Lecture 41

NPTELPhaseII:IITKharagpur:Prof.R.N.Ghosh,DeptofMetallurgicalandMaterialsEngineering||||

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Module 41

Preferred orientation

Lecture 41

Preferred orientation


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Keywords:Anisotropy,itsorigin,texture,effectoftextureonpropertiesofmaterials,texturehardening,polefigures,representationofcrystallographictexture,methodsofdeterminingpolefigure,factorsthatcontrolpreferredorientation,sheetformability,effectoftextureoncreepandmagnetic

propertiesIntroductionMetals are crystalline. Crystals have different properties along different directions. Cubiccrystals having the highest degree of symmetry has three independent elastic constantsalthoughonlytwoareneededforanisotropicmaterial.Theonlytrueisotropiccrystalisthatoftungsten. It isBCC.This isonlyforgeneralcuriosity.Werarelyusesinglecrystal.Mostmetalsaremadeofa largenumberof tinycrystals. If theseare randomlyarranged theaggregate islikely toexhibit isotropicbehavior.Howeveroften it isdifficult toobtainaperfectly randomorientation. Itneedsprecisecontrolofcompositionandseveralprocessingparameterstogetsuchastructure.Theabsenceofperfectrandomorientation isresponsiblefortheanisotropicbehaviorofmostof the commercialmetalsandalloys.Themain sourceofanisotropy is thepreferred arrangement of the various constituents present in the alloy. The purpose of thismoduleistoexplainthefollowingaspectsofpreferredorientation:

Originoftextureorpreferredorientationinmaterial Effectoftextureonthepropertiesandperformanceofengineeringmaterials Evaluationoftexturesinmaterials Texturecontrol Texture:goodorbad?

Originofanisotropy:Crystalline structure is primarily responsible for the anisotropic behavior of engineeringmaterial. Cubic crystal having the highest symmetry has 3 independent elastic constants(stiffnessorcompliance). Ifthere isadefiniterelationbetweenthethreeasgiven inslide1 itcanbesaidtobe isotropic.TungstenhavingBCCstructurefulfillsthiscriterion.Therefore it isisotropic.Most engineering materials are polycrystalline. If these are randomly arranged the overallpropertiesarelikelytobeindependentofdirection.ThisiswhyweonlyneedtospecifyYoungsmodulusandPoissonratio the twoelasticconstants formostof thecases.However thewaymetalsoralloyarecastandsubsequentlyprocessedoftenitdoesnotensureperfectlyrandomorientationof its constituents. Forexampleeven the solidificationofpuremetal inan ingotalthoughstartswiththenucleationofalargenumberoftinyrandomlyarrangedcrystalsatthemoldwallonlyafewofthesehavingfavorableorientationgrowagainstthedirectionofheat


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flowgivingrisetolargecolumnargrains.InthecaseofmetalshavingBCCorFCCstructure[100]axishappenstobethepreferreddirectionofgrowth.

AnisotropyCrystals have limited symmetry elements. Even

cubic crystals have different properties along different directions. Three elastic constants.

Isotropic crystal: 2 elastic constants (W).

Poly-crystals: random orientation: isotropic. However orientation is rarely random.

44 11 12

44 11 12

122

C C C

S S S

C: Stiffness

S: Compliance

Slide1


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Figure1illustrateswiththehelpofasetofsketchestheoriginofpreferredorientationofgrainsin a cast metal. The existence of columnar grains in a large part of the ingot makes itanisotropic.Upset forgingwhere the ingot issubjected to largeplasticdeformationatahightemperature fromalldirectionsby turnmayhelpdevelopastructureconsistingof randomlyorientedgrains so that itbecomes isotropic.Apart fromhotupset forgingmostof theotherdeformation processes are likely to favor preferred orientation of grains and other microconstituents.

Moldwall

Heatflow

Favorablenucleigrowintocolumnargrains

Randomequiaxedgrainsnearthecentreline

Tinygrainswithunfavorableorientationdonotgrow

Microstructureafterupsetforging

Hotupsetforging

Fig1:Columnargrainsdevelopinametalingotasaresultoftheconstraintimposedbyheatflowthroughthemoldwall.Afewofthetinygrainsthatformalongthewallgrowintolargecolumnargrains. [100] is often the direction of growth. Towards the end of solidification homogeneousnucleationalongthecentrelinemayresultinrandomequiaxedgrains.Castmetalsareanisotropicbecauseofthepreferredorientationofthegrains.Microstructureofcastmetalcanbeconvertedintohomogeneousequiaxedgrainsbyupset forging.The sketch at the top right shows thatbychangingthedirectionofappliedstresshow largedeformationcanbegivenwith littlechange inthe shape and size of the casting. Large plastic deformation above the recrystallizationtemperaturehelpsdevelophomogeneousstructureconsistingofrandomlyorientedgrains.Suchastructureisexpectedtobeisotropic.


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Rolling Wiredrawing

Fig2:Showsschematicrepresentationofthedeformationofgrainsduringrollingandwiredrawing.Duringrollingagrain ispressedbyapairofrollssothat ittransforms intoathinplate. Its lengthincreases but itswidth remains nearly unaltered. The length increases at the cost of its height.Duringwiredrawingarodispulledthroughadie.Agrainisthereforesubjectedtoradialpressure.Asaresultitslengthincreasesatthecostofitscrosssectionalareaperpendiculartothedirectionof drawing. In short rolling transform nearly spherical grains into plateswhereaswire drawingtransformsgrainsintofibers.Thedrawingaxisisoftenreferredtoasthefiberaxis.Wiredrawingisdone at room temperature. Therefore it is a coldworkingprocess for steel,CuorAl.However,rolling is done both at room and high temperatures. During hot rolling deformed grains getreplacedby strain free recrystallizedgrains.Theseareequiaxed.Thereforeexaminationofgrainstructureofhot rolledsteelmaynot reveal thedirectionof rolling.Howeversteelhas inclusionsthatgetalignedanddeformedinthedirectionofrolling.Theshapeanddistributionofinclusionsinhot rolled plates or sections clearly reveals the direction of deformation. The alignment ofinclusionsismainlyresponsiblefortheanisotropicbehaviorofhotrolledplates.Inthecaseofcoldworkbothdeformationand thealignmentof inclusionsormicroconstituentscontribute towardsanisotropy.


