Advances in material and friction data for modelling of metal machining

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Shreyes MELKOTE, Wit GRZESIK, José OUTEIRO, Joël RECH, Volker SCHULZE, Helmi ATTIA,

Pedro J. ARRAZOLA, Rachid M'SAOUBI, Christopher SALDANA - Advances in material and

friction data for modelling of metal machining - CIRP Annals - Manufacturing Technology - Vol.

66, n°2, p.731–754 - 2017

Any correspondence concerning this service should be sent to the repository

Advances

in

material

and

friction

data

for

modelling

of

metal

machining

Shreyes

N.

Melkote

(2)

a,

*

,

Wit

Grzesik

(2)

b

,

Jose

Outeiro

(2)

c

,

Joel

Rech

d

,

Volker

Schulze

(2)

e

,

Helmi

Attia

(1)

f

_,

_Pedro-J.

_Arrazola

₍₂₎

g

_,

_Rachid

_M

_’Saoubi

₍₁₎

h

_,

_Christopher

_Saldana

a

a

GeorgeW.WoodruffSchoolofMechanicalEngineering,GeorgiaInstituteofTechnology,Atlanta,Georgia,30332-0405,USA b

DepartmentofManufacturingEngineering&ProductionAutomation,OpoleUniversityofTechnology,5thMikolajczykaSt.,45-271,Opole,Poland c

LaBoMaPLaboratory,ARTS&METIERS,CampusofCluny,RuePortedeParis,F-71250,Cluny,France d_{ENISE(ÉcoleAssociéeàl'EcoleCentraledeLyon),58RueJeanParot,42000,Saint-Etienne,France} e

InstituteforProductionScience,KarlsruheInstituteofTechnology(KIT),Kaiserstraße12,76131,Karlsruhe,Germany f

AerospaceStructures,MaterialsandManufacturingLaboratory,NationalResearchCouncilofCanada/McGillUniversity,Montreal,QC,H3T2B2,Canada g

FacultyofEngineering,MondragonUniversity,Mondragón,20500,Spain h

R&DMaterialsandTechnologyDevelopment,SecoToolsAB,SE-73782Fagersta,Sweden

1. Introduction

Industrialmachiningprocessesareamongthemostcomplex manufacturingprocessestomodelandsimulate.Inmetalcutting, thecomplexitiesstemfromthesevereplasticdeformationofthe metal,andfromtheextremetribologicalconditionspresentatthe tool-workpieceinterfaces[207].Theabilitytoaccuratelymodel and simulate cutting processes such as turning, milling, etc. dependsontheavailabilityofaccuratemathematicalmodelsfor(i) the constitutive response of the deforming material, i.e., a constitutivemodelthatdescribeshowthematerialyieldstrength andfracturebehaviourchangewithdeformationparameterssuch asstrain,strainrate,temperature,microstructure,etc.,and(ii)the frictionatthetoolandworkpieceinterfaces,i.e.,frictionmodel.

Amajorchallengeindevelopingconstitutiveandfrictionmodels formetalcuttingisthedifficultyinacquiringdynamicstress–strain dataandfrictiondata,respectively,thataccuratelyrepresentthe cuttingprocess.Historically,metalcuttingmodellingandsimulation effortshavereliedonstress-straindataderivedfromquasi-static and/ordynamicmaterialstestingtocalibrateconstitutivemodels

[107].Thesedataandassociatedconstitutivemodelsusuallycovera limitedrangeofstrains,strainrates,andtemperaturescomparedto

those occurringin metal cutting. Consequently, theuse of such constitutive models inmachining simulationsgenerally requires extrapolationtohigherstrainsandstrainrates,whichcontributesto inaccuracies in the simulated results. In the case of friction modelling,highlysimplifiedfrictionmodels(e.g.Coulombfriction) areoftenusedinmachiningsimulations.Themainreasonsforthis includelimitedknowledgeofthecomplexfrictionalinteractionsat the tool-work interfaces, and a lack of suitable experimental techniquesformeasuringtherelevantfrictionmodelparameters underconditionsrepresentativeofmetalcutting.

Othertypesof datacriticalfor machiningprocessmodelling andsimulation includetemperature-dependentthermo-physical properties and workpiecemicrostructure data,which are often difficulttofind or measure,for thematerials and deformation conditionsofinterest.Forinstance,recentmicrostructure evolu-tiondependentconstitutivemodelsformetalmachiningrequire microstructuredata(e.g.grainsizeevolutionasafunctionofstrain, strain rate, and temperature) that are not readilyavailable for manyworkmaterialsofpracticalinterest[144].

Theobjectiveofthiskeynotepaperistoreviewandcritically analyserecentadvancesandneedsinmaterial,friction,thermal, and microstructure data and associated models, along with experimental techniques for generating the data needed for accuratelysimulatingthemetalcuttingprocess.

The paper is organized as follows. Section 2 discusses key aspectsofconstitutivedataandmodelsformetalcuttingincluding phenomenological and physically based constitutive models, ARTICLE INFO

Articlehistory:

Availableonline27July2017

Keywords: Machining Modelling Friction

ABSTRACT

Thispaperreviewsrecentadvancesinconstitutiveandfrictiondataandmodelsforsimulationofmetal machining.Phenomenologicalandphysically-basedconstitutivemodelscommonlyusedinmachining simulationsarepresentedanddiscussed.Othertopicsincludeexperimentaltechniquesforacquiringdata necessaryto identifytheconstitutivemodelparameters,andrecent advancesinmodellingof tool-workpiecefrictionandexperimentaltechniquestoacquirefrictiondataundermachiningconditions. Additionally, thermo-physical properties for thermal modelling of the machining process, and microstructure data forthe chipand workpiece togetherwith relevantexperimental methods are discussed.Futureresearchneedsineachofthefocusedareasarehighlighted.

.

* Correspondingauthorat:GeorgiaInstituteofTechnology,GeorgeW.Woodruff SchoolofMechanicalEngineering,813FerstDrive,N.W.Rm.381,MARC,Atlanta, Georgia30332-0405,UnitedStates.Fax:014048949342.

experimentaltechniquesforgeneratingthedatarequiredtofitthe constitutive model parameters, methods for model parameter identification,a criticalassessmentofthedataandmodels, and futureresearch needs and opportunities. Section 3 reviews key aspectsoffrictioninmetalcutting,frictionmodelsandassociated datarequirements,andexperimentalmethodsforgeneratingthe frictiondata.Section4reviewsthermalaspectsofmetalcutting,and thepertinentmodelsanddata.Section5reviewsmicrostructure evolutioninmetal cutting,experimentalmethodsforgenerating relevant microstructure data, and associated models. Section 6concludeswithasummaryofthepaperandafutureoutlook.

2. Constitutivedataandmodels

2.1.Deformationcharacteristicsinmachining 2.1.1. Strains,strainrates,andtemperatures

Metal machining is a severe plastic deformation process characterizedby heterogeneous thermomechanicaldeformation ofthemetalathighdeformationratesleadingtothemodification of the microstructure and material properties. Consequently, constitutivemodellingformetalmachiningrequiresfundamental understanding of the deformation conditions in the relevant deformationzones(Fig.1).

Accurateknowledgeofthestrains,strainrates,andtemperatures arecriticalforunderstandingandcontrollingthemachiningprocess. Largestrains(1–10),strain-rates(upto106_s
1_{)andtemperatures} (_>1000_{C)arereportedinmetalcutting[10].However,itshouldbe}

notedthat the large strains and strain-rates reported are often estimatedusing simplifiedshearplane based analytical models, whichweren’tvalidated usingsuitableexperimental techniques capableofmeasuringsuchvaluesunderpracticalcuttingconditions. Moreover, large temperatures are reported in the secondary deformationzone. In addition, themechanicalbehaviour of the workmaterialinmachiningalsodependsonotherparameterssuch asthemicrostructure(e.g.,dislocationdensity,grainsize,etc.)[144]

andthestate-of-stress[27].Therefore,properidentificationofthe deformationconditionsandtheirrangesinmetalcuttingisessential for the design and selection of suitable mechanical tests to characterizetheworkmaterialbehaviourunderconditions repre-sentativeofmetalcutting.

In-situ experimental techniques such as Particle Imaging Velocimetry(PIV)havebeenusedtocharacterizethestrainand strain-ratedistributionsinmetalcutting[139].Inthistechnique, heterogeneous surface markers in the workpiece surface are trackedusing high-speedimaging (Fig.3). Thestrain fieldsare calculatedusingtherelativedisplacementsoftheheterogeneous surfacemarkers.

UsingPIV,Brownetal.[37]estimatedastrain-rateof20s
1in theprimaryshearzoneandashearstrainof2.05inaOFHCcopper chipataverylowcuttingspeedof0.3m/min.Inordertoestimate thestrainandstrain-rate,theyusedaclassicalshearplanebased analyticalmodel.Huangetal.[113]performedsimilarexperiments

onTi–6Al–4Vatacomparablelowcuttingspeedof0.6m/minand theyestimatedstrain-ratesof40–80s
1andastrainof1.5.

Ingeneral,thePIVtechniqueisrestrictedtomeasurementsat lowcuttingspeedsduetoimagingspeedlimitations.Nevertheless, itisaveryusefulin-situtechniquetounderstandandquantifythe deformationfieldinmetalcutting.

