Experimental and numerical assessment of subsurface plastic deformation induced by OFHC copper machining

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José OUTEIRO, Sébastien CAMPOCASSO, Lamice DENGUIR, Guillaume FROMENTIN, Vincent

VIGNAL, Gérard POULACHON - Experimental and numerical assessment of subsurface plastic

deformation induced by OFHC copper machining CIRP Annals Manufacturing Technology

-Vol. 64, n°1, p.53-56 - 2015

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Administrator : archiveouverte@ensam.eu

Experimental

and

numerical

assessment

of

subsurface

plastic

deformation

induced

by

OFHC

copper

machining

J.C.

Outeiro

(2)

a,

*

,

S.

Campocasso

a,b

,

L.A.

Denguir

a,c

,

G.

Fromentin

a

,

V.

Vignal

c,d

,

G.

Poulachon

(2)

a

a

ArtsetMetiersParisTech,LaBoMaP,RuePortedeParis,71250Cluny,France

b

CEA,DAM,Valduc,21120Is-sur-Tille,France

c_{ICB,UMR6303CNRS–Universite´ deBourgogne,BP47870,21078Dijon,France}

d_{LaboratoireInteractionsMate´riau-Proce´de´-Environnement,LRCLIMPEn8DAM-VA-11-02,France}

1. Introduction

Residualstressandplasticstraindistributionsinthemachined surfaceandsubsurfacearetwokeysurfaceintegrityparameters usedtoevaluatethefunctionalperformanceandlifeof compo-nents[1].Traditionally,muchattentionispaidtotheexperimental measurement (quantification) of residual stresses in machined components,whichisconfirmedbythelargenumberofscientific publicationson residualstressdistributionsfora widerangeof workmaterialsandcuttingconditions(includingtoolgeometry, tool materialand cooling conditions).So far,less attentionhas beenpaidtotheplasticstraindistributioninthemachinedsurface andsubsurfaceofcomponents,whichismainlyduetothelackof scientific techniques suitable for measuring (quantifying) such plasticstrains.However,therapidriseofnewtechniquesbasedon high-speed/high-resolutionimagingdevicesopensnew possibili-tiesforanalysingnotonlytheplasticstrainbutalsothestrain-rate distributionsgeneratedinmetalcutting.Thisinformationisvery useful for validating metal-cutting numerical models and to understandthefundamentalmechanismsoftheplastic deforma-tionofmachinedsurfaces[2].

High-speed/high-resolution imaging techniques, such as the DigitalImagingCorrelation(DIC)andParticleImageVelocimetry (PIV),arecommonlyusedtomeasurethestrainandstrain-ratefields generatedinthechip formationprocess(primaryandsecondary deformationzones)[3]. However,increasedrequirementsinterms

ofthecompletecharacterisationofthemachinedsurfaceintegrity haveledtotheapplicationofsuchtechniquestotheanalysisofthe residual plastic strain distribution in the machined surface and subsurface,too.OneexampleistheworkperformedbyGuoetal.[4], where the DICtechnique was applied tostudythe deformation history ofthe machinedsurface ofbrassand OxygenFree High Conductivity(OFHC)copper.Itisworthnotingthatanextremelylow cutting speed(0.6m/min)wasusedwhencomparedtosuitable cuttingspeeds formachiningthisworkmaterial (around120m/ min). A conclusion of this study was that the magnitude of equivalent plasticstrain in the machinedsurface is identicalto thatobservedinthechip.

In this paper, residual plastic strain distributions in the machined surface and subsurface, induced by the orthogonal cutting of OFHC copper under practical machining conditions (including high cutting speeds), were investigated using both numericalmodellingandexperimentalDICtechniques,includinga similarimagingdevicetothatusedbyHijaziandMadhavan[5]. The numericalresultswerefinally compared tothoseobtained experimentallyintermsofforces,chipcompressionratio,residual plasticstrainandhardnessdistributions.

