Thermomechanical coupling investigation in Ti-6Al-4V orthogonal cutting: experimental and numerical confrontation

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Thermomechanical coupling investigation in Ti-6Al-4V

orthogonal cutting: experimental and numerical

confrontation

Mahmoud Harzallah, Thomas Pottier, Rémi Gilblas, Yann Landon, Michel

Mousseigne, Johanna Senatore

To cite this version:

Mahmoud Harzallah, Thomas Pottier, Rémi Gilblas, Yann Landon, Michel Mousseigne, et al..

Ther-momechanical coupling investigation in Ti-6Al-4V orthogonal cutting: experimental and

numer-ical confrontation. International Journal of Mechannumer-ical Sciences, Elsevier, 2020, 169, pp.105322.

�10.1016/j.ijmecsci.2019.105322�. �hal-02384414�

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Thermomechanical

coupling

investigation

in

Ti-6Al-4V

orthogonal

cutting:

Experimental

and

numerical

confrontation

M. Harzallah

a,b,c,∗

_{, T. Pottier}

a

_{, R. Gilblas}

a

_{, Y. Landon}

b

_{, M. Mousseigne}

b

_{, J. Senatore}

b

a Institut Clément Ader (ICA), Université de Toulouse, CNRS, Mines Albi, UPS, INSA, ISAE-SUPAERO, Campus Jarlard, Albi CT Cedex 09 81013, France b Institut Clément Ader (ICA), Université de Toulouse, CNRS, Mines Albi, UPS, INSA, ISAE-SUPAERO, 3 rue Caroline Aigle, Toulouse 31400, France c Laboratoire Génie de Production (LGP), Université de Toulouse, École Nationale d’Ingénieurs de Tarbes (ENIT), 47 avenue d’Azereix, Tarbes 65016, France

Keywords:

Digital image correlation Infrared thermography Orthogonal cutting Damage Thermomechanical couplings Behavior

a

b

s

t

r

a

c

t

Theconstantindustrialneedofdetaildataonthechipformationmeetswiththelackofaphysicalunderstanding ofthethermo-mechanicalcouplingsduringhardmetalcutting.Inthepresentpaper,numericalandexperimental investigationsatmicroscale(about0.5×0.5mm2_area),_is_performed_in_order_to_highlight_the_mechanisms re-sponsibleforthepoorTi-6Al-4Vmachinability.Inafirststep,strain,strain-rates,temperatures,dissipatedpowers alongwithdisplacements,velocityandcrackpropagationareobtainedateachpixelbymeansofVISIRapparatus. Experimentalobservationshavehighlightedthedependencyofthephysicalphenomenatobothcuttingspeed andrakeangleandprovidevaluableevidencesonthedifferentnatureofthecouplingphenomenon.Secondly,a 3DFEorthogonalcuttingmodelisthendevelopedtobringamulti-scalecomprehensionofTi-6Al-4Vchipgenesis andtopredictthekinematicsandthermalquantities.Thenumericalandexperimentalconfrontationrevealedthe robustnessofthedevelopedFEmodelaswellasitslimits.Hence,theelementdeletionmethodandthefriction modelareidentifiedasthemainweakspotsoftheproposedFEmodel.Finally,aparticularattentionispaidto thechipformationstepsandtheirimpactonthefinalpart.

1. Introduction

Titaniumalloys,althoughwidelyusedintheaerospaceand biomed-icalindustries,areknownfortheirpoormachinability[1].Sucha disad-vantageresultsfrom(i)alowthermalconductivity,(ii)ahighcapacity tomaintainstrengthathightemperatureand(iii)theinabilityto gen-eratecontinuouschip[2,3].

Numerous experimental studieson machining of titanium alloys havebeencarriedoutinordertoinvestigatetheTi-6Al-4Vmachinability andtoenhancethetoollifeaswellasthesurfaceintegrity.Alternatively, severalresearchworkshavebeendevotedtomachiningassistance tech-nicssuchaslaser[4–6],cryogenic[7,8]andHighpressureassistances

[9–11].Ontheotherhand,manyresearchersaddressedcomprehensive andexhaustivestudiesonthephysicalphenomenainvolvedin Ti-6Al-4Vmachining[12,13].Accordingly,threemaintheoriesaredeveloped inorder toexplaintheTi-6Al-4V chipformation[3,14,15]. Theﬁrst onesupposesthatthechipformationisbasedonadiabaticshearband inducedbythethermalandstrainsofteninginthematerial[16,17]. Thesecondtheoryisbasedoncrackspropagationalongtheshearplane

[3,18,19].Itstartsatthetooltipthenreachesthefreesurfaceofthe material.Finally,thelasttheoryisthecombinationofthetwo afore-mentionedtheoriesinwhichtheadiabaticshearbandistheprecursor ofamaterialfailureleadingtocrackpropagation[20,21].

∗_{Corresponding}_author.

E-mailaddress:mahmoud.harzallah@enit.fr(M.Harzallah).

Theunderstandingofthethermo-mechanicalmechanismsinvolved inchipformationisaverytopicalissue.Thelocalizedandrapidnature ofthemachininghaspreventedfromastraightforwardexperimental ac-cesstothesecouplings.Therefore,researcherswidelyinvestigatedthe useofnumericalsimulationinunderstandingthematerialremoval phe-nomenon.Accordingly,manynumericalsimulationsofthemachining processhavebeenperformedinrecentyears.

Inordertodescribetheﬂowbehaviorofthematerialinmachining, severalworksadoptedtheJohnsonCookconstitutivemodel[22].It dis-sociateshardening,viscousandthermalaspectsbythreeindependents terms.Foraluminummachining,Mabroukietal.[23]employedthislaw tounderstandthephysicalphenomenaaccompanyingchipformationat variouscuttingspeed.Atlatietal.[24]adoptedtheJohnsonCooklaw aswellinordertocharacterizethesegmentationprocessinmachining. Ayedetal.[6]developedanorthogonalcuttingFE modelaimingat optimizingtheparametersoflaserassistedtitaniumalloymachining. Becauseofitspopularity,animportantnumberofidentiﬁcationofthis modelhasbeencarriedoutinthelastdecade[25–28].Forthisreason, Ducobuetal.[28]gathered20setsofJohnson–Cookparametersfrom theliterature forTi6Al4Vandconducteda qualitativeand quantita-tiveselectionofthemostrepresentativesetofparametersbycomparing theoutputsofaCoupledEulerian-Lagrangianorthogonalcuttingmodel withtheexperimentalresults.Speciallyforthemachiningsimulation

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ofAISI316Lsteel,Umbrelloetal.[29]exploredtheeﬀectsofﬁve dif-ferentsetsofJ-Cmaterialconstantsusinganorthogonalcuttingmodel andbyassessingthepredictedcuttingforces,chipmorphology, temper-aturedistributionsandresidualstresses.Theauthorsobservedthatall theconsideredprocessoutputand,inparticulartheresidualstressesare verysensitivetotheJohnson–Cook’smaterialconstants.

InspiredfromtheJohnsonCookmodel,Harzallah etal.[20] pro-posedanewbehaviormodelcoupledintemperatureandstrainrate in ordertodescribethecomplexphenomenainduced bymachining. Orthogonalcuttingsimulationsusingthislattermodelprovedits capa-bilitytopredictcorrectlytheTi-6Al-4Vchipformation.Calamazetal.

[15]proposedanewmaterialconstitutivelawtoanalyzethechip for-mationandshearlocalizationwhenmachiningtitaniumalloys.Ducobu etal.[3]conductedanumericalcomparisonbetweentheJohnsonCook modelandthenewbehaviordevelopedbyCalamaz(TanHmodel).They concludedthattakingintoaccountthethermalsofteningisnotsufficient torepresentthetitaniumalloychipformationasthestrainsoftening phenomenamustalsobeconsidered.Nevertheless,therangeofvalidity ofthesemodelsremainsdependentontheexperimentalcalibrationtests andparametersidentification.Severalpioneeringnumericalworkshas alsobeenledatmicroscaleinordertocloselydescribetheinfluenceof microstructureonthethermo-mechanicalresponse[6,30].Theuseof crystalplasticitymodelsisthecommonwaytoimplementthematerial heterogeneityatmicroscalebothfromanallotropicphaseandlattice orientationstandpoint.Suchworkusuallyfocusesonmaterialthat ex-hibitgrainsizeinthesameorderofmagnitudeasthefeedratesuchas Ti17in[6]forinstance.

Thedamagecriterionisthesecondsigniﬁcantmodelingfeature. In-deed,chipformationresultsfrommaterialdecohesion[31].Liuetal.

