XRD-残余应力测试课件

BSSMWorkshop

PARTII

Thesin2ψMethodUsingLaboratoryX-Rays

JudithShackleton

SchoolofMaterials,UniversityofManchesterBSSMWorkshop

PARTII

Thesin2Thesin2ψMethod

WhatareWeMeasuring?WemeasuretheELASTICStrain.WecandetermineMagnitudeofthestress,ItsdirectionItsnature CompressiveortensileWeusetheplanesofthecrystallatticeasanatomicscale“straingauge”Thesin2ψMethod

WhatareWeThesin2ψMethod

HowDoesitWork?WemeasureSTRAIN()notSTRESS()WeCALCULTESTRESSfromtheSTRAIN&theELASTICCONSTANTSWeusetheplanesd{hkl},ofthecrystallatticeasastraingaugeWecanmeasurethechangeind-spacing,dStrain==d/dThesin2ψMethod

HowDoesitChangesind-spacing

withStressConsiderabarwhichisintensionThed-spacingsoftheplanesnormaltotheappliedstressincrease,asthestressistensileThed-spacingsoftheplanesparalleltotheappliedstressdecrease,duetoPoissonstrainChangesind-spacing

withStrMeasuringElastic&

Inelastic

StrainPrimarilywearemeasuringmacrostressesThisisauniformdisplacementofthelatticeplanesThesecauseaVERYSMALLshiftintheposition,theBraggangle2,ofthereflection&wecanmeasurethis(OnlyJust!!)Inelasticstressescausepeakbroadening,whichcanbemeasured.Thisisanextensivesubject,notcoveredhere.MeasuringElastic&

InelastiWhichMaterialsCan

WeMeasure?Worksonanypoly-crystallinesolidwhichgivesahighangleBraggreflectionMetalsCeramics(noteasy!)Multi-phasematerialsNotusuallyappliedtopolymers,asnosuitablereflections,canaddametallicpowder,reportedintheliteratureWhichMaterialsCan

WeMeasurWhyusethesin2

Method

TheAdvantagesMostImportantAstressfreed-spacingisNOTrequiredforthebi-axialcasewhichisalmostalwaysusedOtheradvantagesLowcost(comparedwithneutrons&synchrotrons,butnotholedrilling)Non-destructive,unlikeholedrillingEasytodo&fairlyfoolproof(ifyouarecareful!!)Whyusethesin2

Method

TheDisadvantagesMostImportantSurfacemethodonly,X-raybeampenetrationdepth10to20microns,atbestFordepthprofilingmustelectro-polish,gives1-1.5mmOtherDisadvantagesAffectedbygrainsize,texture(preferredorientation)&surfaceroughnessDoesn’tworkonamorphousmaterials(obviously!!)DisadvantagesMostImportantBasicTheoryConsideraunitcube(quiteabigone!)embeddedinacomponentNotation,(ij)thestresscomponentactingonfaceiindirection(paralleltoaxis)jBasicTheoryConsideraunitcuBasicTheoryThenormalstressesactnormaltothecubefaces&thetwosubscriptsarethesamee.g..(22)Theshearstresses(twistingforces)actparalleltothecubefaces&thetwosubscriptsaredifferente.g.(31)orinthegeneralcase(ij)Wemeasurenormalstresses&shearstresses,butthat’snotwhatwewant,wedon’tgetalloftheinformation!Why??BasicTheoryBasicTheory

NormalStressesFromelastictheoryofisotropicmaterials,the3normalstrainsaregivenby, 11=1 [11-(22+33)]

E 22=1 [22-(33+11)]

E 33=1 [33-(11+22)]

EThestraininanydirectionisafunctionofthestressintheothers!!.Ideally,weshouldmeasuremorethanonedirectionBasicTheory

NormalStressesFrPrincipalStressesWeshouldmeasuremorethanonedirectiontogetacompletepictureofthestressinthecomponentIfwemeasure3directionsormorewecancalculatethePRINCIPALSTRESSESS,thesearethedirectionsonwhichnoshearstressactsWedothisbyrotatingthesamplethroughanangle,initsownplane,exactdetails&diagramslaterPrincipalStressesWeshouldmeHowtheSin2Method

Works

Samplein“BraggCondition”Diffractionvector,normaltosamplesurfacednWemeasurethed-spacingwiththeangleofincidence()&theangleofreflectionoftheX-raybeam(withrespecttothesamplesurface)equal.Theseplanesareparalleltothefreesurface&unstressed,butnotunstrainedAlsocalledfocussedgeometryHowtheSin2Method

Works

SaHowtheSin2Method

WorksDiffractionvector,titledwithrespecttosamplesurfaceTiltthesamplethroughanangleandmeasurethed-spacingagain.Theseplanesarenotparalleltothefreesurface.Theird-spacingischangedbythestressinthesample.dDefocusedgeometryHowtheSin2Method