Recently, Sagapuram [194] used high speed imaging to investigate themechanism of shear-localizedchip formationin orthogonalcuttingofTi–6Al–4Vatcuttingspeedsof0.25m/s–5m/ s. Using a combination ofmarkerdisplacementtechniques and microscopy,theyestimatedtheaverageshearstrainintheshear bandtorangefrom10(at0.25m/s)to40(at5m/s).Shearstrain rateintheshearbandregionwasestimatedtobe4105_s
1_ata cuttingspeedof1m/s.

Outeiro etal. [167]usedthe DigitalImageCorrelation (DIC) technique to estimate subsurface plastic strains produced in orthogonalcuttingofOFHCcopperatacuttingspeedof90m/min. TheyestimatedthemaximumvonMisesequivalentstraintobe 0.25at150

m

mbelowthecutsurfaceforanundeformedchip thickness (h)of 0.2mm (Fig. 2).The authors notethat further improvements in DIC are requiredto determinethemaximum strains,whichoccurnearthemachinedsurface.

Accurate measurements of the cutting temperatures in the primary deformation zone, and in the secondary deformation zone, primarily due to tool-chip friction, are important for understandingtheirimpactontheflowstressoftheworkmaterial duringcutting,andonthetoolwearaswell.Hightemperatures normallyobservedatthetool-chipinterfaceacceleratetoolwear, whichcandegradethemachinedpartsurfaceintegrity.However, the high temperatures in the secondary deformation zone normallydo notaffect workmaterialbehaviour intheprimary deformation zone. As noted by Astakhov [11], under practical cuttingconditions(Pécletnumber,Pe>>10),theheatgenerated intheprimaryand secondarydeformationzonesistransported awayfromthezonesbythefastmovingchipbecausethechip velocityismuchgreaterthantherateofheatconduction.

Thechallengeistomeasurethetemperaturesintheprimary deformationzoneaccuratelyandatasufficientlyhighresolution. Fig.1.Deformationzonesinthemetalcuttingprocess.

Fig.2.PIVtechniqueusedtocharacterizedeformationinmachining:(a)Effective strainratefield,(b)Griddistortion[102].

Fig. 3. Measured and predictedthrough-depth plastic strain distributions at differentuncutchipthicknesses[167].

Davieset al.[65] presented a comprehensivereviewof cutting temperaturemeasurement techniques.Choosinga reliable tem-peraturemeasurementtechniqueisachallengingtaskduetoeach method’smeasuringrangelimits,sensorcapabilities(robustness, influence on process, signal type/sensitivity to noise, response time,anduncertainty),easeofcalibration,cost,size,intrusiveness, etc.Toaddressthisissue,researchersattheNationalInstituteof Standards and Technology (NIST) in the USA have developed special setups for highresolution and highspeed temperature measurement by infrared thermography[117].Fig. 4 shows an example temperature distribution in the primary deformation zone in orthogonal cutting of 7075-T651 Aluminium. It clearly showsthatthepeaktemperatureintheprimarydeformationzone barelyexceeds200C.

2.1.2. Stateofstress

AccordingtoAstakhov[13],metalcuttingcanbeviewedasa formingprocesswheretheexternalenergyappliedtothecutting system causes separation of a layer of material fromthe bulk. Therefore,aprincipaldifferencebetweenmachiningandallother metalformingprocessesisthephysicalseparationofmaterialin theformofachipfromtherestoftheworkpiece.Theprocessof physicalseparationofasolidbodyintotwoormorepartsinvolves fracture,andthus,machiningmustbetreatedasthepurposeful fractureofthelayerbeingremoved.Significantworkonthisview ofmetalcuttinghasbeenreportedbyAtkins[14].Fromthispoint of view, proper modelling of the work material in machining shouldtakeintoaccountnotonlythematerialflowstressunder thedeformationconditionsinmachining,butalsounder condi-tionswherefractureoccurs[169].Bothflowstressandfractureare stronglydependentonthestateofstress[27,169].

Classicalmetalplasticitytheoryassumesthatonlythesecond deviatoricstressinvariant(J2)influencestheyieldsurface,asinthe vonMisesyieldcriterion.Thus,thehydrostaticstress(

s

m)hasa negligible effect on strain hardening, and the flow stress is independentofthethirddeviatoricstressinvariant(J3)[27].The hydrostaticstressisoftenexpressedasadimensionlessquantity calledthestresstriaxialityparameter(

h

),definedinEq.(1).The equivalentstressisoftenincorporatedintothenormalizedLode angleparameter(

u

),definedinEq.(2).

h

¼

s

m

s

ð1Þ

u

¼1

_p

2arccos J3

s

3 " # ð2Þ Recent experiments on plastic deformation of metals have shownthatboththehydrostaticstresseffectandtheeffectofthe third deviatoric stress invariant should be included in the constitutive description of the material [27]. In general, the hydrostaticpressurecontrolsthesizeoftheyieldsurfacewhilethe

Lodeangleparameterisresponsibleforitsshape.Theeffectofthe Lode angle parameter on plastic yielding has been studied by Cazacuetal.[44]andBacherlaandBassani[26].Theseresearchers proposed flow stress models that incorporate thedifference in yieldstrengthincompressionandtension.However,theirmodels donothavetheflexibilitytopredictplanestrainyielding.Sucha generalization was proposed by Bai and Wierzbicki [27] who proposed a newformof anasymmetricmetalplasticitymodel, consideringthestresstriaxiality(

h

)andLodeangleparameter(

u

) effects. Recently, Buchkremer et al. [38] modified the Bai and Wierzbickimodeltoincludestrain-rateandtemperatureeffectsin theflowstresstosimulatelongitudinalturningofAISI1045steel. BaiandWierzbicki[27] alsoproposeda newfracture model that takesintoaccountstresstriaxiality(

h

)and theLodeangle parameter(

u

).However,unliketheJohnson–Cookdamagemodel

[127],theirfracturemodeldoesnotaccountfortheinfluenceof strain-rateandtemperature.

Akeypointofthisdiscussionisthat,totheextentpossible,the role ofstressstateonplasticyieldingand fractureofthemetal shouldbeaccountedforinconstitutivemodelling.Asdiscussed later, constitutive models for metal cutting routinely use flow stress data obtained under uniaxial loadingconditions. This is becauseuniaxialloadingexperimentsareeasiertoconductthan multiaxialloadingexperiments.However,theroleofthestateof stressandfractureinmachiningcannotbeignored.

2.2. Constitutivemodelling

Constitutive modelsdescribetherelationshipbetweenstress and strain. The complexity of these relationships range from isotropicelasticmodelssuitableforlarge-scalestructural model-ling,tocrystalplasticityformulationsdesignedtocapture grain-scale inelastic behaviour. Prior knowledge of the deformation processisrequiredforselectionofanappropriatemodel.

As discussed previously, machining is unique in that the imposed deformations (strains, strain rates, temperatures, and state of stress) produce a complex thermomechanical loading history. Constitutive modelsmayalsobecoupled withinternal statevariable(ISV)modelsthatseektocapturetheevolutionofthe underlying structure-related variables e.g., dislocation density, meangrainsize,texture,etc.withdeformation.Theconstitutive lawsaswellasISVevolution equationsmaybedescribedusing phenomenologicalequations,physically-basedequations,orsome combinationofthetwo.

2.2.1. Phenomenologicalmodels

Phenomenological constitutivemodels arecommonly usedto describe the high strain rate and high temperature flow stress response of metals in machining. These models are termed phenomenological because they describe material behaviour through empiricallyfittedfunctionsof oneormoremacroscopic variablesofdeformationsuchastheplasticstrain(

e

p),plasticstrain

rate(_

e

p),andtemperature(T).Thegeneralformofsuchmodelsis:

s

¼

s



e

p; _

e

p;T;...Þ ð3Þ

Theobjectiveofthispaperisnottoreviewall phenomenologi-calconstitutivemodelsin theliteraturebuttocriticallydiscuss onlythosethatarecommonlyusedinmachiningsimulations.

Table1summarizesthemostfrequentlyused

phenomenologi-cal models used in cutting simulations. All of them assume isotropic deformation behaviour of the work material. Of the modelslistedinTable1,theJ_–Cmodel[126]isthemostwidely usedbecauseofitssimplicityandrelativeeaseofcalibration.Its majordrawbackisthatitispurelyempiricalanditislimitedinits ability toaccurately describe theconstitutive behaviour of the materialoutsidetherangeofthetestdatausedtofitthemodel’s parameters.AsdiscussedbyLeseur[140],theJ–Cmodelisunable tocapturetheincreasedstrainratesensitivityabove103s
1,often attributedtoviscousdragbasedresistancetodislocationmotion. Fig.4.Visible(top)andinfraredtemperaturedistributionin_{C(bottom),obtained}

byhigh-speedvideographyofmetalcutting(rectangleinvisibleimageis0.3mm horizontalinfraredfieldofview)[117].

