BSSMWorkshopBSSMWorkshopPARTIIPARTIIThesinThesin22ψMethodUsingψMethodUsingLaboratoryX-RaysLaboratoryX-RaysJudithShackletonJudithShackletonSchoolofMaterials,UniversityofSchoolofMaterials,UniversityofManchesterManchesterThesinThesin22ψMethodψMethodWhatareWeMeasuring?WhatareWeMeasuring?•WemeasuretheELASTICStrain.WemeasuretheELASTICStrain.–WecandetermineWecandetermine–Magnitudeofthestress,Magnitudeofthestress,–ItsdirectionItsdirection–ItsnatureItsnature•CompressiveortensileCompressiveortensile–WeusetheplanesofthecrystallatticeasanatomicWeusetheplanesofthecrystallatticeasanatomicscale“straingauge”scale“straingauge”ThesinThesin22ψMethodψMethodHowDoesitWork?HowDoesitWork?WemeasureWemeasureSTRAINSTRAIN(()not)notSTRESSSTRESS(())•WeWeCALCULTESTRESSCALCULTESTRESSfromthefromtheSTRAINSTRAIN&the&theELASTICCONSTANTSELASTICCONSTANTS•WeusetheplanesWeusetheplanesdd{hkl}{hkl},ofthecrystallatticeasa,ofthecrystallatticeasastraingaugestraingauge•WecanmeasurethechangeinWecanmeasurethechangeindd-spacing,-spacing,dd•Strain=Strain===d/dd/dChangesind-spacingChangesind-spacingwithStresswithStressConsiderabarwhichisintensionConsiderabarwhichisintension•TheThedd-spacingsoftheplanesnormaltotheappliedstressincrease,asthe-spacingsoftheplanesnormaltotheappliedstressincrease,asthestressistensilestressistensile•TheThedd-spacingsoftheplanesparalleltotheappliedstressdecrease,dueto-spacingsoftheplanesparalleltotheappliedstressdecrease,duetoPoissonstrainPoissonstrainMeasuringElastic&MeasuringElastic&InelasticInelasticStrainStrain•PrimarilywearemeasuringmacrostressesPrimarilywearemeasuringmacrostresses–ThisisauniformdisplacementofthelatticeplanesThisisauniformdisplacementofthelatticeplanes–ThesecauseaVERYSMALLshiftintheposition,theThesecauseaVERYSMALLshiftintheposition,theBraggangle2Braggangle2,ofthereflection&wecanmeasurethis,ofthereflection&wecanmeasurethis(OnlyJust!!)(OnlyJust!!)•Inelasticstressescausepeakbroadening,whichInelasticstressescausepeakbroadening,whichcanbemeasured.Thisisanextensivesubject,notcanbemeasured.Thisisanextensivesubject,notcoveredhere.coveredhere.WhichMaterialsCanWhichMaterialsCanWeMeasure?WeMeasure?–Worksonanypoly-crystallinesolidwhichWorksonanypoly-crystallinesolidwhichgivesahighangleBraggreflectiongivesahighangleBraggreflection•MetalsMetals•Ceramics(noteasy!)Ceramics(noteasy!)•Multi-phasematerialsMulti-phasematerials–Notusuallyappliedtopolymers,asnosuitableNotusuallyappliedtopolymers,asnosuitablereflections,canaddametallicpowder,reflections,canaddametallicpowder,reportedintheliteraturereportedintheliteratureWhyusethesinWhyusethesin22MethodMethodTheAdvantagesTheAdvantages•MostImportantMostImportant–AstressfreeAstressfreedd-spacingisNOTrequiredforthe-spacingisNOTrequiredforthebi-axialcasewhichisalmostalwaysusedbi-axialcasewhichisalmostalwaysused–OtheradvantagesOtheradvantages•Lowcost(comparedwithneutrons&synchrotrons,Lowcost(comparedwithneutrons&synchrotrons,butnotholedrilling)butnotholedrilling)•Non-destructive,unlikeholedrillingNon-destructive,unlikeholedrilling•Easytodo&fairlyfoolproof(ifyouarecareful!!)Easytodo&fairlyfoolproof(ifyouarecareful!!)DisadvantagesDisadvantages•MostImportantMostImportant–Surfacemethodonly,X-raybeampenetrationSurfacemethodonly,X-raybeampenetrationdepth10to20microns,atbestdepth10to20micron...