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Origin of anisotropyCrystallographic anisotropy: texture

Mechanical anisotropy: inclusion shape: MnS

Crystal Drawing Rolling

FCC [111] [100] {100} - {351}

BCC [110] {112} - {100}

HCP [210] {0001}

Metalsareknownforitsductility.Itcanbedeformed intoanyshape.This istruenotonlyfortheexternalshapeofthemetalbutalsofortheindividualgrainswithinit.Thereforetheshapeofthegrain,thedistributionofprecipitatesandinclusionsalthoughmayindicatetheexistenceofanisotropybutitcannotgiveanyideaabouttheorientationofindividualgrains.Theexternalshapesofgrainsmay looksimilartheretheirorientationsmightbedifferent.ThiscanonlybeevaluatedfromXrayorElectronBackScatterDiffraction(EBSD)patterns.Slide2givestheorientationsofgrainsincolddrawnwiresorrolledsheetsofmetals.Inthecaseofwireallthegrainstendtoalignthemselvesinsuchawaythataspecificcrystallographicaxisineachofthesepointalongtheaxisofthewire.Thisisknownasthefiberaxis.Notethattheindicesoffiberaxisdependoncrystalstructure.Forexample inthecaseofFCCstructurethefiberaxis iseither[100]or[111],whereas inthecaseofBCC it is[110].Thesedirectionsarenormaltotheclosepackedplanes.(InFCC(111)planeshavethehighestpackingdensity,and(100)hasthesecondhighestpackingdensity.)Awirehasanaxisymmetricgeometry.Itmightbeenoughtospecifyitsfiberaxis.Howeverinthecaseofarolledsheetyouneedtospecifytheindices of the crystal planes in individual grains that are parallel to the rolled face and theindicesofthedirectionsof individualgrainsalongthedirectionofrolling. Forexample inthecaseoflowcarbonsteelwhichprimarilyconsistsofferritegrainshavingBCCstructurethetopsurface(rolledface)ofeachofthegrainsiseither(110)or(100)whereastherollingdirectionis[110].Thetexturethatdevelopsdependsonthefiveindependentslipsystemsthatcontributetothedeformationofindividualgrains.

Slide2


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Crystal anisotropy: XRD, EBSD, Property

Mechanical anisotropy: Microstructure: Poor transverse /

through thickness property, lamellar tearing

Cause: cold work & annealing, altered by alloy addition

microstructure

Inclusions: control amount shape & size

Slide2suggeststhatapolycrystallinematerialmayexhibitanisotropicbehaviorbecauseofthefollowingtwofactors:

Crystalanisotropyduetopreferredorientationofindividualgrains Mechanicalanisotropyduethepreferredalignmentofmicroconstituentslikeinclusions

Slide2alsosuggestsmethodsforthedetectionofanisotropy.Apartfromdirectdeterminationoftheorientationofgrainsmeasurementofthepropertiessuchasstrength,ductility,magneticpermeability (for ferromagnetic material) or the elastic modulus along different directionscouldalsobeused.

Slide2


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Figure 3 explains with the help of a set of sketches the origin of anisotropy in crystallinematerial. Apart from crystal structure, it depends a lot on the presence of second phaseparticlesor inclusions and the variousprocessing steps a componenthas toundergobeforebeingputtouse.Theproductionofaperfectlyisotropicmaterialtoocanbeachallengingtask.Forexampletomakecoldrolledannealedsteelsheethavingisotropicbehaviorapartfromthethermo mechanical processing parameters you may have to control the shape, size and

(a)Equiaxedgrainshavingrandomorientation

(d)Equiaxedgrainshavingrandomlydistributedglobularsecondphase

(b)Elongatedgrainshavingsimilarorientation

(c)Equiaxedgrainshavingsimilarorientation

(e)Elongatedgrainsandelongatedsecondphase

(a)Equiaxedgrainshavingelongatedsecondphase

Fig3:Showsasetofdiagramstoexplaintheoriginofanisotropy.Randomgrainorientationandrandom distribution of globular second phase (precipitate or inclusions: shown as dark filled inregions) is necessary for isotropic behavior: illustration (a) and (d).Aligned or elongated grainsoftendenotepreferredorientation: lookatsketch (b)eachgrainhassimilarorientation.Yougetsuchastructure indirectionallysolidifiedcastingorcoldrolledparts.Thepresenceof inclusions,secondphaseprecipitatesalongdendriticchannels incastalloysorbetweenelongatedgrains incoldworkedparts (seesketch (e)) isalso responsible foranisotropy.Suchamicrostructuregivespoor through thicknessstrength, toughnessandductility. Thepresenceofequiaxedgrainsdoesnotensure isotropy.Lookatthesketch(c)thegrainsareequiaxedbutallofthesehave identicalorientation. Nucleation of strain free grains during recrystallization is often controlled by thepresenceof inclusionsorprecipitates.Thisoftencontrols theorientationofgrains.Annealingofcoldrolledpartscannotaltertheshapeanddistributionofinclusionsorsegregationsthatareleftbehindevenafterdeformationprocessing. Lookatthesketch(e).Thegrainsofcoldrolledpartsappeartobeequiaxedbutthe inclusionsretaintheirshape.This isresponsiblefor itsanisotropicbehavior.


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distribution of inclusions aswell. Anisotropy is not necessarily bad. It can be beneficial forseveralapplications.Letusnowlookatafewsuchexamples.Texturehardening:Flow stress of a material is an important property. It is the stress at which large plasticdeformation takesplace.Thisoccursby slip.Ametalconsistsofanumberofcrystalshavingdifferentorientation. Itwoulddeformonly ifsliptakesplace ineachofthese.Slipoccurs inacrystal when the resolved shear stress on specific slip system exceeds a critical value. Therelationbetweenappliedandresolvedshearstresswasderivedinmodule9.Itisalsogiveninslide3.Theratioofuniaxialappliedstress()totheresolvedshearstress() isknownastheorientation factor (m). It is the reciprocal of the product coscoswhere, is the anglebetweenthe loadandtheslipplanenormaland istheanglebetweenthe loadandtheslipdirection.Aproductoftwoindependentvariableismaximumwhenthetwoareequal(==45).Thereforethelowestvaluemcanhaveis2.0whereasthehighestvaluecanbeashighasinfinity.Therangedependsontheavailabilityofsufficientnumberofactiveslipsystemineachgrain so that strain continuity ismaintained.Mostmetals have either BCC or FCC structurehavingveryhighsymmetry.Therearevariousoptionstochoose5independentslipsystemstosatisfythecontinuitycriterion.ThereforetherangeofmmaynotbewideinthecaseofmetalshavingFCCorBCCstructure.TheaveragevalueofmforapolycrystallineaggregateconsistingofrandomlyorientedFCCcrystalsis3.1.ItisalsoknownasTaylorfactor.AsagainsttheseHCPstructure can have a verywide range of values form. This is because it has only a limitednumberofslipsystems.Therangeofm(orientationfactor)canbeverywideinthecaseofidealHCPstructure.Seeslide3.


