DeterminingAverageGrainSize1ThisstandardisissuedunderthefixeddesignationE112;thenumberimmediatelyfollowingthedesignationindicatestheyearoforiginaladoptionor,inthecaseofrevision,theyearoflastrevision.Anumberinparenthesesindicatestheyearoflastreapproval.Asuperscriptepsilon(e)indicatesaneditorialchangesincethelastrevisionorreapproval.ThisstandardhasbeenapprovedforusebyagenciesoftheDepartmentofDefense.
e1NOTE—Reference(2)waseditoriallycorrectedinMay2006.
INTRODUCTION
Thesetestmethodsofdeterminationofaveragegrainsizeinmetallicmaterialsareprimarilymeasuringproceduresand,becauseoftheirpurelygeometricbasis,areindependentofthemetaloralloyconcerned.Infact,thebasicproceduresmayalsobeusedfortheestimationofaveragegrain,crystal,orcellsizeinnonmetallicmaterials.Thecomparisonmethodmaybeusedifthestructureofthematerialapproachestheappearanceofoneofthestandardcomparisoncharts.Theinterceptandplanimetricmethodsarealwaysapplicablefordeterminingaveragegrainsize.However,thecomparisonchartscannotbeusedformeasurementofindividualgrains.
1.Scope
1.1Thesetestmethodscoverthemeasurementofaveragegrainsizeandincludethecomparisonprocedure,theplanimet-ric(orJeffries)procedure,andtheinterceptprocedures.Thesetestmethodsmayalsobeappliedtononmetallicmaterialswithstructureshavingappearancessimilartothoseofthemetallicstructuresshowninthecomparisoncharts.Thesetestmethodsapplychieflytosinglephasegrainstructuresbuttheycanbeappliedtodeterminetheaveragesizeofaparticulartypeofgrainstructureinamultiphaseormulticonstituentspecimen.1.2Thesetestmethodsareusedtodeterminetheaveragegrainsizeofspecimenswithaunimodaldistributionofgrainareas,diameters,orinterceptlengths.Thesedistributionsareapproximatelylognormal.Thesetestmethodsdonotcovermethodstocharacterizethenatureofthesedistributions.CharacterizationofgrainsizeinspecimenswithduplexgrainsizedistributionsisdescribedinTestMethodsE1181.Mea-surementofindividual,verycoarsegrainsinafinegrainedmatrixisdescribedinTestMethodsE930.
1.3Thesetestmethodsdealonlywithdeterminationofplanargrainsize,thatis,characterizationofthetwo-dimensionalgrainsectionsrevealedbythesectioningplane.Determinationofspatialgrainsize,thatis,measurementofthe
sizeofthethree-dimensionalgrainsinthespecimenvolume,isbeyondthescopeofthesetestmethods.
1.4Thesetestmethodsdescribetechniquesperformedmanuallyusingeitherastandardseriesofgradedchartimagesforthecomparisonmethodorsimpletemplatesforthemanualcountingmethods.Utilizationofsemi-automaticdigitizingtabletsorautomaticimageanalyzerstomeasuregrainsizeisdescribedinTestMethodsE1382.
1.5Thesetestmethodsdealonlywiththerecommendedtestmethodsandnothinginthemshouldbeconstruedasdefiningorestablishinglimitsofacceptabilityorfitnessofpurposeofthematerialstested.
1.6ThemeasuredvaluesarestatedinSIunits,whichareregardedasstandard.Equivalentinch-poundvalues,whenlisted,areinparenthesesandmaybeapproximate.
1.7Thisstandarddoesnotpurporttoaddressallofthesafetyconcerns,ifany,associatedwithitsuse.Itistheresponsibilityoftheuserofthisstandardtoestablishappro-priatesafetyandhealthpracticesanddeterminetheapplica-bilityofregulatorylimitationspriortouse.
1.8Theparagraphsappearinthefollowingorder:
Section
Scope
ReferencedDocumentsTerminology
SignificanceandUse
GeneralitiesofApplicationSampling
TestSpecimensCalibration
PreparationofPhotomicrographsComparisonProcedure
Number
123456710
ThesetestmethodsareunderthejurisdictionofASTMCommitteeE04onMetallographyandarethedirectresponsibilityofSubcommitteeE04.08onGrainSize.
CurrenteditionapprovedNov.1,2004.PublishedNovember2004.Originallyapprovedin1955.Lastpreviouseditionapproved1996asE112–96e3.
1Copyright©ASTMInternational,100BarrHarborDrive,POBoxC700,WestConshohocken,PA19428-2959,UnitedStates.
1
E112–96(2004)e1Planimetric(Jeffries)ProcedureGeneralInterceptProceduresHeynLinearInterceptProcedureCircularInterceptProceduresHilliardSingle-CircleProcedureAbramsThree-CircleProcedureStatisticalAnalysis
SpecimenswithNon-equiaxedGrainShapes
SpecimensContainingTwoorMorePhasesorConstituentsReport
PrecisionandBiasKeywordsAnnexes:
BasisofASTMGrainSizeNumbers
1112131414.214.3151617181920
AnnexA1
EquationsforConversionsAmongVariousGrainSizeMeasurementsAnnex
A2
AusteniteGrainSize,FerriticandAusteniticSteelsAnnex
A3
FractureGrainSizeMethodAnnex
A4
RequirementsforWroughtCopperandCopper-BaseAlloysAnnex
A5
ApplicationtoSpecialSituationsAnnex
A6
Appendixes:
Appen-ResultsofInterlaboratoryGrainSizeDeterminations
dixX1
ReferencedAdjunctsAppen-dixX2
3.2.2grain—thatareawithintheconfinesoftheoriginal
(primary)boundaryobservedonthetwo-dimensionalplane-of-polishorthatvolumeenclosedbytheoriginal(primary)boundaryinthethree-dimensionalobject.Inmaterialscontain-ingtwinboundaries,thetwinboundariesareignored,thatis,thestructureoneithersideofatwinboundarybelongstothegrain.
3.2.3grainboundaryintersectioncount—determinationofthenumberoftimesatestlinecutsacross,oristangentto,grainboundaries(triplepointintersectionsareconsideredas1-1⁄2intersections).
3.2.4graininterceptcount—determinationofthenumberoftimesatestlinecutsthroughindividualgrainsontheplaneofpolish(tangenthitsareconsideredasonehalfaninterception;testlinesthatendwithinagrainareconsideredasonehalfaninterception).
3.2.5interceptlength—thedistancebetweentwoopposed,adjacentgrainboundaryintersectionpointsonatestlinesegmentthatcrossesthegrainatanylocationduetorandomplacementofthetestline.3.3Symbols:Symbols:aA—AAI,—d—DfG,—,a—,,—,t—,p,0=matrixgrainsinatwophase(constituent)microstructure.=testarea.
=meangraincrosssectionalarea.
=grainelongationratiooranisotropyindexforalongitudinallyorientedplane.=meanplanargraindiameter(PlateIII).=meanspatial(volumetric)graindiameter.=Jeffriesmultiplierforplanimetricmethod.=ASTMgrainsizenumber.=meanlinealinterceptlength.
=meanlinealinterceptlengthoftheamatrixphaseinatwophase(constituent)microstructure.
=meanlinealinterceptlengthonalongitu-dinallyorientedsurfaceforanon-equiaxedgrainstructure.
=meanlinealinterceptlengthonatrans-verselyorientedsurfaceforanon-equiaxedgrainstructure.
=meanlinealinterceptlengthonaplanarorientedsurfaceforanon-equiaxedgrainstructure.
=baseinterceptlengthof32.00mmfordefiningtherelationshipbetweenGand,(andNL)formacroscopicallyormicro-scopicallydeterminedgrainsizebytheinterceptmethod.=lengthofatestline.=magnificationused.
=magnificationusedbyachartpictureseries.
=numberoffieldsmeasured.
2.ReferencedDocuments2.1ASTMStandards:2E3PracticeforPreparationofMetallographicSpecimensE7TerminologyRelatingtoMetallography
E407PracticeforMicroetchingMetalsandAlloys
E562PracticeforDeterminingVolumeFractionbySys-tematicManualPointCount
E691PracticeforConductinganInterlaboratoryStudytoDeterminethePrecisionofaTestMethod
E883GuideforReflected-LightPhotomicrography
E930TestMethodsforEstimatingtheLargestGrainOb-servedinaMetallographicSection(ALAGrainSize)E1181TestMethodsforCharacterizingDuplexGrainSizesE1382TestMethodsforDeterminingAverageGrainSizeUsingSemiautomaticandAutomaticImageAnalysis2.2ASTMAdjuncts:
2.2.1Foracompleteadjunctlist,seeAppendixX23.Terminology
3.1Definitions—Fordefinitionsoftermsusedinthesetestmethods,seeTerminologyE7.
3.2DefinitionsofTermsSpecifictoThisStandard:
3.2.1ASTMgrainsizenumber—theASTMgrainsizenumber,G,wasoriginallydefinedas:
NAE52
G21
(1)
whereNAEisthenumberofgrainspersquareinchat100Xmagnification.Toobtainthenumberpersquaremillimetreat1X,multiplyby15.50.
ForreferencedASTMstandards,visittheASTMwebsite,www.astm.org,orcontactASTMCustomerServiceatservice@astm.org.ForAnnualBookofASTMStandardsvolumeinformation,refertothestandard’sDocumentSummarypageontheASTMwebsite.
2LMMbn
2
E112–96(2004)e1NaNANAaNAENA,NAtNApNiNInsideNInterceptedNLNL,NLtNLpPiPLPL,PLtPLpQ
=numberofagrainsinterceptedbythetestlineinatwophase(constituent)micro-structure.
=numberofgrainspermm2at1X.
=numberofagrainspermm2at1Xinatwophase(constituent)microstructure.=numberofgrainsperinch2at100X.
=NAonalongitudinallyorientedsurfaceforanon-equiaxedgrainstructure.
=NAonatransverselyorientedsurfaceforanon-equiaxedgrainstructure.
=NAonaplanarorientedsurfaceforanon-equiaxedgrainstructure.
=numberofinterceptswithatestline.=numberofgrainscompletelywithinatestcircle.
=numberofgrainsinterceptedbythetestcircle.
=numberofinterceptsperunitlengthoftestline.
=NLonalongitudinallyorientedsurfaceforanon-equiaxedgrainstructure.
=NLonatransverselyorientedsurfaceforanon-equiaxedgrainstructure.
=NLonaplanarorientedsurfaceforanon-equiaxedgrainstructure.
=numberofgrainboundaryintersectionswithatestline.
=numberofgrainboundaryintersectionsperunitlengthoftestline.
=PLonalongitudinallyorientedsurfaceforanon-equiaxedgrainstructure.
=PLonatransverselyorientedsurfaceforanon-equiaxedgrainstructure.
=PLonaplanarorientedsurfaceforanon-equiaxedgrainstructure.
=correctionfactorforcomparisonchartratingsusinganon-standardmagnifica-tionformicroscopicallydeterminedgrainsizes.
=correctionfactorforcomparisonchartratingsusinganon-standardmagnifica-tionformacroscopicallydeterminedgrainsizes.
=standarddeviation.
=grainboundarysurfaceareatovolumeratioforasinglephasestructure.
=grainboundarysurfaceareatovolumeratioforatwophase(constituent)struc-ture.
=students’tmultiplierfordeterminationoftheconfidenceinterval.
=volumefractionoftheaphaseinatwophase(constituent)microstructure.=95%confidenceinterval.=percentrelativeaccuracy.
consistingentirely,orprincipally,ofasinglephase.Thetestmethodsmayalsobeusedforanystructureshavingappear-ancessimilartothoseofthemetallicstructuresshowninthecomparisoncharts.Thethreebasicproceduresforgrainsizeestimationare:
4.1.1ComparisonProcedure—Thecomparisonproceduredoesnotrequirecountingofeithergrains,intercepts,orintersectionsbut,asthenamesuggests,involvescomparisonofthegrainstructuretoaseriesofgradedimages,eitherintheformofawallchart,clearplasticoverlays,oraneyepiecereticle.Thereappearstobeageneralbiasinthatcomparisongrainsizeratingsclaimthatthegrainsizeissomewhatcoarser(1⁄2to1Gnumberlower)thanitactuallyis(seeX1.3.5).Repeatabilityandreproducibilityofcomparisonchartratingsaregenerally61grainsizenumber.
4.1.2PlanimetricProcedure—Theplanimetricmethodin-volvesanactualcountofthenumberofgrainswithinaknownarea.Thenumberofgrainsperunitarea,NA,isusedtodeterminetheASTMgrainsizenumber,G.Theprecisionofthemethodisafunctionofthenumberofgrainscounted.Aprecisionof60.25grainsizeunitscanbeattainedwithareasonableamountofeffort.Resultsarefreeofbiasandrepeatabilityandreproducibilityarelessthan60.5grainsizeunits.Anaccuratecountdoesrequiremarkingoffofthegrainsastheyarecounted.
4.1.3InterceptProcedure—Theinterceptmethodinvolvesanactualcountofthenumberofgrainsinterceptedbyatestlineorthenumberofgrainboundaryintersectionswithatestline,perunitlengthoftestline,usedtocalculatethemeanlinealinterceptlength,—,.—,isusedtodeterminetheASTMgrainsizenumber,G.Theprecisionofthemethodisafunctionofthenumberofinterceptsorintersectionscounted.Apreci-sionofbetterthan60.25grainsizeunitscanbeattainedwithareasonableamountofeffort.Resultsarefreeofbias;repeatabilityandreproducibilityarelessthan60.5grainsizeunits.Becauseanaccuratecountcanbemadewithoutneedofmarkingoffinterceptsorintersections,theinterceptmethodisfasterthantheplanimetricmethodforthesamelevelofprecision.
4.2Forspecimensconsistingofequiaxedgrains,themethodofcomparingthespecimenwithastandardchartismostconvenientandissufficientlyaccurateformostcommer-cialpurposes.Forhigherdegreesofaccuracyindeterminingaveragegrainsize,theinterceptorplanimetricproceduresmaybeused.Theinterceptprocedureisparticularlyusefulforstructuresconsistingofelongatedgrains.
4.3Incaseofdispute,theinterceptprocedureshallbetherefereeprocedureinallcases.
4.4Noattemptshouldbemadetoestimatetheaveragegrainsizeofheavilycold-workedmaterial.Partiallyrecrystallizedwroughtalloysandlightlytomoderatelycold-workedmaterialmaybeconsideredasconsistingofnon-equiaxedgrains,ifagrainsizemeasurementisnecessary.
