AnalyticalstochasticmodelingandexperimentalinvestigationonabrasivewearwhenturningdifculttocutmaterialsF.Halilaa,C.Czarnotab,M.Nouaria,naLaboratoiredEnergetiqueetdeMecaniqueThe oriqueetAppliquee, LEMTACNRS-UMR7563,EcoledesMinesdeNancy,MinesdAlbi,GIP-InSIC,FrancebLaboratoiredEtudedesMicrostructuresetdeMecaniquedesMateriaux, LEM3CNRS-UMR7239,UniversitedeLorraine,Francearticle infoArticlehistory:Received5September2012Receivedinrevisedform25December2012Accepted28 December2012Availableonline11January2013Keywords:CuttingtoolsAbrasivewearWearmodelingStochasticmodelingAbrasiveparticlesTitaniumalloyTi6Al4VabstractToolwearandtoolfailurearecriticalproblemsintheindustrialmanufacturingeldsincetheyaffectthequalityof the machined workpiece(unexpectedsurfacenish ordimensionaltolerance) and raisethe production cost. Improving our knowledge of wear mechanisms and capabilities of wear predictionarethereforeofgreatimportanceinmachining. Thethreemainwearmodesusuallyidentiedatthetool/chipandthetool/workpieceinterfacesareabrasion, adhesionanddiffusion.Besidesthefactthatunderstanding mechanisms that govern these wear mechanisms are still incomplete, the experimentalanalysisisverydifcultbecausefrictioninterfacefeatures(suchastemperature, pressure, particlesembeddedinthecontact y) arenot easilymeasurable. Theobjectiveof this researchworkis todevelop a wear model in which abrasive particles are assumed embedded at the interface between toolandchip. Theseparticlesareconsideredhavingaconical shapeandarecharacterizedbytwomainparameters in the present approach: the corresponding size and apex angle. Wear particles may be seenas non-metallic inclusions or wear debris generatedduring the machining process. Aprobabilitydensity function has been adopted to describe the uctuation of the size and the apex angle of particlesinthecontactarea. Theinuenceoftheadoptedstatisticaldistributionparametersisalsopresented.Theanalytical model gives, asanal result, thevolumeof theremovedmaterial perunit of time.Finally, severalweartestswerecarriedoutconsideringanuncoatedcarbidetoolWC-CoandTi6Al4Vtitaniumalloyasmachinedmaterialtovalidatetheproposedmodel.&2013ElsevierB.V.Allrightsreserved.1. IntroductionThe surface quality of themachined part strongly depends ontool wear. Generally, the main types of wear usually identied areabrasion, adhesionanddiffusionmodes. Thesethreemodes ofwear operate in an interactive way and depend on severalparameters, whichmaketheunderstandingofmechanismsgov-erning themstill incomplete. In addition, the study of thesemechanismsisdifcultbecausefrictioninterfaces(tool/chipandtool/workpieceinterfacesarea)arenoteasilymeasurableduringmachining operations.Toprovidethebeginningof anexplanationtothemechanismoperating during abrasive wear, two fundamental questions raised:Whatiscausingthisabrasionandhowacarbidetool withaveryhighhardnesscanbewornbyabrasion?Which parameters can have a strong inuence on the initiationandthespreadofabrasivewear?To answer these questions, some authors have suggestedconclusionsmainlybasedonexperimental observationsSuh[1]supposedthat asperities of theroughantagonistic surface areresponsible for the process of material removal and henceabrasivewear. Generally, abrasioncanbecausedbytwotypesof abrasive particles. The rst type of particles can be consideredasfreeweardebrisatthetool/workpiececontact. Intheirwork,Akasawa et al. [2] showed that this type of particles canbeexplained by the diffusion wear mode that may lead to aweakening of the cutting tool fromwhichsome particles aredetached and formwear debris. For instance, considering aWCCotool andacarbonsteel workpiece[2], carbonatomsofthe manufactured steel migrate to the cutting tool and the cobalt(binding part of the substrate WCCo) migrates to the workpiece.As a consequence, a weakening of the WC grains takes place, thusfacilitatingthepropagationofcracksandtheformationofwearfragments.The secondtype of abrasive particles is inclusions initiallypresent in the machined material and having a hardness higher orat least equal to the hardness of the tungsten carbide cutting tool.This shows that abrasiondepends onthe machinedmaterial.Marinov [3] reminded that the work material may containContentslistsavailableatSciVerseScienceDirectjournal homepage: www.elsevier.com/locate/wearWear0043-1648/$ - seefrontmatter&2013ElsevierB.V.Allrightsreserved.http://dx.doi.org/10.1016/j.wear.2012.12.055*Correspondingauthor.Tel.: 33329422226;fax: 33329421825.E-mailaddress:mohammed.nouari@insic.fr(M. Nouari).Wear302(2013)11451157exogenous