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Texture hardening

Potential application: dent resistant material. Scope is limited for fcc / bcc metal.

cos cos

1cos cos

PA

m

m = orientation factor

mmin = 2.0

hcp: m: 2-infinity

fcc: m: limited range ~3.1 for random orientation

Textures in metal affect several other properties

Thestrengthening (or theresistance toplasticdeformation)due topreferredorientation isafunctionofmtheTaylorfactor.Theyieldstressofamaterialunderuniaxialloadingisequaltomtimesthecriticalresolvedshearstress .Notethatthecriticalresolvedshearstress is the true material uniaxial tensile or compression test is a function of thecrystallographictexturethematerialhas.Dependingonthemagnitudeofmitcanvarywidely.PolycrystallinemetalhavingidealHCPstructurehasaveryhighpotentialfortexturehardening.Apotentialapplicationisthedevelopmentofdentresistantmaterial.Representationofcrystallographictexture:Stereographicprojection isused to represent theorientationof a single crystal. Figure4 (a)givesanexampleofsuchaprojection.Atinycubehasbeenplacedatitscenter.Ithasashadedtriangletodenotetheorientationof its111plane.(001) istheplaneofprojection. Notethelocationofitsfour111typepoles.Apolycrystallinemetalisanaggregateofalargenumberofgrains.Eachofthesewouldhave4suchpoles. Ifthereare1000grains(crystals)/mm3thereshouldbe4000(111)poles.Figure4(b)showsaschematicrepresentationofthe locationsofsuchalargenumberof(111)polesofapolycrystallineaggregate.Adotinthisdiagramdenotesthe location of one 111 plane.A uniform distributionmeans the absence of any texture orpreferredorientation.Suchdiagramsareknownaspole figures.Theseareused to representthepreferredorientationincrystallinematerials.

Slide3


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Howarepolefiguresgenerated?Pole figure represents the distribution of poles (normal to a specific reflecting plane) on astandardprojection.Thiscanbeconstructedonly if theorientationsofall thecrystalswithinthemetalare known.Themost commonmethod is to trackor record thediffractedbeamsemanatingfromaspecificcrystallographicplaneofthemetalwhenamonochromaticbeamofXray or electron falls on it. Recall that diffraction occurs when the Bragg conditions aresatisfied.Thisisrepresentedasfollows:2 (1)Notethatddenotesinterplanarspacing,istheangleofincidenceandisthewavelengthofincidentbeamofXray.Letusconsideronlythediffractedbeams from (111)planesofaFCCcrystal. Interplanar spacingof (111)planesare fixed. It isequal to/3where adenoteslattice parameter which is fixed. Since a monochromatic beam is used wave length too isconstant.Theangleofincidence(istheonlyvariable.Theconditionsetbyequation1canbesatisfiedonly if thesamplehasa largenumberofcrystals.Youwillgetdiffractedbeamsonlyfrom crystalswhose (111) planes are favorably oriented. This is illustratedwith the help ofdiagramsinFig5.

111

111111

111

(a) (b)

Fig4:(a)Showstheorientationof(111)polesofacubiccrystalonastandard001projection.Acubiccrystalhasfour111poles.Thereforetheprojectionshowstheirlocationswiththehelpof4points. (b) Shows the locations of 111 poles of in a polycrystalline material. These arerepresented as dots as there are several grains having 4 such poles. Uniform distributionindicatesrandomorientation.Thistypeofrepresentationofaparticularpoleinapolycrystallinematerialisknownaspolefigure.


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Figure5explainswith thehelpof a setofdiagramswhy a continuousdiffraction ringon the film isexpectedifthegrainsarerandomlyoriented.Whatwouldyouexpectifthe(111)reflectingplaneswerepreferentiallyorientedwithrespecttothewireaxis?Thisisshownwiththehelpofasetofsketchesinfig6.Thissuggeststhattheintensityofdiffractionspotsisafunctionofcrystalorientation.

(a)

(b)

Wireaxis

Transmittedbeam

Incidentbeam

111planenormal

Diffractedbeam

(111)plane

Incidentbeam

Transmittedbeam

Planenormal

Diffractedbeam

Filmtorecordthediffractedbeam

SectionoftheconeconsistingofthediffractedbeamTransmitted

beam

290

(c)

Fig 5: Shows the directions of diffracted beams originating from awire samplewhere grains arerandomlyoriented.(a)ShowstheBraggconditionunderwhichtherewillbeadiffractedbeamfrom(111)plane.ThecrystalisassumedtobeFCC.(b)Showsa3Dviewofthesetupusedtorecordthediffractionpattern.Asampleconsistingofalargenumbertinycrystalislocatedatthecentreofthereferencesphere.Note that theblue linesdenote theorientationsof the (111)planenormal thatsatisfytheBraggcondition.Theselieonaconewhosesemiapexangle is(90.Thisintersectsthereference sphere along the blue circle. The corresponding diffracted beamswould lie on a conewhosesemiapexangleis2.Theseareshownasgreenarrows.Thisintersectsthereferencespherealong thegreen circle. (c)Shows theorientationof the film to record thediffractionpattern. It isperpendiculartotheaxisof theconemadeofdiffractedbeams representedbygreenarrows. It islocatedatashortdistancefromthecenterofthereferencesphere.Thereforethediffractionpatternwouldbeacircleasshown.