TheoriginalJ–Cmodeldoesnotaccountforsofteningobserved atthestrainsandtemperaturesintheprimaryshearzone,whichis characteristicofmetals thatexhibitshearbanding(e.g.Ti–6Al– 4V).Toaddressthislimitation,Calamazetal.[41]andSimaand

Özel [211]modifiedthe J–Cmodel toaccentuate the softening

behaviouratlargestrainsandtemperatures,therebyenablingthe simulationofshearbandingwithoutamaterialdamagecriterion. Recently, a similarapproach wasused byHor etal.[112] to model the constitutive behaviour of three steels for use in machiningsimulations.Althoughnotphysically-based,the modi-fied J–C model has been shown to work well for simulating segmentedchipformation in cuttingoflow thermal diffusivity metalssuchastitaniumandnickelbasealloys[219].

Umbrello et al.[221] modifiedtheJ–Cmodel toincludethe effectsofworkmaterialhardnessintheflowstress.Theyusedthe modeltopredictthemachinedsurfaceintegrityinhardturningof AISIH13andAISI52100steels.

Maekawaetal.[154]developedflowstressmodelsthataccount forthestrainpathhistorydependenceofflowstress.Asdiscussed byChilds[49],variationsofthemodelhavebeenusedsuccessfully tosimulatethemachiningresponseofcarbonsteelsandtitanium alloys.

There have been other attempts at incorporating the flow softening effect due to physical processes such as dynamic recrystallization.AnexampleistheworkofRhim andOh[187]

whomodifiedtheJ–CmodelusingAvrami-typeArrheniustermsto simulatechipsegmentationincuttingofAISI1045steel. 2.2.2. Physically-basedmodels

The use of physically-based constitutive models in metal cuttingmodellingandsimulation isarelatively recent

develop-ment.Incontrasttophenomenologicalmodels,physically-based constitutivemodelsarebasedonmicrostructuralaspectsofplastic deformation.Theymathematicallydescribetheflowstrengthofa metal as a function of the microscale physical processes responsible for strengthening (e.g. dislocation-obstacle interac-tion) or softening (e.g. dynamic recovery, continuous dynamic recrystallization,grainboundarysliding)ofthemetal.Itis well-known that during plastic deformation the microstructure continuouslyevolvesas thermallyactivatedmobiledislocations interactwithshortrangeandlongrangeobstaclesincludingthe crystallattice,soluteatomsandprecipitates, forestdislocations, and grain boundaries [158]. Strengthening or softening of the metalduetointeractionofmobiledislocationswithobstaclesis governed bythe strain,strainrate, and temperature. A general formofthephysically-basedconstitutivemodelis[158]:

s

¼

s

ð

r

1;

r

2; _

e

p;TÞ ð4Þ

d

r

1

d

e

¼F1ð

r

1;

r

2; _

e

p;TÞ ð5Þ

d

r

2

d

e

¼F2ð

r

1;

r

2; _

e

p;TÞ ð6Þ

where

r

1and

r

2representmicrostructureparameters,e.g.average

dislocationdensityandaveragegrainsize,respectively.Eq.(4)–(6)

aremathematicaldescriptionsoftheevolutionofthe microstruc-ture parameters with strain. It should be noted that these equationsrepresentjustonepossibleformofthephysically-based constitutive model. For example, the flow stress could be dependent on other microstructure parameters, e.g. texture, Table1

Phenomenologicalconstitutivemodelscommonlyusedinmetalcuttingmodellingandsimulation.

Model Prosandcons

Johnson–Cook(J–C)[126]:

s

¼½AþB

e

n_{p 1þC}_ep _ e0 1
T
T0 Tm
T0  m h i

h ProsJ–C:Simpleformwithfewparameters.Easytocalibrate. ProsmodifiedJ–C:Simpleformwithfewparameters.Considers secondorderinteractions.“tanh”termcapturessofteningatlarge strainsandtemperatures,whichallowsshearbandingtobesimulated withoutafailure(damage)criterion.

ModifiedJ–C[41,211]:

s

¼½AþB

e

n pfð

e

pÞ½1þC

e

_ p _

e

0 1
T
T0 Tm
T0
m   hð

e

p;TÞ fð

e

pÞ¼½expð

e

apÞ
1; hð

e

p;TÞ¼½Dþð1
DÞtanhð

e

pþSÞ
c D¼1
_TT m
d ; S¼ _TT m
b

ConsJ–C:Lacksexplicitmicrostructuralbasis.Knowntobeinaccurate athighstrainrates(>103_–104

s
1).Doesnotintrinsicallycaptureshear localizationeffects.Ignoressecondorderinteractionsofstrain,strain-rate, andtemperature.

J–C:Empirical;Widelyused.ModifiedJ–C:Empirical.

ConsmodifiedJ–C:Lacksexplicitmicrostructuralbasis.Moreinvolved modelcalibrationprocedure.

StrainPathDependenceModel[154,55]:

s

¼A1
_

_e

_

e

0 M eaT
_

e

_

e

0 m Z strainpath e
aT=N
_

e

_

e

0 
m=N d

e

" #N A1¼fðT; _

e

Þ

Pros:Modelsthestrainpatheffectanditsdependenceontemperatureandstrain rate.Considerscouplingofstrainratehardeningandthermalsoftening.

Empirical.Well-developedforcarbonsteelsandcertaintitaniumalloys.

Cons:Requiresincrementalstrainingtestswithsimultaneousheatingand quenchingtocapturestrainpathdependence.Lacksexplicitmicrostructuralbasis.

PowerViscosityLaw[156]:

s

¼gð

e

pÞ

G

ð_

e

pÞ

Q

ðTÞ gð

e

pÞ¼

s

0 1þ

e

p

e

0  1 n;

G

ð_

e

pÞ¼

½

₁þ

e

_ p _

e

0



1 m;

Q

ðTÞ¼c0þc1Tþ...

Pros:Simpleformwithrelativelyfewparameters.Easytocalibrate.

Empirical;DefaultmodelinAdvantEdgeFEMsoftware.

Cons:Lacksexplicitmicrostructuralbasis.Ignoressecondorderinteractions.

Modelparametervaluesincommercialsoftware(e.g.ThirdWaveSystemsAdvantEdge) inaccessibletouser.

s

:flowstress;

e

p:plasticstrain;

e

_p:plasticstrainrate;

e

0:referenceplasticstrain;

e

_0:referenceplasticstrainrate;T:absolute

temperature;T0:referencetemperature;Tm:absolutemeltingtemperature;A,B,C,D,M,N,n,m,a,b,c,d:empiricallydeterminedmodel

whose evolution with deformation would then have to be modelled.

Duetotheircomplexity,physically-basedconstitutivemodels haveseenlimiteduseinmetalcuttingmodellingandsimulation. Nevertheless, they are an important advancement since they intrinsicallypermitthesimulationofmicrostructureand mechan-ical properties(e.g. hardness[145], residual stress[66])of the machined surface, and, in addition, they can more accurately describe the material response to loading outside the model calibrationrange.

Examplesofphysically-basedconstitutivemodelsusedinmetal cuttingmodellingandsimulationaregiveninTable2.

TheZerilli_–Armstrong(Z_–A)constitutiveequationsare moti-vated by the well-known theory of thermal activation of dislocations [233]. Theymodel theflow stressas a summation of athermaland thermal stressterms that are functionsof the strain,strainrate,andtemperature.Differencesintheflowstress behaviours of fcc, bcc, and hcp metals are captured by the equations, which account for the couplingof strain hardening, strainratehardening,andthermalsoftening,asappropriateforthe crystalstructureofthemetalunderconsideration[233,232].

TheZ–Amodelshaveseenlimiteduseinmetalcutting.Jaspers andDautzenberg[121]usedtheZ–Aequationstomodeltheflow stressofAISI1045steel(bcc)andAA6082-T6(fcc)andfoundthat whilethemodelforAISI1045steeldescribedtheflowstresswell, thefccequationforAA6082-T6didnot_fitthe_flowstressdatavery well.Childs andRahmad [56] showed that thebccZ–A model, when modified to include an upper yield point at low strains (_<0.05)typicalofcarbonsteels,producedslightly betterresults thanapowerlawmodelforsimulatingtheplanestraincuttingof carbon steels. In later work, they [57] showed that acceptable valuesofforces,shearangle,andshearstresscouldbeobtained through a simpler, albeit heuristic, modification of the strain hardeningexponent.Liuetal.[143]modifiedthehcpZ–Amodelto accountforincreasedsoftening,whichwasattributedtodynamic recoveryandrecrystallizationatlargestrainsandtemperatures,to simulatechipsegmentationinorthogonalcuttingofTi–6Al–4V.

Guoetal.[103]usedtheISVbasedBammann–Chiesa–Johnson

(BCJ)model tosimulatemetal cutting.AlthoughtheBCJmodel

incorporatestheeffectsofseveralphysicalprocessesactiveduring plasticdeformation,itiscomplexandrequiresalargeamountof carefullycontrolledtestdatatofitthe18modelparameters.This makesthemodeldifficulttoestablishandthereforelesspractical. Svobodaetal.[214]usedtheMechanicalThresholdStress(MTS) modeltosimulateorthogonalcuttingof316Lstainlesssteel.They used dislocation density and vacancy concentrationas ISVs to describetheevolutionofmicrostructurewithplasticdeformation. Theirmodelisthefirstdocumentedinstanceofamicrostructure dependent physically-based constitutive model used in metal cuttingsimulation.Inlaterwork,Wedbergetal.[224]extended Svobodaetal.’smodeltoincludetheeffectofdislocationdragon the_flowstressathighstrainrates.Whiletheir_finiteelement(FE) simulation of orthogonalcutting of316L stainlesssteel yielded goodresultsforforcesandchipthickness,itisnotcleariftheir modelscansimulatechipsegmentation,whichisknowntooccur instainlesssteels.