and endogenous non metallic inclusions. Exogenous assoftendogenousinclusions(e.g. suldesandphosphides)donotplayanimportant roleinabrasivewear. Onthecontrary, hardendogenousinclusionssuchassilicateandcarbidesmayhaveamarkedeffect onthewear evolution. Theycaneasilycut andremove a part of material fromthe tool surface. Marinov [3]conductedexperimentstoanalyzetheinuenceof cuttingcon-ditions and abrasive particle characteristics on the abrasive wearof aK20tungstencarbidecuttingtool. Theauthor consideredseveral specimenspreparedbypowdermetallurgyfromahighmanganesesteelandidentiedbydistincttypesofnon-metallicinclusions and different levels of concentration. It was shown thatthe higher the ratio between the non-metallic inclusions hardnessand the cutting tools hardness, the more pronounced the abrasivewear is. Marinov [3] also revealed that the abrasive wearrepresentsingeneral 25%of thetotal rateof wearwhichisincontradiction with a previous study of Ho et al. [4] who found anamount of only 10%. In the case of machining Inconel 718 with atungstencarbidetool, Fockeetal. [5] alsoconrmedthatnon-metallicinclusionsarethecauseofabrasivewear. Jiaandsher[6] focused on the inuence of chemical composition of tungstencarbide tools andthe nature of abrasive particles. Conductingscratchingtestsandusingseveralabrasiveswithdifferenthard-ness, theyconrmedthattheabrasionresistance(inverseoftheremoved volume) of theWCCo toolsdepends ontheir hardnessas well as the hardness of abrasive particles. Saito et al. [7]considering different cemented carbide inserts by varying Cocontent and WC grain size have shown that these two parametershaveasignicant inuenceontheabrasivetoolwear.Cuttingconditions alsohaveastronginuenceonabrasivewear [8]. The effect of temperature, for example, has been studiedbyUsuietal. [9]whodevelopedanempiricalmodeltoanalyzeabrasiveandadhesivewear. Krameret al. [10] consideredthatmechanismscontrollingthetotal wear rate(includingabrasivewear)dependoncuttingconditions. Theauthorsconrmedthatmechanical wear processes, such as abrasion, are dominant at lowcuttingtemperatureandforcuttingspeed. Thus, abrasiveweardepends, indirectly, on the chip sliding velocity and the tool/chipcontactlength.Abrasionmanufacturing, ingeneral, andtheabrasivewearofthe cutting tool, in particular, can be studied by means of differenttechniques.Inthecaseofaconventionalmachining,cuttingtoolwearisacombinationofacomplexseveralmechanisms. Separ-ating the specic actionof one of these wear modes is verydifcult to manage. Moreover conventional tribological testscannot reproduce severe machining conditions (high contactpressure, high temperature, high strain ratey). Nevertheless,some authors (e.g. Kagnaya et al. [11]) used tribological tests likescratch tests, pin-on-disk tests, etc. to predict abrasion tool wearin machining. By this way (knowing the restricted area of such ananalysis), onecancaptureinuencesoftheslidingdistance, theapplied pressure or the nature of the used lubricant (in the case ofan assisted process) as well as material properties and character-istics (hardness, impurities concentration, thermomechanicalbehavior,)ontheabrasivewear. Asaconsequence, cuttingtoolbehaviormaybeanalyzedandtool lifemaybepredictedfromtribological benchtests.Oneof therst empirical equations basedonconventionaltribological tests, governingwearprocesswasgivenbyRabino-wicz[12]andthroughthewellknownArchardequation[13].Inthesemodels,theremovedvolumeofmaterialincreaseslinearlywith the normal applied load and the sliding distance anddecreases as the workpieces hardness is increased. ThroughAbrasive wear tests, Khruschov et al. [14] showed that theabrasionresistancevarieslinearlywiththehardness. TaborandPowell [15] performed scratch tests with spherical indenters andproposedarelationshipwheretheabrasivewearisproportionaltothenormalloadandtotheslidingdistance;itwasalsofoundinverselyproportionaltothehardnessandtheYoungsmodulusofthecountersurface.Thankstothesestudies, answerscanbeproposedtothetwoabovequestions. Abrasionwear iscausedbyabrasiveparticlespresentatthetool-chipandtool-workpieceinterfaces. Particlescanbeeithernon-metallichardinclusionspresent (initially) inthemachined materialor debrisgeneratedbyother wearmodes(adhesion or diffusion modes). Parameters such as hardness,contact pressure, sliding velocity, contact length and temperaturehave a great inuence on the abrasion wear process. However, thetemperaturewill not beconsideredinthedevelopment of theproposedstudywhichtakes intoaccount