4.5Individualgrainmeasurementsshouldnotbemadebasedonthestandardcomparisoncharts.Thesechartswereconstructedtoreflectthetypicallog-normaldistributionofgrainsizesthatresultwhenaplaneispassedthrougha
3
QmsSVSVatVVa95%CI%RA
4.SignificanceandUse
4.1Thesetestmethodscoverproceduresforestimatingandrulesforexpressingtheaveragegrainsizeofallmetals
E112–96(2004)e1three-dimensionalarrayofgrains.Becausetheyshowadistri-butionofgraindimensions,rangingfromverysmalltoverylarge,dependingontherelationshipoftheplanarsectionandthethree-dimensionalarrayofgrains,thechartsarenotapplicabletomeasurementofindividualgrains.
5.GeneralitiesofApplication
5.1Itisimportant,inusingthesetestmethods,torecognizethattheestimationofaveragegrainsizeisnotaprecisemeasurement.Ametalstructureisanaggregateofthree-dimensionalcrystalsofvaryingsizesandshapes.Evenifallthesecrystalswereidenticalinsizeandshape,thegraincrosssections,producedbyarandomplane(surfaceofobservation)throughsuchastructure,wouldhaveadistributionofareasvaryingfromamaximumvaluetozero,dependinguponwheretheplanecutseachindividualcrystal.Clearly,notwofieldsofobservationcanbeexactlythesame.
5.2Thesizeandlocationofgrainsinamicrostructurearenormallycompletelyrandom.Nonominallyrandomprocessofpositioningatestpatterncanimprovethisrandomness,butrandomprocessescanyieldpoorrepresentationbyconcentrat-ingmeasurementsinpartofaspecimen.Representativeimpliesthatallpartsofthespecimencontributetotheresult,not,assometimeshasbeenpresumed,thatfieldsofaveragegrainsizeareselected.Visualselectionoffields,orcastingoutofextrememeasurements,maynotfalsifytheaveragewhendonebyunbiasedexperts,butwillinallcasesgiveafalseimpressionofhighprecision.Forrepresentativesampling,theareaofthespecimenismentallydividedintoseveralequalcoherentsub-areasandstagepositionsprespecified,whichareapproximatelyatthecenterofeachsub-area.Thestageissuccessivelysettoeachofthesepositionsandthetestpatternappliedblindly,thatis,withthelightout,theshutterclosed,ortheeyeturnedaway.Notouch-upofthepositionsoselectedisallowable.Onlymeasurementsmadeonfieldschoseninthiswaycanbevalidatedwithrespecttoprecisionandbias.6.Sampling
6.1Specimensshouldbeselectedtorepresentaverageconditionswithinaheatlot,treatmentlot,orproduct,ortoassessvariationsanticipatedacrossoralongaproductorcomponent,dependingonthenatureofthematerialbeingtestedandthepurposeofthestudy.Samplinglocationandfrequencyshouldbebaseduponagreementsbetweenthemanufacturersandtheusers.
6.2Specimensshouldnotbetakenfromareasaffectedbyshearing,burning,orotherprocessesthatwillalterthegrainstructure.
7.TestSpecimens
7.1Ingeneral,ifthegrainstructureisequiaxed,anyspecimenorientationisacceptable.However,thepresenceofanequiaxedgrainstructureinawroughtspecimencanonlybedeterminedbyexaminationofaplaneofpolishparalleltothedeformationaxis.
7.2Ifthegrainstructureonalongitudinallyorientedspeci-menisequiaxed,thengrainsizemeasurementsonthisplane,oranyother,willbeequivalentwithinthestatisticalprecisionof
4
thetestmethod.Ifthegrainstructureisnotequiaxed,butelongated,thengrainsizemeasurementsonspecimenswithdifferentorientationswillvary.Inthiscase,thegrainsizeshouldbeevaluatedonatleasttwoofthethreeprincipleplanes,transverse,longitudinal,andplanar(orradialandtransverseforroundbar)andaveragedasdescribedinSection16toobtainthemeangrainsize.Ifdirectedtestlinesareused,ratherthantestcircles,interceptcountsonnon-equiaxedgrainsinplateorsheettypespecimenscanbemadeusingonlytwoprincipletestplanes,ratherthanallthreeasrequiredfortheplanimetricmethod.
7.3Thesurfacetobepolishedshouldbelargeenoughinareatopermitmeasurementofatleastfivefieldsatthedesiredmagnification.Inmostcases,exceptforthinsheetorwirespecimens,aminimumpolishedsurfaceareaof160mm2(0.25in.2)isadequate.
7.4Thespecimenshallbesectioned,mounted(ifneces-sary),ground,andpolishedaccordingtotherecommendedproceduresinPracticeE3.Thespecimenshallbeetchedusingareagent,suchaslistedinPracticeE407,todelineatemost,orall,ofthegrainboundaries(seealsoAnnexA3).
TABLE1SuggestedComparisonChartsforMetallicMaterials
NOTE1—Thesesuggestionsarebaseduponthecustomarypracticesinindustry.Forspecimenspreparedaccordingtospecialtechniques,theappropriatecomparisonstandardsshouldbeselectedonastructural-appearancebasisinaccordancewith8.2.
Material
Aluminum
Copperandcopper-basealloys(seeAnnexA4)Ironandsteel:AusteniticFerriticCarburizedStainless
Magnesiumandmagnesium-basealloysNickelandnickel-basealloysSuper-strengthalloysZincandzinc-basealloys
PlateNumberI
IIIorIV
BasicMagnification
100X75X,100X
IIorIVIIVIIIorIIIIIorIIIorII100X100X100X100X100X100X100X100X
8.Calibration
8.1Useastagemicrometertodeterminethetruelinearmagnificationforeachobjective,eyepieceandbellows,orzoomsettingtobeusedwithin62%.
8.2Usearulerwithamillimetrescaletodeterminetheactuallengthofstraighttestlinesorthediameteroftestcirclesusedasgrids.
9.PreparationofPhotomicrographs
9.1Whenphotomicrographsareusedforestimatingtheaveragegrainsize,theyshallbepreparedinaccordancewithGuideE883.
10.ComparisonProcedure
10.1Thecomparisonprocedureshallapplytocompletelyrecrystallizedorcastmaterialswithequiaxedgrains.
10.2Whengrainsizeestimationsaremadebythemoreconvenientcomparisonmethod,repeatedchecksbyindividualsaswellasbyinterlaboratorytestshaveshownthatunlessthe
E112–96(2004)e1FIG.1ExampleofUntwinnedGrains(FlatEtch)fromPlateI.
GrainSizeNo.3at100X
FIG.2ExampleofTwinGrains(FlatEtch)fromPlateII.Grain
SizeNo.3at100X
appearanceofthestandardreasonablywellapproachesthatofthesample,errorsmayoccur.Tominimizesucherrors,thecomparisonchartsarepresentedinfourcategoriesasfollows:310.2.1PlateI—Untwinnedgrains(flatetch).Includesgrainsizenumbers00,0,1⁄2,1,11⁄2,2,21⁄2,3,31⁄2,4,41⁄2,5,51⁄2,6,61⁄2,7,71⁄2,8,81⁄2,9,91⁄2,10,at100X.
10.2.2PlateII—Twinnedgrains(flatetch).Includesgrainsizenumbers,1,2,3,4,5,6,7,8,at100X.
10.2.3PlateIII—Twinnedgrains(contrastetch).Includesnominalgraindiametersof0.200,0.150,0.120,0.090,0.070,0.060,0.050,0.045,0.035,0.025,0.020,0.015,0.010,0.005mmat75X.
10.2.4PlateIV—Austenitegrainsinsteel(McQuaid-Ehn).Includesgrainsizenumbers1,2,3,4,5,6,7,8,at100X.10.3Table1listsanumberofmaterialsandthecomparisonchartsthataresuggestedforuseinestimatingtheiraveragegrainsizes.Forexample,fortwinnedcopperandbrasswithacontrastetch,usePlateIII.
NOTE1—Examplesofgrain-sizestandardsfromPlatesI,II,III,andIVareshowninFig.1,Fig.2,Fig.3,andFig.4.
10.4Theestimationofmicroscopically-determinedgrainsizeshouldusuallybemadebydirectcomparisonatthesamemagnificationastheappropriatechart.Accomplishthisbycomparingaprojectedimageoraphotomicrographofarepresentativefieldofthetestspecimenwiththephotomicro-graphsoftheappropriatestandardgrain-sizeseries,orwithsuitablereproductionsortransparenciesofthem,andselectthe
PlatesI,II,III,andIVareavailablefromASTMHeadquarters.OrderAdjunct:ADJE11201P(PlateI),ADJE11202P(PlateII),ADJE11203P(PlateIII),andADJE11204P(PlateIV).Acombinationofallfourplatesisalsoavailable.OrderAdjunct:ADJE112PS.
3FIG.3ExampleofTwinGrains(ContrastEtch)fromPlateIII.
GrainSize0.090mmat75X
photomicrographwhichmostnearlymatchestheimageofthetestspecimenorinterpolatebetweentwostandards.ReportthisestimatedgrainsizeastheASTMgrainsizenumber,orgraindiameter,ofthechartpicturethatmostcloselymatchestheimageofthetestspecimenorasaninterpolatedvaluebetweentwostandardchartpictures.
5
E112–96(2004)e1FIG.4ExampleofAusteniteGrainsinSteelfromPlateIV.Grain
SizeNo.3at100X
TABLE2MicroscopicallyDeterminedGrainSizeRelationshipsUsingPlateIIIatVariousMagnifications
NOTE1—Firstline—meangraindiameter,d,inmm;inparentheses—equivalentASTMgrainsizenumber,G.NOTE2—MagnificationforPlateIIIis75X(row3data).
Magnification
25X50X75X100X200X400X500X
ChartPictureNumber(PlateIII)
10.015(9.2)0.0075(11.2)0.005(12.3)0.00375(13.2)0.0019(15.2)——
20.030(7.2)0.015(9.2)0.010(10.3)0.0075(11.2)0.00375(13.2)0.0025(14.3)—
30.045(6.0)0.0225(8.0)0.015(9.2)0.0112(10.0)0.0056(12.0)0.0037(13.2)0.003(13.8)
40.060(5.2)0.030(7.2)0.020(8.3)0.015(9.2)0.0075(11.2)0.005(12.3)0.004(13.0)
50.075(4.5)0.0375(6.5)0.025(7.7)0.019(8.5)0.009(10.5)0.006(11.7)0.005(12.3)
60.105(3.6)0.053(5.6)0.035(6.7)0.026(7.6)0.013(9.6)0.009(10.7)0.007(11.4)
70.135(2.8)0.0675(4.8)0.045(6.0)0.034(6.8)0.017(8.8)0.011(10.0)0.009(10.6)
80.150(2.5)0.075(4.5)0.050(5.7)0.0375(6.5)0.019(8.5)0.0125(9.7)0.010(10.3)
90.180(2.0)0.090(4.0)0.060(5.2)0.045(6.0)0.0225(8.0)0.015(9.2)0.012(9.8)
100.210(1.6)0.105(3.6)0.070(4.7)0.053(5.6)0.026(7.6)0.0175(8.7)0.014(9.4)
110.270(0.8)0.135(2.8)0.090(4.0)0.067(4.8)0.034(6.8)0.0225(8.0)0.018(8.6)
120.360(0)0.180(2.0)0.120(3.2)0.090(4.0)0.045(6.0)0.030(7.2)0.024(7.8)
130.451(0/00)0.225(1.4)0.150(2.5)0.113(3.4)0.056(5.4)0.0375(6.5)0.030(7.2)
140.600(00+)0.300(0.5)0.200(1.7)0.150(2.5)0.075(4.5)0.050(5.7)0.040(6.3)
10.5Goodjudgmentonthepartoftheobserverisnecessarytoselectthemagnificationtobeused,thepropersizeofarea(numberofgrains),andthenumberandlocationinthespecimenofrepresentativesectionsandfieldsforestimatingthecharacteristicoraveragegrainsize.Itisnotsufficienttovisuallyselectwhatappeartobeareasofaveragegrainsize.Recommendationsforchoosingappropriateareasforallpro-cedureshavebeennotedin5.2.
10.6Grainsizeestimationsshallbemadeonthreeormorerepresentativeareasofeachspecimensection.
10.7Whenthegrainsareofasizeoutsidetherangecoveredbythestandardphotographs,orwhenmagnificationsof75Xor100Xarenotsatisfactory,othermagnificationsmaybeem-ployedforcomparisonbyusingtherelationshipsgiveninNote
6
2andTable2.Itmaybenotedthatalternativemagnificationsareusuallysimplemultiplesofthebasicmagnifications.
NOTE2—IfthegrainsizeisreportedinASTMnumbers,itisconve-nienttousetherelationship:
Q52log2~M/Mb!
(2)
56.log10~M/Mb!
whereQisacorrectionfactorthatisaddedtotheapparentmicro-grainsizeofthespecimen,asviewedatthemagnification,M,insteadofatthebasicmagnification,Mb(75Xor100X),toyieldthetrueASTMgrain-sizenumber.Thus,foramagnificationof25X,thetrueASTMgrain-sizenumberisfournumberslowerthanthatofthecorrespondingphotomi-crographat100X(Q=−4).Likewise,for400X,thetrueASTMgrain-sizenumberisfournumbershigher(Q=+4)thanthatofthecorrespondingphotomicrographat100X.Similarly,for300X,thetrueASTMgrain-size
E112–96(2004)e1TABLE3MacroscopicGrainSizeRelationshipsComputedforUniform,RandomlyOriented,EquiaxedGrains
NOTE1—MacroscopicallydeterminedgrainsizenumbersM-12.3,M-13.3,M-13.8andM-14.3correspond,respectively,tomicroscopicallydeterminedgrainsizenumbers(G)00,0,0.5and1.0.