WorksDifHowtheSin2Method

WorksWetiltthesamplethroughananglepsi,tomeasuremagnitudethenormal&shearstressesWeusearangeofvaluesof(calledoffsets)forexample,from0to45instepsof5NEVERusethe“DoubleExposureMethod”whichusesjustoneoffsets.Notenoughdatapoints!Werotatethethesamplethroughanangle,todeterminethedirectionsoftheprinciplestressesHowtheSin2Method

WorksWeNoStressFreed-Spacing

Needed

TheApproximationThedepthofpenetrationoftheX-raybeaminthesampleissmall,typically<20Wecansaythatthereisnostresscomponentperpendiculartothesamplesurface,thatis33=0Wecanusethed-spacingmeasuredat=0asthestressfreed-spacingThisisthed-spacingoftheplanesparalleltothesamplesurfaceAreasonableapproximation!!Theerroris<2%,certainlylessthantryingtomakeastressfreestandard!!!NoStressFreed-Spacing

NeedTheEquationforthe

sin2

MethodThesimplestformoftheequationis, = E d-dn (1+)sin2 dnWere=StressindirectionE=Young’smodulus(GPa)=Poisson’sratio=Tiltangle(degrees)d=d-spacingmeasuredattiltangle,(Å)dn=The“stressfreed-spacing”fromourapproximation measuredat=0(Å)StrainTermTheEquationforthe

sin2MeThesin2Plot:TheResults!dnisobtainedbyextrapolatingaplotofd

(orstrain)againstsin2to=0Stressisobtainedfromthegradient,mofthesin2plot = E m (1+)Ifthed-spacingdecreases,thestressiscompressive(planespushedtogether)Ifthed-spacingincreasesthestressistensile(planespulledapart)Thesin2Plot:TheResults!Thesin2Plot:Example

WecanplotSTRAINagainstsin2&obtaintheSTRESSfromthegradientThesin2Plot:ExampleWecaThesin2Plot:ExampleAlso,wecanplotd{hkl}againstsin2&obtainthestressfromthegradient,whichisthesameonbothplotsThesin2Plot:ExampleAlso,General:Stress

DiffractometersBasicallyadaptedpowderdiffractometersCanaccommodatelarger,heaviersamplesMaximumaccessible2angleislargerUsuallyabout1652(checkthisifyoubuyone!!!)Moreaxesofrotationthanastandardpowderdiffractometer,omegaand2canmoveindependentlyGeneral:Stress

DiffractometeThereareTwoBasicTypesLaboratoryBasedSystemsFixedlocationCanusuallybeusedforotherapplications,forexamplephaseidentificationPortablesystemsDesignedspecificallyforresidualstressmeasurementsCancarriedandfixedtoalargecomponent(aircraft!)ThereareTwoBasicTypesLaborDiffractionAnglesused

inStressAnalysisDiffractionAnglesused

inStDiffractionGeometry

SummaryoftheAnglesUsedin

ResidualStressAnalysis

Two-theta(2)

TheBraggangle,anglebetweentheincident(transmitted)anddiffractedX-raybeams.Omega()TheanglebetweentheincidenceX-raybeamandthesamplesurface.Bothomegaandtwo-thetarotateinthesameplane.Phi()Theangleofrotationofthesampleaboutit’ssurfacenormal.Psi()

Anglesthroughwhichthesampleisrotated,inthesin2method.Westartatpsi=0,whereomegaishalfoftwo-thetaandadd(orsubtract)successivepsioffsets,forexample,10,20,30and40Chi()Angleofrotationabouttheaxisoftheincidentbeam.Chirotatesintheplanenormaltothatcontainingomegaandtwo-theta.Thisangleisalsosometimes(confusingly)referredtoasDiffractionGeometry

SummaryoInstrumentation

TheOmegaMethod

PortableSystemsInstrumentation

TheOmegaMethInstrumentationanExample

ofaPortableSystem,Manchester’s

Protoi-XRDInstrumentationanExample

of

DecidingWhattodo?

Weneedtodecidehowtomakeourmeasurements,weneedtomakesomechoices,WhichX-raytubetouse?Whichcrystallographicplanedowechoose?Thebestthingtodoiscopywhatsomeoneelsehasdone!YourresultswillbecomparablewiththosemadebyotherworkersManyIndustrieshave“set”methods

DecidingWhattodo?

Weneed

RadiationSelection

ChoiceofX-RayTube

(Wavelength!)

ALWAYScheckwhatotherpeoplehavedoneinthepastas,generallymeasurementsondifferentplaneswithdifferentwavelengthsarenotcomparable3Considerations(1)Dispersion(2)Fluorescence(3)Choiceofcrystallographicplane

RadiationSelection

Choiceo

RadiationSelection

ChoiceofX-RayTube

(Wavelength!)