[32]conductedanevaluationofsixductilefracturemodelsandtheir applicabilityformetalcuttingsimulation.Amongthesedamage mod-els,theyshowedthattheWierzbickifracturemodel[33]isthemost comprehensivecriteriontodescribethechipremoval.Conversely,its onlydrawbackisthenumberofparameterstobecalibrated(7 param-eters),someofwhicharediﬃculttobeobtainedfromexperiments di-rectly.Mabroukietal.[23]proposedacouplingbetweenmaterial dam-ageevolutionanditsfractureenergytodescribethematerialseparation intheorthogonalcuttingsimulation.Thismodelingstrategyisadopted byseveralresearchersandfordiﬀerentmaterials[6,24,34].Owenand Vaz[31]usedafracturecriterionwithafailuresofteningmodelinorder todescribevoidgrowthmechanismintitaniumalloymachining.

Regardingthefrictionphenomenon,thelackofexperimentaldata atthetool/chipinterfacehasledBäkeretal.[35]toneglectitintheir model.Nevertheless,inmoststudies,theCoulombfrictionmodelis gen-erallyadopted[6,36]. Guoetal.[37]improvedthis approachsince stick-slipphenomenonisobservedat thetool/chip interface.Indeed, aCoulombfrictionlawandaTrescastresslimitmodelareused simul-taneously.Zhangetal.[34]showedthatthesurfacelimitingshearstress islinkedtothecontactpressureandthecoeﬃcientoffriction.Ben Abde-lalietal.[38]andBonnetetal.[39]developedanewfrictionmodelasa functionoftheslidingvelocity.Bothoftheseworksareusingdedicated tribometersforcalibrationsake.However,experimentalcalibrationof suchmodelsremainsweakduetothelackofin-situinformationonthe localslidingvelocity.

Despitetheconstructivecontributionsoftheaforementionedworks toenhancethenumericalmodelprediction,thevalidationand calibra-tionofmachiningsimulationsonaglobalscaleremainsexcessively lim-ited,andisachievedbyafewcomparisonsintermsofcuttingforces andchipmorphology[3,24].Themajorityofthesefindingsarebased onEx-situandpost-morteminvestigationsofthemachining.Itreports atleastasmanyquestionsasanswersbecauseoflackofin-situ informa-tionregardingtemperature,strainfield,strainrateandstresses.Infact, themachiningprocessremainseminentlyathermomechanicalproblem whichrequiressimultaneousmeasurementsofthestrainfieldand tem-peratureinordertoanalyzeanddescribethecouplingsbetweenthem duringthechipformation[19,40,41].

ThankstothermalimagingandDigitalImageCorrelation(DIC) per-formances,strainﬁeldandtemperaturemeasurementsinthemachining processarenowpossibleandoﬀercomplimentaryinformation,atthe microscopiclevel,toenrich,ontheonehandthenumericalsimulation inputs(behavior,damageandfrictionmodels)andontheotherhand theexperimentalandnumericalconfrontations[42,43].

Basedonthisapproach,severaldeviceshavebeensetupallowing toaccesstheregionofcutandthereforetoobservethechipformation mechanismsandextractthethermaland/orkinematicsfields[44].In order toassessthekinematicfieldsduringAISI 1045-HRmachining, HijaziandMadhavan[40]developedacomplexdedicateddevice com-posedoffournon-intensifieddigitalcamerassetindualframemodeto performa4imagesacquisitionat1MHz.Baizeauetal.[45]developed anewsystemforresidualstrainsassessmentduringmachining.This ap-paratusiscomposedbyahighspeedcamera(switchedindoubleframe mode)andalaserflashsystemdedicatedforsceneilluminationwhich synchronized withthetoolposition.During machiningof100CrMo7 material,onlydoubleframesbefore,during,andafterthecutwere cap-turedbythecamera.Suchtechniqueallowstoenhancetheimage qual-ityathighcuttingspeedbutitisnotsufficientforabetterdescription ofthechipformationmechanisms.

Forthethermal fieldsmeasurementduringhigh-SpeedMachining of 6061-T6AluminumAlloy,Kazbanetal.[46]used anoptical sys-tembasedonfocusedarrayofmercury-cadmium-tellurium(HgCdTe) infrareddetectors.Thissystemincludesaconcavemirrorwithan alu-minumcoatingandtwoflatmirrors withagold coatingtoenhance theradiationreflectivity.Althoughitprovidesagoodthermal measure-ment,acarefulopticalalignmentofthesystemisrequiredtoensurethat thedetectorsareproperlyfocusedonthesurfaceoftheworkpieceand properlypositionedaheadofthetooltip.

Inaddition,severalstudiesfocusedonbothmachiningkinematics andthermalﬁeldsusingsomededicatedsystems.Forexample,Zhang etal.[47]usedathermalandahighspeedcameraswhichwereplaced on eachworkpiecesidefor thechipformationmechanismsanalysis. Thislatterstudyadoptedaplanestrainsandstresseshypothesisin or-dertoassociatematerialpointsforeachworkpieceface.Whitentonetal.

[48]developedanewdevicefortheunderstandingofthemachinability differencebetweenironandsteelatmicroscale.Itisbasedona cou-plingbetweenthermalandhighspeedcameraswhichfocusedonthe sameobjective.Thisisasimultaneoussynchronizedvisibleandthermal imagingsystemwhichiscomposedofathermalinfraredcameraanda visiblecamera.Themainlensisa ×15reflectivelensthatpassesboth visibleandinfraredlight.Thecoldmirrorreflectsthevisiblelighttothe visiblecameraandtransmitsinfraredlighttothethermalcamera.

Inspiredfromthelatterdevice,anopticalapparatuscalledVISIRis developedandcalibratedbyHarzallah etal.[49]forasimultaneous in-situchipformationobservationandmeasurements.Accordingly,the presentpaperdealswithanexperimentalandnumericalinvestigation ofkinematicsandthermalfieldsinordertobetterunderstandthechip formationgenesis.Theexperimentalset-up,materialofstudyand post-processingstrategyarefirstlypresented.Then,experimentalresultsare presentedanddiscussed.Inasecondsection,theFEmodelisdetailed andanumerical/experimentalconfrontationisperformed. Theforce, kinematicsandthermalfieldsareusedforcomparisonpurpose.Finally acomprehensivediscussiononthechipgenerationphenomenonis ad-dressed.

2. Experimentalapproach 2.1. Acquisitionandmachiningdevices

ThankstoVISIRapparatus,thesimultaneousmeasurementofstrains, strainratesandtemperaturesattooltipvicinityispossible.The develop-mentandcalibrationsofthisapparatusaredescribedinaprevious com-munication[49].AsdepictedinFig.1bthesceneofcutisilluminated through acollimatedwhite-lightLED(∼ 1 Watt)which isintegrated

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Kistler Table

Thermal camera (Flir SC7000)

High speed Camera (Photron SA3)

Linear axis: max (2 m/s)

a)

_{VISIR apparatus}

IR Camera

CMOS h

ig

h

sp

eed

Cam

era

Si splitter

beam

splitter

Region of

cut

off-axis

parabolic

miror

power LED

+ focus

Schwarzschild

objective

tube lens

VIS optical path

IR optical path

Lightening

b)

Tool

Workpiece

Schwarzschild Objective (x15)

c)

VISIR apparatus

3

1

2

4

5

6

7

8

1

2

3

4

5

6

7

8 d)

Fig.1. Orthogonalcuttingexperimentalsetup:a)linearactuator,cuttingtoolandopticalapparatusb)closeupviewofthecutc)VIS-IRapparatusdetaileddesign d) nomenclature.

withintheVISIRopticalsystem.Theradiationemittedbytheworkpiece andreceivedbythereﬂectiveobjective,overarangeofwavelengths,is dividedintwopathsbythemeanofathinsiliconsplitter.Thislatter hastheparticularitytoreﬂects allofradiationbelow2μmof wave-lengthstothevisibleopticalpathandtransmittherestintheinfrared opticalpathasdescribedintheFig.1c.Then,theradiationsarefocused inthecamerassensorsbymeansofmirrors.Itmustbementionedthat thechromaticaberrationsarecorrectedthroughachromaticlenswhich wereinsertedinbothpaths.

Inordertorespecttheorthogonalcuttingconfiguration,adedicated device,calledDEXTER, madeof afixedtoolandalinearactuatoris used.Thislatterisfixedontheworkingplateofaconventionalmilling machinewhile thetoolis fixedon thespindle headaspresented in

Fig.1a.Cuttingforcesweremeasuredusinga6-components dynamome-ter(Kistler9257A).

2.2. Workpieceandtool

Inthepresentwork,thematerialunderinvestigationisthe Ti-6Al-4V(grade5)titaniumalloy.Itschemicalcompositionwasanalyzedby spark-opticalemissionspectrometryandisreportedintheTable1.It shouldbe mentionedthatthestudiedmaterialistemperedat1000K andthe𝛽-transusisaround1233K.Itsaveragegrainsizeismeasured around19.2μm.

ThemicrostructurehasbeeninvestigatedthroughSEMandis de-scribedinFig.2aandb.Itischaracterizedbyaduplexmicrosturcture composedbyprimary𝛼 grains(hexagonalclose-packedstructure) sur-roundedbytransformed𝛽 grains(bodycentrecubicstructure).