MacroGrainSizeNo.M-0M-0.5M-1.0M-1.5M-2.0M-2.5M-3.0M-3.5M-4.0M-4.5M-5.0M-5.5M-6.0M-6.5M-7.0M-7.5
¯AGrains/UnitAreaNNo./mm20.00080.00110.00160.00220.00310.00440.00620.00880.01240.01750.02480.03510.04960.07010.0990.140
No./in.20.500.711.001.412.002.834.005.668.0011.3116.0022.6332.0045.26.0090.51
¯AverageGrainAreaAmm21290.3912.45.2456.2322.6228.1161.3114.080.57.0240.3228.5120.1614.2610.087.13
in.22.001.411.000.7070.5000.3540.2500.1770.1250.08840.06250.04420.03120.02210.01560.0110310−3M-8.0M-8.5M-9.0M-9.5M-10.0M-10.5M-11.0M-11.5M-12.0M-12.3M-12.5M-13.0M-13.3M-13.5M-13.8M-14.0M-14.3
0.1980.2810.3970.5610.7941.1221.5872.2453.1753.9084.4906.3497.8178.97911.05512.69915.634
128.0181.0256.0362.1512.0724.11024.11448.22048.12521.626.54096.35043.15793.07132.18192.610086.3
5.043.562.521.781.260.10.6300.04450.3150.2560.2230.1570.1280.1110.0910.0790.0
7.8125.5243.9062.7621.9531.3810.9770.6900.4880.3970.3450.2440.1980.1730.1400.1220.099
2.251.1.591.331.120.9940.7940.6670.5610.5060.4720.3970.3580.3340.3010.2810.253
—dAverageDiametermm35.930.225.421.418.015.112.710.78.987.556.355.344.493.783.172.67
in.1.411.191.000.8410.7070.5950.5000.4200.3540.2970.2500.2100.1770.1490.1250.105310−388.474.362.552.4.237.231.226.322.119.918.615.614.113.111.811.09.96
2.001.681.411.191.000.8410.7070.5950.5000.4510.4200.3540.3190.2970.2680.2500.225
—,MeanInterceptmm32.0026.9122.6319.0316.0013.4511.319.518.006.735.6.7.003.362.832.38
in.1.21.00.0.740.630.530.440.370.310.260.220.180.150.130.110.093310−378.766.255.746.839.433.127.823.419.717.716.613.912.511.710.59.848.87
0.5000.5950.7070.8411.001.191.411.682.002.222.382.833.143.363.734.004.44
50.0059.4670.7184.09100.0118.9141.4168.2200.0221.9237.8282.8313.8336.4373.2400.0443.8
¯LNmm−10.0310.0370.0440.0530.0630.0740.0880.1050.1250.1490.1770.2100.2500.2970.3540.420
¯N100mm3.133.724.425.266.257.438.8410.5112.5014.8717.6821.0225.0029.7335.32.05
numberisfournumbershigherthanthatofthecorrespondingphotomi-crographat75X.
10.8Thesmallnumberofgrainsperfieldatthecoarseendofthechartseries,thatis,size00,andtheverysmallsizeofthegrainsatthefineendmakeaccuratecomparisonratingsdifficult.Whenthespecimengrainsizefallsateitherendofthechartrange,amoremeaningfulcomparisoncanbemadebychangingthemagnificationsothatthegrainsizeliesclosertothecenteroftherange.
10.9Theuseoftransparencies4orprintsofthestandards,withthestandardandtheunknownplacedadjacenttoeachother,istobepreferredtotheuseofwallchartcomparisonwiththeprojectedimageonthemicroscopescreen.
TransparenciesofthevariousgrainsizesinPlateIareavailablefromASTMHeadquarters.OrderAdjunct:ADJE112TSfortheset.Transparenciesofindividualgrainsizegroupingsareavailableonrequest.OrderAdjunct:ADJE11205T(GrainSize00),ADJE11206T(GrainSize0),ADJE11207T(GrainSize0.5),ADJE11208T(GrainSize1.0),ADJE11209T(GrainSize1.5),ADJE11210T(GrainSize2.0),ADJE11211T(GrainSize2.5),ADJE11212T(GrainSizes3.0,3.5,and4.0),ADJE11213T(GrainSizes4.5,5.0,and5.5),ADJE11214T(GrainSizes6.0,6.5,and7.0),ADJE11215T(GrainSizes7.5,8.0,and8.5),andADJE11216T(GrainSizes9.0,9.5,and10.0).Chartsillustratinggrainsizenumbers00to10areon81⁄2by11in.(215.9by279.4mm)film.TransparenciesforPlatesII,III,andIVarenotavailable.
410.10Noparticularsignificanceshouldbeattachedtothefactthatdifferentobserversoftenobtainslightlydifferentresults,providedthedifferentresultsfallwithintheconfidencelimitsreasonablyexpectedwiththeprocedureused.
10.11Thereisapossibilitywhenanoperatormakesre-peatedchecksonthesamespecimenusingthecomparisonmethodthattheywillbeprejudicedbytheirfirstestimate.Thisdisadvantagecanbeovercome,whennecessary,bychangesinmagnification,throughbellowsextension,orobjectiveoreyepiecereplacementbetweenestimates(1).510.12Maketheestimationofmacroscopically-determinedgrainsizes(extremelycoarse)bydirectcomparison,atamagnificationof1X,oftheproperlypreparedspecimen,orofaphotographofarepresentativefieldofthespecimen,withphotographsofthestandardgrainseriesshowninPlateI(foruntwinnedmaterial)andPlatesIIandIII(fortwinnedmate-rial).Sincethephotographsofthestandardgrainsizeseriesweremadeat75and100diametersmagnification,grainsizesestimatedinthiswaydonotfallinthestandardASTMgrain-sizeseriesandhence,preferably,shouldbeexpressed
Theboldfacenumbersinparenthesesrefertothelistofreferencesappendedtothesetestmethods.
57
E112–96(2004)e1TABLE4GrainSizeRelationshipsComputedforUniform,RandomlyOriented,EquiaxedGrains
GrainSizeNo.
G
0000.51.01.52.02.53.03.54.04.55.05.56.06.57.07.58.08.59.09.510.010.511.011.512.012.513.013.514.0
¯AGrains/UnitAreaN
No./in.2at100X
0.250.500.711.001.412.002.834.005.668.0011.3116.0022.6332.0045.25.0090.51128.00181.02256.00362.04512.00724.081024.001448.152048.0026.314096.005792.628192.00
No./mm2at1X3.887.7510.9615.5021.9231.0043.8462.0087.68124.00175.36248.00350.73496.00701.45992.001402.91984.02805.83968.05611.67936.011223.215872.022446.431744.1442.963488.1785.8126976.3
¯AverageGrainAreaAmm20.25810.12900.09120.050.04560.03230.02280.01610.01140.008060.005700.004030.002850.002020.001430.001010.000710.000500.000360.000250.000180.000130.00000.0000630.0000450.0000320.0000220.0000160.0000110.000008
µm2258012903291239515620322582281016129114058065570340322851201614261008713504356252178126.163.044.631.522.315.811.17.9
—dAverageDiametermm0.50800.35920.30210.25400.21360.17960.15100.12700.10680.080.07550.06350.05340.04490.03780.03180.02670.02250.010.01590.01330.01120.00940.00790.00670.00560.00470.00400.00330.0028
µm508.0359.2302.1254.0213.6179.6151.0127.0106.8.875.563.553.444.937.831.826.722.518.915.913.311.29.47.96.75..74.03.32.8
—,MeanInterceptmm0.45250.32000.26910.22630.19030.16000.13450.11310.09510.08000.06730.05660.04760.04000.03360.02830.02380.02000.01680.01410.01190.01000.00840.00710.00600.00500.00420.00350.00300.0025
µm452.5320.0269.1226.3190.3160.0134.5113.195.180.067.356.7.0.033.628.323.820.016.814.111.910.08.47.15.95.04.23.53.02.5
¯LNNo./mm2.213.123.724.425.266.257.438.8410.5112.5014.8717.6821.0225.0029.7335.32.0450.0059.4670.7184.09100.0118.9141.4168.2200.0237.8282.8336.4400.0
eitherasdiameteroftheaveragegrainorasoneofthemacro-grainsizenumberslistedinTable3.Forthesmallermacroscopicgrainsizes,itmaybepreferabletouseahighermagnificationandthecorrectionfactorgiveninNote3,particularlyifitisdesirabletoretainthismethodofreporting.
NOTE3—IfthegrainsizeisreportedinASTMmacro-grainsizenumbers,itisconvenienttousetherelationship:
Qm52log2M56.log10M
whereQMisacorrectionfactorthatisaddedtotheapparentgrainsizeofthespecimen,whenviewedatthemagnificationM,insteadofat1X,toyieldthetrueASTMmacro-grainsizenumber.Thus,foramagnificationof2X,thetrueASTMmacro-grainsizenumberistwonumbershigher(Q=+2),andfor4X,thetrueASTMmacro-grainsizenumberisfournumbershigher(Q=+4)thanthatofthecorrespondingphotograph.
(3)
fractureofhardenedsteel(2),involvescomparisonofthespecimenunderinvestigationwithasetofstandardfractures.6IthasbeenfoundthatthearbitrarilynumberedfracturegrainsizeseriesagreewellwiththecorrespondinglynumberedASTMgrainsizespresentedinTable4.Thiscoincidencemakesthefracturegrainsizesinterchangeablewiththeauste-niticgrainsizesdeterminedmicroscopically.Thesizesob-servedmicroscopicallyshallbeconsideredtheprimarystan-dard,sincetheycanbedeterminedwithmeasuringinstruments.
11.Planimetric(orJeffries’)(3)Procedure
11.1Intheplanimetricprocedureinscribeacircleorrect-angleofknownarea(usually5000mm2tosimplifythecalculations)onamicrographorontheground-glassscreenofthemetallograph.Selectamagnificationwhichwillgiveatleast50grainsinthefieldtobecounted.Whentheimageisfocusedproperly,countthenumberofgrainswithinthisarea.Thesumofallthegrainsincludedcompletelywithintheknownareaplusonehalfthenumberofgrainsintersectedbythecircumferenceoftheareagivesthenumberofequivalentwholegrains,measuredatthemagnificationused,withinthearea.IfthisnumberismultipliedbytheJeffries’multiplier,f,inthesecondcolumnofTable5oppositetheappropriatemagnification,theproductwillbethenumberofgrainspersquaremillimetreNA.Countaminimumofthreefieldsto
10.13ThecomparisonprocedureshallbeapplicableforestimatingtheaustenitegrainsizeinferriticsteelafteraMcQuaid-Ehntest(seeAnnexA3,A3.2),oraftertheaustenitegrainshavebeenrevealedbyanyothermeans(seeAnnexA3,A3.3).Makethegrain-sizemeasurementbycomparingthemicroscopicimage,atmagnificationof100X,withthestan-dardgrainsizechartinPlateIV,forgrainsdevelopedinaMcQuaid-Ehntest(seeAnnexA3);forthemeasurementofaustenitegrainsdevelopedbyothermeans(seeAnnexA3),measurebycomparingthemicroscopicimagewiththeplatehavingthemostnearlycomparablestructureobservedinPlatesI,II,orIV.
10.14Theso-called“ShepherdFractureGrainSizeMethod”ofjudginggrainsizefromtheappearanceofthe
8
AphotographoftheShepherdstandardfracturescanbeobtainedfromASTMHeadquarters.OrderAdjunct:ADJE011224.
6E112–96(2004)e1TABLE5RelationshipBetweenMagnificationUsedandJeffries’
Multiplier,f,foranAreaof5000mm2(aCircleof79.8-mm
Diameter)(f=0.0002M2)
MagnificationUsed,M
110255075A1001502002503005007501000
ATABLE6GrainSizeEquationsRelatingMeasuredParametersto
theMicroscopicallyDeterminedASTMGrainSize,G
Jeffries’Multiplier,f,toObtainGrains/mm20.00020.020.1250.51.1252.04.58.012.518.050.0112.5200.0
NOTE1—DeterminetheASTMGrainSize,G,usingthefollowingequations:
NOTE2—Thesecondandthirdequationsareforsinglephasegrainstructures.
NOTE3—Toconvertmicrometrestomillimetres,divideby1000.NOTE4—AcalculatedGvalueof−1correspondstoASTMG=00.
Equation
¯A)−2.954G=(3.321928log10N
¯L)−3.288G=(6.3856log10N
G=(6.3856log10PL)−3.288G=(−6.3856log10,)−3.288
UnitsNAinmm−2¯Linmm−1N
PLinmm−1,inmm
At75diametersmagnification,Jeffries’multiplier,f,becomesunityiftheareausedis5625mm2(acircleof84.5-mmdiameter).
ensureareasonableaverage.Thenumberofgrainspersquaremillimetreat1X,NA,iscalculatedfrom:
NA5fNInside1
SNIntercepted
2D(4)
wherefistheJeffries’multiplier(seeTable5),NInsideisthenumberofgrainscompletelyinsidethetestcircleandNInterceptedisthenumberofgrainsthatinterceptthetestcircle.
¯,isthereciprocalofNA,thatis,1/NATheaveragegrainarea,A
,whilethemeangraindiameter,d,aslistedonPlateIII(see
¯.Thisgraindiameterhasno10.2.3),isthesquarerootofA
physicalsignificancebecauseitrepresentsthesideofasquare
¯,andgraincrosssectionsarenotsquare.grainofareaA
11.2Toobtainanaccuratecountofthenumberofgrainscompletelywithinthetestcircleandthenumberofgrainsintersectingthecircle,itisnecessarytomarkoffthegrainsonthetemplate,forexample,withagreasepencilorfelttippen.Theprecisionoftheplanimetricmethodisafunctionofthenumberofgrainscounted(seeSection19).Thenumberofgrainswithinthetestcircle,however,shouldnotexceedabout100ascountingbecomestediousandinaccurate.Experiencesuggeststhatamagnificationthatproducesabout50grainswithinthetestcircleisaboutoptimumastocountingaccuracyperfield.Becauseoftheneedtomarkoffthegrainstoobtainanaccuratecount,theplanimetricmethodislessefficientthantheinterceptmethod(seeSection12).
11.3Fieldsshouldbechosenatrandom,withoutbias,asdescribedin5.2.Donotattempttochoosefieldsthatappeartobetypical.Choosethefieldsblindlyandselectthemfromdifferentlocationsontheplaneofpolish.
11.4Byoriginaldefinition,amicroscopically-determinedgrainsizeofNo.1has1.000grains/in.2at100X,hence15.500grains/mm2at1X.Forareasotherthanthestandardcircle,determinetheactualnumberofgrainspersquaremillimetre,NA,andfindthenearestsizefromTable4.TheASTMgrainsizenumber,G,canbecalculatedfromNA(numberofgrainsper2mmat1X)using(Eq1)inTable6.
12.GeneralInterceptProcedures
12.1Interceptproceduresaremoreconvenienttousethantheplanimetricprocedure.Theseproceduresareamenabletousewithvarioustypesofmachineaids.Itisstronglyrecom-9
mendedthatatleastamanualtallycounterbeusedwithallinterceptproceduresinordertopreventnormalerrorsincountingandtoeliminatebiaswhichmayoccurwhencountsappeartoberunninghigherorlowerthananticipated.
12.2Interceptproceduresarerecommendedparticularlyforallstructuresthatdepartfromtheuniformequiaxedform.Foranisotropicstructures,proceduresareavailableeithertomakeseparatesizeestimatesineachofthethreeprincipaldirections,ortorationallyestimatetheaveragesize,asmaybeappropri-ate.
