1、Designation: E2283 08 (Reapproved 2014)Standard Practice forExtreme Value Analysis of Nonmetallic Inclusions in Steeland Other Microstructural Features1This standard is issued under the fixed designation E2283; the number immediately following the designation indicates the year oforiginal adoption o
2、r, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope1.1 This practice describes a methodology to statisticallycharacterize the distrib
3、ution of the largest indigenous nonme-tallic inclusions in steel specimens based upon quantitativemetallographic measurements. The practice is not suitable forassessing exogenous inclusions.1.2 Based upon the statistical analysis, the nonmetalliccontent of different lots of steels can be compared.1.
4、3 This practice deals only with the recommended testmethods and nothing in it should be construed as defining orestablishing limits of acceptability.1.4 The measured values are stated in SI units. For mea-surements obtained from light microscopy, linear feature pa-rameters shall be reported as micro
5、meters, and feature areasshall be reported as micrometers.1.5 The methodology can be extended to other materials andto other microstructural features.1.6 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this
6、standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2E3 Guide for Preparation of Metallographic SpecimensE7 Terminology Relating to MetallographyE45 Test Methods for Determini
7、ng the Inclusion Content ofSteelE178 Practice for Dealing With Outlying ObservationsE456 Terminology Relating to Quality and StatisticsE691 Practice for Conducting an Interlaboratory Study toDetermine the Precision of a Test MethodE768 Guide for Preparing and Evaluating Specimens forAutomatic Inclus
8、ion Assessment of SteelE1122 Practice for Obtaining JK Inclusion Ratings UsingAutomatic Image Analysis (Withdrawn 2006)3E1245 Practice for Determining the Inclusion or Second-Phase Constituent Content of Metals by Automatic ImageAnalysis3. Terminology3.1 DefinitionsFor definitions of metallographic
9、termsused in this practice, refer to Terminology, E7; for statisticalterms, refer to Terminology E456.3.2 Definitions of Terms Specific to This Standard:3.2.1 Af the area of each field of view used by the ImageAnalysis system in performing the measurements.3.2.2 Ao control area; total area observed
10、on one specimenper polishing plane for the analysis. Aois assumed to be 150mm2unless otherwise noted.3.2.3 Ns number of specimens used for the evaluation. Nsis generally six.3.2.4 Np number of planes of polish used for theevaluation, generally four.3.2.5 Nf number of fields observed per specimen pla
11、ne ofpolish.Nf5AoAf(1)3.2.6 Ntotal number of inclusion lengths used for theanalysis, generally 24.N 5 NsNp(2)3.2.7 extreme value distributionThe statistical distributionthat is created based upon only measuring the largest feature ina given control area or volume (1,2).4The continuous random1This pr
12、actice is under the jurisdiction of ASTM Committee E04 on Metallog-raphy and is the direct responsibility of Subcommittee E04.09 on Inclusions.Current edition approved Oct. 1, 2014. Published December 2014. Originallyapproved in 2003 last previous edition approved in 2008 as E228308. DOI:10.1520/E22
13、83-08R14.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.3The last approved version of this historical standa
14、rd is referenced onwww.astm.org.4The boldface numbers in parentheses refer to the list of references at the end ofthis standard.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1variable x has a two parameter (Gumbel) Extreme ValueDistr
15、ibution if the probability density function is given by thefollowing equation:fx! 51FexpS2x 2 DG3expF2expS2x 2 DG(3)and the cumulative distribution is given by the followingequation:Fx! 5 exp2exp2x 2 !/! (4)As applied to this practice, x, represents the maximumferet diameter, Length, of the largest
16、inclusion in each con-trol area, Ao, letting:y 5x 2 (5)it follows that:Fy! 5 exp2exp2y! (6)andx 5 y1 (7)3.2.8 the location parameter of the extreme value distri-bution function.3.2.9 the scale parameter of the extreme value distribu-tion function.3.2.10 reduced variateThe variable y is called the re
17、ducedvariate. As indicated in Eq 6, y is related to the probabilitydensity function. That is y = F(P), then from Eq 6, it followsthat:y 52ln2lnFy! 52ln2lnP! (8)3.2.11 plotting positionEach of the N measured inclusionlengths can be represented as xi, where 1 i N. The datapoints are arranged in increa
18、sing order such that:x1# x2# x3# x4# x5.# xNThen the cumulative probability plotting position for datapoint xiis given by the relationship:Pi5iN11(9)The fraction ( i /(N + 1) is the cumulative probability.F(yi)inEq 8 corresponds to data point xi.3.2.12 mean longest inclusion lengthLis the arithmetic