Recently, Liu et al. developed a MTS based ISV model for simulatingcontinuouschipformationinOFHCcopper[146]and segmentedchipformationinpuretitanium[159].Intheirmodel, theflowstressisafunctionofmicrostructure,whichisdescribed bytheevolutionofthedislocationdensityandthemeangrainsize. The effects ofdislocation drag,dynamic recovery, anddynamic recrystallizationarealsoconsidered.Belowacriticalgrainsize,an inverseHall-Petcheffect,attributedtograinboundarysliding,is includedinthemodeltosimulatesegmentedchipformation[159].

Fig.5showsthemodel’sabilitytosimulateseveregrainrefinement intheshearbandregionofthechip.Themodelhasalargenumber ofparameterswhoseidenti_ficationisnon-trivial.

Dingand Shin [68]used Estrinet al.’s[74]unifiedmodel of plasticitytodescribetheflowstressasafunctionofdislocation densityevolution.Intheirmodel,dislocationdensityisthesole microstructureparameter.Thegrainsizeisassumedtoequalthe evolveddislocationcellsize,whichisinverselyproportionaltothe squarerootofthetotaldislocationdensity.DingandShinshowed theirmodelwasabletoaccuratelysimulatethecuttingforceand strainevolutionintheprimaryshearzoneinorthogonalcuttingof puretitanium[69],albeitatverylowcuttingspeedswhereshear bandsdonotform.Itisunclearhoweveriftheirconstitutivemodel Table2

Physically-basedconstitutivemodelsusedinmetalcuttingmodellingandsimulation.

Model Prosandcons

Zerilli–Armstrong(Z–A)[232]:

s

¼

s

aþBe
bTþB0pffiffiffiffiffi

e

pe
aT

s

a¼

s

Gþkdl
1=2;

b

¼

b

0

b

1ln

e

_p;

a

¼

a

0

a

1ln

e

_p

Pros:Relativelysimpleform.Considerscoupledstrainrateandthermaleffectson flowstress.Accountsfortheinitialmicrostructureofthemetal.Considersrelevant secondorderinteractions.

Generalformofequationforbcc,fcc,andhcpmetals. Limiteduseinmachining.

Cons:Mustbemodifiedforincreasedsofteningatlargestrainsandhigh temperaturestosimulatechipsegmentationwhennotusingadamagemodel.

Bammann–Chiesa–Johnson(BCJ)[103]: _

s

¼

l

tr_ðDe

ÞI þ2

m

lDe;De¼D
Dp

Pros:Accountsforhardeningandrecovery(staticanddynamic)processes.

Basedonmicrostructure-propertyrelationships. Usesinternalstatevariables.

Cons:Complexmodelwithmanymaterialparameters.Microstructure parametersarenotexplicitlymodelled.Extensivetestdataneededtofit themodelparameters.

MechanicalThresholdStress(MTS)Model[84]:

s

¼

s

aþ

s

th

s

a¼

a

Gbpffiffiffiffi

r

;

s

th¼

s

0

½

1

ð

kT g0Gb 3ln _

e

0 _

e

Þ

1=q



1=p ;d_d

s

_e

¼

Q

0

Q

rð_

e

;T;sÞ

Pros:Explicitlyaccountsformicrostructureevolutionwithdeformationandits impactontheflowstress.Canbeadaptedtoincludevariousmicromechanical physicssuchasrecoveryandrecrystallization,dislocationdragresistanceathigh rates,andgrainboundarysliding.

Basedonthermalactivationtheoryofplasticdeformation.

Cons:Moreinvolvedparameteridentification.

s

:_flowstress;

s

G: athermal stress due to dislocation-grain boundary interaction;

s

_ :time derivative of Cauchy stress tensor (rate form);

s

0

:mechanicalthresholdstress(flowstressat0K);

Q

0:hardening(dislocationaccumulation)rate;

Q

r:dynamicrecoveryrate;

e

p:plastic

strain;

e

_p:plasticstrainrate;

e

0:referenceplasticstrain;

e

_0:referenceplasticstrainrate;T:absolutetemperature;D:totaldeformation

tensor;De:elasticdeformationtensor;Dp:plasticdeformationtensor;

l

;

m

l:Lame’constants;G:shearmodulus;b:magnitudeof

Burger’svector;

r

:dislocationdensity;l: average grainsize; k: Boltzmann’sconstant;g0:normalized activationenergy at 0K; B,B0,

b

0,

b

1

iscapableofsimulatingshear localizationseenin manymetals includingpuretitanium,especiallyathighercuttingspeeds.

Atmani et al. [17] usedthe original MTS model with Estrin et al._’s [74] microstructure evolution model to simulate grain refinement in orthogonal cuttingof OFHC copper. Their model showsgoodagreementwithexperimentaldata.Denguiretal.[66]

integrated the effects of the state of stress and dynamic recrystallization in the J–C model to simulate the machined surfaceintegrityinorthogonalcuttingofOFHCcopper.

It isclearfromtheprecedingdiscussionthatresearchersare tryingtodevelopincreasinglycomplexphysically-based constitu-tivemodelsformachiningsimulation.It isanticipatedthat this trendwillcontinueinthenearfuture,andwillbedrivenbythe metalmachiningneedsoftheindustrialsector.

2.3. Experimentaltechniquesfordeterminingthemechanical behaviourofmetalsincutting

Developmentandcalibrationofconstitutivemodelsformetal cuttingrequires representative experimental data.During metal cutting,thedeformationhistoryoftheworkmaterialiscomplexand rangesfromroomtemperatureandquasi-staticconditionsaheadof thedeformationzonetohightemperaturesanddynamicratesinthe primaryandsecondarydeformationzones.Additionally,thestateof stressin metalcuttingis alwaysmultiaxialwith a wide rangeofstress triaxialityandLodeangles.Therefore,theexperimentaltechniques used to determine the mechanical behaviour of metals shouldbe able toaccuratelyreproducethestrains,strainrates,temperatures,and statesofstressinmetalcutting.

2.3.1.Quasi-staticanddynamictests

Conventionalcross-headdevicessuchservo-hydraulicor screw-driventestframesarecapableofperforminguniaxialandmulti-axial experiments to large strains in the quasi-static regime (10
5– 100_s
1_{).Elevatedtemperaturescanbeachievedwhencoupledwith} induction or furnace heating. Thermal–mechanical simulators (Gleeble systems) can be used to perform large strain uniaxial compressiontestsatelevatedtemperaturesandstrainratesupto 101–102

s
1(Fig.6).However,thestrainratesproducedinthesetests

areusuallylowerthanthoseproducedinmetalcutting.Therefore, dynamicorimpacttestingtechniquesareneeded.

Themostcommondynamicmaterialtestingtechniqueisthe Split-HopkinsonPressureBar(SHPB),alsoreferredtoasaKolsky bar[131], whichcangeneratestrain ratesontheorderof103_– 104s
1.VariantsoftheoriginalSHPBtechniqueallowfortensile andtorsionloadings[163].Dependingonthematerial,thestrains imposed in these experiments are usually much less than 1. However,repetitivetestingonasinglesamplecanbeusedto impose larger accumulated strains. The use of a hat-shaped specimen permits the study of shear banding at large strains

[4].Suchspecimenshavebeenusedtostudythesusceptibilityof variousalloystoadiabaticshearbandfailure[160].

According to Burns et al. [39], the traditional elevated temperatureKolskybardoesnotaccountforthecombinationof highheatingrates(>1000_{C/s) andhighloadingrates(10}4

/s) seen in machining.Using an electrical pulse-heatedKolsky bar setup(Fig.7),theyshowedthattheflowstressofarapidlyheated near-eutectoid steel decreased by 50% due to time-dependent thermally-activatedmicrostructureevolution, which isnot cap-turedbythestandardJ–Cconstitutivemodel.

Achieving higher strain rates (106–108

s
1) than normally possiblewitha SHPBapparatusrequiresshockinducingimpact tests[79].Thesetestsaremultiaxialinnatureandthereforethe flowstresscurvescannotbedirectlyinferred.Onepopular high-ratetestingtechniqueistherod-on-rigid-anvilorTaylorimpact experiment,where aprojectileis launchedat arigidboundary, which produces a deformed sample. Even though flow stress curvescannotbeextractedfromthesetests,constitutivemodels canbe“tuned”tomatchtheshape of thedeformedsample, as showninFig.8.However,tilldate,suchtestingmethodshavenot Fig.5. (a)Opticalmicrograph ofchipmicrostructure in theshearband, and

simulated (b) grain size and (c) dislocation density distribution (cutting speed=100m/min,uncutchipthickness=0.2mm)[159].