2. Experimentalandnumericalprocedures

2.1. Workmaterial,cuttingtoolsandcuttingparameters

Orthogonal cutting tests on flat specimens of OFHC copper (annealed,averagegrainsizeof50

mm

andaveragehardness of 46HB)witha sizeof40(L)mm15(H)mm4(W)mmwere performed in planing configuration. The uncoated cemented ARTICLE INFO

Keywords: Machining Deformation

Finiteelementmethod(FEM)

ABSTRACT

StraindistributionsinthemachinedsurfaceandsubsurfaceofOFHCcopperworkpiecesweredetermined experimentallyandthroughnumericalsimulations.Anexperimentalsetup,comprisingadoubleframe cameraandapulsedlaser,wasdevelopedtomeasurethedisplacementfieldsusingthedigitalimage correlation(DIC)technique;straindistributionswerethencalculated.Anumericalorthogonalcutting model was alsodeveloped andapplied inorderto predictsuchdistributions.Comparisonbetween simulatedandmeasuredresultsenabledanunderstandingofthefundamentalmechanismsofplastic deformationofthemachinedsurfaceofOFHCcopper.

* Correspondingauthor.

tungstencarbidecuttingtoolshadanedgeradius(rn)of82

mm,

aflankangle(a)of108andtworakeanglevalues(g=208and308).To minimise lateral burr formation and its consequences on strain distribution,a weak inclination angle(ls) of28 was usedin the

experiments. The cutting speed (vc) and width of cut (ap) were

maintained constant, equal to 90m/min and 4mm (ap=W),

respectively.Inordertoevaluatetheinfluenceofcuttingconditions onthestraindistributionsinducedinthemachinedsubsurface,three valuesofuncutchipthickness(h)wereused(0.05,0.1 and0.2mm). Thecombination of these hand

g

values enabledus tovary the severity of the cutting process and its consequences on strain distribution.Lowtemperaturepressurisedair(328C,6bar)was appliedtominimisetheadhesionphenomenonbetweenthetooland theworkmaterial.Foreachsetofcuttingconditions,fivetestswere performed.

2.2. Experimentalset-upandparameters

Theabove-mentionedorthogonalcuttingtestsusingaplaning configurationwereperformedonaDMGDMC85Vmillingmachine (linearmotordrivesystem),equippedwithaspecially-designed experimentalset-upformeasuringthedisplacementfieldsonthe lateral specimen faces during cutting. The cutting speed was applied to the tool (attached to the milling head), while the workpiecewasmaintainedstatic(attachedtothemillingtable).A LaVisionImagersCMOSdouble-framecamera(25602160pixel sensorwitha dynamic rangeof16 bits)and aLitron NS30-15 (Nd:YAG)dual-pulsedlaserwereusedtocapturetheimagesused afterwards for the Digital Image Correlation (DIC). Using a Mitutoyo ML 10 telecentric lens, the field of view size was 1.7mm1.4mm, with a resolution of 0.66

mm/pixel.

This equipmentenablesimagepairstobecapturedwithafrequency of15Hz, precluding anycontinuousacquisition duringcutting. Therefore four image pairs (denoted P0, P1, P2 and P3) were acquiredforeachtest.Eachpaircontainstwoframes(f0andf1), withaninter-frametimeof15

ms.

Theacquisitionprocedurewas basedonthefollowing:

Twopairsbeforethecuttingtest,denotedP0{f0,f1}andP1{f0, f1},allowingmeasurementuncertaintiestobeevaluated. Onepairduringthecuttingtest,denotedP2{f0,f1},enablingthe

chipformationtobeanalysed.

Onepairaftertheendofthecuttingtest,denotedP3{f0,f1}. WhenDICisperformedbetweenimagesP1f0andP2f0,thetotal strains induced by cutting can be measured. However, the objective of the present research is to determine the residual plasticstrainsintheworkpieceaftercutting.Therefore,DICwas performedbetweenimagesP1f0andP3f0.Thedisplacementfields weremeasuredusingCorreliQ4_{software[6],withanuncertaintyof}

around0.16

mm

(evaluatedbyDICcalculationsperformedusing imagesP0f0andP1f0),or8103_{instrainforanelementsizeof}

32 pixels.Thentheresidualplasticstraincomponents(exx,eyy,exy

andeyx)andtheequivalent(vonMises)residualplasticstrain(eeq)

distributionswerecalculated. AKistler 9119AA2dynamometer, witha 5019A charge amplifier, wasalso used to measure the forces.