19、average of the set of N maximum feret diameters of themeasured longest inclusions.LH51N(i51i5NLi(10)3.2.13 standard deviation of longest inclusion lengthsSdev is the standard deviation of the set of N maximum feretdiameters of the measured longest inclusions.Sdev 5F(i51NLi2 LH!2/N 2 1!G0.5(11)3.2.14
20、 return periodthe number of areas that must beobserved in order to find an inclusion equal to or larger than aspecified maximum inclusion length. Statistically, the returnperiod is defined as:T 511 2 P(12)3.2.15 reference area, Arefthe arbitrarily selected area of150 000 mm2. Arefin conjunction with
21、 the parameters of theextreme value distribution is used to calculate the size of thelargest inclusion reported by this standard. As applied to thisanalysis, the largest inclusion in each control area Aoismeasured. The Return Period, T, is used to predict how large aninclusion could be expected to b
22、e found if an area Areflargerthan Aowere to be evaluated. For this standard, Arefis 1000times larger than Ao. Thus, T is equal to 1000. By use of Eq 12it would be found that this corresponds to a probability valueof 0.999, (99.9 %). Similarly by using Eq 6 and 7, the length ofan inclusion correspond
23、ing to the 99.99 % probability valuecould be calculated. Mathematically, another expression for thereturn period is:T 5ArefAo(13)3.2.16 predicted maximum inclusion length, Lmaxthe lon-gest inclusion expected to be found in area Arefbased upon theextreme value distribution analysis.4. Summary of Prac
24、tice4.1 This practice enables the experimenter to estimate theextreme value distribution of inclusions in steels.4.2 Generally, the largest oxide inclusions within the speci-mens are measured. However, the practice can be used tomeasure other microstructural features such as graphite nod-ules in duc
25、tile iron, or carbides in tool steels and bearing steels.The practice is based upon using the specimens described inTest Method E45. Six specimens will be required for theanalysis. For inclusion analysis, an area of 150 mm2should beevaluated for each specimen.4.3 After obtaining the specimens, it is
26、 recommended thatthey be prepared by following the procedures described inMethods E3 and Practice E768.4.4 The polished specimens are then evaluated by using theguidelines for completing image analysis described in PracticesE1122 and E1245. For this analysis, feature specific measure-ments are requi
27、red. The measured inclusion lengths shall bebased on a minimum of eight feret diameter measurements.4.5 For each specimen, the maximum feret diameter of eachinclusion is measured. After performing the analysis for eachspecimen, the largest maximum feret diameter of the measuredinclusions is recorded
28、. This will result in six lengths. Theprocedure is repeated three more times. This will result in atotal of 24 inclusion lengths.4.6 The 24 measurements are used to estimate the values of and for the extreme value distribution for the particularmaterial being evaluated. The largest inclusion Lmaxexp
29、ectedto be in the reference area Arefis calculated, and a graphicalrepresentation of the data and test report are then prepared.4.7 The reference area used for this standard is 150 000mm2. Based upon specific producer, purchaser requirements,other reference areas may be used in conjunction with this
30、standard.E2283 08 (2014)24.8 When required, the procedure can be repeated to evalu-ate more than one type of inclusion population in a given set ofspecimens. For example, oxides and sulfides or titanium-carbonitrides could be evaluated from the same set of speci-mens.5. Significance and Use5.1 This
31、practice is used to assess the indigenous inclusionsor second-phase constituents in metals using extreme valuestatistics.5.2 It is well known that failures of mechanical components,such as gears and bearings, are often caused by the presence oflarge nonmetallic oxide inclusions. Failure of a compone
32、nt canoften be traced to the presence of a large inclusion. Predictionsrelated to component fatigue life are not possible with theevaluations provided by standards such as Test Methods E45,Practice E1122, or Practice E1245. The use of extreme valuestatistics has been related to component life and in
33、clusion sizedistributions by several different investigators (3-8). The pur-pose of this practice is to create a standardized method ofperforming this analysis.5.3 This practice is not suitable for assessing the exogenousinclusions in steels and other metals because of the unpredict-able nature of t
34、he distribution of exogenous inclusions. Othermethods involving complete inspection such as ultrasonicsmust be used to locate their presence.6. Procedure6.1 Test specimens are obtained and prepared in accordancewith E3, E45 and E768.6.2 The microstructural analysis is to be performed usingthe types