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Factorsthatcontrolpreferredorientation:

Dotsdenote111polesthatdonotcontributetodiffraction

111polesthatsatisfyBraggcondition

WireaxisIncidentbeam

Wireaxis

Transmittedbeam

Incidentbeam

111planenormal

Diffractedbeam

Projectionplane

LocationsthatsatisfyBraggcondition

WireaxisIncidentbeam

Locationsof111poles

(a) (b)

(c) Diffractionspots

Transmittedbeam

(d)

AA

BB

A

B

Fig6:(a)Showsa3Dsetuptorecordthediffractionpatternofawiresampleplacedatthecentreofareferencesphere.Thesurfaceoftheblueconeisgeneratedbythenormaltothe(111)planessatisfyingthe Bragg condition for diffraction. The red dashed lines denote the incident and the transmittedbeams. The surface of the green cone consists of the diffracted beams from (111) planes that arefavorablyoriented. (b)Gives thestereographicprojectionof the referencesphere in (a).Lookat thepairofblackdashed lineswitharrowheadsoriginating fromapointonthesphere in (a). It joinsthepointfromwheretheprojectionhasbeentakentoapointonthebluecirclerepresentingthelocationsofthe(111)polesonthereferencesphere.Thetwopointsin(a)aremarkedasAandB.ThelocationsofthesetwopolesontheplaneofprojectionareAandB.Theverticaldashedlinemarkedasthewireaxisin(a)isagreatcircleoraplane.Thisexplainstherelationbetweenthetwodiagrams(a)and(b).Thelatteristhestereographicprojectionoftheformer.Thebluesmallcircledenotesthe locationsof(111)thatsatisfytheBraggcondition.Theuniformdistributionofbluedots indicatesthat(111)polesare uniformly distributed. (c) Shows what happens when (111) plane normal from all the grainssubtendadefiniteanglewith thewireaxis.The two firmblue linesdenoting the locationsof (111)polesintersectthebluedashedcircleatfourpoints.(d)Showsthatdiffractionpatternshouldconsistofonlyfourspots.


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The origin of crystal texture lies in theway amaterial ismade. It develops right from thesolidificationstageitself.Thepresenceofcolumnargrainsinacaststructureisanindicationofpreferredorientation.Howeveritmaygetalteredduringsubsequentprocessing.Dependingontheprocessingrouteanengineeringmaterialmayhaveperfectlyrandomtoperfectlyalignedstructure.Apartfromconventionalcastingorcoldworkpreferredorientation(ortexture)canalsodevelopduringdirectionalsolidification,electrodepositionandzonerefining.Recall thatzonerefiningisamethodofpurificationofmetal.Athinmoltenzoneisformedatoneendofabarmadeofcommerciallypuremetalanditismadetomovealongitslengthuntilitreachesitsother end. Impurities get partitioned into the molten pool. The purity increases with thenumberoftimestheprocess isrepeated. Itfinallyresults inasolidhavingtwodistinctzones:onewhich isextremelypureand theotherhavingall the impurities thatwerepresent in theinitial stock. Slide 4 gives the factors that control texture in metals during deformationprocessing.

Factors controlling textureCold work

Alloy: Copper & Brass

Re-crystallization: inclusions / ppts

Secondary re-crystallization

TD

RD

(111) Pole figure

Coldwork:Duringcoldwork the shapeand theorientationof thegrainskeepchanging.Themagnitudeofchangeisafunctionoftheamountofcoldwork.Forexampleinthecaseofwiredrawing as the amount of reduction increases individual grains orient themselves in such amanner thataparticulardirection inallof them tend tobecomeparallel to thedirectionofdeformationorthewireaxis.Thisiscommonlyknownasitsfiberaxis.Thephysicalpropertyofthe wire (elastic modulus for example) is likely to be same as that along its specificcrystallographic axis. Figure 6(c) shows how the orientation of a particular direction getsconcentratedwithinaspecificregionofthestandardprojectionandfig6(d)givesthenatureofthe diffraction pattern. The shape and the size of the diffraction spots describe the exact

Slide4


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orientationofthegrains.Asetfourperfectdots(orspots)mayrepresentthatthewireaxisisexactly[100],whereasthepresenceoffoursmallarcslyingalongtheimaginarydiffractionringindicatethat[100]directionsinallthegrainsliewithinafewdegreesofthewireaxis.Incaseofcoldrolledsheetspecifyingtherollingdirectionmaynotbeenough.Youneedtospecifyeithertheindicesofthetransversedirectionorgivetheindicesoftheplanesthatareparalleltotherolledsurface.Slide4givesatypicalrepresentationof(111)polefigureofarolledsheet.Thisdenotesthattherollingdirection(RD)is[001]andtheindicesofcrystalplanesthatareparalleltotherolledsurfaceare(100).Thisisusuallydenotedas{001}.Alloyaddition(Cu&Brass):Slide5givesthetypicalpolefigureplotsofcoldrolledcopperandbrass.Thisshowsthatalloyadditioncanalterthenatureoftexturefoundaftercoldwork.Thisis certainlynotunexpected.Theoriginof texture isassociatedwith themicromechanismofdeformation.Alloyadditionaffectsstacking faultenergy.Alphabrasshas lowerstacking faultenergythanthatofpurecopper.Thismakescrossslipdifficult.Asaresultthesetofslipplanescontributingtowardsdeformationarelikelytobedifferent.Thisaffectstheevolutionoftextureduringcoldwork.Thesketchesshownarepurelyschematic.Theactualpolefiguresmayhaveaset of contours representing the intensity of diffraction pattern or the density of particularpolesorientedalongspecificregionsoftheprojection.

(111) Pole Figure: effect of CW , alloying & annealing

TD

RD

TD

RD

Cu Brass

Annealed

Cold worked

Annealing: On annealing cold worked grains are replaced by new strain free recrystallizedgrains.Theorientationofthesedependsontheamountofpriorcoldworkandthepresenceofinclusionsortinysecondphaseparticles.Iftherearenoinclusionsandtheamountofcoldworkislesstheorientationofrecrystallizedgrainsislikelytoberandom.Howeverinthepresenceof

Slide5


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inclusions andhigh amountof coldwork a texture that is totallydifferent from that in coldworkedmetalmaydeveloponannealing.Slide5showstheeffectofannealingontheevolutionoftextures inCu&brass.Ofteneven iftheannealingtexturemaybeweakbutonprolongedannealing only the grains that are preferentially oriented with respect to the inclusionscontinue to grow at the expense of the others. This is often referred to as secondary recrystallization.Awellknownexamplesecondaryrecrystallizationisthedevelopmentofaverycoarsegrainstructurehaving(110)[001]textureinironsiliconalloy.Application: Preferred orientation or crystallographic texture in engineering material is notnecessarilybad.Thereareapplicationswhereitmightbebeneficial.Oneofthemostcommonexamplesisthatofcoldrolledgrainorientedsteel(CRGO)thatareusedastransformercore.Itis subjected to repeatedmagnetization and demagnetization. Soft magnetic material is theidealchoice.[001] isthemostpreferreddirectionforeasymagnetizationordemagnetization.(110)[001] is the preferred texture. This develops easily as a result of secondary recrystallizationinironsiliconalloy.Howeverifyouarelookingforasoftmagneticmaterialforarotor inamotorthismaynotbethe idealchoice.Thedirectionofmagnetizationwouldkeepchangingperiodically.Thereforea softmagneticmaterialhaving isotropicbehaviorwouldbepreferable.Coldrollednonoriented(CRNO)steelsheetsarethebestchoice.Letusnowlookattwoexampleswhereevolutionofpreferredtexturehassignificantlyimprovedtheperformanceofengineeringmaterials.