Themachinedspecimen(100× 40× 3mm3₎_was_polished_and_etched

in ordertoreveal themicrostructureprovidinganaturalspecklefor digitalimagecorrelation(DIC).

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Table1

ChemicalcompositionofthestudiedTi-6Al-4Vtitaniumalloy.

Ti % Al % V % Fe % Nb ppm Si ppm Cr ppm Cu ppm Ni ppm Pd ppm Mo ppm Co ppm C ppm B ppm

88,98 6,395 4,282 0,156 410 280 180 180 130 120 110 110 72 29

Fig.2. (a)InitialmicrostructureofthemachinedTi-6Al-4V(grade5)-equiaxstructure(b)𝛼 and𝛽 phasesofthematerial.

Table2

Cuttingvelocity,feedandrakeanglesused.

𝛾 (°) feed (mm) Vc ( m min −1₎ Test 1 ₁₅ 3 Test 2 _0.25 15 Test 3 ₀ 3 Test 4 15

Twouncoatedcarbidetoolswereusedwithtwodiﬀerentrakeangles (𝛾 =0◦,15◦).Theybothpresentaclearanceangleof𝛼 =11◦andaradius edgearound20μm.

2.3. Acquisitionandmachiningconditions

Inordertoovercomethemotionblurphenomenonthatoccurs dur-ingimagerecording,agoodcompromise betweentheparametersfor eachcamera(integrationtime,acquisitionfrequency,resolution,...)and cuttingconditions(cuttingspeed,feed,...)mustbeachieved.Therefore, opticalandmachiningparametersareﬁxedrespectivelyforeachtestas describedinTables2and3.Foreachtool,afeedof0.25mmisselected andtwocuttingspeeds(Vc)areinvestigated.

ThehighspeedcameraonthevisibleopticalpathisaPhotron Fast-camSA3.ItsacquisitionfrequencyFwassetto6000fpsandthe expo-suretime(it_vis)variesbetween30and50μsdependingonthecutting

speed.AFlirSC7000thermalcamerawasusedintheinfraredpath(IR). Itissetat600fpsandanexposuretimeof𝑖𝑡𝐼𝑅 =30μsprovidinga ther-malimagesizeof160×128pix2_._The_simultaneous_cameras_triggering

wasconductedthroughadedicatedboxsynchronization.

Formagniﬁcationassessmentpurpose,themetricratio(R)was eval-uatedforthevisiblecamera(PhotronFastcamSA3)at1.133μm/pixand at1.981μm/pixforthethermalcamera.Readerscouldreferto[49]for thethermalcameracalibration.

2.4. Experimentalpost-processing

2.4.1. Digitalimagecorrelationandkinematicﬁeldscalculations

Thedigitalimagecorrelation(DIC)isperformedusing7Dsoftware

[50].Asdetailedinapreviouswork[49],thesizeofthesubsetis opti-mizedthroughtwoapproaches(MeanIntensityGradientandRigidbody methods).Hence,itissetto16×16pixforastandarddeviationofthe measureddisplacementsabout0.03pix.However,cumulatingsuch er-rorover50imagesleadtoamaximalerrorof1.5pixandthereforelead toerrorsonstrainbelow10%(ifa16×16pixextensiometricbasisis used).

Theincrementalcorrelationwasusedforkinematicﬁelds calcula-tions(i.e.displacements,strainandstrainrate).Thisapproachis recom-mendedinthecaseoflargedeformation,highstrainrate,out-of-plane motionandmaterialdecohesion[19,51].Incontrast,itrequiresaproper numericalprocessinginordertocomputethecumulateddisplacements andstrains.Accordingly,thecumulateddisplacementstrategydetailed Table3

Opticalparametersusedforeachtest.

itIR (μs) itvis (μs) R (μm/pix) Image IR size (pix × pix) Image visible size (pix × pix) F (fps)

IR visible IR visible

Test 1 50 512 × 512

Test 2 ₅₀ 30 _1.981 _1.133 _{160 × 128} 384 × 352 ₆₀₀ ₆₀₀₀

Test 3 50 512 × 512

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in[19,49]wasusedinordertoenhancetheassessmentofthekinematic fields.Furthermore,theuseofsuchastrategyoffersastraightforward comparisonbetweenexperimentalresultsandnumericalsimulationsin termsoflogarithmicequivalentstrain(HENKY)Handequivalentstrain rateD.It’sworthmentioningthatthestrainratetensoriscalculated bymeansofthedisplacementincrements(ΔU_x,ΔU_y).Theknowledge ofthisparameteroffersastraightforwardaccesstothevelocityfields VxandVy.Assumingaconstantcaptureratesoftheimages,it there-forecomes𝑉𝑥 =Δ𝑈_𝑥∕Δ𝑡and𝑉𝑦 =Δ𝑈_𝑦∕Δ𝑡.Thenthecomponentsofthe strainratetensorDare:

⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ 𝔻𝑥𝑥 (𝑥𝑘 ,𝑦𝑘 ,𝑘)= 𝜕𝑉 𝑥(𝑥 𝜕𝑥 𝑘,𝑦 _𝑘𝑘,𝑘 ) 𝔻𝑦𝑦 (𝑥𝑘 ,𝑦𝑘 ,𝑘)= 𝜕𝑉 𝑦(𝑥 _𝜕𝑦𝑘,𝑦 𝑘,𝑘 ) 𝑘 𝔻𝑥𝑦 (𝑥𝑘 ,𝑦𝑘 ,𝑘)=1 2 (_𝜕𝑉 𝑦(𝑥 𝑘,𝑦 𝑘,𝑘 ) 𝜕𝑥 𝑘 + 𝜕𝑉 𝑥(𝑥 𝑘,𝑦 𝑘,𝑘 ) 𝜕𝑦 𝑘 ) (1)

where(x_k,y_k)arethegridcoordinates(identicalforeveryimagepair) fortheimagek.Readerscanreferto[19]formoredetails.

2.4.2. Energybalanceanalysis

Comingfromfirstandsecondlawsofthethermodynamic,theheat equationis thebasicingredienttoinvestigate thethermomechanical aspectofthecuttingprocess.Thespecificformofthevolumeheat dif-fusionequationintheLagrangianconfigurationappliedtoa2D ther-mographicframeworkcanbeexpressedas:

𝝆𝐂𝐩 ( 𝜕̄𝜃 𝜕𝑡 +⃗𝑣⋅ ⃗∇̄𝜃 ) −𝑘1 ( ⃗∇̄𝜃)2−𝐤Δ2̄𝜃 + 2ℎ𝜃 𝑒 + 2𝜎𝜖 𝑒 (̄𝑇4−𝑇𝑟 4) ⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟ Experimentalevaluation = 𝑤′_𝑐ℎ=𝛽(𝜎 ∶ ̇𝜖_𝑝) ⏟⏞⏞⏞⏞⏞⏞⏞⏞⏟⏞⏞⏞⏞⏞⏞⏞⏞⏟ Numericalevaluation (2) where:

• ̄𝜃 =̄𝑇(𝐱,𝐭)−𝑇₀isthediﬀerencebetweenthecurrentandtheinitial temperatureT₀.

• _𝝆𝐂_𝐩(𝜕 ̄𝜃 𝜕𝑡 +𝑣∇̄𝜃

)

istheintertialtermthatlinksthetemperature evo-lutionatagivenlocation(x,t).Variablevstandsforthevelocity vectorﬁeld.

• 𝑘₁(⃗∇̄𝜃)2−𝐤Δ2̄𝜃 isthediﬀusion(Laplace’s)term.Notethat∇isthe

twodimensionnalgradient andΔ2 thetwo-dimensionnalLaplace

operator.

• 2ℎ𝜃 𝑒 +

2𝜎𝜖

𝑒 (𝑇4−𝑇𝑟 4)aretheconvectiveandradiativeheatlossesover

thefront andbackfaces of the sample. 𝜎 stands for the Stefan-Boltzmanconstant. histheheattransfercoeﬃcientchosen tobe equal50Wm−2_K−1_._T

r istheroomtemperature.However,this

quan-tityhasbeenassessedandcomparedtolaplacianandinertialterms inpreviouswork[49].Accordingly,itwasneglegtedinthepresent analysis.

• _𝑤′

𝑐ℎ=𝑑1=𝛽

(

𝜎 ∶ ̇𝜖𝑝 )istheheatsourcetermandequalstheintrinsic

dissipationd1inabsenceofthethermoelasticcouplings.𝛽,𝜎, ̇𝜖𝑝 are

respectivelytheTaylorQuinneyfactor,theCauchystresstensorand thestrainratetensor.

• Thematerial parameters arethen 𝝆 =𝜌1𝜃 +𝜌0 the massdensity, 𝐂𝐩=𝐶1𝜃 +𝐶0 thespeciﬁcheat,𝐤=𝑘1𝜃 +𝑘0 thethermal

conduc-tivity.Accordingto[52,53],theywerechosentoevolvelinearlyas afunctionoftemperature(seeTable5).

