ASTM_E_2283_-_08_2014.pdf

Designation:E228308(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 or,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 distribution 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.1.3 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 micrometers,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 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 Determining 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 Inclusion Assessment of SteelE1122 Practice for Obtaining JK Inclusion Ratings UsingAutomatic Image Analysis(Withdrawn 2006)3E1245 Practice for Determining the Inclusion or Second-Phase Constituent Content of Metals by Automatic ImageAnalysis3.Terminology3.1 DefinitionsFor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 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 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 plane 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 practice 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/E2283-08R14.2For 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 standard 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 States1 variable x has a two parameter(Gumbel)Extreme ValueDistribution 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 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 reducedvariate.As indicated in Eq 6,y is related to the probabilitydensity function.That is y=F(P),then from Eq 6,it followsthat:y 5 2ln2lnFy!5 2ln2lnP!(8)3.2.11 plotting positionEach of the N measured inclusionlengths can be represented as xi,where 1 i N.The data