Sheetforming:Developmentofdeepdrawingqualitysteel Hightemperaturematerial:Developmentofdirectionallysolidifiedsuperalloy

Deepdrawing:This isoneofthemostcommonsheetformingtechniques.Ittransformsadiscmadeofathinmetalsheetintoatumbler.Thisisillustratedwiththehelpofasetofsketchesinslide6.LetDbethediameterofthedisctobeformedintoaoneendclosedhollowcylinderofdiameterd.D/disknownasthedrawingratio.Themaximumpermissiblevalueofthisratioisameasureof thedeepdrawingabilityof the steel. It isknownas limitingdrawing ratio (LDR).ComponentslikeLPGcylinders,colddrinkcontainersaremadefromdeepdrawingqualitysteel.HighLDRmeansgooddeepdrawability.


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Sheet forming

A disc to be formed into a tumbler: process called

deep drawing

D

d

Drawing ratio: D/d

High uniform elongation

Minimum strain in thickness direction

Equal strain along all planar directions

No yield point phenomenon

Blank

PunchBlank

Slide 6 also gives a list of factors that could ensure high yield (orminimum rejection) andsurfacequalityofthedeepdrawnproduct.Thefirstthree is insomewayconnectedwiththecrystallographic texturepresentwithin the sheetwhereas the lastone isassociatedwith theyieldpointphenomenoninlowcarbonsteel.Highuniformelongation:Slide6showswith thehelpofasketchhowadisc shapedblank isplacedbetweenapairofguideswhileapunchpushesitwithinadie.Astheblankgetspushedintothediecavitymaterialmustflowuniformlyfromalldirections.Ameasureofthisabilityisthe uniform ductility of the material. This is the strain beyond which local deformation orneckingsetsin.Youmayrecallthattheflowstress()ofamaterialisgivenby whereisthetruestrain,kdenotesthestressat=1andnisameasureoftrueuniformstrain.Ahighnmeanshighuniformstrainorhighresistancetolocalizeddeformation.High plastic strain ratio: Good sheet formability also means that during deep drawing thereductioninthickness(t)shouldbeaslowaspossibleincomparisontothereductionalongitswidth (w).This isbestdescribedbyaparameter calledplastic strain ratio.This isdefinedasfollows: ln

/ln

(2)

Inequation2,w0andt0denotetheinitialwidthandthicknessofthetensiletestspecimen.Bothw and t denote the width and the thickness of the test specimen at peak stress (thiscorresponds to itsUTS).However the reduction in thickness oftenmay bemore difficult tomeasureasitmaybeverysmall.Thereforeoftenitisestimatedfromuniformelongation.Theexpressionwhich ismore convenient toestimateR isgiven in slide7.This isderivedon the

Slide6


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basisof the assumption that the volume remains constantduringdeformation.Note that l0denotesinitiallengthandlisthelengthjustbeforeneckingorlocaldeformation.

How do you satisfy these?Plastic strain ratio: R = w/t = ln(w0/w)/ln(t0/t)

Samples drawn along diff

orientations

Tensile test

RD

TD Initial dimensions l0, w0, t0Final dimensions: l,w,t

Thin sheets: difficult to measure thickness

R = ln(w0/w)/ln(lw/l0w0)

0 45 9024

R R RR

Theplasticstrainratioalsodependsontheorientationofthetestspecimen.ThesketchinSlide7giveshowthespecimensaremadefromarolledsheet.R0representstheplasticstrainratioobtainedfromaspecimenalignedalongtherollingdirection.R90denotestheplasticstrainratioalongthetransversedirection.Therearetwopossiblewaysyoucanmakeaspecimenwhosetensileaxis subtendsanangleof45with the rollingdirection.R45denotes theplastic strainratio along these two directions. The average of the four is known as . Slide 7 gives theexpressionusedtodetermine .Slide8showsthatthecorrelationbetweenLDRand ismoredependablethanthatbetweenLDRand%elongation.Ahigh meansbetterdeepdrawability.Thisisoftheorderof11.4inthecaseofrimmingsteelwhereasitis1.41.8inthecaseofAlkilledsteel.Thisispossiblydueto thepresenceof tinyparticlesofAlN.Therearesteelshavingstillhigher (~2).Theseareoftenreferredtoasextradeepdrawingqualitysteel.

Slide7


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R bar vs. LDR

LDR

Rba

r

%El

Rimming steel: Rbar ~ 1-1.4, Killed steel Rbar ~ 1.4-1.8

R bar has better correlation with drawability

% El

R

Planarisotropy:Thematerialshouldhavesimilar alongallplanardirections.Whathappensifthematerialdoesnotfulfillthiscriterionhasbeenexplainedinfig7.Thisleadstononuniformplanardeformation.Thistypeofdefectisknownasearring.Themagnitudeof isafunctionoftheorientationofthespecimen.Letthemaximumandtheminimumvaluesofbeandrespectively. The difference between the two is known asR. This is given by .Thisdefinesthedegreeofplanarisotropy.ForplanarisotropyR=0.Thisiswhatoneshouldlookforwhileselectingamaterialhavinggoodsheetformability.AhighRmeanshighplanaranisotropy.Suchmaterialsare susceptible toearring.The3most importantcriteria forgooddeepdrawabilityare:

Highn:gooduniformductility(measureofstretchability) High :highthroughthicknessstrength LowR:planarisotropy