Ratherthantemperatureandkinematicsﬁeldsanalysis,theobjective oftheexperimentalpartistoassessthelefthandsidetermsfromthe measuredquantities(̄𝑇(𝐱,𝐭)andT₀)inordertoprovideanestimationof theinvolvedpowerinthecuttingphenomenon𝑤′

𝑐ℎ.Itisthencompared

withtherighthandsidetermwhichisevaluatednumericallyfromthe intrinsicdissipationd₁(seeSection5.6).

Table4

Thenumberofthecaptured im-ages for the analyzed segment chip. Number of images IR Visible Test 1 5 58 Test 2 1 10 Test 3 6 62 Test 4 1 11 3. Experimentalresults

Onlyonesegmentisinvestigatedformeachcapturedvideo.For read-ingandcomparisonpurpose,imagesarelabelledbytheirnumberand thepercentageof thesegmentformation.Theﬁrstimage(0%)being theimagewherethesegmentﬁrsttouchesthetoolandthelastimage (100%)beingtheimageexhibitingadisplacementof50μmafterthe segmentbeingfullyformed.TheTable4resumethenumberofimages obtainedforeachtest.

Asmentionedinthepreviouswork[49],onlyonethermalimageis acquiredduringtheprocessat15m/min.Itcorrespondstoa40% pro-gressionofthesegment.Consequently,otherthermalimagesfromother measuredsegmentswhichhave,approximately,thesamesizewere se-lectedfortheanalysis.Itshouldbementionedthatnoimportantdrift ofthethermomechanicalquantitieswasobservedduringthecut.

However,experimental investigationson thechipgenesislead to splitthemechanismintothreesuccessivesteps[3,19,20].During the ﬁrststage(i.e.compressionstep),ahighcompressionstateonthe mate-rialisinducedbythetoolandlocatedaroundthecuttingedge.The seg-mentstorestheelasticenergywhileplasticitydevelopsintheprimary shearzone.Anoutofplaneswellingofthesegmentisclearlyvisiblein thisphase.Theendofthisstageisdeﬁnedbytheshearplanecreation andtheuprisingofamicrocrackatthetooltip.Duringtheshearphase, thecrackinitiatesatthetooltipandevolvesinsidetheshearzone to-wardthefreechipsurface.Finally,thesegmentisfullyformedandslips onboththecuttingfaceandthenextsegment(tobeformed). Simul-taneously,thetooltipstartsthecompressionphaseofthenextone.As depictedinFig.3theclassicalstepsofthechipformationwereobserved andanalysedforeachtest.

SuchgraphresultingfromaDICanalysisbasedonminorandmajor strains(notpresentedhere)asdetailedin[19,20].Itisclearly percepti-blethatthethreesuccessivessub-processesarehighlyinﬂuencedbythe cuttingconditions.Firstly,itcanbepointedoutthatthecompression phaseismoreimportantwithanullrakeangle.Thelongdurationof thecompressionphaseleadstoarapidshearphaseandtoaparticular chipgenesisway.Indeed,duringthecompressionphase,thesegment storeselasticenergywhichisthendissipatedinthenextstages.Hence, thelongerthecompressionphaselaststhefasteristhesegmentejection (i.e.shortshearandextractionphases).

Thecompressionphaseisalsoaﬀectedbythecuttingvelocity.As shownin thetests 1and3(𝑉𝑐=3mmin−1₎_,_this _phase_lasts_longer

thaninthecaseoftests2and4(𝑉𝑐=15mmin−1₎_.

Ontheotherhand,itcanbeseenthatcrackpropagationisdelayed whenlowcuttingspeedareinvolved.Thisobservationbringstolight thecuttingvelocityeﬀectinthestrainlocalizationandthusonthecrack propagation.Therakeangleeﬀectonthestrainlocalizationandcrack propagationisclearlyshownintheFig.3.Acurvedstrainlocalization zoneisalwaysobservedwithanullrakeanglewhereasitislinearwith arakeangleof15∘_._This_crack_path_transition_from_curved_to_linear_may

resultsfromtheshapeofthetriaxialityzone.Asdetailedin[19,20],a hydrostaticpressurezoneislocatedatthetooltipwhichishigher(in termsofmagnitudeandgeometry)inthecaseofnullrakeanglethan thepositiveone(duetotheadditionalcompressioninducedbytherake

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80% 80%

80%

Fig.3.5instantsnapshotpicturesacquiredduringthegenerationofonesegmentforthefourinvestigatedcuttingconditions.Thedistinctionbetweenthethree phasesoftheprocessreliesonthecrackpropagation.Thetimeelapsedin-betweencrackinitiationandcompletiondeﬁnestheshearphase.

angle).Duringthesegmentgeneration,thecrackskirtsthetriaxiality zoneinordertoreachthefreesidesurface.Thislatterbeingnarrower forastherakeangleincrease,thecrackcanreachthefreesurfacein astraightmanner.Consequently,thelargeristhetriaxialityzonethe morecurvedisthecrackpath.

3.1. Kinematicﬁelds

Fig.4presents theevolution ofthe logarithmicequivalentstrain (a.k.aHencky’sstrain)duringchipsegmentformation.Strain localiza-tionsareclearlyhighlightedbysignificantstrainmagnitudes(upto1.7). Duringcompressionphase,thestrainmagnitudeislowandseemshighly heterogeneousinspaceandintime.Then,thestrainlocalizationstarts tomoveforwarduptotheshearplanecreation.Finally,astrainingband isobservedwhichisfixedinspaceandonlyfluctuatesinmagnitudeover time.Thestrainlocalizationthicknessishighlydependentonthecutting speedforbothrakeangles.Itdecreasesasthecuttingspeedincreases. Thisinformationprovesthatstrainlocalizationismainlyresultsfrom thecuttingspeedwhilestrainmagnitudeisinfluencedprimarilybythe rakeanglevariationandatlesserscalebythecuttingvelocity.Onthe otherhand,itcanbenoticedthatthechipbulk(i.e.thesidesurfaceof thechipwhichlocatedawayfromthefirstandsecondshearzones)is notsignificantlydeformedwhenthecuttingspeedvaries.Conversely,it seemstobeinfluencedbythevariationoftherakeangle.

Thestrainratesarealsogreatlyinfluencedbythecuttingspeed.A highstrainratesmagnitudeisobservedforearlystageofthesegment chipformation(~ 20%).Thisphenomenonplaysaleadroleforstrain localizationandcrackpropagationsincetheequivalentstrainatfailure decreasesathighcuttingspeed.Consequently,itleadstoarapid seg-mentchipformation.However,therakeangleinfluenceonthestrain rateisnotnegligible[19,49].Adropof50%inthestrainrateis ob-servedatlowcuttingvelocity.Conversely,thiseffectisnotobservedat 15mmin−1_where_a_comparable_magnitude_is_obtained.

3.2. Thermalﬁelds

Fig.5depictsthetemperatureandintrinsicdissipationdistributions duringchipsegmentformation.Thetemperatureincreaseswiththe cut-tingvelocityaugmentationandat alesser scalewiththerakeangle diminution.

Atlowcuttingspeedandusinga0∘_rake_angle,_no_clear_localization_is

foundbefore60%ofsegmentformation.However,byvaryingtherake angleto15∘_,_an_earlier_temperature_localization_is_observed_(i.e._at_40%

ofthesegmentformation).Foralltests,themaximumtemperaturedoes notevolvesigniﬁcantlyduringthesequence,onlyrangingfrom590K to633K.However,thetemperaturegradientissigniﬁcantinspace.The min/maxrangewithinthesameimageisaround573Kmm−1_._Indeed,

themaintemperatureriseseemstooccurduringthetransitofa mate-rialpointthroughtheprimaryshearzone.Italsoshouldbementioned thatthemaximumtemperaturelocationislocatedintheprimaryshear zone(ZI).SuchﬁndingsleadtoconsiderthatheatgeneratedinZI(from plasticityanddamage)ismoreimportantthaninthesecondaryand ter-tiaryshearzoneswherefrictionisoftenassumedtoplayaleadingrole. Itcanbeexplainedbytheshortperiodofmachining(∼ 1.2s)which cor-respondstoatransitionalstage.Itisworthremindingthatonlyasmall partofthesecondaryshearzoneiscapturedbythethermalcamera dur-ingtheprocess.Indeed,furtherinvestigationswithathermalimageof thewholesceneofcutneedtobeconductedtobeconclusiveonthis matter.

