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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,(?)dn=The“stressfreed-spacing”fromourapproximation measuredat=0(?)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-raytubeofwavelength2.2897?Ifweintroduceastressof200MPa,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-OmegaInstrumentMisalignment-RecommendedStandardsAstressfreepowderNotaneasythingtomakeBewarestressesduetofilingandoxidationCanbecombinedwithresinforeaseofuseAstressedstandardBecareful,alwaysmeasureinthesamedirectionShotpeenedsamplesaregoodUsuallyverifiedbyRound-RobintestsNocertifiedstandards(???)OnesetforeachtubeanodeInstrumentMisalignment-RecomAtypicalExampleofa
StressProfileina
ShotPeenedSampleAshotpeenedsurface,depthprofiledbyElectro-polishing
AtypicalExampleofa
StressProblems!!!Goodone,thematerialhasasmallgrainsize(<100)isisotropic,ratherthantextured&there’snoshearstress.Ideal!Texture,the“wiggle”OursampleisnotisotropicShearStress,thepositive&negativeplotssplitProblems!!!Goodone,themaShearStresses
sin2SplittingPositiveandnegativegivedifferentresultswhenashearstressispresent(orsampleisnotcorrectlypositioned,alwayscheck!)FunctionofthedirectionofthemeasurementShearStresses
sin2SplittingConclusionsThesin2
methodworkswellifyouarecarefulChecktoseewhat’sbeendonebyothersDon’treinventthewheelChooseyouX-raytubewithcarePositionthesamplecarefullyThinkaboutthedirectionsyouwishtomeasureMeasureasufficientrangeof2&countforasufficienttimeCheckyoupeakfittingDotheresultsmakesense?????? ConclusionsThesin2methodwThankYou&Happy
Landings!
ThankYou&Happy
Landings!
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,(?)dn=The“stressfreed-spacing”fromourapproximation measuredat=0(?)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-raytubeofwavelength2.2897?Ifweintroduceastressof200MPa,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,mostinstrumentshavedepthgaugeorapointerBecarefulthatthesampleisasflataspossib
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