12.3ThereisnodirectmathematicalrelationshipbetweentheASTMgrainsizenumber,G,andthemeanlinealintercept,
¯(Eq1)unliketheexactrelationshipbetweenG,NAE,NAandA
fortheplanimetricmethod.Therelationship
p¯,54A
SD½
(5)
betweenthemeanlinealintercept,,,andtheaveragegrain
¯,isexactforcirclesbutnotquiteexactforastructureofarea,A
uniformequiaxedgrains(seeA2.2.2).Consequently,therela-tionshipbetweentheASTMgrainsizenumberGandthemeanlinealintercepthasbeendefinedsothatASTMNo.0hasameaninterceptsizeofprecisely32.00mmforthemacroscopi-callydeterminedgrainsizescaleandof32.00mmonafieldofviewat100Xmagnificationforthemicroscopicallydeterminedgrainsizescale.Thus:
,0
G52log2—,G510.0022log2,¯LG510.0012log2N
(6)(7)(8)
¯Lareinmillimetresat1Xorwhere,0is32mmand—,andN
numberofinterceptspermmforthemacroscopicallydeter-minedgrainsizenumbersandinmillimetresornumberpermmonafieldat100Xforthemicroscopicallydeterminedgrainsizenumbers.Usingthisscale,measuredgrainsizenumbersarewithinabout0.01Gunitsofgrainsizenumbersdeterminedbytheplanimetricmethod,thatis,wellwithintheprecisionofthetestmethods.AdditionaldetailsconcerninggrainsizerelationshipsaregiveninAnnexA1andAnnexA2.
—12.4Themeaninterceptdistance,,,measuredonaplanesectionisanunbiasedestimateofthemeaninterceptdistancewithinthesolidmaterialinthedirection,orovertherangeof
E112–96(2004)e1directions,measured.Thegrainboundarysurfacearea-to-volumeratioisgivenexactlybySv=2NLwhenNLisaveragedoverthreedimensions.Theserelationsareindependentofgrainshape.
13.Heyn(4)LinealInterceptProcedure
13.1Estimatetheaveragegrainsizebycounting(ontheground-glassscreen,onaphotomicrographofarepresentativefieldofthespecimen,oronthespecimenitself)thenumberofgrainsinterceptedbyoneormorestraightlinessufficientlylongtoyieldatleast50intercepts.Itisdesirabletoselectacombinationoftestlinelengthandmagnificationsuchthatasinglefieldwillyieldtherequirednumberofintercepts.OnesuchtestwillnominallyallowestimationofgrainsizetothenearestwholeASTMsizenumber,atthelocationtested.Additionallines,inapredeterminedarray,shouldbecountedtoobtaintheprecisionrequired.Theprecisionofgrainsizeestimatesbytheinterceptmethodisafunctionofthenumberofgraininterceptionscounted(seeSection19).Becausetheendsofstraighttestlineswillusuallylieinsidegrains(see14.3),precisionwillbereducediftheaveragecountpertestlineislow.Ifpossible,useeitheralongertestlineoralowermagnification.
13.2Makecountsfirstonthreetofiveblindlyselectedandwidelyseparatedfieldstoobtainareasonableaverageforthespecimen.Iftheapparentprecisionofthisaverage(calculatedasindicatedinSection15)isnotadequate,makecountsonsufficientadditionalfieldstoobtaintheprecisionrequiredforthespecimenaverage.
13.3Aninterceptisasegmentoftestlineoverlayingonegrain.Anintersectionisapointwhereatestlineiscutbyagrainboundary.Eithermaybecounted,withidenticalresultsinasinglephasematerial.Whencountingintercepts,segmentsattheendofatestlinewhichpenetrateintoagrainarescoredashalfintercepts.Whencountingintersections,theendpointsofatestlinearenotintersectionsandarenotcountedexceptwhentheendappearstoexactlytouchagrainboundary,when1⁄2intersectionshouldbescored.Atangentialintersectionwithagrainboundaryshouldbescoredasoneintersection.Anintersectionapparentlycoincidingwiththejunctionofthreegrainsshouldbescoredas11⁄2.Withirregulargrainshapes,thetestlinemaygeneratetwointersectionswithdifferentpartsofthesamegrain,togetherwithathirdintersectionwiththeintrudinggrain.Thetwoadditionalintersectionsaretobecounted.
13.4Theeffectsofmoderatedeparturefromanequiaxedstructuremaybeeliminatedbymakinginterceptcountsonalinearraycontaininglineshavingfourormoreorientations.ThefourstraightlinesofFig.57maybeused.Theformofsucharraysisnotcritical,providedthatallportionsofthefieldaremeasuredwithapproximatelyequalweight.Anarrayoflinesradiatingfromacommonpointisthereforenotsuitable.ThenumberofinterceptsistobecountedfortheentirearrayandsinglevaluesofNLand,determinedforeacharrayasawhole.
13.5Fordistinctlynon-equiaxedstructuressuchasmoder-atelyworkedmetals,moreinformationcanbeobtainedbymakingseparatesizedeterminationsalongparallellinearraysthatcoincidewithallthreeprincipaldirectionsofthespeci-men.Longitudinalandtransversespecimensectionsarenor-mallyused,thenormalsectionbeingaddedwhennecessary.Eitherofthe100-mmlinesofFig.5maybeappliedfivetimes,usingparalleldisplacements,placingthefive“+”marksatthesamepointontheimage.Alternatively,atransparenttestgridwithsystematicallyspacedparalleltestlinesofknownlengthcanbemadeandused.
14.CircularInterceptProcedures
14.1UseofcirculartestlinesratherthanstraighttestlineshasbeenadvocatedbyUnderwood(5),Hilliard(6),andAbrams(7).Circulartestarraysautomaticallycompensatefordeparturesfromequiaxedgrainshapes,withoutoverweightinganylocalportionofthefield.Ambiguousintersectionsatendsoftestlinesareeliminated.Circularinterceptproceduresaremostsuitableforuseasfixedroutinemanualproceduresforgrainsizeestimationinqualitycontrol.
14.2HilliardSingle-CircleProcedure(6):
14.2.1Whenthegrainshapeisnotequiaxedbutisdistortedbydeformationorotherprocesses,obtaininganaveragelinealinterceptvalueusingstraighttestlinesrequiresaveragingofvaluesmadeatavarietyoforientations.Ifthisisnotdonecarefully,biasmaybeintroduced.Useofacircleasthetestlineeliminatesthisproblemasthecirclewilltestallorientationsequallyandwithoutbias.
14.2.2Anycirclesizeofexactlyknowncircumferencemaybeused.Circumferencesof100,200,or250mmareusuallyconvenient.Thetestcirclediametershouldneverbesmallerthanthelargestobservedgrains.Ifthetestcircleissmallerthanaboutthreetimesthemeanlinealintercept,thedistributionofthenumberofinterceptsorintersectionsperfieldwillnotbeGaussian.Also,useofsmalltestcirclesisratherinefficientasagreatmanyfieldsmustbeevaluatedtoobtainahighdegreeofprecision.Asmallreferencemarkisusuallyplacedatthetopofthecircletoindicatetheplacetostartandstopthecount.Blindlyapplytheselectedcircletothemicroscopeimageataconvenientknownmagnificationandcountthenumberofgrainboundariesintersectingthecircleforeachapplication.Applythecircleonlyoncetoeachfieldofview,addingfieldsinarepresentativemanner,untilsufficientcountsareobtainedtoyieldtherequiredprecision.Thevariationincountspertestcircleapplicationdecreasesasthecirclesizeincreasesand,ofcourse,isaffectedbytheuniformityofthegrainsizedistribu-tion.
14.2.3Aswithallinterceptprocedures,theprecisionofthemeasurementincreasesasthenumberofcountsincreases(seeSection19).Theprecisionisbasedonthestandarddeviationofthecountsofthenumberofinterceptsorintersectionsperfield.Ingeneral,foragivengrainstructure,thestandarddeviationisimprovedasthecountpercircleapplicationandthetotalcount(thatis,thenumberofapplications)increase.Hilliardrecom-mendedtestconditionsthatproduceabout35countspercirclewiththetestcircleappliedblindlyoveraslargeaspecimenareaasfeasibleuntilthedesiredtotalnumberofcountsisobtained.
10
Atrue-sizetransparencyofFig.5isavailablefromASTMHeadquarters.OrderAdjunct:ADJE11217F.
7E112–96(2004)e1NOTE1—Ifreproducedtomakestraightlinesmarkedlength:Straightlinestotal:500mm
Circlesare:
Circumference,mm,
250.0166.783.3Total500.0
Diameter,mm
79.5853.0526.53
NOTE2—SeeFootnote9.
FIG.5TestPatternforInterceptCounting
14.3AbramsThree-CircleProcedure(7):
14.3.1Basedonanexperimentalfindingthatatotalof500countsperspecimennormallyyieldsacceptableprecision,Abramsdevelopedaspecificprocedureforroutineaveragegrainsizeratingofcommercialsteels.Useofthechi-squaretestonrealdatademonstratedthatthevariationofinterceptcountsisclosetonormal,allowingtheobservationstobetreatedbythestatisticsofnormaldistributions.Thusbothameasureofvariabilityandtheconfidencelimitoftheresultarecomputedforeachaveragegrainsizedetermination.
14.3.2Thetestpatternconsistsofthreeconcentricandequallyspacedcircleshavingatotalcircumferenceof500mm,asshowninFig.5.Successivelyapplythispatterntoatleastfiveblindlyselectedandwidelyspacedfields,separatelyrecordingthecountofintersectionsperpatternforeachofthetests.Then,determinethemeanlinealintercept,itsstandarddeviation,95%confidencelimit,andpercentrelativeaccuracy.
11
Formostwork,arelativeaccuracyof10%orlessrepresentsanacceptabledegreeofprecision.Ifthecalculatedrelativeaccuracyisunacceptablefortheapplication,countadditionalfieldsuntilthecalculatedpercentrelativeaccuracyisaccept-able.Thespecificprocedureisasfollows:
14.3.2.1Examinethegrainstructureandselectamagnifi-cationthatwillyieldfrom40to100interceptsorintersectioncountsperplacementofthethreecircletestgrid.Becauseourgoalistoobtainatotalofabout400to500counts,theidealmagnificationisthatwhichyieldsabout100countsperplacement.However,asthecountperplacementincreasesfrom40to100,errorsincountingbecomemorelikely.Becausethegrainstructurewillvarysomewhatfromfieldtofield,atleastfivewidelyspacedfieldsshouldbeselected.Somemetallographersfeelmorecomfortablecounting10fieldswithabout40to50countsperfield.Formostgrainstructures,atotalcountof400to500interceptsorintersections
E112–96(2004)e1TABLE795%ConfidenceInternalMultipliers,t
No.ofFields,n
567101112
t2.7762.5712.4472.3652.3062.2622.2282.201
No.ofFields,n
1314151617181920
t2.1792.1602.1452.1312.1202.1102.1012.093
FIG.6AverageInterceptCountson500mmTestPattern
over5to10fieldsproducesbetterthan10%relativeaccuracy.Fig.6showstherelationshipbetweentheaverageinterceptcountandthemicroscopicallydeterminedASTMgrainsizenumberasafunctionofmagnification.
14.3.2.2Blindlyselectonefieldformeasurementandapplythetestpatterntotheimage.Atransparencyofthepatternmaybeapplieddirectlytothegroundglass,ortoaphotomicrographwhenpermanentrecordsaredesired.Directcountingusingaproperlysizedreticleintheeyepieceisallowable,butitmayherebeexpectedthatsomeoperatorswillfinddifficultyincountingcorrectlyatthecountdensityrecommended.Com-pletelycounteachcircleinturn,usingamanuallyoperatedcountertoaccumulatethetotalnumberofgrainboundaryintersectionswiththetestpattern.Themanualcounterisnecessarytoavoidbiastowardunrealagreementbetweenapplicationsortowardadesiredresult,andtominimizememoryerrors.Theoperatorshouldavoidkeepingamentalscore.Whenatallycounterisused,scoreanyintersectionofthecirclewiththejunctionofthreegrainsastworatherthanthecorrectvalueof11⁄2;theerrorintroducedisverysmall.14.3.3Foreachfieldcount,calculateNLorPLaccordingto:
N¯L5iNL/MP¯L5iPL/M(9)(10)
15.StatisticalAnalysis
15.1Nodeterminationofaveragegrainsizecanbeanexactmeasurement.Thus,nodeterminationiscompletewithoutalsocalculatingtheprecisionwithinwhichthedeterminedsizemay,withnormalconfidence,beconsideredtorepresenttheactualaveragegrainsizeofthespecimenexamined.Inaccordancewithcommonengineeringpractice,thissectionassumesnormalconfidencetorepresenttheexpectationthattheactualerrorwillbewithinthestateduncertainty95%ofthetime.
15.1.1Manyspecimensvarymeasurablyingrainsizefromonefieldofviewtoanother,thisvariationbeingresponsibleforamajorportionoftheuncertainty.Minimumeffortinmanualmethods,toobtainarequiredprecision,justifiesindividualcountswhoseprecisioniscomparabletothisnaturalvariability(6).Thehighlocalprecisionthatmaybeobtainedbymachinemethodsoftenwillyieldonlyasmallincreaseinoverallprecisionunlessmanyfieldsalsoaremeasured,butdoeshelpdistinguishnaturalvariabilityfrominaccuraciesofcounting.15.2Afterthedesirednumberoffieldshavebeenmeasured,
¯Aor—,fromtheindividualfieldcalculatethemeanvalueofN
valuesaccordingto:
(Xi¯5Xn(12)
¯isthemeanandnwhereXirepresentsanindividualvalue,X
isthenumberofmeasurements.
15.3Calculatethestandarddeviationoftheindividualmeasurementsaccordingtotheusualequation:
¯!2(~Xi2X
s5n21FG½
(13)
whereNiandPiarethenumberofinterceptsorintersections
countedonthefield,Listhetotaltestlinelength(500mm)andMisthemagnification.
14.3.4Calculatethemeanlinealinterceptvalueforeachfield,—,by:
11—,5¯5¯NLPL
(11)
wheresisthestandarddeviation.
15.4Calculatethe95%confidenceinterval,95%CI,ofeachmeasurementaccordingto:
95%CI5
t·s=n(14)
wherethe·indicatesamultiplicationoperation.Table7listsvaluesoftasafunctionofn.
15.5Calculatethepercentrelativeaccuracy,%RA,ofthemeasurementsbydividingthe95%CIvaluebythemeanandexpressingtheresultsasapercentage,thatis:
%RA5
95%CI
·100¯X
(15)
TheaveragevalueofndeterminationsofNL,PL,or—,is
usedtodeterminethemicroscopicallymeasuredASTMgrainsizeusingtheequationsinTable6,thedatashowngraphicallyinFig.6,orthedatainTable4.
12
15.6Ifthe%RAisconsideredtobetoohighfortheintendedapplication,morefieldsshouldbemeasuredandthe
E112–96(2004)e1calculationsin15.1-15.5shouldberepeated.Asageneralrule,a10%RA(orlower)isconsideredtobeacceptableprecisionformostpurposes.