Converselytotemperature,alocalizationoftheintrinsicdissipation isobservedatearlystageofchipsegmentformation.Sucheffectis de-tectedespeciallyathighcuttingspeed.Thedissipatedpowerevolution canbedescribedthroughthreestages:atfirst ~ 20%,thedissipated powerislowandisconcentratedatthetooltip.Then,fromaprogression in-between~ 20%to~ 60%,thedissipatedpowerincreasesandmoves towardthemiddleoftheprimaryshearzone.Duringthefinalstageof thesegmentchipformation,itisseenfromthelatestimagesthateven whilethecrackpropagationiscompleted,andthatstrainaccumulation stalls,thegeneratedpowerremainshigh.Thethermal source magni-tudeincreasesby43%whenmultiplyingby5thecuttingspeedanda smallreductionisobservedbyvaryingtherakeangleto0∘_._These

obser-vationsseemnotsurprisingconsideringthehighlocalizationobserved witharakeangleof15∘_and_especially_at_high_cutting_speed._In

addi-tion,itisclearlyperceptiblethattheadditionalcompressioninduced bythenullrakeangledisruptstheshearmechanismsandconsequently thelocalizationphenomena.Theheatsourceinthiscaseseemsmore importantinthespacebutwithasmallermagnitudethaninthecaseof tests1and2.

Itshouldbementionedthatthegenerationofsegmentnoverlaps withtheonegeneration𝑛−1.ItisvisiblefromFig.5at10%(forall

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Fig.4. 5instantimagesofthestrainandstrain-rateﬁeldsdistributionsduringthegenerationprocessofonesinglesegment.Thefourcuttingconditionsunder investigationaredepicted(3m∕min−15m∕minand0◦−15◦).

machiningcondition)thattwoheatsourcesareactivesimultaneously: theupperonecorrespondingtotheslidingofsegment𝑛−1andslightly beaneaththedissipationduetotheearlystageofcompressionin seg-mentn.theinputmechanicalpowerissplitintwolocations,theﬁrst consistsintheslidingofthesegmentn-1overthesegmentnandthe secondistheearlystageofgeneratingsegmentn.

Thepreviousexperimentalsectionbringstolightthe thermomechan-icalaspectoftheTi-6Al-4Vchipformation.Thekinematicsand ther-malﬁeldsevolutionsarepresentedanddiscussed.Thestrain localiza-tionphenomenonplaysanimportantroleintheshearplanecreation. Itsmagnitudeismainlypilotedbythecuttingvelocityanditsshapeis stronglyrelatedtothecuttinggeometry(i.e.therakeangleandfeed).

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Fig.5. 5instantimagesofthetemperatureandintrinsicdissipationdistributionsduringthegenerationprocessofonesinglesegment.Thefourcuttingconditions underinvestigationaredepicted(3m∕min−15m∕min and 0◦−15◦).

Fromathermalstandpoint,themaximumtemperatureisusually lo-catedintheprimaryshearzone.Itsmagnitudeismainlyinﬂuencedby thecuttingspeedandatalesserscalebytherakeangle.Byhighlighting bothFigs.4and5,onecanthereforeprovethattheequivalentstrainat failureissmallerathighcuttingspeedeventhoughthetemperaturein theprimaryshearzoneishigher.Thisresulttestiﬁesthelossof

ductil-ityofmaterialfollowingacompetitionwiththestrainsofteninginthis rangeofthermomechanicalloading.

Thespeciﬁcpowerisalsoinﬂuencedbythemachiningparameters. Thethinstrainingbandinducedathighcuttingspeedleadstoahigh concentrationoftheintrinsicdissipation.However,thedissipationin thesegmentbulkandinthesub-surfaceisfarfromnegligible.Further

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Fig.6. Geometryandboundaryconditionsusedfortheimplementationofa3DFEorthogonalcuttingmodel.

investigationsarerequiredtolinkthisphenomenontothesurface in-tegrity(i.e.residualstresses,...)ofthegeneratedsurface.

4. Numericalapproach

4.1. 3Dgeometricﬁnite-element(FE)model,boundaryconditionsand meshsensitivity

The3Dgeometricmodelproposedconsistsinacarbidecuttingtool andapartmadeofTitaniumalloyTi-6Al-4V.Theworkpiecetomachine ismodelledasaparallelepipedmeasuring10mminlength,1.7mmin heightand1.5mminwidth(𝑤=3mmbutaplaneofsymmetryis de-ﬁned).Itwascreatedbyasinglepartinordertorespectthephysical phenomenainordertoavoidmanymodelinghypotheses.Thetool ge-ometryandthecuttingconditionsarethesameasfortheexperimental study.

AsdetailedinFig.6,the3Dﬁniteelementmodeliscreatedunder symmetricconditioninordertoinvestigatetheevolutionofthechip mechanismeither underplanestrain assumption(center of thechip

𝑧=𝑤∕2)andplanestressassumption(sidefreesurface𝑧=0).Theback surfaceofthetoolislockedover6dof.Thebottomsurfaceofthe work-pieceisonlyfreetotranslatealongtheXaxis.Thedisplacementofthe nodesonthebacksurfaceoftheworkpieceisimposedwithaconstant velocitythatequalsthedesiredcuttingspeed.However,heattransferis allowedonlybetweenthetwoparts.

3Dcontinuumelementsunderreducedintegration(C3D8RT)were adoptedforthermomechanicalﬁeldscalculation.Regardingthe hour-glasscontrol,arelaxstiﬀnessmethodisusedtopreventhourglassingas recommendedbyBargeetal.[54].

Tomakeacompromisebetweenbothcomputingcostandaccuracy, ameshsensitivityanalysisiscomputedusinganiterativemethod. Ac-cordingly,aseriesofsimulationsarecarriedoutbyvaryingthe charac-teristiclengthofelement(L)from55μmto5μmwithanincerementof 5μm.Foreachsimulation,bothaverageandmaximumofthecutting forces(xdirection)arerecordedfortheerrorcalculation.Hence,the

erroriscalculatedbetweentwosuccessivesmeshsize(i.e.iand𝑖−1) asfollows: 𝑀𝑒𝑠ℎ𝑒𝑟𝑟𝑜𝑟𝑖 (%)= √₍ 𝑎𝑣𝑒𝑟𝑎𝑔𝑒(𝐹𝑐)_𝑖−𝑎𝑣𝑒𝑟𝑎𝑔𝑒(𝐹𝑐)_𝑖−1 𝑚𝑎𝑥(𝐹𝑐)_𝑖 )2 × 100 𝑤ℎ𝑒𝑟𝑒𝑖=0𝑡𝑜10 (3)

AsdepictedinFig.7,theerrorseemstobestablefrom25μmofthe meshlengthforacomputingtimeof3hand37min.Inaddition,the chipformationshowsthatfrom thisvalueofthecharacteristicmesh lengthcanwellcapturetheshearlocalizationandthecrackpropagation onthechip.Consequently,themeshsize25×25×115μm3_was_chosen

intheregionofinterestandbeyondthiszoneacoarsestmeshisadopted whichisrangesin-between(200× 300× 115−500× 300× 115μm3_).

4.2. Materialconstitutiveanddamagelaws

Themechanicalbehaviorofthecarbidetoolismodelledbya clas-sicalthermo-elasticlaw.Themechanicalparametersoftheworkpiece andthecarbidetool(WC)aregiveninTable5.

Sincethetightcouplingbetweenphenomena(mainlybetween tem-peratureandstrainrate)thatoccursduringthechipformation,the mas-teryofworkpiecebehavioranddamageevolutionisessential.Therefore, theworkpiecebehaviorismodelledbyamodiﬁedLudwicklaw under-takingatightcouplingbetweentemperatureandstrainrate.Thismodel ispresentedintheEq.(4)oftheequivalentplasticﬂowstress.

𝜎 =𝐴(̇𝜀,𝑇)+𝐵(̇𝜀,𝑇).𝜀𝑛 (̇𝜀 ,𝑇 ) ₍₄₎

where𝐴(̇𝜀,𝑇),𝐵(̇𝜀,𝑇), 𝑛(̇𝜀,𝑇)arerespectivelytheyield strength,the hardeningmodulusandthehardeningcoeﬃcientandexhibita depen-dencyonboththestrainrateandtemperature.However,theevolutions ofeachparameteraccordingtothesetwoquantitiesweredescribedby abilinearinterpolationasdetailedinapreviouswork[20].

Thedamagemodelingclassicallyreliesonacumulativeformulation ofthedamageinternalvariableD,ofwhichtheevolutionthroughout

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Fig.7. Meshsizesensitivityanalysis. Depic-tionoftheevolutionsof:(i)theerroronthe globalcuttingforceand(ii)theCPUtime,asa functionofthemeshsize.(CPUcharacteristics: AMDopteron6376/2processors16Cores/ 2.3GHZ/RAM132Go).

Table5

MechanicalandthermalpropertiesofthecarbidetoolandTi-6Al-4Vworkpiece(20◦C−550◦C)[6,52,53].