Slide8


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Inaddition to theseBCCmetals suchas steelmust satisfyanadditional requirement.This isassociatedwiththeyieldpointphenomenon.InthepresenceofinterstitialsoluteelementsBCCmetalsexhibityieldpointelongation.This leads to the formationof localdeformationbandscalledstretcherstrains.Thismakestheproductunacceptable.Thisisillustratedwiththehelpofsketches inslide9.Thesketchonthe leftgivesatypicalstressstrainplotof lowcarbonsteel.Theoccurrenceofsharpyieldpointandthesubstantialyieldpointelongationisresponsibleforthestrainmarksontheformedproduct.Thisphenomenonisduetothepresenceofinterstitialcarbon andnitrogen atoms in solid solution. In thepresenceof interstitial solute atoms thedislocations inBCCcrystalareeffectivelypinned.Theupperyieldpoint is thestressatwhichthese are unpinned. This suddenly produces a large number of mobile dislocations. Theirsubsequentmovement results in significantyieldpointelongationuntil theseareblockedbyinteractionsbetweendislocations.Thereafterthestressstartsincreasingwithstrain.Iftheloadiswithdrawnaftertheyieldpointelongationandthesampleisreloadedagainitwillnotexhibitanyyieldpointphenomenon.Thissuggests thatcoldworkedsteeldoesnotshowyieldpointphenomenon. However it may reappear after prolonged holding at room temperature orthermalexposure(100150C).Howcanweavoidthepresenceofsharpyieldpointinsteel?Sincethisisassociatedwiththepresenceofinterstitialsoluteelementsoneofthepossiblewayscouldbecompleteremovalofsuchelements.Forexample interstitial free (IF)steeldonotexhibityieldpointphenomenon.Analternativemethodcouldbe to fix interstitialatomsasprecipitates so that therearenotenoughatomstopinthedislocations.AnexampleistheadditionofTiorNb.Thetwohaveveryhigh affinity for carbon. Steels having such strong carbide formers do not have sharp yieldpoint.Thethirdoptionispriorcoldwork(~2%)littlebeforethesheetformingoperation.Thisisoftenknownas temper rolling.However thewaiting time (or the transit time)after suchanoperation should not be long as yield point may reappear due to the time dependentmovement(diffusion)ofinterstitialatomsevenatroomtemperature.

Discbeforedeformation

Goodformability

Poorformability

Fig7: Shows theeffectofplanar isotropyon theshapeofthefinalproduct.Ifplanarductilityofthedisc is identical along alldirectionson theplane,thetopedgeofthecylinder isuniform. If it isnotso it results in an uneven top edge. This type ofdefect intheformedproduct isknownasearring.Ifsuchadefectdevelopsthetopedgeneedstobecropped.Thisisresponsibleforlowyield.Themainreason for its occurrence is the lack of planarisotropy.


21

Yield point problem: steel (bcc)

Temper rolling

IF steel + Ti / Nb

Stretcher strain marksStrain aging

Temper rolling

Strain

Stre

ss

How to avoid it ?

Effectof textureoncreep:Timedependentdeformationorcreep isprimarily responsible forthe lossof loadbearingcapacityofhightemperatureengineeringmaterials.Thereareseveralwaysofimprovingthecreepresistance.Afewofthesewerediscussedinmodule40.Themainfocus howeverwas on steel. This ismade of several grains although the grain sizemay berelativelycoarse.Thebulkofcreepfailuresoriginatefromgrainboundaries.Thereforeoneofthe ways to improve the creep resistance is to make the grain boundaries stronger. Alloyadditionthatpromotesformationofgrainboundaryprecipitateisthemostcommonoption.Analternativeapproachistocontrolthenatureandtheorientationofgrainboundarieswithinthealloy.Whatwouldhappenifthereisnograinboundary?Thisisillustratedinslide10.Thesketchon the leftshows thatgrainboundaries inpolycrystallinemetalsperpendicular tothe direction of loading are the most preferred sites for the nucleation of creep cavities.Therefore it has relatively poor creep resistance. The absence of such boundaries indirectionally solidified alloys makes these more creep resistant. The absence of grainboundariesaltogetherasinsinglecrystalcangivestillhighercreepresistance.Currentlysinglecrystalsuperalloybladesarethemostpopularmaterialforgasturbineblades.Creepresistantmaterialsareextremelydifficulttoformbecauseofitsveryhighstrength.Theseareusedinascastform.Precisionornearnetshapecastingtechniquesareusedtomakethese.This is based on investment casting or lostwax process.Molten alloy poured into ceramicmolds iscooledslowlyunderacontrolledthermalgradient.Thesolidificationstarts fromoneendand thesolid liquid interfacemoves in thedirectionof the thermalgradient.Usually thecubeaxisisthemostpreferreddirectionofgrowth.Ithasrelativelylowelasticmodulus.Apartfromgoodrupturestrengthitgivesveryhighthermalfatigueresistancetoo.

Slide9


22

Effect of texture on creep

GB under tension: sites for cavities

Poly-crystal DS alloy

Few GB under

tension

Cast single crystal super-alloy blades: excellent creep resistance: aero gas turbines

Single crystal

No high angle GB

Evolution of superalloy

1940 2000700

1050

Wrought alloy

Cast DS alloy

SC

Tem

p ca

pabi

lity

Year of introduction

Conventionally cast

Slide11 showshow theperformanceofNibase superalloy since its inception in1940shasimprovedovertheyears.Thisisrepresentedintermsofthetemperaturecapabilityofthealloy.PolycrystallineorwroughtNiCralloyhavingTi/Alastheprecipitationhardeningelementswasamongst the first tobeusedasaerogas turbineblades. Inorder to improve it temperature

Slide10

Slide11


23

capabilityseveralstrategieswereadopted.Thefactorsthatcansignificantlyimprovethecreepresistanceofthealloyareasfollows:

Solidsolution(matrix)strengthener:Cr,Co,Mo,W former(precipitate):Al,Ti,Nb,Ta GBstrengthener:B,Zr,C,Hf Carbideformers:Cr,Ti,Mo,W,Nb,Hf,Ta Oxidescaleformer:Cr,Al

Toimprovethetemperaturecapabilityofwroughtalloysaverylargenumberofalloyadditionswerenecessary.Castsinglecrystalalloydoesnothaveanyhighanglegrainboundary. Itonlyhascoherentprecipitates inamatrixof.Thevolumefractionofcanbeashighas70%.Theseareextremelystableathightemperature.Thisisprimarilyresponsibleforitsgoodcreepresistance.Theabsenceofgrainboundaries in superalloymakesadditionofgrainboundarystrengthener or carbide formers redundant. Single crystal superalloys are therefore muchleanerincomposition.Electrical steel:Grainoriented silicon steel isusedas transformer core tominimize the coreloss.Slide12givesatypicalBHloopofaferromagneticmaterial.Theslopeofthelinearpartoftheplotisknownaspermeability.Theareawithintheloopisameasureofcoreloss.Thisislowfor softmagneticmaterial havinghighpermeability, low coercivity (Hc) and low remanence(Br).The seconddiagram in slide12gives the initialpartof theBHcurve for threedifferenttypesofsteel.Highcarbonsteelhasthelowestpermeability.Itisnotasoftmagneticmaterial.In comparison 3.2%Si NO (nonoriented) steel has higher permeability. It is a better softmagneticmaterial. Ifyoucandevelop (110) [001]texture inthissteel itspermeabilitycanbesignificantly improved. This type of texture is commonly known as cube on edge or Gosstexture.ThiswasfirstdiscoveredbyNormanPGoss.


