XRD--残余应力测试

BSSMWorkshopPARTIIThesin2ψMethodUsingLaboratoryX-RaysJudithShackletonSchoolofMaterials,UniversityofManchesterThesin2ψMethodWhatareWeMeasuring?•WemeasuretheELASTICStrain.–Wecandetermine–Magnitudeofthestress,–Itsdirection–Itsnature•Compressiveortensile–Weusetheplanesofthecrystallatticeasanatomicscale“straingauge”Thesin2ψMethodHowDoesitWork?WemeasureSTRAIN()notSTRESS()•WeCALCULTESTRESSfromtheSTRAIN&theELASTICCONSTANTS•Weusetheplanesd{hkl},ofthecrystallatticeasastraingauge•Wecanmeasurethechangeind-spacing,d•Strain==d/dChangesind-spacingwithStressConsiderabarwhichisintension•Thed-spacingsoftheplanesnormaltotheappliedstressincrease,asthestressistensile•Thed-spacingsoftheplanesparalleltotheappliedstressdecrease,duetoPoissonstrainMeasuringElastic&InelasticStrain•Primarilywearemeasuringmacrostresses–Thisisauniformdisplacementofthelatticeplanes–ThesecauseaVERYSMALLshiftintheposition,theBraggangle2,ofthereflection&wecanmeasurethis(OnlyJust!!)•Inelasticstressescausepeakbroadening,whichcanbemeasured.Thisisanextensivesubject,notcoveredhere.WhichMaterialsCanWeMeasure?–Worksonanypoly-crystallinesolidwhichgivesahighangleBraggreflection•Metals•Ceramics(noteasy!)•Multi-phasematerials–Notusuallyappliedtopolymers,asnosuitablereflections,canaddametallicpowder,reportedintheliteratureWhyusethesin2MethodTheAdvantages•MostImportant–Astressfreed-spacingisNOTrequiredforthebi-axialcasewhichisalmostalwaysused–Otheradvantages•Lowcost(comparedwithneutrons&synchrotrons,butnotholedrilling)•Non-destructive,unlikeholedrilling•Easytodo&fairlyfoolproof(ifyouarecareful!!)Disadvantages•MostImportant–Surfacemethodonly,X-raybeampenetrationdepth10to20microns,atbest–Fordepthprofilingmustelectro-polish,gives1-1.5mm–OtherDisadvantages•Affectedbygrainsize,texture(preferredorientation)&surfaceroughness•Doesn’tworkonamorphousmaterials(obviously!!)BasicTheory•Consideraunitcube(quiteabigone!)embeddedinacomponent•Notation,(ij)thestresscomponentactingonfaceiindirection(paralleltoaxis)jBasicTheory•Thenormalstressesactnormaltothecubefaces&thetwosubscriptsarethesame–e.g..(22)•Theshearstresses(twistingforces)actparalleltothecubefaces&thetwosubscriptsaredifferent–e.g.(31)orinthegeneralcase(ij)•Wemeasurenormalstresses&shearstresses,butthat’snotwhatwewant,wedon’tgetalloftheinformation!Why??BasicTheoryNormalStresses•Fromelastictheoryofisotropicmaterials,the3normalstrainsaregivenby,11=1[11-(22+33)]E22=1[22-(33+11)]E33=1[33-(11+22)]E•Thestraininanydirectionisafunctionofthestressintheothers!!.Ideally,weshouldmeasuremorethanonedirectionPrincipalStresses•Weshouldmeasuremorethanonedirectiontogetacompletepictureofthestressinthecomponent•Ifwemeasure3directionsormorewecancalculatethePRINCIPALSTRESSESS,thesearethedirectionsonwhichnoshearstressacts•Wedothisbyrotatingthesamplethroughanangle,initsownplane,exactdetails&diagramslaterHowtheSin2MethodWorksSamplein“BraggCondition”Diffractionvector,normaltosamplesurfacednWemeasurethed-spacingwiththeangleofincidence()&theangleofreflectionoftheX-raybeam(withrespecttothesamplesurface)equal.Theseplanesareparalleltothefreesurface&unstressed,butnotunstrainedAlsocalledfocussedgeometryHowtheSin2MethodWorksDiffractionvector,titledwithrespecttosamplesurfaceTiltthesamplethroughanangleandmeasurethed-spacingagain.Theseplanesarenotparalleltothefreesurface.Theird-spacingischangedbythestressinthesample.dDefocusedgeometryHowtheSin2MethodWorks•Wetiltthesamplethroughananglepsi,tomeasuremagnitudethenormal&shearstresses–Weusearangeofvaluesof(calledoffsets)forexample,from0to45instepsof5–NEVERusethe“DoubleExposureMethod”whichusesjustoneoffsets.Notenoughdatapoints!•Werotatethethesamplethroughanangle,todeterminethedirectionsoftheprinciplestressesNoStressFreed-SpacingNeededTheApproximation•ThedepthofpenetrationoftheX-raybeaminthesampleissmall,typically20•Wecansaythatthereisnostresscomponentperpendiculartothesamplesurface,thatis33=0•Wecanusethed-spacingmeasuredat=0asthestressfreed-spacing–Thisisthed-spacingoftheplanesparalleltothesamplesurface•Areasonableapproximation!!Theerroris2%,certainlylessthantryingtomakeastressfreestandard!!!TheEquationforthesin2Method•Thesimplestformoftheequationis,=Ed-dn(1+)sin2dnWere–=Stressindirection–E=Young’smodulus(GPa)–=Poisson’sratio–=Tiltangle(degrees)–d=d-spacingmeasuredattiltangle,(Å)–dn=The“stressfreed-spacing”fromourapproximationmeasuredat=0(Å)StrainTermThesin2Plot:TheResults!•dnisobtainedbyextrapolatingaplotofd(orstrain)againstsin2to=0•Stressisobtainedfromthegradient,mofthesin2plot=Em(1+)Ifthed-spacingdecreases,thestressiscompressive(planespushedtogether)Ifthed-spacingincreasesthestressistensile(planespulledapart)Thesin2Plot:ExampleWecanplotSTRAINagainstsin2&obtaintheSTRESSfromthegradientShotPeenedSteely=-0.0028x-2E-05-0.00090-0.00080-0.00070-0.00060-0.00050-0.00040-0.00030-0.00020-0.000100.000000.00000.05000.10000.15000.20000.25000.3000Sin2psiStrainThesin2Plot:Example•Also,wecanplotd{hkl}againstsin2&obtainthestressfromthegradient,whichisthesameonbot