Properties Material

Ti-6Al-4V WC

Young modulus E (GPa) 118 . 8 − 0 . 09 .𝑇 705 Density 𝝆(kg m −3 ) _{4452 − 0 . 1 𝑇} _15,700 Poisson’s ratio ϑ 0.33 0.23 Specific heat 𝑪 𝒑 ( J −1 K −1 ) _{552 . 8 + 0 . 358 .𝑇} _{−2 . 10}−4 .𝑇 2 + 0 . 313 .𝑇 + 220 Thermal conductivity 𝒌 (W m −1 𝐾 −1 ) _{6 . 58 + 0 . 0057 .𝑇} _{−8 . 10}−5 .𝑇 2 + 0 . 07 .𝑇 + 43 . 1 Expansion Coefficient 𝜶𝒅 ( K −1 ) 1 . 15 −5 _{5 . 10}−6 Room temperature 𝑇 𝑟 ( K ) 293 293 Fusion temperature 𝑇 𝑓 ( K) 1903 − Taylor-Quinney coefficient 0.8 −

plasticityisdeﬁnedasafunctionoftheincrementofplasticstraind𝜀p

by:

̇𝐷 =𝑑𝜀𝑝

̄𝜀𝑓 (5)

Suchformalismrequiresagoodassessmentofthestrainatfailurē𝜀𝑓 .In

fact,theshearnatureofthemechanismandthenarrowrangeofstress triaxiality𝜂 involvedin cutting(𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑒𝑙𝑦−0.33<𝜂 <0.33)have ledtoconsidermaxshearfailurecriterionaswellsuitedforthis inves-tigation[20].Thislawcanbedescribedasafunctionofthenormalized Lodeanglē𝜃 byEq.(6).

̄𝜀𝑓 = ⎡ ⎢ ⎢ ⎢ ⎣ √ 3𝜏_𝑓(̇𝜀,𝑇) 𝐵(̇𝜀,𝑇)𝑐𝑜𝑠(𝜋 ̄𝜃 6 ) −𝐴_𝐵(₍̇𝜀_̇𝜀,_,𝑇_𝑇)₎ ⎤ ⎥ ⎥ ⎥ ⎦ −1 𝑛(̇𝜀,𝑇) (6)

Thestrainrateandtemperaturedependencyisthusaddressedthrough the material parameters and the maximum shear stress at failure

𝜏𝑓 (̇𝜀,𝑇).Thelatteristheonlyparametertocalibrateandisdescribed

asafunctionoftemperatureandstrainratebyabilinearinterpolation asdetailedin[20].TheplaneequationisrecalledinEq.(7)whereas theparametersvaluesusedinsimulationsarespeciﬁedinTable6.Itis importanttonotethatthedamageandbehaviorlawsaresuccessfully implementedintheFEmodelbymeansofVUMATsubroutine.

𝐴,𝐵,𝑛,𝜏𝑓 =−𝑎.𝑇−𝑏.𝑙𝑛(̇𝜀_𝑝)−𝑐 (7)

Table6

Behavioranddamagelawparameters[20].

A (Pa) B (Pa) n 𝜏f (Pa)

a 9 . 36 𝑒 + 005 5 . 57 𝑒 + 05 9 . 46 𝑒 − 05 7 . 1716 𝑒 + 05

b −1 . 45 𝑒 + 08 4 . 66 𝑒 + 07 4 . 23 𝑒 − 02 9 . 3088 𝑒 + 07

c −8 . 65 𝑒 + 08 −6 . 39 𝑒 + 08 −0 . 365 6 . 9573 𝑒 + 08

4.3. Contactconditionsandfrictionmodeling

Inadditiontobehavioranddamagelaws,thesimulationofthechip formationprocessalsorequiresagooddescriptionoftheinteraction be-tweenthetoolandworkpiece.Therefore,aparticularattentionispaidto thefrictionmodel.Asprovedbyseveralauthors,thetool/chipinterface canbedividedintwodistinctregionswherethetribologicalbehavior isclearlydiﬀerent[55–57].Theﬁrstregion(i.e.stickregion)islocated aroundthetooltipandischaracterizedbyastrongmaterialadhesion duetohighcontactpressure.Thesecondregion(i.e.slipregion)is char-acterizedbyaslidingmotionofthechipalongtherakeface.

Inthepresentstudy,anewstick-slipfrictionmodelisproposedas formulatedinEq.(8)anddescribedinFig.6(detailA).Accordingly, thestickregionwasdescribedbyaTrescafrictionlawwithacoeﬃcient valuem_kequaltotheunity[27].Ontheotherhand,theslidingregion ismodelledbyamodiﬁedCoulombfrictionlawwhichfriction param-eter𝜇 isdescribedasafunctionoftheslidingvelocityV_slasproposed in[58].𝜎n and𝜏 representrespectivelythenormalandshearfriction

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stresses. ⎧ ⎪ ⎨ ⎪ ⎩ |𝜏|=−𝑚_𝑘.√𝜎𝑛 3. ⃖⃖⃖⃗ 𝑉 𝑠𝑙

||⃖⃖⃖⃗𝑉 𝑠𝑙||∶Trescafrictionlaw(forstickregion)

|𝜏|=−𝜇(𝑉_𝑠𝑙).𝜎_𝑛. ⃖⃖⃖⃗𝑉 𝑠𝑙

||⃖⃖⃖⃗𝑉 𝑠𝑙||∶ModiﬁedCoulombfrictionlaw(forslidingregion)

(8) AspointedoutbyBodwenandTabor[59],theapparentfriction pa-rameterresultsfromtwocontributions.Itincludesononehandthe ad-hesivephenomena,thatareaﬀectedbythematerialpropertiessuchas hardness,asperities,andontheotherhandtheplasticdeformationof theworkmaterial,whichcannotbeneglectedundersuchseverecontact conditions.Basedonthisconsideration,severalstudiesprovedthatthe adhesivepartoftheapparentfrictionparameteriscloseto90%inthe caseoftitaniumalloyTi-6Al-4V[58,60].Accordingly,onlythe adhe-sivepartisintroducedinsimulations.Thefrictionlawissuccessfully implementedinthenumericalmodelthroughVfricusersubroutine.

Anotherimportantfeatureofthemodelistheheatpartition coeﬃ-cient𝛽p .Itdeﬁnestheratioofthefrictionthermalpowerthatspreads

withinthetoolT (andthus 1−𝛽_𝑝withintheworkpieceW).Several modelshaveproposeddifferentapproachesintheassessmentofsuch coefficient[61,62].ThemostrecentapproachesreliesontheThermal ContactResistance(TCR)whichassessmentisadedicated experimen-talchallengeinitsownright[63,64].Inthepresentwork,theoriginal approachproposedbyBlok[61]andJaeger[62]hasbeenchosen.This latterdoesnotrequiretheevaluationoftheTCRbutratherdefines𝛽p

asaratioofthermaleﬀusivitesofthetool𝜁T andworkpiece𝜁W inthe

caseofadynamiccontact.Suchdeﬁnitionhasalreadybeensuccessfully implementintheﬁeldsofcuttingsimulation[3,38]andreads:

𝛽𝑝 = 𝜁𝑇

𝜁𝑇 +𝜁_𝑊×√𝑃𝑒

where 𝜁𝑖 =√𝝆_𝑖.𝑪𝒑_𝑖.𝒌_𝑖and𝑃𝑒 =𝐿×𝑉𝑠 ×𝝆𝑊 ×𝑪𝒑𝑊

4×𝒌_𝑊 𝑖=𝑇,𝑊 (9) where, Pe is the Peclet number, V_s the sliding velocity and L the contact width. The evaluation of the Peclet number re-quires the input of the sliding velocity which is an experimen-tal blind spot. Accordingly, four values of 𝛽p was calculated:

at (20◦C∕3mmin−1_,₅₀₀◦_C_∕3_m_min−1_;₂₀◦_C_∕15_m_min−1_,₅₀₀◦_C_∕15

mmin−1).ThematerialparametersforTungstenCarbideandTi-6Al-4V werethoseofTable5.Theobtainedvalues(0.58,0.56,0.75,0.74)was averagedtoobtainavalueof𝛽𝑝 =0.66whichwassetinthemodel.Its shouldbementionedthat90%oftheplasticworkinducedbyfrictions phenomenaisconvertedintoheat[3,20].

5. Numericalandexperimentalconfrontation

TheuseofcoupledmeasurementandFEsimulationsconstitutesa powerfultoolforinvestigationsandprovidesapreciousinsightofchips generationphenomenonfromwhich someconclusionscan be drawn butitalsobringsmanysubsequentquestions.Thepresentsectiondeals withthenumericalandexperimentalresultsobtainedfromorthogonal cuttingoftitaniumalloyTi-6Al-4V.Thecomparisonbetweenthetwo approachesisperformedthroughseveralaspects.Accordingly,the rel-ativeerroriscalculatedasdescribedinEq.(10).

𝐸𝑟𝑟𝑜𝑟(%)= √ √ √ √(𝑚𝑎𝑥(𝑂𝑢𝑡𝑝𝑢𝑡_𝑛𝑢𝑚)−𝑚𝑎𝑥(𝑂𝑢𝑡𝑝𝑢𝑡_𝑒𝑥𝑝) 𝑚𝑎𝑥(𝑂𝑢𝑡𝑝𝑢𝑡_𝑒𝑥𝑝) )2 × 100 (10) Thechipmorphologyisdiscussedandcuttingforcesarethus mon-itored andcompared.Moreover, aparticularattentionis paidtothe thermalaspectintermstemperatureevolutionandintrinsicdissipation duringthechipgeneration.