Fig.6.Ti–6Al–4Vflowstresscurvesat1303KproducedusingtheThermecmaster-Z thermal-mechanicalsimulator[149].

Fig.7.SchematicoftheNISTelectricalpulse-heatedKolskybarsetup[39].

Fig.8.Experimentalandsimulatedhcptitaniumsamplesobtainedinreverse anvil-on-rodimpacttests[157].

Fig.9.Experimentaltechniquesfordifferentstrainrateregimes(adaptedfrom

beenutilizedbythemachiningresearchcommunity.Otherhigh ratetestsincludeballisticpenetrationtestsandplateimpacttests

[137].Asummaryofthemajortestingregimesandtheassociated

materialstestmethodsisgiveninFig.9. 2.4. Identificationofconstitutivemodelparameters

Thechoiceofaconstitutivemodelisextremelyimportantto accurately describe the mechanical behaviour of the work material. Equally important is the identification of constitutive modelparameters.Theseparametersareusuallyidentifiedfrom experimental data obtained from mechanical [111] and/or machining tests [172]. Different methods, including direct and inversemethods,canbeusedtoidentifythemodelparameters

[28].

The direct method consists of explicitly determining the constitutivemodelparametersasafunctionofthemodelvariables. Thismethodcanbeappliedtosimpleconstitutivemodelswithfew parameters(e.g.,thepowerlaw).Forcomplexconstitutivemodels with many parameters, the inverse method, which utilizes optimization-basedapproaches,isthebestsolutionforidentifying themodelparameters.Theinversemethodconsistsofsimulating the experimental test by modifying the constitutive model parameters iteratively to minimizethe difference between the predicted and measured data [28]. Several optimization-based methods(seeTable3)canbeusedforthispurpose[45,222].

Thederivative-freesearchand gradient-basedalgorithmsare relativelysimple tousebutthey dependstronglyontheinitial guess and tend to converge to the local minima. However, derivative-freesearchmethodsaresimplertousethan gradient-basedmethodssincetheydon’tneedtocomputederivatives.Both algorithmsarestronglydependentonuserskills.Germainetal.

[85] used the Levenberg_–Marquardt algorithm to identify the optimalJ–Cmodelparametersfortwotitaniumalloysusingdata fromcompressiontestsathighstrain-ratesandtemperatures.

EvolutionaryalgorithmssuchasGeneticAlgorithms(GA)and ParticleSwarm Optimization (PSO)are morerobust than other algorithms since they use mechanisms to improve the initial solutionand, in general, do not converge tothe local minima. However,theyarecomputationallyexpensiveandconvergenceto theglobalminimumisnotalways guaranteed.Özel andKarpat

[171] used a cooperative PSO algorithm on SHPB test data to

identifytheJ_–Cmodelcoef_ficientsforseveralworkmaterials. Hybridapproachesthatcombinetheadvantagesoftwoormore algorithms,suchastherobustnessofevolutionaryalgorithmsand theperformanceofgradient-basedalgorithms,canalsobeused. Chaparroetal. [45]used bothgradient-based and evolutionary algorithmstoidentifytheconstitutivemodelparametersforan Aluminium alloy using flow stress data obtained from tension tests,anddatafrommonotonicandBauschingersheartests.

Depending on userskills and methods used to identify the modelparameters,theresultsobtainedfromthesealgorithmscan varygreatly.Thiscontributestotheinconsistenciesoftenobserved inthemodelparametersreportedinliterature[45].

2.5. Criticalassessmentofmaterialbehaviourandconstitutive models

The accuracyof constitutive modelsand associated data for metal cutting simulations depends greatly on [107,49]: (i) the materials testing techniqueandthethermo-mechanicalloading conditionsutilized toobtaintheflowstressdatausedtofitthe modelparameters,(ii)themodelchosenandthephysicstherein, especially when extrapolatingthemodel outside itscalibration range, (iii) prior processing history and microstructure of the materialusedtogeneratetheflowstressdata,and(iv)themodel parameteridentificationalgorithmemployed.

Itiscommonplaceformachiningresearcherstofitconstitutive models to high strain rate data obtained from uniaxial SHPB compression tests performed overa range of temperatures. As pointed out byChilds [49], suchmodelsyieldacceptable shear stressvalues for theprimaryshearzone where thestrainsand temperaturesaregenerallylowerthanatthetool-chipinterface. However, theflow stresscorresponding totemperaturesat the tool-chipinterfacetendstobeoverestimatedbythemodeldueto the inability of standard dynamic material tests to faithfully reproduce the higher strains and temperatures seen in the secondaryshearzone.

Thedependenceoftheaccuracyofmachiningsimulationson thetestmethodandtheassociatedloadingconditionscanbeseen

fromtheworkofHoretal.[112],whereaJ–Cmodelfittedwith

dynamicsheartestdatayieldedpeaktemperaturesclosertothe experimentalvaluethanamodelfittedwithdynamiccompression data.Eventhoughthestressstateinmetalcuttingismultiaxial, acceptablepredictions(_<10–15%error)oftheforces,shearangle, and deformedchipthicknesscanbeobtainedfromconstitutive equationsfittouniaxialflowstressdata(mostlyfromquasi-static and/ordynamiccompressiontests).Horetal._’s[112]resultsalso suggest that the primary deformation mode (compression vs. shear) in the materials test may be important for accurate predictionofquantitiessuchastemperatures,strains,etc.

Thechoiceofaconstitutivemodelcanimpacttheaccuracyof machining simulations, as discussed by a number of authors

[41,211,112,103,121,209,81,52,1].Fig.10showsacomparisonofflow stresscurves andmachiningsimulationsusingtwo constitutive modelsforOFHCcopper.

Table3

Optimisation-basedmethods. Method Algorithm Gradient-based Steepestdescent

Newtonandquasi-Newton Levenberg–Marquardt

Sequentialquadraticprogramming

Globallyconvergentmethodofmovingasymptotes Derivative-freesearch Patternsearch

Rosenbrock Simplex Powell

Evolutionaryalgorithms Geneticalgorithms Particleswarmoptimization

Simulatedannealing Fig. 10. Influence of constitutive model on the flow stress and machining simulationsforOFHCcopper[66].

Thedeformationphysicscontainedinthemodelalsoimpactsthe simulationaccuracy.ThiscanbeseeninFig.11whereanMTS-type model for OFHC copper with and without dislocation drag is compared against experimental data. The work of Childs and Rahmad[56]alsohighlightstheimportanceofincludingthecorrect deformation physicsintheconstitutivemodeltoensuretheaccuracy ofcuttingsimulations.Intheabsenceofadamageevolutionmodel, Melkoteetal.[159]showedthataninverseHall-Petcheffectmustbe includedintheconstitutivemodeltocaptureshearbandsformedin thecuttingofpuretitanium.Thisneedissupportedbyevidenceof severegrainrefinementintitaniumchips[205].

Researchers inthemachiningcommunity routinelyuseflow stressdatafromliteraturetofit constitutivemodels.Often,the processing history and microstructure of the material used to generatetheflowstressdataareunknown,leadingtopotentially significant differences between the microstructures of the materialsusedtogeneratetheflowstressandthecuttingdata, respectively.Thiscanleadtoerroneousconstitutivemodellingand inaccuratecuttingsimulations.Forexample,itiswell-knownthat the heat treatment process routes greatly influence the bulk microstructureand its deformation response. This is especially true of Ti–6Al–4V, Ni-based super alloys, and steels. Fig. 12

illustratesthedependenceofflowstressofTi–6Al–4Vontheinitial microstructure.Itisthereforeimperativeforresearcherstoensure consistencyintheinitialmicrostructureswhen usingdatafrom literature and to report the prior heat treatment and initial microstructureoftheworkmaterial.

Since chip formation in metal cutting involves physical separation of the material from the bulk, proper constitutive modellingshouldaccount for notonly thematerial flowstress undermachiningconditions,butalsoforaphysically-meaningful damagemodelorcriterionformaterialseparation(fracture)[169]. Themethodforconstitutivemodelparameteridentificationcan yieldnon-uniquemodelparametersforagivenmaterial.Itisnot uncommontofindreportsofdifferentmodelparametervaluesfor thesamematerial.Reasonsforthenon-uniquenessofthemodel parametersinclude thenonlinear optimizationmethodused to determinetheirvalues[172],thetypeofflowstressdatausedtofit themodel(e.g.compressionvs.shear)[112,111],andtherangesof strains,strainrates,andtemperaturesproducedintheflowstress determination tests. For a given constitutive model, a detailed

sensitivity analysis and validation against experimental data, similartothatreportedbyChilds[51],isnecessarytoidentifythe modelparametervaluesthatyieldphysicallymeaningfulresults. Insummary,constitutivemodeldevelopmentformetalcutting modellingandsimulationcontinuestobeanactiveresearcharea. Whilethemajorfocusofrecentworkisondeveloping physically-basedconstitutivemodels,theuseofsimplermodels(e.g.,J–C)is very common. This is due to the ready availability of model parametervaluesforcommonengineeringmetalssuchascarbon steels,aluminiumalloys,andcertainsuperalloys(e.g.Ti–6Al–4V), aswellastheeaseofparameteridentificationforsuchmodels. 2.6. Futureneedsandopportunities

1. Asystematic and detailed comparison of therelative perfor-manceofdifferentconstitutivemodelsinsimulatingthemetal cuttingprocess.

