second smallest is
inclusions in steels and other metals because of the unpredict-
ranked number 2 etc.
able nature of the distribution of exogenous inclusions. Other
6.7 The probability plotting position for each inclusion is
methods involving complete inspection such as ultrasonics
basedupontherank.TheprobabilitiesaredeterminedusingEq
must be used to locate their presence.
9: P = i/(N + 1). Where 1# i# 24, and N = 24.
i
6. Procedure
6.8 A graph is created to represent the data. Plotting
positions for the ordinate are calculated from Eq 8: y =
6.1 Testspecimensareobtainedandpreparedinaccordance
i
−ln(−ln(P)).Thevariable yinthisanalysisisreferredtoasthe
with E3, E45 and E768.
i
Reduced Variate (Red. Var.). Typically the ordinate scale
6.2 The microstructural analysis is to be performed using
ranges from −2 through +7. This corresponds to a probability
the types of equipment and image analysis procedures de-
range of inclusion lengths from 0.87 through 99.9%. The
scribed in E1122 and E1245.
ordinate axis is labeled as Red. Var. It is also possible to
6.3 Determine the appropriate magnification to use for the
include the Probability values on the ordinate. In this case, the
analysis. For accurate measurements, the largest inclusion
ordinatecanbelabeledProbability(%).Theabscissaislabeled
measured should be a minimum of 20 pixels in length. For
asInclusionLength(mm);theunitsofinclusionlengthshallbe
specimenscontainingrelativelylargeinclusions,objectivelens
micrometers.
having magnifications ranging from 10 to 203 will be ad-
equate. Generally, for specimens with small inclusions, an 6.9 Estimation of the Extreme Value Distribution Param-
objective lens of 32 to 803 will be required. The same eters:
magnification shall be used for all the specimens to be 6.9.1 Several methods can be used to estimate the param-
analyzed.
eters of the extreme value distribution. Using linear regression
6.4 Using the appropriate calibration factors, calculate the to fit a straight line to the plot of the Reduced Variate as a
area of the field of view observed by the image analysis
function of inclusion length is the easiest method; however, it
system, A. For each specimen, an area of 150 mm shall be is the least precise. This is because the larger values of the
f
evaluated.UsingEq1,thenumberoffieldsofviewrequiredto
inclusion lengths are more heavily weighted than the smaller
perform the analysis is N = A / A = 150 / A. N should be inclusion lengths. Two other methods for estimating the
f o f f f
rounded up to the next highest integer value; that is, if N is
parametersarethemethodofmoments(mom),andthemethod
f
calculated to be 632.31, then 633 fields of view shall be of maximum likelihood (ML).The method of moments is very
examined.
easytocalculate,butthemethodofmaximumlikelihoodgives
6.5 Image Analysis Measurements: estimates that are more precise. While both methods will be
6.5.1 In this practice, feature specific parameters are mea-
described, the maximum likelihood method shall be used to
sured for each individual inclusion. The measured inclusion calculate the reported values of d and l for this standard.
lengths shall be based on a minimum of eight feret diameters.
(Since the ML solution is obtained by numerical analysis, the
6.5.2 For each field of view, focus the image either manu- valuesof dand lobtainedbythemethodofmomentsaregood
allyorautomatically,andmeasurethemaximumferetdiameter
guesses for starting the ML analysis.)
ofeachdetectedoxideinclusion.Themeasuredferetdiameters
6.9.2 Moments Method—It has been shown that the param-
are stored in the computer’s memory for further analysis. This
eters for the Gumbel distribution, can be represented by:
procedure is repeated until an area of 150 mm is analyzed.
Sdev 6
=
6.5.3 In situations where only a very few inclusions are
d 5 (14)
mom
p
contained within the inspected area, the specimen can first be
and
observed at low magnification, and the location of the inclu-
sionsnoted.Theobservedinclusionscanthenberemeasuredat
–
l 5 L 20.5772· d (15)
mom mom
high magnification.
where the subscript mom indicates the estimates are based
6.5.4 Afterthespecimenisanalyzed,usingtheaccumulated
on the moment method.
data, the maximum feret diameter of the largest measured
inclusion in the 150 mm area is recorded. This procedure is 6.9.3 Maximum Likelihood Method—This method is based
repeated for each of the other five specimens. on the approach that the best values for the parameters d and l
6.5.5 The specime
...