Designation: E112 − 13Standard Test Methods forDetermining Average Grain Size1This standard is issued under the fixed designation E112; 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.This standard has been approved for use by agencies of the U.S. Department of Defense.INTRODUCTIONThese test methods of determination of average grain size in metallic materials are primarilymeasuring procedures and, because of their purely geometric basis, are independent of the metal oralloy concerned. In fact, the basic procedures may also be used for the estimation of average grain,crystal, or cell size in nonmetallic materials. The comparison method may be used if the structure ofthe material approaches the appearance of one of the standard comparison charts. The intercept andplanimetric methods are always applicable for determining average grain size. However, thecomparison charts cannot be used for measurement of individual grains.1. Scope1.1 These test methods cover the measurement of averagegrain size and include the comparison procedure, the planim-etric (or Jeffries) procedure, and the intercept procedures.These test methods may also be applied to nonmetallicmaterials with structures having appearances similar to those ofthe metallic structures shown in the comparison charts. Thesetest methods apply chiefly to single phase grain structures butthey can be applied to determine the average size of a particulartype of grain structure in a multiphase or multiconstituentspecimen.1.2 These test methods are used to determine the averagegrain size of specimens with a unimodal distribution of grainareas, diameters, or intercept lengths. These distributions areapproximately log normal. These test methods do not covermethods to characterize the nature of these distributions.Characterization of grain size in specimens with duplex grainsize distributions is described in Test Methods E1181. Mea-surement of individual, very coarse grains in a fine grainedmatrix is described in Test Methods E930.1.3 These test methods deal only with determination ofplanar grain size, that is, characterization of the two-dimensional grain sections revealed by the sectioning plane.Determination of spatial grain size, that is, measurement of thesize of the three-dimensional grains in the specimen volume, isbeyond the scope of these test methods.1.4 These test methods describe techniques performedmanually using either a standard series of graded chart imagesfor the comparison method or simple templates for the manualcounting methods. Utilization of semi-automatic digitizingtablets or automatic image analyzers to measure grain size isdescribed in Test Methods E1382.1.5 These test methods deal only with the recommended testmethods and nothing in them should be construed as definingor establishing limits of acceptability or fitness of purpose ofthe materials tested.1.6 The measured values are stated in SI units, which areregarded as standard. Equivalent inch-pound values, whenlisted, are in parentheses and may be approximate.1.7 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.1.8 The paragraphs appear in the following order:Section NumberScope 1Referenced Documents 2Terminology 3Significance and Use 4Generalities of Application 5Sampling 6Test Specimens 7Calibration 8Preparation of Photomicrographs 9Comparison Procedure 10Planimetric (Jeffries) Procedure 11General Intercept Procedures 12Heyn Linear Intercept Procedure 13Circular Intercept Procedures 14Hilliard Single-Circle Procedure 14.21These test methods are under the jurisdiction of ASTM Committee E04 onMetallography and are the direct responsibility of Subcommittee E04.08 on GrainSize.Current edition approved Oct. 1, 2013. Published February 2014. Originallyapproved in 1955. Last previous edition approved 2012 as E112 – 12. DOI:10.1520/E0112-13.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1Copyright ASTM International Provided by IHS under license with ASTM Licensee=University of Alberta/5966844001, User=sharabiani, shahramfsNot for Resale, 03/14/2014 11:10:37 MDTNo reproduction or networking permitted without license from IHS--`,,,,`,`````,,`,,`,,`,`,,,```,-`-`,,`,,`,`,,`---Abrams Three-Circle Procedure 14.3Statistical Analysis 15Specimens with Non-equiaxed Grain Shapes 16Specimens Containing Two or More Phases or Constituents 17Report 18Precision and Bias 19Keywords 20Annexes:Basis of ASTM Grain Size Numbers AnnexA1Equations for Conversions Among Various Grain Size Measurements AnnexA2Austenite Grain Size, Ferritic and Austenitic Steels AnnexA3Fracture Grain Size Method AnnexA4Requirements for Wrought Copper and Copper-Base Alloys AnnexA5Application to Special Situations AnnexA6Appendixes:Results of Interlaboratory Grain Size Determinations AppendixX1Referenced Adjuncts