2. Knowledgeofwhichconstitutivemodel—phenomenologicalor physicallybased—touseforagivenengineeringalloyoverthe rangeofeconomiccuttingconditionsforthealloy.Adatabaseof validatedflow stress models for commonengineering alloys could be created by CIRP and made available to industry practitionersandtheacademicresearchcommunity.

3. Developmentofamaterialstestingtechniquethatiseconomical andiscapable ofcapturing therangesof strains,strainrates, temperatures,and thestate of stress routinely seenin metal cutting.

4. Better understanding of the effects of heat treatment and startingmicrostructuresonthematerialflowstress.

5. Development of material damage (fracture) models that are applicabletometalcutting.

3. Frictiondataandmodels

3.1. Tribologicalphenomenaatthetool-workmaterialinterface 3.1.1. Frictioninmetalcuttingprocess

Friction between contacting bodies is important in all engineering applications where solid metallic surfaces are in slidingcontactwitheachother.Thisisparticularlyimportantin metal cutting where the plastic deformation of the softer counterpart (work material) takes place under high normal pressure. Thesize of contact(contact length) isdetermined by thecuttingbehaviour,andcontacttakesplaceonboththerakeand flank faces depending on the cutting conditions. Energy is dissipated during relative motion of the contacting surfacesof thetool, thechip,andthefreshly formedmachinedsurface.In addition, friction is influenced by tool wear, which increases energy consumption.The dimensionlessfrictionquantity is the coefficientoffriction,definedastheratioofforcesactingparallel (F)andperpendicular(N)totheinterfacebetweenthetwobodies inrelativemotion(

m

=F/N).

Ingeneral,threegenericphysicalmechanismsareresponsible forfriction(Fig.13),namely[110]:

-Adhesion (

m

a), which involves the shearing of micro-welded junctions formed by contacting surface asperities at high pressureandtemperature.

Fig.12.FlowstresscurvesforthreedistinctTi–6Al–4Vmicrostructuresobtained fromdifferentheattreatments[201].

Fig.11.EffectofdislocationdragphysicsinMTS-typeconstitutivemodelforOFHC copper[146].

-Plastic deformation of asperities (

m

d), causing material flow when abodyslides overanother,whichis responsiblefor the staticcoefficientoffriction.

-Ploughingactionofroundedcuttingedges(

m

p),whichproduces agrooveduetoplasticflowbutwithoutremovingmaterial.

Thedominantmechanism of slidingfriction tendstobe the adhesiveinteractionbetweenthesurfaceasperities,especiallyfor non-viscoelasticmaterials.However,roughercontactingsurfaces and tool wear result in more intense plastic deformation of asperities,whichincreasesthefriction.

Adhesionand plastic deformationasthedominantfrictional phenomenaare integratedin a molecular-mechanicaltheoryof frictiondevelopedbyKragelskyetal.[136].Thisfrictionconcept wasusedtopredicttheroughnessheight[90].Thepresenceofthe threebasicfrictionmechanismswasconfirmedinamacroscopic concept of friction, called the genesis of friction [213]. The followingtypicalvaluesofthethreecomponentsofthecoefficient offrictionwereexperimentallydetermined(maximumvaluesin brackets):

m

a=0–0.4(0.51),

m

d=0–0.43(0.75),and

m

p=0–0.4(1.0). Accordingly,animportantmechanismoffrictionisploughingof thecontactingsurfacesbythehardasperitiesandwearparticles. However, its participation depends on the tribological contact conditions. The presence of low-friction coatings and fluid lubricantsdrasticallyreducesfriction.

Frictionmodellingisaverydifficulttaskduetoanumberof potentialinfluencingfactorsincludingthecontactmicrogeometry (surfaceroughness),relativemotion(constancyofmotion,surface velocity),appliedforces(contactpressure, constancyof applied forces),temperature(thermaleffectsonthematerialandlubricant properties), and stiffness and vibration (contact compliance, damping of frictional vibrations, feedback between frictional stimulusandstructuralresponse).

In general, the values of the coefficient of friction used in analytical and numerical modelling of metal cutting are much lowerthanthosemeasuredinorthogonalcuttingtests.Themodels assume

m

=0–0.5(0.6),whereas experimentallyobtainedvalues canexceed1andsometimesapproach2(3)[12].

3.1.2. Conceptoffrictionatthemacroscopicscale

Underhighlyloadedconditionsatthechip-toolcontact,thereis aregionofcompleteplasticcontact,whichrestrictslubricationby fluids or gases during continuous chip formation. The friction stressbetweenthechipandtoolisequaltotheshearyieldstressof the chip at the prevalent strain, strain-rate, and temperature. Lubricationtypicallyreducesthetool-chipcontactlength.Within thereducedcontactlength,thefrictionstressishigherthanunder normalcontactconditions.However,solidlubricationispossiblein thecaseofafree-machiningmetal[55,50].

Ininterruptedcutting,suchasinmilling,therecanbeaninitial periodoflubricatedcuttingduringwhichpre-existing lubricant filmsarewornaway.ThiswasexploredinthecontextofMinimum QuantityLubrication(MQL)inRef.[116].

t

¼min:ð

ms

n;

s

=

ffiffiffi 3 p

Þ ð7Þ

Eq.(7)isawell-knownfrictionlaw.Thefrictionstress

t

isthe lowerof

ms

nand

s

=

ffiffiffi 3 p

where

m

isthefrictioncoefficient,

s

nisthe normal stress between the chip and the tool, and

s

is the equivalentflowstressofthechipmaterial(forafree-machining material,

s

=pffiffiffi3 may be corrected bya factor m<1). This law recognises the changing contact conditions at the chip-tool interfaceasthe distancefromthe cuttingedgeincreases, from

t

¼

s

=pffiffiffi3nearthecuttingedgeto

t

¼

ms

ntowards theendof

contact.InFEsimulationsofdrymachiningofaseriesofcarbon andlowalloysteels,goodagreement withexperimentalresults wasobtainedbyassumingafrictioncoef_ficientgreaterthan1.0

[57]. This is in agreement with the results presented in Refs.

[55,50,48]. The assumption is also applicable to the

micro-machiningofsteelandbuilt-up-edgeformationinthecuttingof steel[53].

Animprovedfrictionmechanismthatintegratestheeffectsof adhesion and ploughing can be derived from a slip-line field analysisofthecontactbetweenarigid-plasticplaneandarigid wedge-shapedasperity[134].Theslidingofahardmetalsurface overasoftsurfaceisassumedtoresultfromthepushingofwaves ofplasticallydeformedmaterialinthesoftsurfaceaheadofthe asperitiesonthehardsurface.

3.2. Frictionmodels

3.2.1. Reviewofexistingtool-chipinterfacefrictionmodels

Realisticcharacterizationofthefrictionalinteractionbetween thechipandthetoolisnecessarytomodelthebehaviourofthe secondarydeformationzone.

Inthepast,andincurrentpractice,thetoolrakefacefrictionhas beenmodelledintermsofaconstantcoefficientoffrictionbased ontheCoulombfrictionmodel.

Theaveragecoefficientoffrictionatthetool-chipinterfacecan becalculatedfromthecuttingforcesorfromtheaveragetool-chip contactstresses(see Fig.14)[92].Therelationshipbetweenthe frictionforceFgandthenormalforceFgNyieldsanaveragefriction

coefficientattherakefaceasfollows:

m

g ¼ Fg FgN¼ Fc sin

g

0þFf cos

g

0 Fc cos

g

0
Ff sin

g

0 ð8Þ where Fc isthecuttingforce,Ff is thefeedforce,and

g

0 isthe

orthogonalrakeangle.

Themodellinkingtheaverageshear(

t

f)andnormalstresses

(

s

n)actingontherakefaceisgivenby:

m

c¼

t

tAp

s

tAp¼

t

f

s

n ð9Þ

whereApistheapparentareaofcontact,

t

tand

s

t aretheshear

strengthandyieldstressofthesofter(chip)material.

Fig.14.(a)Merchant’sshearplanemodelofforcesinthechipformationzone,and (b)Zorev’scontactstressdistributionmodel[92].

Zorev’ssticking-slidingmodelshowninFig.14bdistinguishes thezoneofsticking(seizureorplasticcontact)nearthetooledge and sliding (elastic contact) beyond the sticking region. The compressivenormalstressismaximumatthecuttingedgeand falls to zero at the end of tool-chip contact. The shear stress exhibitsaplateauinthestickingzoneanddecreasesinthesliding zone.Thedistributionofnormalstressesisgivenby:

s

c¼

s

cmaxðx=lcÞn ð10Þ

wherelcisthetool-chipcontactlength,xisthedistancefromthe chipseparationpoint,andnisanexponentparameter.

Intheslidingzone,thestressdistributionsatis_fiestheCoulomb frictionlawasfollows:

t

c¼

ms

c ð11Þ

Intheslidingregion,theratiooftherealcontactareaArtothe apparentcontactareaApisverysmallandtheCoulomb–Amonton lawdescribesthefrictionbehaviour.Incontrast,in thesticking regionAr/Ap continuously increases and, in the vicinity of the cuttingedge,itapproaches1.Thismeansthatthecoefficientof frictionreachesthetheoreticalmaximumof0.577,whichsatisfies thevonMisesplasticflowrule.