24

Electrical steelsCRGO: texture: transformer {011}

CRNO: random: rotors

B wb/m2

H A/m

Soft magnet: high & low hysteresis

B

H

3.5Si + GO

3.2Si + NOHC

steel

Magnetically soft // RD: GO

BrHc

B = H

TwotypesoftexturescanbedevelopedinSisteel.Oneknownasnormaltexturehas(100)orthe cube planes aligned parallel to the rolled face. This is represented as (100) [001]. ThesecondtexturecommonlycalledGossorcubeonedgetexturehasthecubeplanesparalleltotheedgeof the sheet.This is represented as (110) [001].ThepresenceofGoss texture canimprovemagneticfluxdensity(B)orthemagneticpermeabilitysignificantly.Theoriginoftextureinsteeldependsoncoldworkandannealing.Slide13showshowVickershardness (VH)changeswithannealing temperature.Theannealing time isheldconstant.Thecoldworkedgrainsarereplacedbystrainfreegrainsofferritesoonafterrecrystallization.Atthisstagethepredominanttexture is(100)[001]whereastheGosstexture isrelativelyweak.HoweverduringthesecondaryrecrystallizationstagethegrainshavingGoss texturegrowaslargegrainsattheexpenseoftheother.

Slide12


25

Re-crystallization texture

VH

TAnnealing of CW steel

Re-crystallization

Secondary re-cryst.

f

lnD

f

lnDSecondary

recrystallization

Goss texture obtained by abnormal grain growth: secondary re-crystallization

Re-crystallization

The figureon the top right inslide13givesgrainsizedistribution justafterrecrystallization.Mostofthefinergrainshavenormalstructure.VeryfewgrainshavetheGosstexture.Howeveraftersecondaryrecrystallizationthecoarsegrainsgrowsignificantlyattheexpenseofthefinerones.Asaconsequencethereisasignificantincreaseinitsmagneticpermeability.Summary:Inthismodulewe lookedattheoriginofanisotropy inengineeringmaterials thataremostlymadeofa largenumberofcrystals.This isduetopreferredorientationof individualgrainsorthe shape, size and the distribution of its micro constituents. Apart from measurement ofpropertiesalongdifferentdirectionsthepresenceoftexturecanbedetectedfromtheintensityofXraydiffractionlines.Randomlyorientedgrainsgivecontinuousdiffractionringwhereasinthe presence of preferred orientation the pattern consists of isolated spots aligned alongimaginary rings.The informationobtained fromXraydiffraction is reported in the formofapole figure.This is a graphical representationof thedistributionof thepolesof aparticularcrystallographicplaneonastereographicprojection.Thecrystallographictexturethatdevelopsinamaterialdependson severalprocessingparameters.Thesecanbecontrolled todevelopfavorable texture for a varietyofapplications.Theoccurrenceofunevenedgesduringdeepdrawingofthinsteelsheetintocupsortumblerisduetothelackofplanarisotropy.Thistypeproblemiscommonlyknownasearring.Welookedathowsuchproblemcanbeovercome.Theroletexture inthedevelopmentofsoftmagneticmaterialandcreepresistantsuperalloyhasalsobeendiscussed.

Slide13


26

Exercise:1. Is it possible to infer whether a hot rolled steel plate would exhibit poor through

thicknessductilitybylookingatitsopticalmicrostructure?2. Whyshouldpolycrystallinealloyshavedifferentpropertiesindifferentdirections?3. Why are nickel base single crystal super alloys the most preferred material for gas

turbineblades?4. Which crystallographic direction of Nickel base superalloy should have the highest

strength?5. Whichpropertieswillyou look forwhile selecting steel fordeepdrawingapplication?

Givereasons.Answer:

1. The presence of inclusion (mostly MnS) elongated along the direction of rolling isresponsible for poor through thickness ductility of steel plate. Microstructure of alongitudinalsectionwouldshowelongatedinclusions.Theratioofitslengthtothicknessdependsonthetotaldeformationtheplatehasundergone.

2. Themainreasonsforpolycrystallinealloysexhibitingdifferentpropertiesalongdifferentdirections are (a) preferred orientation due to either cold work or recrystallizationtexture(b)presenceofelongatedinclusions.

3. Gas turbine blades have towithstand high stresses at elevated temperature (850C).Therefore themainmechanism of failure is creep. This occurs through nucleation&growthofcavities.Grainboundariesarethemostpreferredsitesforcavitation.Absenceof such sites in single crystal gives it the best creep resistance. Apart from this thecrystal axishavingmaximum creep strength isoriented along themaximumprincipalstresstoexploititsanisotropicbehavior.

4. Nickel base superalloy has face centered cubic structure. Its preferred slip systemis111110. The axis having maximum strength should have minimum Schmidsfactor.hasminimumSchmidsfactor.

5. Deep drawing is a sheet forming process. The material should have high throughthicknessstrengthsothatduringformingthereisminimumlossofthickness.Whereasalongplanardirection itshouldhave identical formability.PlasticstrainratioRgivesameasureof formability.Deepdrawinggradeofsteelmusthavehigh andminimum


27

R.The formerensuresminimum thickness strainwhereas the latter indicatesplanarisotropy(thisisneededtoavoidearringproblem).

Appendix

Representationofpreferredorientationinsheetmetal

Theoriginandtheimportanceofpreferredorientationhavebeenexplainedindetailinthismodule.Alittlemoredetailsontherepresentationpreferredorientationinsheetmetalisgiveninthissection.In the case of a wire representation of preferred orientation is rather simple. It might besufficienttoknowwhichcrystallographicdirection ineachgrain isalignedalongthewireaxis.Howeverknowledgeofpreferredorientation insheetmetal isalsoofconsiderable interest. Itaffectscloselyrelatedtoitsformability.Hereitisnecessarytodescribetheorientationofgrainsalong threedirections: rollingdirection (RD), transversedirectionandnormaldirection (ND).These are perpendicular to each other. Figure A1 (a) shows pole figure of sheet metal. Itdisplays the locationofaparticularpole (forexample111) inastereographicprojectionwithrespecttothethreeaxesND,RD&TD.FigureA1(b)representsthecorrespondinginversepolefigureofND.Itsuggeststhatthetopfaceofmostofthegrainsinthesheetisacubeplane.Todescribethepreferredorientationofasheetyouneed3inversepolefiguresoneeachforND,RDandTD.