¯Aor—15.7ConvertthemeanvalueofN,totheASTMgrain
sizenumber,G,usingTable4ortheEqsinTable6.16.SpecimenswithNon-equiaxedGrainShapes
16.1Ifthegrainshapewasalteredbyprocessingsothatthegrainsarenolongerequiaxedinshape,grainsizemeasure-mentsshouldbemadeonlongitudinal(,),transverse(t)andplanar(p)orientedsurfacesforrectangularbar,plateorsheettypematerial.Forroundbars,radiallongitudinalandtrans-versesectionsareused.Ifthedeparturefromequiaxedisnottoogreat(see16.2.2),areasonableestimateofthegrainsizecanbedeterminedusingalongitudinalspecimenandthecirculartestgrid.Ifdirectedtestlinesareusedfortheanalysis,measurementsinthethreeprincipaldirectionscanbemadeusingonlytwoofthethreeprincipaltestplanes.16.2PlanimetricMethod:
16.2.1Whenthegrainshapeisnotequiaxedbutelongated,makegraincountsoneachofthethreeprincipalplanes,thatis,planesofpolishonlongitudinal,transverseandplanar-orientedsurfaces.Determinethenumberofgrainspermm2at1Xonthe
¯A,,N¯Atlongitudinal,transverse,andplanarorientedsurfaces,N
¯Ap,respectively,andcalculatethemeannumberofgrainsandN
¯A,fromthethreeN¯Avaluesfromtheprincipalperunitarea,N
planes:
¯5~N¯A,·N¯At·N¯Ap!1/3N
(16)
where·indicatesamultiplicationoperationandthebar
aboveeachquantityindicatesanaveragevalue.
16.2.2Areasonableestimateofthegrainsizecanbemade¯A,aloneifthedeparturefromanequiaxedshapeisnotfromN
excessive(#3:1aspectratio).
¯Afromthe16.2.3CalculateGfromthemeanvalueofN
averagesmadeoneachfield.Performthestatisticalanalysis(15.1-15.5)onlyontheindividualmeasurementsoneachfield.16.3InterceptMethod:
16.3.1Toassessthegrainsizeofnon-equiaxedgrainstructures,measurementscanbemadeusingcirculartestgridsorrandomlyplacedtestlinesoneachofthethreeprincipaltestplanes,orbyuseofdirectedtestlinesineitherthreeorsixoftheprincipaldirectionsusingeithertwoorthreeoftheprincipaltestplanes,seeFig.7.Forspecimenswherethedeparturefromanequiaxedshapeisnotsevere(#3:1aspectratio),areasonableestimateofthegrainsizecanbemadeusingacirculartestgridonthelongitudinalplaneonly.
16.3.2Thegrainsizecanbedeterminedfrommeasurementsofthemeannumberofgrainboundaryintersectionsperunit
¯L,orthemeannumberofgrainsinterceptedperunitlength,P
¯L.Bothmethodsyieldthesameresultsforasinglelength,N
¯LorN¯Lcanbedeterminedusingeitherphasegrainstructure.P
testcirclesoneachoftheprincipalplanesordirectedtestlinesineitherthreeorsixoftheprincipaltestdirectionsshowninFig.7.
NOTE1—Measurementsofrectangularbar,plate,striporsheettypespecimenswithnon-equiaxedgrainstructures.
FIG.7SchematicShowingtheSixPossibleDirectedTestLine
OrientationsforGrainSizeMeasurement
¯Lor16.3.3ForthecaseofrandomlydeterminedvaluesofP
¯Lonthethreeprincipalplanes,computetheaveragevalueN
accordingto:
¯5~P¯L,·P¯Lt·P¯Lp!1/3P
(17)
13
E112–96(2004)e1or
¯5~N¯L,·N¯Lt·N¯Lp!1/3N
(18)
——¯LorN¯LAlternatively,calculate,,,,tand,pfromtheP
valuesoneachplaneusing(Eq11).Then,calculatetheoverall
—meanvalueof,from:
—,5~—,,·—,t·—,p!1/3
(19)
16.3.4Ifdirectedtestlinesareusedintheprincipaldirec-tionsontheprincipalplanes,onlytwooftheprincipalplanes
arerequiredtoperformdirectedcountsinthethreeprincipaldirectionsandobtainanestimateofthegrainsize.
16.3.5Additionalinformationongrainshapemaybeob-—tainedbydetermining,parallel(0°)andperpendicular(90°)tothedeformationaxisonalongitudinallyorientedsurface.Thegrainelongationratio,ortheanisotropyindex,AI,canbedeterminedfrom:
——AI,5,,~0°!/,,~90°!
(20)
16.3.5.1Thethree-dimensionalmeangrainsizeandshapemayalsobedefinedbythedirectedmeanlinealinterceptvaluesonthethreeprincipalplanes.Thesevalueswouldbeexpressedas:
—,,~0°!:—,,~90°!:—,,~90°!
(21)
16.3.5.2Anotherapproachthatcanbeusedistonormalize
thethreeresultsbydividingeachbythevalueofthesmallestwiththeresultsexpressedasratios.16.3.6Themeanvalueof—,forthemeasurementsinthethreeprincipaltestdirectionsisobtainedbyaveragingthe
¯Lvalues(asshownin(Eq22))andthen¯L,orPdirectedN
—computing,fromthismeanvalue;or,bycalculatingdirected—,valuesineachofthethreeprincipaldirectionsandthenaveragingthemaccordingto(Eq23):
¯L,~0°!·P¯Lt~90°!·P¯Lp~90°!!1/3¯P5~P
(22)
¯L.ForcomputingthegrandThisisdoneinlikemannerforN
mean—,fromthedirectedmeanvalues,use:
—
,5~—,,~0°!·—,t~90°!·—,p~90°!!1/3
(23)
Unlessstatedotherwise,theeffectiveaveragegrainsizeshall
bepresumedtobethesizeofthematrixphase.
17.2Theidentityofeachmeasuredphaseandthepercent-ageoffieldareaoccupiedbyeachphaseshallbedeterminedandreported.ThepercentageofeachphasecanbedeterminedaccordingtoPracticeE562.
17.3ComparisonMethod—Thecomparisonchartratingproceduremayprovideacceptableprecisionformostcommer-cialapplicationsifthesecondphase(orconstituent)consistsofislandsorpatchesofessentiallythesamesizeasthematrixgrains;or,theamountandsizeofthesecondphaseparticlesarebothsmallandtheparticlesarelocatedprimarilyalonggrainboundaries.
17.4PlanimetricMethod—Theplanimetricmethodmaybeappliedifthematrixgrainboundariesareclearlyvisibleandthesecondphase(constituent)particlesaremainlypresentbetweenthematrixgrainsratherthanwithinthegrains.Determinethepercentageofthetestareaoccupiedbythesecondphase,forexample,byPracticeE562.Alwaysdeter-minetheamountofthephaseofleastconcentration,usuallythesecondphaseorconstituent.Then,determinethematrixphasebydifference.Next,countthenumberofmatrixgrainscompletelywithinthetestareasandthenumberofmatrixgrainsintersectingthetestareaboundary,asdescribedinSection11.Thetestareamustbereducedtothatcoveredonlybythematrixphasegrains.Theeffectiveaveragegrainsizeisthendeterminedfromthenumberofgrainsperunitnetareaofthematrixphase.Statisticallyanalyzethenumberofgrainsperunitareaoftheamatrixphase,NAa,fromeachfieldmeasurementusingtheapproachdescribedinSection15.
¯Aa,determinetheeffectiveThen,fromtheoverallaverage,N
grainsizeofthematrixusingTable4ortheappropriateequationinTable6.
17.5InterceptMethod—Thesamerestrictionsregardingapplicability,asstatedin17.4,pertaintothismethod.Again,theamountofthematrixphasemustbedetermined,asdescribedin17.4.Atestgridconsistingofoneormoretestcircles,suchasshowninFig.5,isused.Forthisapplication,countthenumberofmatrixgrains,Na,interceptedbythetestline.Determinethemeaninterceptlengthofthematrixphaseaccordingto:
~VVa!~L/M!—,a5Na
wherethe·indicatesamultiplicationoperation.
16.3.7Themeangrainsizeisdeterminedfromtheoverall
¯Lor,usingTable4ortheequationsinTable¯L,NaveragesofP
6.Additionalinformationonthemeasurementofgrainsizefornon-equiaxedstructurescanbefoundinAnnexA1ofTestMethodsE1382.
16.4Statisticalanalysisshouldbeperformedonthedatafromeachplaneoreachprincipaltestdirectionaccordingtotheprocedurein15.1-15.5.
17.SpecimensContainingTwoorMorePhasesor
Constituents
17.1Minoramountsofsecondphaseparticles,whetherdesireableorundesireablefeatures,maybeignoredinthedeterminationofgrainsize,thatis,thestructureistreatedasasinglephasematerialandthepreviouslydescribedplanimetricorinterceptmethodsareusedtodeterminethegrainsize.
14
(24)
wherethevolumefractionoftheamatrix,VVa,isexpressedasafraction,ListhetestlinelengthandMisthemagnifica-tion.ThegrainsizeoftheagrainsisdeterminedusingTable4ortheequationinTable6.Inpractice,itisinconvenienttomanuallydeterminethevolumefractionoftheaphaseandthenumberofagrainsinterceptingthetestlineforeachfield.Ifthisisdone,themeanlinealinterceptlengthoftheaphaseforeachfieldcanbedeterminedandthisdatacanbestatisticallyanalyzedforeachfieldaccordingtotheproceduredescribedinSection15.IfVVaandNaarenotmeasuredsimultaneouslyforthesamefields,thenthestatisticalanalysiscanonlybeperformedontheVVaandNadata.
17.6Itisalsopossibletodetermine—,bymeasurementofindividualinterceptlengthsusingparallelstraighttestlinesappliedrandomlytothestructure.Donotmeasurethepartial
aE112–96(2004)e1interceptsattheendsofthetestlines.Thismethodisrathertediousunlessitcanbeautomatedinsomeway.TheindividualinterceptsareaveragedandthisvalueisusedtodetermineGfromTable4ortheequationinTable6.Theindividualinterceptsmaybeplottedinahistogram,butthisisbeyondthescopeofthesetestmethods.
18.Report
18.1Thetestreportshoulddocumentallofthepertinentidentifyinginformationregardingthespecimen,itscomposi-tion,specificationdesignationortradename,customerordatarequester,dateoftest,heattreatmentorprocessinghistory,specimenlocationandorientation,etchantandetchmethod,grainsizeanalysismethod,andsoforth,asrequired.
18.2Listthenumberoffieldsmeasured,themagnification,andfieldarea.Thenumberofgrainscountedorthenumberofinterceptsorintersectionscounted,mayalsoberecorded.Foratwo-phasestructure,listtheareafractionofthematrixphase.18.3Aphotomicrographillustratingthetypicalappearanceofthegrainstructuremaybeprovided,ifrequiredordesired.18.4Listthemeanmeasurementvalue,itsstandarddevia-tion,95%confidenceinterval,percentrelativeaccuracy,andtheASTMgrainsizenumber.
18.4.1Forthecomparisonmethod,listonlytheestimatedASTMgrainsizenumber.
18.5Foranon-equiaxedgrainstructure,listthemethodofanalysis,planesexamined,directionsevaluated(ifapplicable),thegrainsizeestimateperplaneordirection,thegrandmeanoftheplanarmeasurements,andthecomputedorestimatedASTMgrainsizenumber.
18.6Foratwo-phasestructure,listthemethodofanalysis,theamountofthematrixphase(ifdetermined),thegrainsizemeasurementofthematrixphase(andthestandarddeviation,95%confidenceinterval,andpercentrelativeaccuracy),andthecomputedorestimatedASTMgrainsizenumber.
18.7Ifitisdesiredtoexpresstheaveragegrainsizeofagroupofspecimensfromalot,donotsimplyaveragetheASTMgrainsizenumbers.Instead,computeanarithmetic
¯Aor,valuesaverageoftheactualmeasurements,suchas,theN
perspecimen.Then,fromthelotaverage,calculateorestimate
¯AortheASTMgrainsizeforthelot.ThespecimenvaluesofN
,mayalsobestatisticallyanalyzed,accordingtotheapproachinSection15,toevaluatethegrainsizevariabilitywithinthelot.
19.PrecisionandBias
19.1Theprecisionandbiasofgrainsizemeasurementsdependontherepresentativenessofthespecimensselectedandtheareasontheplane-of-polishchosenformeasurement.Ifthegrainsizevarieswithinaproduct,specimenandfieldselectionmustadequatelysamplethisvariation.
19.2Therelativeaccuracyofthegrainsizemeasurementoftheproductimprovesasthenumberofspecimenstakenfromtheproductincreases.Therelativeaccuracyofthegrainsizemeasurementofeachspecimenimprovesasthenumberoffieldssampledandthenumberofgrainsorinterceptscountedincrease.
19.3Biasinmeasurementswilloccurifspecimenprepara-tionisinadequate.Thetruestructuremustberevealedandthe
15
grainboundariesmustbefullydelineatedforbestmeasurementprecisionandfreedomfrombias.Asthepercentageofnon-delineatedgrainboundariesincreases,biasincreasesandpre-cision,repeatability,andreproducibilitybecomepoorer.
19.4Inaccuratedeterminationofthemagnificationofthegrainstructurewillproducebias.
19.5Ifthegrainstructureisnotequiaxedinshape,forexample,ifthegrainshapeiselongatedorflattenedbydeformation,measurementofthegrainsizeononlyoneplane,particularlytheplaneperpendiculartothedeformationdirec-tion,willbiastestresults.Grainshapedistortionisbestdetectedusingatestplaneparalleltothedeformationdirection.Thesizeofthedeformedgrainsshouldbebasedonmeasure-mentsmadeontwoorthreeoftheprincipalplaneswhichareaveragedasdescribedinSection16.
19.6Specimenswithaunimodalgrainsizedistributionaremeasuredforaveragegrainsizeusingthemethodsdescribedinthesetestmethods.Specimenswithbimodal(ormorecom-plex)sizedistributionsshouldnotbetestedusingamethodthatyieldsasingleaveragegrainsizevalue;theyshouldbecharacterizedusingthemethodsdescribedinTestMethodsE1181andmeasuredusingthemethodsdescribedinTestMethodsE112.ThesizeofindividualverylargegrainsinafinegrainedmatrixshouldbedeterminedusingTestMethodsE930.
19.7Whenusingthecomparisonchartmethod,thechartselectedshouldbeconsistentwiththenatureofthegrains(thatis,twinnedornon-twinned,orcarburizedandslowcooled)andtheetch(thatis,flatetchorgraincontrastetch)forbestprecision.