The maximum value of the friction coefficient can also be determinedby[92]:

m

cmax¼1=½2ð1:3

g

0Þ ð12Þ

where

g

0istheorthogonalrakeanglemeasuredinradians.

Forconstantshearfrictionalongtheentiretool-chipinterface, frictionisdeterminedusingashearfrictionfactormasfollows:

t

¼mk ð13Þ

wherekistheshearflowstrengthoftheworkmaterialatthe tool-chipinterface.Typically,mrangesfrom0.1to0.8(0.9)[80].For m=1,plasticcontact(seizure)occurs.

ShirakashiandUsui[210]derivedafrictionstressequationas follows:

t

f¼kð1
e
msn=kÞ ð14aÞ

where

t

fand

s

narethefrictionandnormalstresses,respectively.

InEq.(14a)thefrictionandnormalstressesarefittedtodata

fromasplittoolexperimentfor

a

-brass,purealuminium,andS15C lowcarbonsteel.TheequationreducestoEq.(11)atlowvaluesof

s

nandsaturatesattheshearflowstresskathighvaluesof

s

n.

Further modification of Eq. (14a) concerns the transition between

t

f¼

ms

n and mkdue tothe factthat for free-cutting

steelsthesaturationvalueisnotkbutmk.Bymultiplyingkwitha frictionfactorm,where0_<m_<1,amodi_fiedequationisobtained:

t

f¼mkð1
e
msn=mkÞ ð14bÞ

Alternatively,thelimitingfrictionstressatapointinthe chip-toolcontactcanbereplacedby

s

=pffiffiffi3,where

s

istheequivalent flowstress[50],yieldingthefollowingequation:

t

f¼

s

ffiffiffi

3

p 1
eð
msn ffiffi3

p

=sÞ _ð15Þ

A furtherimprovement ofthe frictionmodel isto replacea constantfrictioncoefficientbyonethatincreaseswiththeeffective plasticstrain:

m

¼

m

0ð1þ

e

pÞ ð16Þ

Taking into consideration the fact that in cutting a newly createdsurfacedirectlycontactsthetool face,Iwataet al.[118]

proposedthefollowingempiricalequation:

t

f¼ Hv 0:07
 tanh 0:07

m

p Hv
 MPa _ð17Þ

whereHvistheVickershardnessoftheworkpiecematerial,andp isthecontactpressureinMPa.

In the molecular-mechanical theory of friction, the total coefficient of friction consists of the adhesion and mechanical componentsasfollows[136,90]:

m

¼

m

aþ

m

m ð18Þ

The friction components

m

a and

m

m are derived in Ref.

[90].Anothermodelwithatransitionzonewasproposedrecently byZhou[236].

Thecoefficientoffrictionforthewavecontactmodelproposed byKopalinskyandOxleyisgivenby[134]:

m

¼_AA _cossin

a

_a

þ_þ cos_{sin ðarc}ðarc cos_cos f_f

a

_a

Þ_Þ ð19Þ where A¼1þp

2þarc cos f
2

a

2:arc sin ½ð1
fÞ
1=2

sin

a

,fisthenormalizedfilmstrengthgivenbyf¼

t

=k,

t

is theshear strengthof thefilm,k istheshear flowstressof the deformingmaterial,and

a

isasurfaceroughnessparameter.For 0f<1,

m

liesintherange0

m

<1.Forfulladhesion,

m

isclose to1.Ontheotherhand,forasmallresidualploughingcomponent of friction,

m

¼cot

a

[115].The asperitydeformation modelhas beenfoundtobeingoodagreementwithexperimentalresults. 3.2.2. Comparativeassessmentofexistingfrictionmodels

Thedistributionofthenormalandshearstressesontherake faceofacuttingtool,shownschematicallyinFig.14b,hasbeen verifiedtodeterminetherealpatternofstresschangesalongthe tool_’s rake and _flank faces. In these experiments, the stress distributionatorverynearthecuttingedge,obtainedfromasplit toolandphotoelasticitytechnique,isnotveryaccurate.

Fig.15 shows several examples of the tool rake face stress distributionsobtainedfordifferentmaterialsusingthesplittool technique.Thecontactstressesarenormalizedbytheshearflow strengthk,andthedistancefromthecuttingedgeisnormalizedby thechipthickness.Inmostcases,thenormalstressrisestoapeak nearthecuttingedgeandrangesfrom0.7kto2.5k.However,for nonferrous metals such as aluminium and copper, the normal stresstendstoavisibleplateau.

Ingeneral,duringmetalcutting,themeancoefficientoffriction issubstantiallyaffectedbythecuttingspeed(partlyduetothermal softening),thefeedrate(viathenormalload),therakeangle(by controlling the intensityof plastic deformation in theprimary deformation zone), and by modification of the tribological conditionsthroughlow-frictioncoatings[92].ForAISI1045and AISI304steelsandanumberofsingleandmultilayertoolcoatings,

Fig.15.Experimentallydeterminedcontactstressesfor(a)non-ferrous,and(b) ferrousmetals,usingthesplittooltechnique[92].

ithasbeenshownthatthereductionincontactareaandthermal softeningoftheworkpieceinfluencethecontactstressesandthe frictionalbehaviour[12,99].

3.3. Experimentalmethodsfordeterminingthefrictiondatafor machining

Determinationofthefrictioncoefficientinmachiningcanbe realizedbyatleastthreedifferentmethods:

-cuttingforcemeasurements, -conventionaltribometer,

-specialtribometerdesignedforcuttingapplications.

Thefirstapproachisusuallybasedontheturning[172,50,99,95]

orthemillingprocess[197].Thecuttingforces,chipdimensions, and the tool-chip contact surface are measured and analysed. However,thefrictioncoefficientvariesalongthecontact[184,212]

duetovariationofthelocalslidingvelocity,contactpressure,and temperature.Consequently,thisapproachisunabletodistinguish betweenthe sticking and sliding zones of contact. In order to overcomethisproblem,authorsuseeitherasplittooloranalytical models. A proposal to improve this method by combining interrupted turning with in-depth analysis of the secondary deformationzonehasbeenpresented[151].

Thesecondapproachfordeterminingthefrictioncoefficientuses conventional tribometers without surface refreshment and is independentofanycuttingprocess.Themostcommontribometer isthepin-on-disc,whichiseasytouse.Thediscismadeofthework materialwhilethepinismadefromthecuttingtoolmaterial.This approachhasbeenusedbyseveralresearchers[199].Commercial cuttingtoolinsertsmayalsobeusedinsteadofpins.Unfortunately, suchtribometers donotsimulatetherelevanttribologicalconditions at the tool-work interface in cutting. However, it has been documented[199,35]thatsuchfrictiondatacanaidinimproving theaccuracyofnumericalsimulationsofcutting.

The third approach involves the use of special tribometers (Fig.16) thatsimulate open tribological conditionswith differentsliding velocitiesandcontactpressures.Apopularconfiguration(Fig.16b) usesapinplacedjustafteracuttingtoolduringthemachiningofa tubeface[166].Inthis case,thepinrubsagainstacontinuously refreshedsurfaceandtheslidingspeedsandcontacttemperatures replicate dry machining.However, thecontact pressuresin this methodareonlyaround15MPawhereasthecontactpressuresin cuttingareontheorderofafewGPa.Severaldevices[212,229]have beendevelopedtoincreasethecontactpressureunderhighsliding velocitiesortoinvestigatetheeffectsoflubrication.

The experimental set-up shown in Fig. 16f is similar to orthogonal cutting of a disc using a real cutting tool with an extremely negative rake angle [180]. However, during a single rotationoftheworkpieceand thevery shortcontacttime, itis difficulttoachieveasteadythermalstate.Thismethodwasfurther refinedbyusingabroachingmachine[181].

Asanalternative,anopentribometersimulatingthecontact conditions in cutting over a longer time scale (Fig. 16e) was proposed [60].A cylindricalpin rubs ona freshsurface during rotationandthesurfacerefreshmentisdiscontinuous.Alargefeed of the pin enables a helical movement in order to avoid superposition of the scratches produced on the cylinder. This tribo-set-up,installedonalathe,canyieldsufficientlyhighsliding velocities(several hundredm/min).It shouldbenotedthatthe surfacehastoberegeneratedpriortoanewfrictiontest.

TheopentribometerwasimprovedbyZemzemietal.[230],and subsequentlybyClaudinetal.[60]soastoreachhighercontact pressuresandslidingvelocities.Inaddition,italsoprovides,via specialinstrumentation,theheatpartitionattheinterface,which isakeythermalparameterinnumericalsimulationsofcutting.