5.1. Chipmorphology

Fig.8depictsthenumericalchipmorpholgyaswellasthedamage ﬁelds obtained forthefourmachiningconditions. Alltheperformed cuttingtestsledtoserratedchips,generatedfromquasi-periodiccracks propagation. Chipssegmentsareseparatedbydamagedzones which emphasizethemagnitudeofthethermo-mechanicalloadingsandcracks propagationshistoryinducedduringtheprocess.Thecrackinitiatesat thesidefree surface,closetothetooltip andpropagateswithin the material.

Theclassicaldependencybetweenthecuttingspeedandthechip sizeis alsofound.The chipsizedecreasesasthecutting speedrises Fig.8. Chipmorphologiesobtainedfromthe FEmodelforthefourcuttingconditions.

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Fig.9. NumericalvonMisesstressandstresstriaxialityﬁeldsforthediﬀerentmachiningconditionsat80%ofthesegmentformation.

Table7

Meanvaluesanderrorsofexperimentalandnumericalforcesunderallmachiningconditions.

𝛾 ( ∘₎ _{feed (mm)} _{Vc (m min}−1 ) 𝐹𝑐

exp Average Fcnum Average Fc error % 𝐹 𝑓 exp Average Ffnum Average Ff error %

Test 1 15 0.25 3 1463 1329 9.15 693 627 9.52

Test 2 15 1233 1153 6.48 512 473 7.61

Test 3 0 3 1611 1528 5.15 789 733 7.09

Test 4 15 1516 1435 5.34 745 689 7.51

higherresultinganimportantnumberofchipsegments.Itshouldbe mentionedthatasigniﬁcanttransversaldeformationofthechipsurface (outofplane)isobservedforallcuttingconditions.Asprovedbyseveral authors,thislatterphenomenonseemsaﬀectedmainlybytherakeangle andatalesserscalebythecuttingspeed[19,20,49].

Damageismainlyconcentratedintheprimaryandsecondaryshear zones.Thinbandsareobservedinthecaseoftestsperformedwith pos-itiverakeangleandspeciallyat15𝑚.𝑚𝑖𝑛−1_. _In_the_case_of _third_and

fourthtests,ahighermagnitudeofdamageisobservedinthechipbulk. AsillustratedbyFig.9a,theuseofanullrakeanglegivesbirthtoan additionalstressinthechipsegmentduringtheprocesswhichinduces deformationofthechipbulkandcreationofastronghydrostatic com-pressivezoneatthetooltip.

Fig.9b,showsthecomputedstresstriaxiality(triax)at80%ofthe chipevolutionfordifferentcuttingconditions.Itcanbeseenthatthe mechanicalloadingsdifferwiththerakeanglechanges.Forapositive rakeangle,itisclearlyfoundthatshearistheleadingmodeoffailure. However,acompressive/shearstateisnoticeableinthecaseofthethird andfourthtests.Duetothiseffect,thenumericalmaterialelementsare highlydeformedandstackedthereforeremovingasignificantpartof thedepictedcrackpathline.Ahydrostaticcompressivezoneisobserved nearbythetooltip.Itsshapeandmagnitudeseemsstronglyaffectedby therakeangleandatalesserscalebythecuttingspeed.Basedonthese observations,itappearsthattheshapeoftheshearplanemainlyresults fromtheshapeofthehydrostaticcompressivezone.Inthecaseofthe firstandthesecond tests,a simpleandlinearevolutionof thecrack propagationpathisobserved.Bycontrast,acurvedcrackpathshapeis foundinthecaseoftests3and4.Accordingly,thecrackpropagation seemstoavoidthehydrostaticcompressivezoneinordertoreachthe freesideofmaterial.Thesenumericalobservationsareverysimilarto theexperimentalones.Inaddition,itjustifiestheparticularchipshape foundwithnullrakeangleandbringstolightseveralchallengesabout theinfluenceofthehydrostaticpressureontheshapeandgeometryof theshearbandespecially, inthecaseof anisotropicmaterialswhere therelationbetweenstressandstraintriaxialityisnolongerstraight forward.

5.2. Cuttingforces

Asmentionedintheabovecuttingforcesaremeasuredthrough 6-componentsdynamometer (Kistler9257A).Unfortunately, itsnatural frequency (7kHz)istoolow incomparisonwithchipformation fre-quency.Inaddition,thegenerationof segmentnpartiallyoverlapin timebythegenerationofsegments𝑛−1and𝑛+1. Thisjustiﬁesthe diﬃcultyinpost-processingmacroscopicforcesusingsuchdevice. Con-sequently,onlyaveragesofthecuttingandfeedforcesareconsidered andcomparedasdetailedinTable7.

Itcanbenotedthatbothcuttingandfeedforcesareaﬀectedmainly bytherakeangleandthecuttingvelocity.Itincreasesbyvaryingthe rakeangletowardnullvalueorbydecreasingthecuttingvelocity. Re-gardingthisissue,the3Dnumericalmodelpresentsagoodagreement withanacceptableerror.However,thenumericalforcesare underes-timatedinallsimulatedcases.Inaddition,theerrorseemstobemore meaningfulinthecaseofthefeedforceandspeciallyforthetest1.This underestimationcanbeoriginatingfrommanysources.Infact,the con-tactconditionsarehighlyinﬂuencedbytherakeanglevariationwhich isnottakenintoaccountinthisFEmodel.Inaddition,theuseofthe elementdeletionmethod,theassumptionofaconstantcuttingvelocity, andthechosenmeshsizecanalsobetheoriginoftheobtainederror. Ontheotherhandthecomputedcuttingforcesprovideabettermatch oftheexperimentaloneswhentherakeangleequals0∘_.

5.3. Logarithmicstrain(Heq)

Fig.10aandballowthecomparisonbetweennumericaland exper-imentalstrainsinthechipsegment.Overalltests,thenumerical log-arithmicstrainseemsunderestimated.Eventthoughtheerrorissmall fortests3and4(~ 10%),itismorepronouncedinthecaseofpositive rakeangle(~ 24%).Thiserrorcanbemainlyattributedtothe simu-lationtechnique.Sincetheerodingelementtechniqueisemployedin FEsimulations,thestrainhighestcumulationisdiscardedalongwithits bearingelement.AsdepictedinFig.10c,agoodagreementbetween nu-mericalandexperimentalstrainpathsisobserved.Bycontrast,apartof

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Fig.10. Numericalandexperimentaldistributionsofthelogarithmicstrainﬁelds:Comparisonsat80%ofthesegmentformationandforalltests.(a)Numerical distributionofthelogarithmicstrain(b)Experimentaldistributionofthelogarithmicstrain(c)Logarithmicstrainpathsextractedfromthenumericalandexperimental results(seethearrowsdirections).Thenumericalstrainpeaksareerodedbythenumericalelementdeletiontechnique.

Fig.11. Numericalandexperimentaldistributionsofthestrainrateﬁelds:comparisonsat80%ofthesegmentformationandforalltests:a)numericalresultsb) experimentalresults.

thenumericalresponseisnotfound.Thisﬁndingleadstoconsiderthat thenumericalpeaksareremovedbytheerosionelementtechnique. De-spitethenumericalartifact,theFEmodelpresentsagoodsensitivityon thelogarithmicstrainasafunctionofthecuttingconditions.Alikethe experimentalobservations,themodelpredictsthatthestrainmagnitude decreasesbyvaryingtherakeanglefrom0∘_to₁₅∘_.

5.4. Strainrate(Deq)

Numericalandexperimentalstrain rateﬁelds at80%of thechip segmentformationaredepictedinFig.11.Thehighmagnitudeofthe strainrateislocatedmainlyintheprimaryandsecondaryshearzones. Althoughthespatialevolutionofthestrainrateiscorrectlypredicted byFE numericalmodel,anoverestimationis notedoveralltestsand especiallyfortest3.

This error can be induced by the friction model. Since the fric-tionmodelis composedbytwodistinctregions,thelimitinbetween theselattersisarbitrarilyselected.Consequently,theplasticstrainand strainrateinducedbyfrictionatthetooltipandinthesecondaryshear zoneseeminﬂuenced bythis arbitraryzonedistinction.Thispointis thereforeaclearperspectiveofthepresentwork.Asdeclaredin[49], theVISIRdeviceisfocusedmainlyintheprimaryshearzone. Accord-ingly,thesecondaryshearzoneisnotbringtotheforeinthepresent paper.

However,itisworthnoticingthattheFEandexperimentalshear an-glebandsaredifferent.Thisdifferencecanbeexplainedbythecomplex pathofthecrackwhichisnotretranscribedproperlybytheFEmodel. Infact,theuseofelementdeletioninducesvariationsontheshearangle andthus,onthekinematicfieldsevolution.