onlythemechanicalabrasivewearmode.Inthepresentpaper,anewanalyticalabrasivewearmodelisproposed and applied to analyze physical wear phenomenaoccurring during the machining of titaniumalloy Ti6Al4VbyWCCocarbide tools.Thepaperisorganizedasfollow:First of all, a Representative Volume Element (RVE) describingthe contact area is presented and general equations areformulated. Then, it addressed the description of the proposedmodelbasedonananalyticalapproachincludingastatisticaldescriptionofparticlesembeddedinthecontactarea.Specialattention has been paid on the particles morphology andcontactpressure.A sensitivity study isproposed in order to highlight the effectof model parameters on the cumulative overall abrasive wear.Finally, experimental cutting tests with WCCo insertsmachiningrefractorytitaniumalloysarepresentedanddis-cussed. Thetestedmaterialsarecharacterizedbyanesizedmicrostructure(grainsizeintheorderof 1 mm)withahighhardnesslevel,inorder toexhibitabrasionphenomenonTo validate the modeling, machining tests were performedwithout lubrication(drycutting) underdifferent cuttingcondi-tions. Uncoated WCCo tools with different geometries werechosentostudythewearbehavioroftheinsert. Cuttingforces,pressure, friction and tool damage were deeply analyzed. A part oftheexperimental studyfocuses onSEMandEDSpost-mortemanalyses of thewear patterns exhibitedbytheinserts duringmachining tests. Results were then compared qualitatively to thetheoretical modeling developed in this work. Experimentsrevealed that during machining the a-b alloy, different tool wearmodes canbe exhibiteddepending onthe consideredcuttingcondition. It was clearly shown that diffusion was not fullyactivated even for high levels of cutting temperatures, whileabrasion and excessive chipping were the most important failuremechanisms for WCCocutting tools. The paper discusses allfactorsleadingtosuchoccurrencesandstudiestheinuenceofcuttingconditionsandsomemicrostructureparametersonthetooleffectivenessandfailure modes.2. Problem description2.1. RepresentativevolumeelementRVEDuringmachining, thechipows onthetools facewithaslidingvelocitydenotedbyVcandexercisingaboveanapparentpressure denoted by P0. By adopting a homogenization procedure,itwasassignedtoeachmaterial pointof thiscontactchiptoolinterfacearepresentativevolumeelementRVEshowninFig. 1.Withinthis RVEwedenote byNbr thenumber of potentiallyabrasive particles per unit area present at the tool/workpieceF.Halilaetal./Wear302(2013)11451157 1146interface. Dependingoncuttingconditions andmaterial para-meters, only a given number Nactof Nbr is actually active.Potentially abrasive particles are closely related to the workpiecematerialmicrostructure(impuritiesmeansizeandshape y).AsillustratedinFig. 1, theinactiveparticlesareincontactneitherwith the tool nor with the chip. In the case of this study, adoptinga stationary and established contact, the number Nact of particlesperunitareaistimeindependentandmaybeexpressedas:NactNactPo,Vc,ka,kt,kc,ks 1whereP0isthepressureappliedontheremoteboundaryoftheRVE corresponding to the Tool/chip contact pressure (seen as theapparent pressure) and Vc is the chip velocity. Quantities, ka, kt, kcandksrepresentmicrostructural andgeometrical parametersofabrasiveparticles, tool mechanical properties, chipmechanicalpropertiesandstatistical parameters.Fig.1illustratestheRVEinthecaseofmachiningprocess.Itshouldbehighlightedherethataccordingtomanyauthors[1618], abrasivewear canbeeither twobodyor threebodyabrasion. Intwo-bodyabrasion, abrasiveparticlesareembeddedin the chip so that they will slide without rotation on the tool facewithVc(velocity of the sliding chip). Inthree-body abrasion,particlesarefreeinthechip/tool contactzone. However, inthepresent study, it is assumed that wear is mainly due to two-bodyabrasionsothat thenumber of abrasives involvedinthepro-cessesofabrasionisthenumberNactoftheactiveparticles.2.2. ParticlesmorphologyAs previously underlined, abrasion wear mode has been foundto be causedeither by wear debris involvedat the tool/chipcontact zone or by non-metallic inclusions embedded in themachined material. As an illustration, Fig. 2 shows different typesof hardparticlesthatcanbetrappedintothetool/chipcontactand may cause abrasive wear (potentially abrasive particles).Fig. 2(a) showsgrainsdetachedfromWCgrainsinthecuttingtool [11]. Fig. 2(b) illustrates abrading particles (wear debris) leftattheendofadryslidingweartest(cold worktoolsteelslidingona ferritic carbonsteel) [19]. Fig. 2(c) and(d) depicts non-metallic inclusionsinitiallypresent intheworkpiece[20,5].As seenonFig. 