In order to identify the appropriate friction model, several friction tests under the relevant sliding velocities and contact pressures must be carried out [184]. Because of the very high contactpressures,severeplasticdeformationoccurs.Hence,these tribometersmeasure an apparentfriction coefficient that often overestimatesthefrictioncoefficient.Therefore,post-treatmentof thetestdataisnecessarytoextracttherelevantinterfacialfriction coefficientfromtheapparentfrictioncoefficientasillustratedin

Fig.17.Thisidenti_ficationcanbeperformedthroughanumerical modelofthefrictiontestorthroughananalyticalmodelbasedon geometricalobservationsofthescratchesproduced[60]. 3.4. Othervariablesinfrictionidentification

3.4.1. Effectofworkmaterialanditsmicrostructure

Identification of thefriction model bymeansof the experi-mentalmethodsdiscussedinsection3.3isfraughtwithchallenges sincefrictiondependsonalargenumberoffactorssuchas: workmaterialcompositionandmicrostructure,

cuttingtoolsubstrate,coating,surfacetexture,and lubricantcompositionandapplicationtechnique.

Regardingtheinfluenceoftheworkmaterial,Fig.18showsthe frictional behaviourofa TiNcoated carbide toolwithapparent

Fig.16.Opentribometersfordeterminingfrictionincutting.Designedby(a)Olsson etal.[166],(b)Zemzemietal.[229],(c)Smolenickietal.[212],(d)Hedenqvistand Olsson[108],(e)Claudinetal.[60],(f)Pulsetal.[180].

Fig.17.Proceduretoidentifyfrictionmodelsfromlaboratorytestsasproposedby Zemzemietal.[229].

Fig. 18.Evolutionoftheapparentfrictioncoefficientwithslidingvelocityforvarious materialpairs[84,60].

frictioncoefficients

m

appthatvarysignificantlyfrom0.1to0.7. Thedifferencesbetweentheworkmaterialsaresignificantforlow sliding velocities under dry conditions. Ferritic-pearlitic and austeniticsteelsyieldmuchhigherfrictioncoefficientscompared tomartensitic steels[95].Athighslidingvelocities,thefriction coefficientsconvergetolowervalues(0.2).Moreover,allwork materialswithasimilarmicrostructuredonotsatisfythesame friction model. For instance, a small percentage of CaMnS inclusionslowersthefrictionsignificantlyatlowslidingspeeds, whereassimilarinclusionsdonotaffectthefrictionalbehaviourof austeniticgradesofsteel.

3.4.2. Effectofcuttingfluids

The influence of cutting fluids on the friction coefficient is showninFig.19.Itcanbeseenthattheuseofalubricantoilcauses alargedecreaseinthefrictioncoefficient,especiallyatlowsliding speeds.Incontrast,theeffectisreducedathigherslidingspeeds comparedtothedrycase.Inthepresenceofalubricant,thefriction coefficientremainsconstantaround0.1irrespectiveofthesliding velocity(Fig.19a).Itshouldbenotedthatthefrictionbehaviour stronglydependsontheamountoflubricantsupplied,itsviscosity, andthecontactduration.Itwasshownthattheoilwasevacuated ina few tenths ofa second duethe highcontactpressure and slidingvelocity[60].Ontheotherhand,oilwillpenetratethe tool-chip interfaceif the contact is longer than a second (turning, drilling, etc.). In interrupted cutting processes, the contact is lubricatedbeforeeachcuttingperiod.Theamountofoildeposited attheinterface(beforecutting)dependsstronglyonthecutting speed.Athighcuttingspeeds,theinterfaceisstarvedofoil,which leadstodrysliding.Incontrast,atlowcuttingspeeds,thecontactis fullylubricated.Moreover,oilviscositystronglyinfluencesfriction inMQLbymodifyingthegenerationofoilmist(dropletsizeand/or flowrate)irrespectiveofitscomposition(Fig.19b).

The effects of liquidnitrogen (LN2)or gaseous nitrogenand solidCO2onthelubricationmodeandfrictionarestillunclear.It has been reported that LN2 significantly lowers friction in machining of Inconel 718, probably due to oxygen starvation

[184].Intitaniummachining,anoxidizedsurfacestronglymodifies thefrictionbehaviour[60].

3.4.3. Effectofcuttingspeed

Simulation ofhighspeedmachiningatcuttingspeedshigher than1000m/min[92]needsfrictiondatathat aresubstantially modifiedbythestrainrateandtemperature.Itwasdocumented thatfrictioncoefficientsformetallicworkmaterialsconvergeto 0.2 in dry sliding, which corresponds to a semi-solid friction regimeasassumedinRef.[164].

3.4.4. Effectoftoolcoatings

It is well-known that cuttingtool coatingscan significantly modifythefrictionalbehaviouratthetool/workmaterialinterface

[99,185].Theinfluenceofthesubstrateisalsoverysignificant.It wasshownin Ref.[231]thata CBNsubstrateyieldsaverylow friction coefficient of 0.1–0.2 when machining Inconel 718, whereasTiAlNcoatedcarbidetoolsexhibit

m

valuesof0.2–0.4. Incontrast,HSSandcarbidesproducesevereadhesionandhigh frictioncoefficientswhereasPCDyieldsaself-lubricatedcontact whenmachiningaluminiumalloys[77].

Anextensivecharacterizationoftoolcoatingswasreportedin Refs. [99,91]. The characterization was based on mechanical, thermal and energy considerations according to the complex frictionmodelsreviewedinSection3.2.

For difficult-to-cut alloys, operations that require specially coatedtoolsareakeyissueforbothtoolmanufacturersandend users[202].Typically,coatingsarefirstdepositedonsamples,and tests and correlations betweenthe outcomes of thelaboratory tests and the results of cutting tests are established. In Refs.

[202,203], methodologies for classifying the performance of

cuttingtool coatings werepresented.For example, theratioof ballwearareatothesampletracedepthwas usedtorankthe cuttingperformance of nanostructured TiN+AlTiN,TiN+AlTiN +MoS2andCrN+CrN:C+CcoatingsdepositedonWC-Coinserts

[202].

3.5. ImplementationoffrictioninFEsoftware 3.5.1. FrictioneffectsinFEmodellingofmachining

Asdiscussedearlier,theuseoffrictioncoefficientsbasedonthe Coulomb frictionlawtorepresentthecontact conditionsatthe tool-chipandtool-workpieceinterfacesforallcuttingregimesis unrealistic.Asaresult,differentfrictionmodelsareoftenusedin FEsimulationsofmetalcutting.

InFEmodellingofmetalcutting,thelocalfrictionatthe tool-chipinterfaceisoftenmodelledbythemodifiedCoulombfriction law,wherethefrictionstressislimitedbythecurrentshearflow stress of the work material

t

f¼minð

t

;

ms

nÞ where

t

f is the

friction(shear)stress,

s

nisthenormalcontactstress,

m

isthelocal

frictioncoef_ficient,and

t

¼

s

=p3ffiffiffiistheshear_flowstressofthe workmaterialatthecontactinterface.

Thedualzoneideawasusedtodevelopbothnumericaland analyticalmodelsforthetool-workcontactfriction.Moufkietal.

[162]proposedthemeanfrictioncoefficienttobedependenton

themeantemperature.Özlüetal.[174]usedafrictionmodelthat separatedthefrictioncoefficientintotwocomponents—apparent andslidingfrictioncoefficients.Thefirstcomponentisgivenbythe ratioofthetotalfrictionandnormalforcesactingontheentirerake facewhereasthesecondcomponentisgivenbytheratioofthe frictionandnormalforcesactingintheslidingregion.

Todate,mostof theanalyses oftool-chipcontacthavedealt withthedeterminationofthefrictioncoefficient.Shietal.[208]

analysedtheeffectsofamodi_fiedCoulombfrictionlawatthe tool-chipinterfaceviaa2DFEmodelforrakeanglesrangingfrom15to 30andafrictioncoefficientrangingfrom0.0to0.6.Themaximum temperature,tool-chipcontactlength,shearangle,andthecutting forceswerefoundtobestronglydependentonthecoefficientof friction.

Arrazola and Özel[8] used thegeneral purposeFE software ABAQUS(Explicitv6.1)toconductadetailedsensitivityanalysisof frictionandotherparametersinorthogonalcutting.Theyshowed that,apartfromthefrictioncoefficient(

m

),otherinputparameters suchasthethermalconductance(KI),theheatpartitioncoefficient (

G

),andthepercentageoffrictionenergytransformedintoheat (

h

)havesignificantinfluenceontheresults(seeTable4).

Amongallthecontactparameters,thefrictioncoefficienthad thegreatestinfluence.However,itwasobservedthatallcontact parametershadalargeinfluenceonthemaximumtoolrakeface temperature(To).Itwasfoundthat(i)thefrictioncoefficientwas theonlyparameterthatinfluencedthetool-chipcontactlength, and(ii)evenforhighvaluesofthefrictioncoefficient,thetool-chip contact lengthwas lowerthan experimentallyobserved values. This could be a reason for the lower thrust force predictions commonlyobserved in FEsimulations ofmetal cutting.In fact, these two aspects are major issues in FE modelling of chip formation, particularly when tryingtomodel the effectof tool wear(especially,craterwear).

Inordertosolvethisproblem,Arrazolaetal.[7]showedthatthe useofavariablefrictioncoefficientdecreasedtheerrorsbetween thesimulatedandmeasuredfeed/thrustforcesto10%.

Fig.19.Influenceoflubricationandoilviscosityonfriction:(a)fulllubrication,(b) MQL[40].