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Fig.12. Numericalandexperimentaldistributionofthetemperaturefieldsat80%ofthesegmentformationandforalltests:a)numericalthermalfieldsb) experimentalthermalfields.

Fig.13. TheevolutionoftheintrinsicdissipationduringchipsegmentformationinthecaseofTest1.(a)numericalresults(b)experimentalresults.

5.5. TemperatureT

Numerical and experimental temperature ﬁelds are presented in

Fig. 12. Overall, the experimental temperature seems correctly esti-matedundera relativeerror inferiorto12%.Experimentally,itcan beseenthatthemaximaltemperatureisalwayslocatedintheprimary shearzone.Bycontrast,thenumericalmaximaltemperatureismainly localizedinbothprimaryandsecondaryshearzones.Thisobservation (alongwiththepreviousstatementconcerningthestrainrates)shows thatthechosenmodelingofthetribologicalinterface,although improv-ingthesegmentationquality,generatesmanyerrorsinthekinematic andthermalﬁelds.

Consequently,thislatterpointleadstoconsiderthatthetribological behaviorrequiresarigorouscharacterizationandidentiﬁcationinterms offrictionandheatpartitionsmodelsforbettermodelingthechip-tool interface.

5.6. Thermaldissipation

Theintrinsicdissipationstaystheprincipalfactorfortemperature riseduringmachining.Thisphenomenonisanalyzedandcomparedby twostrategiesasmentionedaboveinEq.(2).

Fig.13promptstheexperimental andnumericalintrinsic dissipa-tionevolutionduringchipsegmentformation.Despitethesmall over-estimationinthesecondaryshearzone,theexperimentaldistribution ofthis phenomenonseems correctlypredictedbythenumerical

sim-ulation.Thedissipationinitiatesatthetooltipvicinityandmovesin thestrainingbandtowardsthefreesurface.Foreachsegment forma-tionstep,apeakofthermaldissipationisobservedwhichisfollowed bycrackpropagation.Thisﬁndingstendtoprovethatthethermal dis-sipationisnotinducedonlybytheplasticdeformationandthefriction phenomenabutalsobythefailurephenomenon[65–67].

AsdepictedinFig.14,thethermaldissipationmagnitudeis explic-itlyrelatedtomachiningconditions.Asmallincreaseofthedissipation magnitudebyvaryingtherakeangleto0∘_is_noticed._In_addition,_the

chipbulkseemsdeeplyaﬀectedbytheanglevariationwheresome dissi-pationzonesareobserved.Withtheincreaseofthecuttingspeed(tests 2and4),ahighelevationoftheintrinsicdissipationisnotedwitha smalldissipationdistributioninthechipbulk.Thisconstatationproves thatthecuttingvelocityisthekeydriverforthestrainlocalization.It’s worth mentioningthatthekinematicandthermalﬁeldsanalysiswas focusedonlyontheplanofthecapturedimagesandthus,theinternal strainwasnotanalyzedinthisstudy.

6. FEmodelcontributiontothesurfaceintegrityontheﬁnalpart

Amongtheaimsofthiscontributionistheunderstandingofthe phys-ical phenomenainducing thesegmented chipduringmachining. For that,experimentalandnumericalinvestigationsofthekinematicsand thermalﬁeldswereperformedinordertoachievethisgoal.

However,thechipformationmechanismanalysisinitselfisnotthe ﬁnalgoal,butit’sanunavoidablestrategytowardbetter

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understand-Fig.14. Experimentalandnumericalconfrontationintermsofintrinsicdissipationﬁeldsduringthechipsegmentformation(at80%ofevolution):(a)numerical results(b)experimentalresults.

Fig.15. Damageevolutionproﬁlealongthegeneratedsurfaceandinvestigationoftheimpactofthediﬀerentchipformationphasesonthesurfaceintegrity.Case oftest2(𝑉𝑐=15mmin−1_,_{𝛾 =}₁₅◦_,_𝑓₌₀_.₂₅_mm).

ingoftheﬁnalsurfacegenerationanditsintegrity.Accordingly,the exploitationofthepresentedmodelallowsthepredictionof thechip segmentationeﬀectonthemachinedsurface.

Fig.15depictsthedamagedistributioninthefinalpart.Arippled damagetendencyisobservedalongthepredefinedpathwhichreflects therepetitiveaspectofthisphenomenon.Surprisingly,thistendencycan becorrelatedwiththechipformationsteps(i.ecompression,shearand extraction).Itturnsoutthatthethreestepsofthechipgenesisarethe sourceofthiskindofdamagetendency.Firstly,it’sclearlyperceptible thatthecompressionphaseinducesalwaysthemostimportant dam-agemagnitude.Infact,duringthisphasethesegmentstorestheelastic energywhich willbe dissipatedintheotherstages.Asresults,many phenomenaareobserved,mainly:(i)theoutofplanedeformation phe-nomenonwhichimpactsthefinalpartin theform ofaburr,(ii)the highestintrinsicdissipationandforcelevels,(iii)thedevelopmentofthe shearplaneandtheactivationofthecrackpropagationphenomenon. Thesephenomenacanexplainthehighlevelofthedamageonthe

fi-nalpartduringthisphase.Oncetheshearplaneiscreated,thesegment slidesonitandthedamagedropssignificantly.Atthefinalstep,the seg-mentbreaksfreefromthecontactzoneandcontinuestoslideonboth thecuttingfaceandonthenextsegment.Hence,aprogressiveincrease ofthedamageisobservedwhichcorrespondstothechipsegment ex-tractionbutalso(andprobablymoresignificantly)theinitiationofthe nextone.

Itisworthnoticingthattheanalyzedmachiningvideosshowthat thesecondandthethirdsteps(i.eshearandextraction)arestrongly conditionedbytheﬁrststep.Consequently,onecanthereforeassume thatthecontrolofthecompressionchipformationphasecanimprove thesurfaceintegrity.

7. Conclusionandoutlooks

ThepresentworkdealswiththeTi-6Al-4Vchipformationproblem. Itproposes,ononehand,acoupledin-situmeasurementofthermaland

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kinematicﬁeldsatmicro-scaleandontheotherhand,anumerical inves-tigationinordertorestitutetheexperimentalphenomena.This contri-butionprovidesavaluableinsightonthethermomechanicalcouplings andthusgivesanewunderstandingof theTi-6Al-4V chipformation mechanisms.

Inthefirstsection,thestrain,strain-rates,temperaturesalongwith intrinsicdissipationfieldsarepresentedanddiscussed.The experimen-talobservationshighlightedthedependencyofthephysicalphenomena tothemachiningparameters (i.e.cutting speedandtherake angle). Accordingly,itbringstolightthecuttingspeedeffectonthestrain lo-calizationandalsothegeometricaspectoftheshearanglebymeans oftherakeanglevariation.Inaddition,thecrackpropagationanalysis conductedinthisworkemphasizedtheeffectoftherakeangleonthe chipsegmentshape.

Forconfrontationsake,a3Dorthogonalcuttingmodelissetupand computedforthesamecuttingconditionsasin thepresented experi-ments.Insummary,itcanbesaidthatsimulationresultsshowagood agreementwithexperiments.Itpermitstopredictthechipformation morphology,thermalandkinematicsfieldsunderanacceptableerror. Inaddition,itprovidesapreciousinsightregardingthechipformation genesisanditsinfluenceonthesurfaceintegrity.Its3Daspectwhich liberatestheclassicalplanestrainhypothesisanditssimplemodeling ofbehaviorandmaterialfailureareamongthestrengthspointsofthis FEmodel.However,severalpointsshouldbeimprovedforabetterchip formationpredictionandotherconfigurations(cuttingvelocity,rake an-gle,feed...)canofcoursebeinvestigatedbythesamemeanandwould berequiredtofullyvalidatetheproposedapproach.

TwomaindrawbackscanbesingledoutofthepresentedFE orthogo-nalcuttingmodel.Theﬁrstoneisthelackofknowledgeonthe tribolog-icalbehaviorofthetungstencarbideandthetitaniumalloyTi-6Al-4V. Indeed,thedeterminationoffrictionandtheheatpartitionevolutions isanexperimentalchallengeandconstitutesaperspectiveofthiswork. Forthispurpose,theuseofopentribometerthatenablestoreproduceas faithfullyaspossiblethecuttingcondition(i.e.contactpressure,sliding velocity,...)seemsinevitable.

TheseconddrawbackoftheproposedFEmodelisthematerial sep-arationtechnique. Itisadirectconsequenceofthechosennumerical procedureandinducesalackofinformationintheprimaryshearzone asdiscussedabove.Otherthanelementdeletion,thenodesplittingand theadaptativeremeshingtechniquespresentaspowerfulalternativeto overcometheproblem[68–70].Indeed,acorrectionofthisnumerical artefactshouldbeaddressedinfutureworks.

DeclarationofCompetingInterests

Theauthorsdeclarethattheyhavenoknowncompetingﬁnancial interestsorpersonalrelationshipsthatcouldhaveappearedtoinﬂuence theworkreportedinthispaper.

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