AppendixX22. Referenced Documents2.1 ASTM Standards:2E3 Guide for Preparation of Metallographic SpecimensE7 Terminology Relating to MetallographyE407 Practice for Microetching Metals and AlloysE562 Test Method for Determining Volume Fraction bySystematic Manual Point CountE691 Practice for Conducting an Interlaboratory Study toDetermine the Precision of a Test MethodE883 Guide for Reflected–Light PhotomicrographyE930 Test Methods for Estimating the Largest Grain Ob-served in a Metallographic Section (ALA Grain Size)E1181 Test Methods for Characterizing Duplex Grain SizesE1382 Test Methods for Determining Average Grain SizeUsing Semiautomatic and Automatic Image Analysis2.2 ASTM Adjuncts:2.2.1 For a complete adjunct list, see Appendix X23. Terminology3.1 Definitions—For definitions of terms used in these testmethods, see Terminology E7.3.2 Definitions of Terms Specific to This Standard:3.2.1 ASTM grain size number—the ASTM grain sizenumber, G, was originally defined as:NAE5 2G21(1)where NAEis the number of grains per square inch at100X magnification. To obtain the number per square milli-metre at 1X, multiply by 15.50.3.2.2 grain—an individual crystal with the same atomicconfiguration throughout in a polycrystalline material; thegrain may or may not contain twinned regions within it orsub-grains.3.2.3 grain boundary—a very narrow region in a polycrys-talline material corresponding to the transition from onecrystallographic orientation to another, thus separating oneadjacent grain from another; on a two-dimensional planethrough three-dimensional polycrystalline materials, the grainedges between adjacent grains surrounding a single grain makeup the outline of the two-dimensional grains that are observedin the light microscope and are measured or counted by theprocedures in this test method.3.2.4 grain boundary intersection count, P—determinationof the number of times a test line cuts across, or is tangent to(tangent hits are counted as one (1) intersection) grain bound-aries (triple point intersections are considered as 1-1⁄2 intersec-tions).3.2.5 grain intercept count, N—determination of the numberof times a test line cuts through individual grains on the planeof polish (tangent hits are considered as one half an intercep-tion; test lines that end within a grain are considered as one halfan interception).3.2.6 intercept length—the distance between two opposed,adjacent grain boundary intersection points on a test linesegment that crosses the grain at any location due to randomplacement of the test line.3.3 Symbols:α = matrix grains in a two phase (constituent)microstructure.A = test area.A¯= mean grain cross sectional area.AIℓ= grain elongation ratio or anisotropy index for alongitudinally oriented plane.d¯= mean planar grain diameter (Plate III).D¯= mean spatial (volumetric) grain diameter.f = Jeffries multiplier for planimetric method.G = ASTM grain size number.ℓ¯= mean lineal intercept length.ℓ¯α= mean lineal intercept length of the α matrixphase in a two phase (constituent) microstruc-ture.ℓ¯ℓ= mean lineal intercept length on a longitudi-nally oriented surface for a non-equiaxedgrain structure.ℓ¯t= mean lineal intercept length on a transverselyoriented surface for a non-equiaxed grainstructure.ℓ¯p= mean lineal intercept length on a planar ori-ented surface for a non-equiaxed grain struc-ture.ℓ0= base intercept length of 32.00 mm for definingthe relationship between G and ℓ (and NL) formacroscopically or microscopically deter-mined grain size by the intercept method.L = length of a test line.M = magnification used.Mb= magnification used by a chart picture series.n = number of fields measured.Nα= number of α grains intercepted by the test linein a two phase (constituent) microstructure.NA= number of grains per mm2at 1X.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at

[email protected] For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.E112 − 132Copyright ASTM International Provided by IHS under license with ASTM Licensee=University of Alberta/5966844001, User=sharabiani, shahramfsNot for Resale, 03/14/2014 11:10:37 MDTNo reproduction or networking permitted without license from IHS--`,,,,`,`````,,`,,`,,`,`,,,```,-`-`,,`,,`,`,,`---NAα= number of α grains per mm2at 1X in a twophase (constituent) microstructure.NAE= number of grains per inch2at 100X.NAℓ= NAon a longitudinally oriented surface for anon-equiaxed grain structure.NAt= NAon a transversely oriented surface for anon-equiaxed grain structure.NAp= NAon a planar oriented surface for a non-equiaxed grain structure.NI= number of intercepts with a test line.NInside= number of grains completely within a testcircle.NIntercepted= number of grains intercepted by the test circle.NL= number of intercepts per unit length of testline.NLℓ= NLon