Beforetheorthogonalcuttingtests,thelateralspecimenfaces underobservationbythecamerawereblastedwithglass micro-beads,andallthespecimenswereannealed(4508Cduring2h).As aconsequence,asurfaceroughnesssuitableforDICwasobtained, correspondingtoSa,SpdandSpcequalto2.24

mm,

401peaks/mm2

and 358mm1_{, respectively. These parameters were measured}

usingaVeecoWykoNT1100interferometer. 2.3. Numericalmodelsandparameters

AnumericalmodelbasedontheArbitraryLagrangian–Eulerian (ALE) formulation was developed and applied to simulate the surfaceandsubsurfaceplasticdeformation,inducedbyorthogonal

cutting process of OFHC copper. The commercial FEA software ABAQUS/Explicit and a plane-strain mechanical analysis were used.To model theviscoplasticbehaviourof OFHCcopper, the Johnson-Cook constitutive model was employed [7], which is representedbyEq. (1),where ¯

s

istheequivalentstress(MPa), ¯

e

is theequivalentplasticstrain, ˙¯

e

istheequivalentplasticstrainrate (s1_{), ˙¯}

_e0

_{isthereferenceequivalentplasticstrainrate(0.01s}1_),Tis

thetemperature(8C),Tmisthemeltingtemperatureofthework

material(10838C)andTroomistheroomtemperature(208C).A,B,

C,nand marematerialparameters,which wereobtained from experimental quasi-static and dynamic compression tests at different strain rates and temperatures. They are equal to 90MPa,500MPa,0.022,0.52 and0.83,respectively.

¯

s

¼ ðAþB¯

e

n_Þ |fflfflfflfflfflffl{zfflfflfflfflfflffl} Strainhardeningeffect

1þCln

e

˙¯ ˙¯

e0

    |fflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl} Strain-rateðviscosityÞeffect 1 TTroom TmTroom  m   |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} Thermalsofteningeffect

(1) Theelasticandthermalpropertiesoftheworkmaterialwere obtainedfromexperimentaltestson thesameworkmaterialas thatusedinthemachiningtests.Thetoolwasmodelledaselastic, itsthermalandelasticpropertiesbeingobtained fromliterature

[8].Concerningthetribologicalcharacteristicsofthetool–chipand tool–workpieceinterfaces,Zorev’smodelwasused[9]. Thevalue ofthefrictioncoefficientwasdeterminedfromtribologicaltests describedin[10]. Thesetestsenabledthedeterminationofthe apparent frictioncoefficient(mapp), which includesboth

contri-butions of interfacial (local) adhesive phenomena (madh) and

macroscopic plastic deformation (mplast). For the numerical

simulation,

m

adhshouldbeused;fortherangeofslidingvelocities

and contact pressures applied in the machining tests, this coefficientcanberepresentedasafunctionoftheslidingvelocity (vs),givenbythefollowingequation:

madh

¼c1þ c2

1þ½ðvsc3Þ=c42 (2)

where thecoefficients ci(i=1,...,4) are equal to0.787, 0.185,

0.764 and0.362,respectively.Itisworthnotingthattheproposed equationfollowsthegeneraltrendofthefrictioncoefficientwith respecttotheslidingvelocityfoundbyZorev[9].Concerningthe limit shear stress (tlimit), this is equal to theyield shear stress

ðty¼

sy=

pffiffiffi3Þ and wascalculated based on the estimatedyield stress (sy) of the deformed superficial layers of the chip and

machined surface. This estimation was based on the relation betweentheVickershardness(HV)andtheyieldstress(sy),which

wasproposedbyKrishnaet al.[11]andgivenbythefollowing equation:

sy

¼1:97HV (3)