28

Althoughnormalandinversepolefiguresadequatelydescribeorientationsofindividualgrainsinasheetwithrespecttoits3referenceaxes(ND,RD&TD)thereisanothermorepopularwaytorepresentit.ThisisbasedonEuleranglesrepresentingspecificrotations(1,,2)requiredtoalign the cubeaxesof individualgrains to coincidewith the referenceaxes.Eachgrain islikelytohaveaspecificsetofEulerangles.ThenumberofgrainshavingEulerangleswithin1,,2and1+d1,+d,2+d2 inaunitvolumedenotesanorientationdistribution function(ODF).

ND TD

RD001 101

111

ND

FigA1: Illustrates the differencebetween a pole figure (a) and an inverse pole figure (b). Theformershowsthelocationofagivenplanenormalwithrespecttothesampleaxes.Inthiscaseitshowsthe locationof111poles. UsuallyforFCCmetalthreecommonpolefiguresarethoseof100,110and111.Inversepolefiguregivesthelocationofasampleaxiswithrespecttothecrystalaxes.ThelocationofNDisdisplayedin(b)withrespecttotheorientationofthecrystalaxes.Itisan inverseof (a). Inordertodescribethetextureorpreferredorientation inasheetproduct,3inversepolefiguresarerequired;oneeachforND,RDandTD.

(a) (b)


29

FigA3:Explainswiththehelpofastereographicprojectionhowthecrystalaxesmayhavetoberotated togetalignedalong the three laboratory referenceaxes (ND:planenormal,RD: rollingdirection and TD: transverse direction). The points denoted by unfilled circle are the initiallocationsofthecubepoles;theunfilledtrianglesarethelocationafterarotationof1aboutND,thefilledtrianglesarethelocationafterarotationofaboutRDand2isthefinalrotationaboutND.ThesethreeanglesareknownastheEulerangles.TheprojectionplaneisND.

1

1 1

2

2

TD

RD

ZS

YS

XSXC

YC

ZC

ZS

YSXS XC

YC

ZC

ZS

YSXS XC

YC

ZC

(a)

ZS

YSXSXC

YC

ZC

(b) (c)

(d)FigA2:Showsasetofrotationsabouttwoaxes(ZS&YS)sothat the crystalaxes (XCYCZC)become coincidentwith thesampleaxes.(XSYSZS)denotesthelaboratoryreferenceaxesandthecuberepresentsacrystal.ForarolledsheetZSisND,YSisRDandXSisTD.


30

FigureA2represents theorientationofaspecificcrystal (Xc,Yc,Zc)withrespect toasetof3laboratoryreferenceaxes(Xs,Ys,Zs).Thefirstrotation1 isaboutZssothatcrystalaxisZc liesalongtheplaneXsZs.ThesecondrotationisaboutYssothatZcgetsalignedalongZs.Thefinalrotation2 is aboutZs.As a resultof these three rotations the crystal gets alignedwith thelaboratory referenceaxes. FigureA3 showsa setof3 rotations thatareneeded so that thecrystal getsalignedwith the laboratory reference axes.A stereographicprojectionmayhelpyouappreciatetheconceptofEuleranglesusedtodenotetheorientationofaspecificgrainoracrystal.

FigureA4representslocationofindividualgrainsinEulerspace.ItalsointroducestheconceptODFasan integralfunction.The individualpointswithinthecubedenote locationofgains. IntheabsenceofanytextureorpreferredorientationtheseareuniformlydistributedintheentireEuler space. FigureA5 (a) showsa situationwhere thesepointsareclusteredwithincertainregionsof this space. There is also amarkeddifference in the concentrationof suchpointswithintheseclusters.This isan indicationofthepresenceofpreferredorientationortexture.FigureA5 (b)givesa sectionalviewof figA5 (a)ata specificvalueof. It suggests that themagnitude ODF is high in certain areas. The distribution of points within these clusters isconvertedintocontours.Atsetofsuchmapsatregularintervalsofangle(givesacompletedescriptionoftexture.ItcanbeusedtopredictpropertieslikeelasticmodulusfromODF.

g

FigA4:Showsthelocationsofdifferentlyorientedcrystals present in the sample in Euler space. Inthis case the points are uniformly distributed. Itsuggeststhatthegrainsarerandomlyoriented.Afunction f(g)denotes the volume fractionor thenumberofgrainslocatedwithinasmallvolumeatthe tip of the vector g. The integral overaregiongivesthenumberofcrystalspresentin this part of the Euler space. It is commonlyknownasODF:OrientationDistributionFunction.If the grains are randomly oriented ODF is aconstant. It is independentof location.Howeverin the presence of preferred orientation it is afunction of Euler angles. The points denotingcrystal orientation will no longer be uniformlydistributed.Theseareusuallyfoundconcentratedincertainregions.


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Additionaltestsforsheetmetalformability

Formabilityofsteelbyandlarge isinverselyproportionaltoitsstrength.Interstitialfreesteelhaving littleCorNhas lowstrength (YS


32

isnosolidpunchtheresultisnotaffectedbyfriction.IftheheightofthedomeisHanddisthediameter of the disc, the ratioH/d is defined as stretchability. In away it is similar to LDR(Limitingdrawratio).Bendability:Itmeasurestheabilityofasheettowithstandbending.Whenasheetisbenttheouterfiberissubjectedtomaximumtensilestress.Ifitexceedsacriticalvaluefractureappearsat itsouter face.Thisdependsofbendingradius (r),bendangle,sheet thickness (t)and flowstressofmaterial.Theratior/twheretisthesheetthicknessiscalledbendability.Smallerratiomeansbetterbendability.Flangeability:Itisevaluatedbyholeexpansiontest.Adischavingaholeofdiameterd0isheldatitsouteredgeinafixturewhileaconicalpunchisusedtoexpandthehole.Thesheetwouldbendandtheholewouldexpand.Theedgeoftheholeissubjectedtomaximumdeformation.Ifdfisthediameteroftheholeatwhichacrackdevelops,theratiodf/d0givesameasureoftheflangebilityofsteel.

Hd

d0df

t

2r

(a) (b) (c)

FigA6:Asetofsketchesillustratinghowthefollowingtestsareperformedonsheetmetal:(a)Stretchability=H/d(b)Bendability=r/t(c)Flangeability=df/d0

Keywords :IntroductionOrigin of anisotropy:Texture hardening:Representation of crystallographic texture:How are pole figures generated?Summary:Exercise:Answer:AppendixAdditional tests for sheet metal formability

Lecture 41

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Transcript of Lecture 41