a longitudinally oriented surface for anon-equiaxed grain structure.NLt= NLon a transversely oriented surface for anon-equiaxed grain structure.NLp= NLon a planar oriented surface for a non-equiaxed grain structure.PI= number of grain boundary intersections with atest line.PL= number of grain boundary intersections perunit length of test line.PLℓ= PLon a longitudinally oriented surface for anon-equiaxed grain structure.PLt= PLon a transversely oriented surface for anon-equiaxed grain structure.PLp= PLon a planar oriented surface for a non-equiaxed grain structure.Q = correction factor for comparison chart ratingsusing a non-standard magnification for micro-scopically determined grain sizes.Qm= correction factor for comparison chart ratingsusing a non-standard magnification for mac-roscopically determined grain sizes.s = standard deviation.SV= grain boundary surface area to volume ratiofor a single phase structure.SVα= grain boundary surface area to volume ratiofor a two phase (constituent) structure.t = students’ t multiplier for determination of theconfidence interval.VVα= volume fraction of the α phase in a two phase(constituent) microstructure.95 %CI = 95 % confidence interval.%RA = percent relative accuracy.4. Significance and Use4.1 These test methods cover procedures for estimating andrules for expressing the average grain size of all metalsconsisting entirely, or principally, of a single phase. The grainsize of specimens with two phases, or a phase and aconstituent, can be measured using a combination of twomethods, a measurement of the volume fraction of the phaseand an intercept or planimetric count (see Section 17). The testmethods may also be used for any structures having appear-ances similar to those of the metallic structures shown in thecomparison charts. The three basic procedures for grain sizeestimation are:4.1.1 Comparison Procedure—The comparison proceduredoes not require counting of either grains, intercepts, orintersections but, as the name suggests, involves comparison ofthe grain structure to a series of graded images, either in theform of a wall chart, clear plastic overlays, or an eyepiecereticle. There appears to be a general bias in that comparisongrain size ratings claim that the grain size is somewhat coarser(1⁄2 to 1 G number lower) than it actually is (see X1.3.5).Repeatability and reproducibility of comparison chart ratingsare generally 61 grain size number.4.1.2 Planimetric Procedure—The planimetric method in-volves an actual count of the number of grains within a knownarea. The number of grains per unit area, NA, is used todetermine the ASTM grain size number, G. The precision ofthe method is a function of the number of grains counted. Aprecision of 60.25 grain size units can be attained with areasonable amount of effort. Results are free of bias andrepeatability and reproducibility are less than 60.5 grain sizeunits. An accurate count does require marking off of the grainsas they are counted.4.1.3 Intercept Procedure—The intercept method involvesan actual count of the number of grains intercepted by a testline or the number of grain boundary intersections with a testline, per unit length of test line, used to calculate the meanlineal intercept length, ℓ¯. ℓ¯is used to determine the ASTMgrain size number, G. The precision of the method is a functionof the number of intercepts or intersections counted. A preci-sion of better than 60.25 grain size units can be attained witha reasonable amount of effort. Results are free of bias;repeatability and reproducibility are less than 60.5 grain sizeunits. Because an accurate count can be made without need ofmarking off intercepts or intersections, the intercept method isfaster than the planimetric method for the same level ofprecision.4.2 For specimens consisting of equiaxed grains, themethod of comparing the specimen with a standard chart ismost convenient and is sufficiently accurate for most commer-cial purposes. For higher degrees of accuracy in determiningaverage grain size, the intercept or planimetric procedures maybe used. The intercept procedure is particularly useful forstructures consisting of elongated grains (see Section 16).4.3 In case of dispute, the planimetric procedure shall be thereferee procedure in all cases.4.4 No attempt should be made to estimate the average grainsize of heavily cold-worked material. Partially recrystallizedwrought alloys and lightly to moderately cold-worked materialmay be considered as consisting of non-equiaxed grains, if agrain size measurement is necessary.4.5 Individual grain measurements should not be madebased on the standard comparison charts. These charts wereconstructed to reflect the typical log-normal distribution ofgrain sizes that result when a plane is passed th