35、of equipment and image analysis procedures de-scribed in E1122 and E1245.6.3 Determine the appropriate magnification to use for theanalysis. For accurate measurements, the largest inclusionmeasured should be a minimum of 20 pixels in length. Forspecimens containing relatively large inclusions, objec
36、tive lenshaving magnifications ranging from 10 to 20 will be ad-equate. Generally, for specimens with small inclusions, anobjective lens of 32 to 80 will be required. The samemagnification shall be used for all the specimens to beanalyzed.6.4 Using the appropriate calibration factors, calculate thea
37、rea of the field of view observed by the image analysissystem, Af. For each specimen, an area of 150 mm2shall beevaluated. Using Eq 1, the number of fields of view required toperform the analysis is Nf= Ao/ Af= 150 / Af. Nfshould berounded up to the next highest integer value; that is, if Nfiscalcul
38、ated to be 632.31, then 633 fields of view shall beexamined.6.5 Image Analysis Measurements:6.5.1 In this practice, feature specific parameters are mea-sured for each individual inclusion. The measured inclusionlengths shall be based on a minimum of eight feret diameters.6.5.2 For each field of view
39、, focus the image either manu-ally or automatically, and measure the maximum feret diameterof each detected oxide inclusion. The measured feret diametersare stored in the computers memory for further analysis. Thisprocedure is repeated until an area of 150 mm2is analyzed.6.5.3 In situations where on
40、ly a very few inclusions arecontained within the inspected area, the specimen can first beobserved at low magnification, and the location of the inclu-sions noted. The observed inclusions can then be remeasured athigh magnification.6.5.4 After the specimen is analyzed, using the accumulateddata, the
41、 maximum feret diameter of the largest measuredinclusion in the 150 mm2area is recorded. This procedure isrepeated for each of the other five specimens.6.5.5 The specimens are then repolished and the procedureis repeated until each specimen has been evaluated four times.This will result in a set of
42、24 maximum feret diameters. Foreach repolishing step, it is recommended that at least 0.3 mmof material be removed in order to create a new plane ofobservation.6.5.6 The mean length, L, is then calculated using Eq 10.6.5.7 The standard deviation, Sdev, is calculated using Eq11.6.6 The 24 measured in
43、clusion lengths are sorted in ascend-ing order. An example of the calculations is contained inAppendix X1. The inclusions are then given a ranking. Thesmallest inclusion is ranked number 1, the second smallest isranked number 2 etc.6.7 The probability plotting position for each inclusion isbased upo
44、n the rank. The probabilities are determined using Eq9: Pi= i /(N + 1). Where 1 i 24, and N = 24.6.8 A graph is created to represent the data. Plottingpositions for the ordinate are calculated from Eq 8: yi=ln(ln(Pi). The variable y in this analysis is referred to as theReduced Variate (Red. Var.).
45、Typically the ordinate scaleranges from 2 through +7. This corresponds to a probabilityrange of inclusion lengths from 0.87 through 99.9 %. Theordinate axis is labeled as Red. Var. It is also possible toinclude the Probability values on the ordinate. In this case, theordinate can be labeled Probabil
46、ity (%). The abscissa is labeledas Inclusion Length (mm); the units of inclusion length shall bemicrometers.6.9 Estimation of the Extreme Value Distribution Param-eters:6.9.1 Several methods can be used to estimate the param-eters of the extreme value distribution. Using linear regressionto fit a st
47、raight line to the plot of the Reduced Variate as afunction of inclusion length is the easiest method; however, itis the least precise. This is because the larger values of theinclusion lengths are more heavily weighted than the smallerinclusion lengths. Two other methods for estimating theparameter
48、s are the method of moments (mom), and the methodof maximum likelihood (ML). The method of moments is veryeasy to calculate, but the method of maximum likelihood givesestimates that are more precise. While both methods will bedescribed, the maximum likelihood method shall be used tocalculate the rep
49、orted values of and for this standard. (Sincethe ML solution is obtained by numerical analysis, the valuesE2283 08 (2014)3of and obtained by the method of moments are goodguesses for starting the ML analysis.)6.9.2 Moments MethodIt has been shown that the param-eters for the Gumbel distribution, can be represented by:mom5Sdev =6(14)andmom5 LH2 0.5772mom(15)where the subscript mom indicates the estimates are basedon the moment method.6.9.3 Maximum Likelihood MethodThis method is basedon the appro
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