3. Resultsanddiscussion

3.1. Chipcompressionratioandcuttingforce

Chipcompressionratio(CCR)isaquantitativemeasurementof thetotalplasticdeformationreachedinthecuttingprocessandis usuallygivenbytheratiobetweenthechipthickness(hch)andh

[12]. However, duetotheirregularchipthicknessandslightly largerchipwidthwhencomparedtothewidthofcut,theCCRwas calculated bydividing thechipcross-sectionbythe uncutchip cross-section.Fig.1ashowsboththemeasuredandpredictedCCR fortworakeanglesandtwouncutchipthicknessvalues.Forthe samecuttingconditions,theCCRpredicted bytheALEmodelis similartothat measured,exceptfor

g

beingequal to208and h equalto0.05mm.Moreover,fortherangeof

g

andhusedinthis study, the most important parameter affecting the CCR is

g.

Therefore, itis expected thatthe deformationin themachined surfacewillbemoreintenseandwillaffectdeepermateriallayers as

g

isdecreased.

The cutting force applied to the cutting tool was also experimentally measured and numerically predicted. Fig. 1b shows both measured and predicted cutting force(Fc) for two

rakeangles and twouncut chipthicknessvalues. Forthesame cuttingconditions,theFcpredictedbytheALEmodelissimilarto

thatmeasured.Fcincreasesas

g

isdecreasedandashisincreased,

withtheothercuttingconditionsremainingconstant.

AlthoughtheALEmodel predictsthecuttingforcesand CCR reasonably well, for a complete validation of this model a comparisonbetweenpredicted andmeasured machinedsurface integrityfeatures(includingplasticdeformation)isrequired. 3.2. Residualplasticstraindistributioninthemachinedsurfaceand subsurface

Fig.2shows anexampleof eeqdistributionin themachined

subsurface,calculatedfromtheresidualplasticstraincomponents, assumingplanestrainconditions[12]. For therange ofcutting conditionsusedin this study,it wasnot possibletoobtainthe plasticstraindistributioninalayerclosertothesurfacewithoutan excessivedistortionoftheglobalDICtechniquemesh,inducedby thehighstrainvalues.Dependingonthecuttingconditions,the thicknessofthislayervariedfrom40 to300

mm.

Fromthesestraindistributions,in-depthprofileswere calcu-latedby averaging thestrains for each subsurface layer. Fig.3

showsanexampleofthein-depthprofilesoftheplasticstrains obtainedexperimentallyandbynumericalsimulation.Thisfigure shows a good qualitative agreement between measured and predicted results. In particular, the predicted in-depth strain profilesfollow the general trend of thosemeasured fordepths greaterthan100

mm.

Thisfigurealsoshowsthattheshearstrain component(exy)ismuchhigherthantheothers,suggestingthat

shearistheprincipaldeformationmodeofthemachinedsurface. Moreover,sincefortherangeofcuttingconditionsinvestigatedthe

shear strain component eyx is zero and the normal strain

componentsareverylow(exxandeyy),thepredominant

deforma-tionmodeseemstobesimpleshear.

Fig.4showsbothpredictedandmeasuredin-depthprofilesof eeqfor

g

equalto308andhvaryingfrom0.05 to0.2mm.Although

experimentally no strain distribution is known closer to the surface,thepredictedin-depthprofilesofeeqcapturequitewellthe

in-depth evolution ofthe measured eeq, fordepths higher than

100

mm.

Indeed, these predicted in-depth profiles of eeq pass

throughthelowerboundaryofeachplasticstraindomain,which correspondstoagivenvalueofh. Asalsoshowninthisfigure,the magnitudeofeeqandthethicknessofthedeformedlayerincrease

withh. Atthesurface,theequivalentplasticstrainspredictedby the ALE numerical model can reach values of around 2 to 3, dependingonthecuttingconditions,andtheyalsoincreasewithh. Thepredictedhighplasticstrainvaluesatthemachinedsurface supportthehypothesisofthesevereplasticdeformation(SPD)of themachinedsurface.Althoughthishypothesiscannotbeverified using the present DIC technique, the plastic strains found experimentally by Guo et al. [4] for the same work material and similar cutting conditions (except the cutting speed), are similartothosepredictedusingthepresentALEnumericalmodel.