19.8Grainsizeratingsusingthecomparisonchartmethodbyanindividualmetallographerwillvarywithin60.5Gunits.Whenanumberofindividualsratethesamespecimen,thespreadinratingsmaybeasgreatas1.5to2.5Gunits.
19.9Thefracturegrainsizemethodisonlyapplicabletohardened,relativelybrittle,toolsteels.Specimensshouldbeintheas-quenchedorlightlytemperedconditionsothatthefracturesurfaceisquiteflat.Anexperiencedmetallographercanratetheprior-austenitegrainsizeofatoolsteelwithin60.5GunitsbytheShepherdfracturegrainsizemethod.19.10Aroundrobintestprogram(seeAppendixX1),analyzedaccordingtoPracticeE691,revealedarathercon-sistentbiasbetweencomparisonchartratingsusingPlateIandgrainsizemeasurementsusingboththeplanimetricandinter-ceptmethods.Chartratingswere0.5to1Gunitcoarser,thatis,lowerGnumbers,thanthemeasuredvalues.
19.11Grainsizesdeterminedbyeithertheplanimetricorinterceptmethodsproducedsimilarresultswithnoobservedbias.
19.12Therelativeaccuracyofgrainsizemeasurementsimprovedasthenumberofgrainsorinterceptscountedincreased.Forasimilarnumberofcounts,therelativeaccuracyofinterceptmeasurementswasbetterthanthatofplanimetricmeasurementsofgrainsize.Fortheinterceptmethod,10%RA(orless)wasobtainedwithabout400interceptorinter-sectioncountswhilefortheplanimetricmethod,toobtain10%RA,orless,about700grainshadtobecounted.Repeatabilityandreproducibilityofmeasurementsimprovedasthenumber
E112–96(2004)e1ofgrainsorinterceptscountedincreasedandwasbetterfortheinterceptmethodthanfortheplanimetricmethodforthesamecount.
19.13Theplanimetricmethodrequiresamarkingoffofthegrainsduringcountinginordertoobtainanaccuratecount.Theinterceptmethoddoesnotrequiremarkinginordertogetanaccuratecount.Hence,theinterceptmethodiseasiertouseandfaster.Further,theroundrobintestshowedthattheinterceptmethodprovidesbetterstatisticalprecisionforthesamenumberofcountsandis,therefore,thepreferredmeasurementmethod.
19.14Anindividualmetallographercanusuallyrepeatplanimetricorinterceptgrainsizemeasurementswithin60.1Gunits.Whenanumberofmetallographersmeasurethesamespecimen,thespreadofgrainsizesisusuallywellwithin60.5Gunits.
20.Keywords
20.1ALAgrainsize;anisotropyindex;areafraction;ASTMgrainsizenumber;calibration;equiaxedgrains;etchant;grainboundary;grains;grainsize;interceptcount;interceptlength;intersectioncount;non-equiaxedgrains;twinboundaries
ANNEXES
(MandatoryInformation)
A1.BASISOFASTMGRAINSIZENUMBERS
A1.1DescriptionsofTermsandSymbols
A1.1.1Thegeneraltermgrainsizeiscommonlyusedtodesignatesizeestimatesormeasurementsmadeinseveralways,employingvariousunitsoflength,area,orvolume.Ofthevarioussystems,onlytheASTMgrainsizenumber,G,isessentiallyindependentoftheestimatingsystemandmeasure-mentunitsused.TheequationsusedtodetermineGfromrecommendedmeasurements,asillustratedinFig.6andTable2andTable4,aregiveninA1.2andA1.3.ThenominalrelationshipsbetweencommonlyusedmeasurementsaregiveninAnnexA2.Measurementsthatappearintheseequations,orinequationsinthetext,areasfollows:
A1.1.1.1N=Numberofgrainsectionscountedonaknowntestarea,A,ornumberofinterceptscountedonaknowntestarrayoflength=L,atsomestatedmagnification,
¯.M.TheaverageofcountsonseveralfieldsisdesignatedasN
A1.1.1.2Aftercorrectionformagnification,NAisthenum-berofgrainsectionsperunittestarea(mm2)at1X;NListhenumberofgrainsinterceptedperunitlength(mm)oftestlinesat1X;andPListhenumberofgrainboundaryintersectionsperunitlength(mm)oftestlineat1X.
—
A1.1.1.3—,=1/NL=1/PLwhere,isthemeanlinealinterceptlengthinmmat1X.
¯isthemeanareaofthegrain¯=1/NAwhereAA1.1.1.4A
—
sections(mm2)at1X.Themeangraindiameter,d,isthe
¯.GrainsizevaluesonPlateIIIareexpressedinsquarerootofA
termsofd¯.NotethatTable2liststheequivalentASTMgrainsizenumberforeachchartpictureandforseveraldifferentmagnifications.
A1.1.1.5Theletters,,tandpareusedassubscriptswhenassessingthegrainsizeofspecimenswithnon-equiaxedgrainstructures.Thethreesubscriptsrepresenttheprincipalplanesforrectangularbar,plate,sheet,orstripspecimens,thatis,thelongitudinal(,),transverse(t)andplanar(p)surfaces.Theyaremutuallyperpendiculartoeachother.Oneachplane,therearetwoprincipaldirectionsthatareperpendiculartoeachother(asillustratedinFig.7).
A1.1.1.6Thenumberoffieldsmeasuredisdesignatedbyn.
16
A1.1.1.7Otherspecificdesignationsaredefinedbyequa-tionswhichfollow.
A1.2InterceptMethods:A1.2.1Metricunits,—,inmillimetresat100Xformicro-scopicallydeterminedgrainsizesand—,mat1Xformacro-scopicallydeterminedgrainsizes,areusedwiththefollowing
——
equationrelating,or,mtoG.Formacroscopicallydeter-—minedgrainsizes,,misinmmat100X:
,0
G52log2—,m
(A1.1)
forG=0,,0isestablishedas32.00andlog2,0=5.
G5110.00022log2,m—
G5110.000026.39log10,m
(A1.2)(A1.3)
Formicroscopicallydeterminedgrainsizes,,¯isinmillime-tresat1Xand:
G5–3.287726.39log10—,¯LG5–3.287712log2N¯LG5–3.287716.39log10N
(A1.4)(A1.5)(A1.6)
¯LisdeterminedinsteadofN¯L,substituteP¯LforN¯LinEqIfP
A1.5andEqA1.6.
A1.3PlanimetricMethod:
¯AEinnumberpersquareinchesatA1.3.1Englishunits,N
100Xformicroscopicallydeterminedgrainsizesandat1Xformacroscopicallydeterminedgrainsizes,areusedwiththe
¯AEtoG:followingequationsrelatingN
¯AEG51.0001log2N¯AEG51.00013.3219log10N
(A1.7)(A1.8)
¯AisexpressedintermsofthenumberofgrainspersquareIfN
millimetresat1X,formicroscopicallydeterminedgrainsizes,then:
E112–96(2004)e1¯AG52.954213.3219log10N
(A1.9)
A2.EQUATIONSFORCONVERSIONSAMONGVARIOUSGRAINSIZEMEASUREMENTS
A2.1ChangeofMagnification—Iftheapparentgrainsize
hasbeenobservedatmagnificationM,butdeterminedasifatthebasicmagnificationMb(100Xor1X),thenthesizevalueatthebasicmagnificationisasfollows:A2.1.1PlanimetricCount:
NA5NA0~M/Mb!2
(A2.1)
¯51/NAA
(A2.7)
¯istheaveragegraincrosssectionalarea.whereA
A2.2.2InterceptWidthofaCircularGrainSection:
p—¯,54A
SD1/2
(A2.8)
whereNA0isthenumberofgrainsperunitareaat
magnificationMb.
A2.1.2InterceptCount:
Ni5Ni0~M/Mb!
(A2.2)
Themeaninterceptdistanceforpolygonalgrainsvariesaboutthistheoreticalvalue,beingdecreasedbyanisotropybutincreasedbyarangeofsectionsizes.Thewidthcomputedby(EqA2.8)is0.52%smallerthanthewidthassignedtoGby(EqA1.4)inA1.2.1(D=+0.015ASTMNo.).
A2.3Otherusefulsizeindicationsaregivenbythefollow-ingequations:
¯,ofsimilarsizeA2.3.1Thevolumetric(spatial)diameter,D
spheresinspaceis:
¯51.5—D,
(A2.9)
whereNi0isthenumberofgrainsinterceptedbythetestline
(theequationforPiandPi0isthesame)atmagnificationMb.A2.1.3AnyLength:
,¯5,¯0Mb/M
(A2.3)
where,¯0isthemeanlinealinterceptatmagnificationMb.
A2.1.4ASTMGrainSizeNumber:
G5G01Q
(A2.4)
where:
Q=2log2(M/Mb)
=2(log2M−log2Mb)
=6.39(log10M−log10Mb)
whereG0istheapparentASTMgrainsizenumberatmagnificationMb.
A2.1.5Grainspermm2at1Xfromgrainsperin.2at100X:
NA5NAE~100/25.4!2
NA515.5NAE
(A2.5)(A2.6)
Similarrelationshipsbetween—,,determinedonthetwo-¯,havedimensionalplaneofpolish,andthespatialdiameter,D
beenderivedforavarietyofpotentialgrainshapes,andvariousassumptionsabouttheirsizedistribution.Anumberofformu-lae,suchasequation(EqA2.7),havebeenproposedwithdifferentmultiplyingfactors.Areasonableestimateofthe
¯,baseduponthetetrakaidecahedronshapespatialdiameter,D
modelandagrainsizedistributionfunction(8),is:
¯D51.571,¯
(A2.10)
whereNAisthenumberofgrainspermm2at1XandNAEis
thenumberofgrainsperin.2at100X.
A2.2Othermeasurementsshowninthetablesmaybecomputedfromthefollowingequations:A2.2.1AreaofAverageGrain:
A2.3.2Forasinglephasemicrostructure,thegrainbound-arysurfaceareaperunitvolume,SV,hasbeenshowntobeanexactfunctionofPLorNL:
SV52PL52NL
(A2.11)
whileforatwophasemicrostructure,thephaseboundarysurfaceareaperunitvolumeoftheaphase,SVa,is:
SVa52PL54NL
(A2.12)
A3.AUSTENITEGRAINSIZE,FERRITICANDAUSTENITICSTEELS
A3.1Scope
A3.1.1Becauseitissometimesnecessarytosubjectmate-rialtospecialtreatmentsortechniquesinordertodevelopcertaingraincharacteristicspriortotheestimationofgrainsize,theessentialdetailsofthesetreatmentsaresetforthinthefollowingsections.
A3.2EstablishingAusteniteGrainSize
A3.2.1FerriticSteels—Unlessotherwisespecified,auste-nitegrainsizeshallbeestablishedbyoneofthefollowingprocedures:
NOTEA3.1—Theindicationsofcarboncontentsintheprocedureheadingsareadvisoryonly.Numerousmethodsareinuseforestablishingaustenitegrainsize,andaknowledgeofgraingrowthandgraincoarsen-ingbehaviorishelpfulindecidingwhichmethodtouse.Thesizeofaustenitegrains,inanyparticularsteel,dependsprimarilyonthetempera-turetowhichthatsteelisheatedandthetimeitisheldatthetemperature.Itshouldberememberedthattheatmosphereinheatingmayaffectthegraingrowthattheoutsideofthepiece.Austenitegrainsizeisalsoinfluencedbymostprevioustreatmentstowhichthesteelmayhavebeensubjectedas,forexample,austenitizingtemperature,quenching,normal-izing,hotworking,andcoldworking.Itisthereforeadvisable,when
17
E112–96(2004)e1testingforaustenitegrainsize,toconsidertheeffectsofpriororsubsequenttreatments,orboth,ontheprecisepiece(ortypicalpiece)thatisunderconsideration.
A3.2.1.1CorrelationProcedure(CarbonandAlloySteels)—Testconditionsshouldcorrelatewiththeactualheat-treatmentcycleusedtodevelopthepropertiesforactualservice.Heatthespecimensatatemperaturenotover50°F(28°C)abovethenormalheat-treatingtemperatureandfornotover50%morethanthenormalheat-treatingtimeandundernormalheat-treatingatmosphere,thenormalvaluesbeingthosemutuallyagreedupon.Therateofcoolingdependsonthemethodoftreatment.MakethemicroscopicalexaminationincompliancewithTable1.
A3.2.1.2CarburizingProcedure(CarbonandAlloySteels;CarbonGenerallyBelow0.25%)—ThisprocedureisusuallyreferredtoastheMcQuaid—EhnTest.Unlessotherwisespecified,carburizethespecimensat1700625°F(927614°C)for8horuntilacaseofapproximately0.050in.(1.27mm)isobtained.Thecarburizingcompoundmustbecapableofproducingahypereutectoidcaseinthetimeandatthetemperaturespecified.Furnacecoolthespecimentoatempera-turebelowthelowercriticalatarateslowenoughtoprecipitatecementiteintheaustenitegrainboundariesofthehypereutec-toidzoneofthecase.Whencool,sectionthespecimentoprovideafresh-cutsurface,polish,andsuitablyetchtorevealthegrainsizeofthehypereutectoidzoneofthecase.MakeamicroscopicalexaminationincompliancewithTable1.WhiletheMcQuaid-Ehntestwasdesignedforevaluatingthegraingrowthcharacteristicsofsteelsintendedforcarburizingappli-cations,usuallysteelswith<0.25%carbon,itisfrequentlyusedtoevaluatesteelswithhighercarboncontentsthatwillnotbecarburized.Itmustberecognizedthatthegrainsizeofsuchsteelswhenheattreatedfromaustenitizingtemperaturesbelow1700°FmaybefinerinsizethanthatobtainedbytheMcQuaid-Ehntest.
A3.2.1.3MockCarburizingProcedure—TheheattreatmentdescribedinA3.2.1.2isperformedbutacarburizingatmo-sphereisnotusedandthespecimenmustbequenchedfromthemockcarburizingtemperatureataratefastenoughtoformmartensite,ratherthanslowlycooledaftercarburizing.Thespecimenissectioned(carefulabrasivecut-offcuttingisrequiredtopreventburning),polishedandetchedwithareagentthatwillrevealtheprior-austenitegrainboundaries(suchassaturatedaqueouspicricacidwithawettingagent,seePracticeE407).MockcarburizingissometimespreferredbecausethedepthofthecarburizedcaseproducedbytheMcQuaid-Ehntestmaybequitethinwithsomesteels.Withamockcarburizedspecimen,allofthegrainsonthecrosssectioncanbeexamined.Problemssuchasbandedgrainsize,duplexorALAgrains(seeTestMethodsE1181)aremoreeasilydetectedwithamockcarburizedspecimenduetothemuchgreatersurfaceareaforexamination.