Wecanmeasurethestressinavarietyofmaterials(i.e.ferrite,austenite,nickel,aluminium,corundumetc)usingthesamediffractometer,bychangingtheX-raytube&consequentlythewavelengthoftheX-rays.MostresidualstressdiffractometerswillhaveaselectionofX-raytubesavailableHowdowechoose?????

RadiationSelection

Choiceo

ChoiceofX-RayTube

(1)Dispersion

Weneeda2angle,ideally>1402Thechangeind-spacing,duetostrain,isverysmall,typicallyinthethirddecimalplaceThedispersionofthediffractionpatternismuchgreaterathigh2angles.Thesmallchangesind-spacingcanonlybedetectedatangles>125°2

ChoiceofX-RayTube

(1)Dis

ChoiceofX-RayTube

(1)Dispersion

AnExample

Ifwehaveareflectionfromferrite{211}at1562.UsingradiationfromachromiumanodeX-raytubeofwavelength2.2897ÅIfweintroduceastressof200MPa,givenYoung’smodulusof220GPa,whatisthechangeinthe2angle?Answer,thenew2angleis155.51Thedifferenceis0.48NOTMUCH!!!

ChoiceofX-RayTube

(1)Disp

ChoiceofX-RayTube

(2)SampleFluorescence

IftheK-1componentoftheincidentX-raybeamcausesthesampleemititsownfluorescentX-rays,DONOTUSEITX-raypenetrationdepthwillbeverysmall<5microns&NOTrepresentativeofthebulkPeaktobackgroundratiowillbeterribleMaydamagesensitivedetectors

ChoiceofX-RayTube

(2)Samp

ChoiceofX-RayTube

(3)ChoiceofCrystallographic

Plane

ForaccuratecomparisonwithotherpeoplesdataCHECKwhichplaneshavebeenusedhistorically!!MeasurementsmadeonplaneswithdifferentMiller{hkl}indicesarenotusuallycomparable.Ifthesampleistextured(preferredorientation)selectasetofplaneswithahighmultiplicity

ChoiceofX-RayTube

(3)ChoiChoiceofMeasurement

Conditions:SummaryAsksomeonewhohasexperiencewiththatparticularmaterialDon’tre-inventthewheelChooseradiationtypecarefullyAvoidX-raytubeswhichcauseK-1fluorescenceLot’sof“tricksofthetrade”seetheNPLGoodPracticeGuideforResidualStressMeasurementsusingthesin2MethodChoiceofMeasurement

ConditiDataCollection

PositioningtheSampleSamplemustbecentreofrotationofthegoniometer,mostinstrumentshavedepthgaugeorapointerBecarefulthatthesampleisasflataspossible,bentsampleswillgiveartificialshearstressesForcurvedandunevensamplesrestricttheirradiatedareaHoopdirection,Spotsize<R/4,whereR=radiusofcurvatureAxialdirection,Spotsize<R/2DataCollection

PositioningthDataCollection

Makesurethatyoucollectdataoverasufficient2range!Includethebackgroundonbothsidesofthepeak.Canbedifficultasinelasticisusuallypresent&thiscausespeakbroadening.Peakscanbeupto102Countforasufficienttimetoensureadequatestatistics,need>1000countatthetopofthepeakifpossibleDataCollection

MakesurethatDataProcessingALWAYSCHECKTHISSTAGENeedaprogramwithgoodgraphicsStagesinthedataprocessingBackgroundstrippingK-2stripping(onlyifK-2peakisvisible)LorentzPolarisationCorrectionPeakfittingtolocatemaximumCriticalStage,checktheresultsonthescreen.Avarietyofpeakmodelsareavailablemostofwhichwillwork.UsuallyuseGaussian,don’tuseparabolaGoodqualitydatacanbefittedwithmostmodels,thisisagoodtest!DataProcessingALWAYSCHECKTHHowPrecisearethe

ResultsGenerallythere’salotofscatteronsin2plots!TheerrorbarsprintedoutbymostPC’sarejustthestandarddeviationofthepointsfromthefittedlineandtendunderestimatetheerrorsLargeerrorbarsarenotnecessarilyunacceptableandaredueto,Texture,largegrainsize,poorpeakfittingetcForexample,20050MPaisquitenormalCheckthepeaksonthescreen!Valuesoflessthan50MPa,canusuallybethoughtofaszero,thisdependsontheinstrument

Toconfirmsuchlowreadingsmakeseveralmeasurements&seeiftheyallcomeoutwiththesamesign(i.e.allcompressive)HowPrecisearethe

ResultsGeInstrumentMisalignment-Omega-2misalignments-Omega-misalignments(sideinclinationmethod)Instrumentmisalignmentcauses,ShiftsinthepositionsofthereflectionsandincorrectstressvaluesThepositiveandnegativemeasurementsgivedifferentpeakpositions,thisiscalledsplittingWemustmeasureatleasttwostandardstoverifythatthemachineisworkingcorrectlyInstrumentMisalignment-OmegaI