Fig. 5 shows the same measured in-depth profiles of eeq

represented inFig.4,but withrespecttothenormalised depth, whichwasobtainedbydividingthedepth(d)byh.Thedotsshown inFig.5representtheexperimentaleeqvaluesforeachlevelofh,

while the black line represents a fitting curve for all thedata, obtainedusingtheequationdetailedinthefigure.Thismeansthat for the same cutting conditions but for a different h, the eeq

Fig.2.Subsurfacedistributionoftheequivalentresidualplasticstrainforg=308 andh=0.1mm.

Fig.3.In-depthprofilesoftheplasticstraincomponentsforg=308andh=0.1mm. Fig.1.Measuredandpredicted(a)CCRand(b)cuttingforce(Fc)asafunctionofthe

toolrakeangleanduncutchipthickness.

Fig.4.Measuredandpredictedin-depthplasticstraindistributionswithrespectto theuncutchipthickness.

distributioniscontrolled bythenon-dimensionalparameter, d/ h. IdenticalresultswerealsoobtainedbyGuoetal.[4]ataverylow cuttingspeed(0.6m/min).

As farasthe influenceof

g

isconcerned, Fig.6 shows both predicted and measured in-depthprofiles of eeq for h equal to

0.05mmand

g

varyingfrom208to308.Asshowninthisfigure,eeq

increasesas

g

isdecreased from308to208.Atthesurface, the equivalentplasticstrainspredictedbytheALEnumericalmodel canreachvaluesofaround3.4 fortheseverestcuttingconditions (lowest

g

=208, and highest h=0.2mm), which confirms the severityoftheplasticdeformationofthemachinedsurface.

In order to compare the thickness of the deformed layer measured by DICwiththat measured using anothertechnique, micro-hardnessmeasurementswerealsoperformed.Fig.7shows anin-depthprofileofVickersmicro-hardnessfor

g

equalto308and hequalto0.2mm.Thehardnessisgreateratthemachinedsurface, reaching 1105HV, and decreases as the depth is increased, stabilisingaroundavalueof704HV.Sincehardnessisrelatedto strainhardening, thismeans that strains should followthe same variations as hardness. Therefore, depending on the hardness measurement, the thicknessof the deformed layer (tEXP-HV) is in

thiscaseabout1000

mm.

AsshowninFig.4,asimilarvaluewasalso obtainedusingtheDICtechnique,whichmeansthatthistechnique capturestheplasticdeformationfieldquitewell.

4. Conclusionsandoutlook

ADICexperimentaltechniqueandnumericalmodellingwere appliedtoevaluatetheresidualplasticstraindistributioninthe machinedsurface andsubsurface of OFHCcopper, machinedat practicalcuttingspeeds.Thepredictedequivalentplasticstrainis higheratthemachinedsurface,reachingvaluesbetween1.8 and 3.4,whichconfirmsthesevereplasticdeformationofthemachined surface.Moreover,basedonthedistributionoftheplasticstrain components, the predominant deformation mode seems to be simple shear. Both the plastic strain and the thickness of the deformedlayerincreasewhentheuncutchipthicknessincreases andwhentherakeangledecreases.

Although the DIC technique requires only two images to capture the plastic deformation with good accuracy, further improvements are required in order to determine the strains closertothesurface.

Acknowledgments

Theauthorswould liketothankRe´myBesnardand Thomas BaizeaufortheirhelponimplementingtheDICtechnique. AppendixA.Supplementarydata

Supplementarydataassociatedwiththisarticlecanbefound, intheonlineversion,atdoi:10.1016/j.cirp.2015.04.080.

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Fig.6.Measuredandpredictedin-depthplasticstraindistributionsasafunctionof therakeangle.

Fig.5.Equivalentplasticstrainwithrespecttothenormaliseddepth.

Fig.7.Measuredin-depthVickersmicro-hardnessdistributioninthemachined surface.