A3.2.1.4HypoeutectoidSteels(CarbonandAlloySteels0.25to0.60%Carbon)—Unlessotherwisespecified,heatspecimensofsteelswithacarboncontentof0.35%orlessat1625625°F(885614°C);heatspecimensofsteelwithacarboncontentofover0.35%at1575625°F(857614°C)foraminimumof30minandcoolinairorquenchinwater.
18
Thehighercarbonsteelsinthisrangeandalloysteelsoverapproximately0.40%carbonmayrequireanadjustmentincoolingpracticetooutlineclearlytheaustenitegrainbound-arieswithferrite.Insuchcasesitisrecommendedthatafterholdingthespecimenfortherequiredtimeatahardeningtemperature,thetemperaturebereducedtoapproximately1340625°F(727614°C)for10min,followedbywateroroilquench.Whencool,sectionthespecimentoprovideafresh-cutsurface,polish,andsuitablyetchtorevealtheaustenitegrainsizeasoutlinedbyprecipitatedferriteinthegrainboundaries.MakethemicroscopicalexaminationincompliancewithTable1.
A3.2.1.5OxidationProcedure(CarbonandAlloySteels0.25to0.60%Carbon)—Polishoneofthesurfacesofthespecimen(approximately400-gritor15-µmabrasive).Placethespecimenwiththepolishedsideupinafurnace,and,unlessotherwisespecified,heatat1575625°F(857614°C)for1handquenchincoldwaterorbrine.Polishthequenchedspecimentorevealtheaustenitegrainsizeasdevelopedintheoxidizedsurface.MakethemicroscopicalexaminationincompliancewithTable1.
A3.2.1.6DirectHardeningSteels(CarbonandAlloySteels;CarbonGenerallyBelow1.00%)—Unlessotherwisespeci-fied,heatspecimensofsteelswithacarboncontentof0.35%orlessat1625625°F(885614°C);heatspecimensofsteelswithacarboncontentofover0.35%at1575625°F(857614°C)forsufficienttimeandquenchataratetoproducefullhardening.Polishthequenchedspecimenandetchtorevealthemartensiticstructure.Temperingfor15minat450625°F(232614°C)priortoetchingimprovesthecontrast.MakethemicroscopicalexaminationincompliancewithTable1.
A3.2.1.7HypereutectoidSteels(CarbonandAlloySteels;CarbonGenerallyOver1.00%)—Useaspecimenapproxi-mately1in.(25.4mm)indiameteror1in.squareforthistest.Unlessotherwisespecified,heatthespecimenat1500625°F(816614°C)foraminimumof30min,andfurnacecooltoatemperaturebelowthelowercriticaltemperatureatarateslowenoughtoprecipitatecementiteintheaustenitegrainbound-aries.Whencool,sectionthespecimentoprovideafresh-cutsurface,polish,andsuitablyetchtorevealtheaustenitegrainsizeasoutlinedbyprecipitatedcementiteinthegrainbound-aries.MakethemicroscopicalexaminationincompliancewithTable1.
A3.2.2AusteniticSteels—Withausteniticmaterials,theac-tualgrainsizeofthemetalhasbeenestablishedbypriorheat-treatment.
A3.3RevealingtheGrainSize
A3.3.1FerriticSteels—Forrevealingaustenitegrainsizethefollowingmethods(seeNoteA3.1)aregenerallyused:A3.3.1.1OutliningtheGrainswithCementite—Inthehy-pereutectoidzoneofacarburizing(McQuaid—Ehntest)pro-cedureorinhypereutectoidsteelscooledfromtheausteniticcondition,theaustenitegrainsizeisoutlinedbythecementitewhichprecipitatedinthegrainboundaries.Itisthereforepossibletoratethegrainsizebyetchingthemicrographicspecimenwithasuitableetchant,suchasnital,picral,oralkalinesodiumpicrate.(SeePracticeE407.)
E112–96(2004)e1A3.3.1.2OutliningtheGrainswithFerrite—Inthehypoeu-tectoidzoneofacarburizedspecimen,theaustenitegrainsizeisoutlinedbytheferritethatprecipitatedinthegrainbound-aries.Ferritesimilarlyoutlinestheformeraustenitegrainsinamedium-carbonsteel(approximately0.50%carbon),whenithasbeencooledslowlyfromtheausteniterange.Inlow-carbonsteels(approximately0.20%carbon),coolingslowlyfromtheausteniterangetoroomtemperature,theamountofferriteissolargethattheformeraustenitegrainsizeismasked;inthiscase,thesteelmaybecooledslowlytoanintermediatetemperature,toallowonlyasmallamountofferritetoprecipitate,followedbyquenchinginwater;anexamplewouldbeapiecepreviouslyheatedto1675°F(913°C),transferredtoafurnaceatbetween1350to1450°F(732to788°C),heldatthistemperatureforperhaps3to5min,andthenquenchedinwater;theaustenitegrainsizewouldberevealedbysmallferritegrainsoutlininglow-carbonmartensitegrains.
A3.3.1.3OutliningtheGrainsbyOxidation—Theoxidationmethoddependsonthefactthatwhensteelsareheatedinanoxidizingatmosphere,oxidationtakesplaceinpartpreferen-tiallyalongthegrainboundaries.Acommonprocedure,therefore,istopolishthetestspecimentoametallographicpolish,heatitinairatthedesiredtemperatureforthedesiredlengthoftime,andthenrepolishthespecimenlightlysoasmerelytoremovescale;whereupontheaustenitegrainbound-ariesarevisibleasoutlinedbyoxide.
A3.3.1.4OutliningMartensiteGrainswithFinePearlite—Amethodapplicableparticularlytoeutectoidsteels,whichcannotbejudgedsoreadilybysomeothermethods,iseithertohardenabarofsuchasizethatitisfullyhardenedattheoutsidebutnotquitefullyhardenedintheinterior,ortoemployagradientquenchinwhichtheheatedpieceisforaportionofitslengthimmersedinwaterandthereforefullyhardened,theremainderofthepieceprojectingabovethequenchingbath,beingthereforenothardened.Witheithermethodtherewillbeasmallzonewhichisalmostbutnotquitefullyhardened.Inthiszone,theformeraustenitegrainswillconsistofmartensitegrainssurroundedbysmallamountsoffinepearlite,thusrevealingthegrainsize.Thesemethodsarealsoapplicabletosteelssomewhatlowerandhigherthantheeutectoidcomposition.
A3.3.1.5EtchingofMartensiteGrains—Theformerauste-nitegrainsizemayberevealedinsteelsfullyhardenedtomartensitebyusinganetchingreagentthatdevelopscontrastbetweenthemartensitegrains.Temperingfor15minat450°F(232°C)priortoetchingdistinctlyimprovesthecontrast.Areagentthathasbeenrecommendedis1gofpicricacid,5mLofHCl(spgr1.19),and95mLofethylalcohol.Analternateapproachistouseanetchantthatrevealstheprior-austenitegrainboundariespreferentially.Manyetchantshavebeen
developedforthispurpose(seePracticeE407andstandardtextbooks).Themostsuccessfulconsistsofsaturatedaqueouspicricacidcontainingawettingagent,usuallysodiumtride-cylbenzenesulfonate(thedodecylversionalsoworkswell).Specimensshouldbeintheas-quenchedconditionortemperednotaboveabout1000°F.Successwiththisetchantdependsuponthepresenceofphosphorusinthealloy($0.005%Prequired).Resultsmaybeenhancedbytemperingthesteelbetween850and900°Ffor8hormoretodrivephosphorustothegrainboundaries.Forsteelswithsubstantialalloyaddi-tions,itmaybenecessarytoaddafewdropsofhydrochloricacidtotheetchant(per100mLofetchant).Etchingusuallytakesatleast5min.Theetchantwillattacksulfideinclusions.Lightlyre-polishingthespecimenonastationarywheeltoremovesomeoftheunimportantbackgrounddetailmaymakeiteasiertoseethegrainboundaries.
A3.3.2AusteniticSteels—Forrevealingthegrainsizeinausteniticmaterials,asuitableetchingtechniqueshallbeusedtodevelopgrainsize.Recognizingthattwinningtendstoconfusereadingofgrainsize,theetchingshouldbesuchthataminimumamountoftwinningisevident.
A3.3.2.1StabilizedMaterial—Thespecimen,astheanode,maybeelectrolyticallyetchedinawatersolutioncomposedof60%concentratednitricacidbyvolume,atambienttempera-ture.Tominimizetheappearanceoftwinning,alowvoltage(1to11⁄2V)shouldbeused.Thisetchantisalsorecommendedforrevealingferritegrainboundariesinferriticstainlesssteelsandisusedidentically.
A3.3.2.2UnstabilizedMaterial—Thegrainboundarymaybedevelopedthroughprecipitationofcarbidesbyheatingwithinthesensitizingtemperaturerange,482to704°C(900to1300°F).Anysuitablecarbide-revealingetchantshouldbeused.
A3.4ReportingtheGrainSize
A3.4.1FerriticSteels—Duplex,ormixedgrain-sizedstruc-ture(seeTestMethodsE1181)whenobserved,shallbereportedwithtworepresentativerangesofgrainsizenumbers.Wheneverheat-treatmentsotherthanthecarburizing(McQuaid—Ehntest)procedureareemployedtodevelopaustenitegrainsize,acompletereportshallbemadewhichincludes:
A3.4.1.1Temperatureusedinestablishingthegrainsize,A3.4.1.2Timeattemperatureusedinestablishingthegrainsize,
A3.4.1.3Methodofrevealinggrainsize,andA3.4.1.4Grainsize.
A3.4.2AusteniticSteels—Indeterminingthesizeofauste-niticgrains,thetwinboundarieswithinagrainshallnotbecounted.
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E112–96(2004)e1A4.FRACTUREGRAINSIZEMETHOD8A4.1Thefracturegrainsizemethod,developedbyArpi(9),andShepherd(2),employsagradedseriesoftenfracturedspecimenstoestimatetheprior-austenitegrainsizeofsteelspecimens(seeFootnote11forapplicablematerials)bycomparison.Carburizedcasesofcarbonandalloysteelsmayalsobeevaluatedforprior-austenitegrainsizebythismethod(butnotthelow-carboncore).
A4.2ThetenfracturedspecimensarenumberedfromonetotenwherethenumberscorrespondtoASTMgrainsizenumbers.Thesampletoberatedisfractured,usuallytrans-versetothehotworkingdirection,andthefractureiscomparedtothetentestfracturesoftheShepherdseries.9Thefractureappearanceofthespecimenisratedtothenearestwholenumberofthestandard,butinterpolationtoone-halfnumbersispermitted.Itisalsopossibletorateduplexconditionswhenthefractureexhibitstwodifferentfracturepatterns.
A4.3Specimenscanbefracturedbystrikingthefreeend,whilerestrainingtheotherend,orbythree-pointbendingusingapress,oratensilemachine(loadedincompression)oranyothersuitablemethod.Notchingofspecimensorrefrigeration
Thismethodisapplicableonlytohigh-hardness,brittlesteelswithapredomi-nantlymartensitemicrostructure,suchastoolsteels,high-carbonsteelsandmartensiticstainlesssteels,andshouldbedonewiththespecimenintheas-quenchedorlightlytemperedcondition.9ForthoseindividualswhodonotpossessaShepherdstandardseries,aphotographicreproductionisavailablefromASTMHeadquarters.OrderADJE011224.
8priortofracturing,orboth,helpstoensureaflatfracture.ForfurtherinformationseeVanderVoort(10).
A4.4Thespecimentoberatedmustbepredominantlymartensitic,althoughlargeamountsofretainedaustenitedonotinvalidatetheresults.Appreciableamountsofresidualcarbidearealsopermitted.However,diffusioncontrolledtransformationproducts,suchasbainite,pearlite,orferrite,ifpresentinamountsmorethanafewpercent,changethenatureofthefractureappearanceandinvalidatefracturegrainsizeratings.Excessivetemperingofmartensitictoolsteelstructuresalsoaltersthefractureappearanceandinvalidatesfracturegrainsizeratings.Ratingsaremostaccurateforas-quenchedorlightlytemperedspecimens.Flat,brittlefracturesaredesiredtoobtainthebestaccuracy.
A4.5Studieshaveshownthatfracturegrainsizeratingsoffullyhardened,as-quenchedtoolsteelscorrelatewellwithmicroscopicallymeasuredprior-austenitegrainsizeratings.Formosttoolsteels,thefracturegrainsizeratingwillbewithin61unitofthemicroscopicallydeterminedprior-austenitegrainsizenumber,G.
A4.6Thefracturegrainsizemethodcannotbeusedtorategrainsizesfinerthanten.Fracturesofspecimenswithprior-austenitegrainsizesfinerthantencannotbediscriminatedbyeyeandwillberatedasiftheywereatengrainsize.Fracturescoarserthanagrainsizenumberofonewillappeartobecoarserthanonebutcannotbeaccuratelyratedbythismethod.
A5.REQUIREMENTSFORWROUGHTCOPPERANDCOPPER-BASEALLOYS
A5.1Forwroughtcopperandcopper-basealloyproductsunderthejurisdictionofCommitteeB-5onCopperandCopperAlloys,itismandatorythatthefollowingproceduresbefollowed:
A5.1.1ThespecimenshallbepreparedinaccordancewithPracticeE3.
A5.1.2Thespecimenusedforthecomparisonmethodshallbecontrastetched,andcomparedwithPlateIII,or,ifgivenaflatetch,comparedwithPlateII.
A5.1.3Thegrainsizeshallbeexpressedastheaveragegraindiameterinmillimetres;forexample,0.025-mmaveragegraindiameter.Themeaningofthisexpressionisthediameteroftheaveragecrosssectionofgrainslyingintheplaneofthemetalbeingexamined.
A5.1.4Mixedgrainsizes(seeTestMethodsE1181)aresometimesencountered,particularlyinhot-workedmetal.Theseshallbeexpressedbygivingtheestimatedareapercent-agesoccupiedbythetworangesofsizes.Forexample,50%of0.015mm;and50%of0.070mm;or,ifarangeexists,40%of0.010to0.020mm;and60%of0.090to0.120mm.
A5.1.5Fordeterminingcomplianceofrequirementsforgrainsizewiththespecifiedlimits,theestimatedvalueshallberoundedinaccordancewith:
GrainSize
Upto0.055mm,inclOver0.055mm
CalculatedorObservedValuetoWhichGrainSize
ShouldbeRounded
tothenearestmultipleof0.005mmtothenearest0.010mm
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E112–96(2004)e1A6.APPLICATIONTOSPECIALSITUATIONS
A6.1Numerousspecificpracticesforgrainsizemeasure-menthavebecomeestablishedinvarioussegmentsofthemetalsandmaterialsindustries.Thepresentlistingofstandardmethodsisnotintendedtoimplythatanysuchspecificpracticeshouldbeabandonedwhenexperiencehasshownthatpracticetobeadequatefortheintendedapplication.Itis,however,stronglyrecommendedthatthestatisticalprocedureofSection15beappliedtothedatafromthesetraditionalpracticesinordertoensurethattheyyieldaconfidencelimitthatisadequateforcurrentrequirements.
A6.2ItischaracteristicofmanyspecialpracticesthattheyreportanumericalresultthatisnotconvenientlyrelatedtocommonlyusedsizescalessuchasareshowninTable4.Continuedusageofthecustomarynumbersisjustifiedonthegroundsthateithertheyhaveinherentmeaningintheirowncommunity,orthattheyhaveacquiredmeaningthroughlongusage.Itis,however,stronglyrecommendedthatsuchmea-surementsbemadecomprehensibletoawideraudiencefirstbyreexpressionononeofthepreferredmetricscales(asusedinTable4),andthenbyconversiontothecorrespondingASTMgrainsizenumbers.Wheretheoriginalmeasurementsrepre-sentsomeformofinterceptorplanimetriccountitmaybesaidthattheASTMgrainsizenumberhasinfactbeendetermined.Wheretheoriginaldataareofadifferentnature,itshouldbestatedthatthemeasurementisequivalenttoASTMgrainsize
No.“x”.ConversionsmaybemadeeitherthroughTable4orthroughtherelationsshowninAnnexA1andAnnexA2.A6.3Examples:
A6.3.1Example1—TheSnyderandGraffprocedure(11)remainsingeneralusageforestimatingtheausteniticgrainsizeoftoolsteels.ThisisaspecificversionoftheHeyninterceptmethod(see13.1)inwhichthereportednumberistheaveragenumberofinterceptswitha5-in.(127-mm)testlineappliedtoanimageat1000X.ThiscountismoreimmediatelyusefulthantheASTMgrainsizenumberitself,asimportantchangesofqualityareassociatedwithachangeofabouttwoASTMsizenumbers,whichdifferenceisnotwellresolvedonthelogarith-micsizescaleorbycomparisonorplanimetricmethods.TheSnyderandGraffsizenumberwillbecomemeaningfultoothersbymultiplyingbythefactor7.874toyieldNLpermillimetre,afterwhichTable4willindicate,forexample,thatS&GNo.15isASTMgrainsizeNo.10.5.Furthermore,astheprecisionofthispracticedoesnotattain2%ofthecount,the5-in.(127-mm)testlinecouldbereplacedbya125-mmtestlinewithoutinvalidatingpastrecords,makingthemultiplier8.0,whereuponthetotalinterceptcountoneighttestlinesequalsNLdirectly.TheconfidencelimitevaluationinSection15canbeappliedtosingletestlines,ortototalsonfixednumbersoflinesineachlocalarea.
APPENDIXES
(NonmandatoryInformation)
X1.RESULTSOFINTERLABORATORYGRAINSIZEDETERMINATIONS10X1.1Thisinterlaboratorytestprogramwasconductedtodevelopprecisionandbiasestimatesforthemeasurementofgrainsizebythechartcomparisonmethod,bytheplanimetricmethod,andbytheinterceptmethod.
X1.2Procedure
X1.2.1Photomicrographs(8by10in.)oftwodifferentferriticstainlesssteels,fourofonespecimenatdifferentmagnificationsandthreeoftheotherspecimenatdifferentmagnifications,wereratedforgrainsizeusingthechartmethodwithPlateIandbytheplanimetricandinterceptmethods.AdrawingofthegrainboundariesofaspecimenofausteniticHadfield’smanganesesteel,withagraincontrastetch,wasalsoevaluatedbyallthreemethods.Anumberofothermicrographswereratedonlybythecomparisonmethod.Ineachcase,thegrainboundarieswereclearlyandfullydelineated.
X1.2.2Fortheplanimetricmethod,eachraterwasgivenan8by10in.clearplastictemplatewithfive79.8mmdiametertestcirclesandagreasepencil.Fortheinterceptmethod,eachraterwasgivenasinglethree-circletemplate.
X1.2.3Fortheplanimetricmethod,thetemplatewasdroppedontothephotographandtapeddowntopreventmovement.Becausethecirclesgridandthemicrographwerenearlythesamesize,gridplacementshouldberatherconsis-tentbetweenraters.Fortheinterceptmethod,theratersdroppedtheirgridontothemicrographfivetimesatrandom.Itwasassumedthatthisdifferenceinplacementmethodwouldreducethevariabilityoftheplanimetricmethodrelativetotheinterceptmethod.
X1.3Results
X1.3.1Figs.X1.1andX1.2showthegrainsizeratingsforthetwoferriticstainlesssteels,identifiedasSeriesAandB,asafunctionofthemagnificationofthemicrographs,fortheplanimetricandinterceptmethods.Threepeoplealsomadeimageanalysismeasurementsoftheimages.Ascanbeseen,thetightestspreadoccurred,forbothsetsofmicrographs,atamagnificationofabout400Xwheretheaveragegraincountper
21
SupportingdatahavebeenfiledatASTMInternationalHeadquartersandmaybeobtainedbyrequestingResearchReportRR:E04-1005.
10E112–96(2004)e1planimetricmeasurementwasabout30to35andtheaveragenumberofinterceptsorinterceptswasabout40to50perthree-circleapplication.
X1.3.2Figs.X1.3andX1.4showhowthepercentrelativeaccuracyofthemeasurementsvariedwiththenumberofgrainscounted,Fig.X1.3,andwiththenumberofinterceptsorintersectionscounted,Fig.X1.4.Allofthemeasurementdataareincluded.NotethatapercentRAof10%,orless,isobtainedwhenabout700ormoregrainsarecountedbytheplanimetricmethodandwhenabout400grainboundaryintersectionsorgraininterceptsarecountedfortheinterceptmethod.Becausethegrainsmustbemarkedoffonthetemplateastheyarecountedtoensurecountingaccuracyintheplanimetricmethod,whilemarkingisnotneededfortheinterceptmethod,itisclearthattheinterceptmethodisamoreefficientmethod.
X1.3.3TablesX1.1andX1.2listtheresultsoftheanalysisofrepeatabilityandreproducibilityaccordingtoPracticeE691.Ingeneral,theinterceptmethodoutperformedtheplanimetricmethodinthisstudy.
X1.3.4Fig.X1.5showsaplotoftheplanimetricversustheinterceptgrainsizeratingforeachmicrographbyeachrater.Notethatthedataarescatteredatrandomaroundtheone-to-onetrendline.Thisindicatesthattherewasnobiasinthegrainsizemeasurementsbyeithermethod.
X1.3.5Eachmicrographthatwasratedforgrainsizecouldbeconsideredintwoways,firstasaratingforthetruemagnificationofthemicrographandsecondforaratingasifthemicrographwasat100X.Forevaluationofthecomparisonmethod,itwasassumedthateachmicrographwasat100X.
Theinterceptandplanimetricdatawerealsocomputedusingthisassumption.Figs.X1.6andX1.7showplotsofthechartcomparisonratingsversustheplanimetricandinterceptratings,assumingallmicrographswereat100X.Notethatthedataarenotscatteredatrandomaroundtheone-to-onetrendline.Thisclearlyshowsthatbiasisoccurringinthechartcomparisonratings,whichweretypically0.5to1Gunitlower,thatis,coarser,thantheplanimetricorinterceptmeasurements.Thesourceofthisbiasisunderstudy.
FIG.X1.1GrainSizeMeasurementsfortheSeriesAFerritic
StainlessSteelSpecimens
FIG.X1.2GrainSizeMeasurementsfortheSeriesBFerritic
StainlessSteelSpecimens
22
E112–96(2004)e1NOTE1—Theimageanalysisresultsforthesamemicrographs.
FIG.X1.3RelationshipBetweentheNumberofGrainsCountedandthePercentRelativeAccuracyforthePlanimetricMethod
NOTE1—Theimageanalysisresultsforthesamemicrographs.
FIG.X1.4RelationshipBetweentheNumberofInterceptsorIntersectionsCountedandthePercentRelativeAccuracyforthe
InterceptMethodTABLEX1.1ResultsofASTMGrainSizeRoundRobin(PlanimetricMethod)
ImageA1A2A3A4B1B2B3
No./sq.mm846.831.611046.978.491054.121069.411184.01
ASTMG6.776.757.086.987.097.117.26
AverageNo.1918.0474.5150.535.5608.5152.541.5
Repeatability95%CL106.11209.68499.42785.07342.214.60435.21
Reproducibility95%CL
266.56239.884.10765.18344.35452.27403.98
Repeatability
%RA
12.5325.2147.7080.2332.43.4436.76
Reproducibility
%RA
31.4928.8546.7278.2032.6742.2934.12
23
E112–96(2004)e1TABLEX1.2ResultsofASTMGrainSizeRoundRobin(InterceptMethod)
ImageA1A2A3A4B1B2B3
,¯(µm)29.929.827.229.026.126.726.6
ASTMG6.846.857.116.937.237.177.18
AverageIntercepts811.5396.0222.5102.0450.0223.5113.0
Repeatability95%CL
3.255.658.2814.904.966.198.84
Reproducibility95%CL
9.376.338.1616.467.967.019.86
Repeatability
%RA
10.8718.9630.4351.3719.0123.2033.24
Reproducibility
%RA
31.3521.2430.0056.7730.5126.2637.08
FIG.X1.5ComparisonoftheGrainSizeMeasurementsforEachMicrographbyEachOperatorbythePlanimetricandIntercept
Methods
NOTE1—Chartplotsbyeachraterandassumesthemicrographsareat100Xmagnification.Thedatagenerallyfalltoonesideoftheonetoonetrendlineindicatingabias.
FIG.X1.6PlotoftheComparisonChartGrainSizeRatingsforEachMicrographVersusthePlanimetricMethodRatingforEach
Micrograph
24
E112–96(2004)e1FIG.X1.7PlotoftheComparisonChartGrainSizeRatingsforEachMicrographVersustheInterceptMethodRatingforEach
Micrograph
X2.REFERENCEDADJUNCTS
X2.1ThefollowingisacompleteandupdatedlistofadjunctsreferencedinTestMethodsE112.AlladjunctsareavailablefromASTM.
Adjunct:
Combinationof18Components
CombinationofPlatesI,II,III,andIVPlateIonlyPlateIIonlyPlateIIIonlyPlateIVonly
CombinationTransparencies,(PlateI)00through10Transparency,GrainSize00Transparency,GrainSize0Transparency,GrainSize0.5
OrderAdjunct:ADJE112CSADJE112PSADJE11201PADJE11202PADJE11203PADJE11204PADJE112TSADJE11205TADJE11206TADJE11207T
Transparency,Transparency,Transparency,Transparency,Transparency,Transparency,Transparency,Transparency,Transparency,Fig.5only
GrainGrainGrainGrainGrainGrainGrainGrainGrain
Adjunct:
Size1.0Size1.5Size2.0Size2.5
Sizes3.0,3.5,andSizes4.5,5.0,andSizes6.0,6.5,andSizes7.5,8.0,andSizes9.0,9.5,and
Adjunct:
4.05.57.08.510.0
Adjunct:
ShepherdSeriesReproduction
OrderAdjunct:ADJE11208TADJE11209TADJE11210TADJE11211TADJE11212TADJE11213TADJE11214TADJE11215TADJE11216TOrderADJ:E11217FOrderADJ:ADJE011224
REFERENCES
(1)Hull,F.C.,Transactions,“ANewMethodforMakingRapidandAccurateEstimatesofGrainSize,”AmericanInstituteofMiningandMetallurgicalEngineers,Vol172,1947,p.439.
(2)Shepherd,B.F.,“TheP-FCharacteristicofSteel,”Transactions,TransactionsoftheAmericanSocietyofMetals,Vol22,December1934,pp.979–1016.
(3)Jeffries,Z.,Kline,A.H.,andZimmer,E.B.,“TheDeterminationoftheAverageGrainSizeinMetals,”Transactions,AmericanInstituteofMiningandMetallurgicalEngineers,Vol54,1917,pp.594–607.(4)Heyn,E.,“ShortReportsfromtheMetallurgicalLaboratoryoftheRoyalMechanicalandTestingInstituteofCharlottenburg,”Metallog-raphist,Vol5,1903,pp.37–.
(5)Underwood,E.E.,andCoons,W.C.,“TheRoleofQuantitativeStereologyinDeformationTwinning,”DeformationTwinning,Gordon
andBreach,NewYork,1965,pp.405–429.
(6)Hilliard,J.,“EstimatingGrainSizebytheInterceptMethod,”MetalProgress,Vol85,May19.
(7)Abrams,H.,“GrainSizeMeasurementbytheInterceptMethod,”Metallography,Vol4,1971,pp.59–78.
(8)Mendelson,M.I.,“AverageGrainSizeinPolycrystallineCeramics,”J.AmericanCeramicSociety,Vol52,August1969,pp.443–446.(9)Arpi,R.,“TheFractureTestasUsedforToolSteelinSweden,”Metallurgia,Vol11,No.65,March1935,pp.123–127.
(10)VanderVoort,G.F.,“GrainSizeMeasurement,”PracticalApplica-tionsofQuantitativeMetallography,ASTMSTP839,1984,pp.85–181.
(11)Snyder,R.W.,andGraff,H.F.,“StudyofGrainSizeinHardened
HighSpeed,”MetalProgress,Vol33,1938,pp.377–380.
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E112–96(2004)e1ASTMInternationaltakesnopositionrespectingthevalidityofanypatentrightsassertedinconnectionwithanyitemmentionedinthisstandard.Usersofthisstandardareexpresslyadvisedthatdeterminationofthevalidityofanysuchpatentrights,andtheriskofinfringementofsuchrights,areentirelytheirownresponsibility.
Thisstandardissubjecttorevisionatanytimebytheresponsibletechnicalcommitteeandmustbereviewedeveryfiveyearsandifnotrevised,eitherreapprovedorwithdrawn.YourcommentsareinvitedeitherforrevisionofthisstandardorforadditionalstandardsandshouldbeaddressedtoASTMInternationalHeadquarters.Yourcommentswillreceivecarefulconsiderationatameetingoftheresponsibletechnicalcommittee,whichyoumayattend.IfyoufeelthatyourcommentshavenotreceivedafairhearingyoushouldmakeyourviewsknowntotheASTMCommitteeonStandards,attheaddressshownbelow.
ThisstandardiscopyrightedbyASTMInternational,100BarrHarborDrive,POBoxC700,WestConshohocken,PA19428-2959,UnitedStates.Individualreprints(singleormultiplecopies)ofthisstandardmaybeobtainedbycontactingASTMattheaboveaddressorat610-832-9585(phone),610-832-9555(fax),orservice@astm.org(e-mail);orthroughtheASTMwebsite(www.astm.org).
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