2, particles of a givenmaterial may havevarious shapes and sizes. For example, Luo and Dornfeld [21], in awork dealing with the modeling of the CMP (Chemical MechanicalPolishing) process, haveconsideredthat abrasiveparticlesmayCHIPTOOLThree-body abrasionInactive particlesTwo-body abrasionPApparent contact pressurePoVFcFfCHIPTOOLWORKPIECEActive abrasive particlesFig. 1. Representative volume element (RVE) in the case of orthogonal cutting, containing Nbr abrasive particles (active and inactive). P0 is the apparent contact pressure,Pisthe realcontactpressure,Fccuttingforce,Fffeedforce,VcuttingspeedandVcisthechipvelocity.Sulfide inclusion Debonding of aWC fragmentFragmented WC grainWear debris2ma bc dFig. 2. SEM images and optical micrographs of specimens showing different origins of abrasive particles: (a) WC fragments obtained from a pin-on disk test (WC6%Co/AISI 1045) [11]. (b) Abrading particle left at the end of dry sliding wear test [19]. (c) Non-metallic Sulde inclusion observed in the machined steel K1050 with a CVD-TiNcoatedHSSturninginsert[20].(d)Opticalmicrographshowingan embeddedtitaniumcarbideinclusioninamatrix ofInconel718[5].F.Halilaetal./Wear302(2013)11451157 1147havesymmetricconicalorsphericalshape. Lorentzonetal. [22]haveusedanumerical methodtostudytheeffect of asingleembeddedhardcarbideparticleontool wear. Heconsideredaconical shape of the hard particle. In the case of the present study,each abrasive particle is considered having a conical shapeidentiedby a size R andanapex anglej(Fig. 3). Becauseparticlesshapehasasignicant impact onabrasivewear [21],several authors assumedthat geometrical parameters of theseparticles(size, apexangley) followastatistical distributioninthecontactarea[23,24]. Adoptingasamepointofview, andinordertotakeintoaccountthegreatrangeinparticlesizesandshapes, R and j are assumed here to follow a statistical distribu-tion.Detailsofcalculationwillbepresentedinalatersection.2.3. Realpressure/apparentpressureThe study of the contact mechanics [25] showed that thesurfacecontactbetweentwosolidsisdiscontinuousandthatthereal contact area A is, in some circumstances, a small fraction of theapparent contact area A0. In 1966, Greenwood and Williamson [26]have developed one of the rst models of elastic contact between arough surface and a smooth one. Intheir model, the authorsdescribed the rough surface by the height distribution of thecontactingasperitiessupposedhavingaspherical shapeat theirsummits.Itwasfoundthat theapparentpressureP0, correspond-ing to the apparent contact area A0, and the real pressure P,corresponding to the real contact area A, applied on rough surfaceasperities are related through the following equation:A0APP0c 2InEq. (2), cr1is aconstant that depends ontheYoungsmodulusandthePoissonsratioof thetwoelasticsurfaces, theradius of the asperities and their distribution on the surface [26].Although it appears that the contact between two bodies islimitedtomicroscopicasperities, it iscommonlyassumedthattheforcesaredistributedoverthetotal apparentarea. Suchanapproximationis not so far fromreality inmachining wherecontactpressuremayreachhighlevels[27], inducingacrushingof asperities andatteningof contactingsurfaces. As aconse-quence, theactual andapparent contact areasaresimilarsuchthatitcanbeconsidered thatc1inEq.(2).3. Modeling3.1. BehaviorofoneactiveabrasiveparticleThe interaction between two neighboring abrasive particles isdisregarded here, such that the overallabrasive wear isobtainedby volume averaging over the total number Nbr of abrasiveparticles. The behavior of one abrasive particle, assumed isolatedinaslidingcontact, ispresentedinthis section.3.1.1. Plasticdeformationinthechip/abrasiveandtool/abrasivecontactThe understanding of the deformation mode that occurs at theparticle/tool interface is important for the determination of overallabrasive wear. If the deformation is elastic (Hertzian elasticdeformation), fewor no abrasion occurs. In this paper, it isassumedthat thedeformationoccurringattheparticle/tool andparticle/chip interfacesis purely plastic.This choice is justied bytworeasons;therstisthatthedeformation at interfacescannotbe elastic since the Hertz contact pressure is higher than the owstress [28] due tothe highpressure at the chip/tool interfacegenerated during machining. The second reason is that the conicalshape induces an instantaneous elastoplastic (for moderate appliedpressure) or fully plastic (for high level of applied pressure)deformationmodeundertheindentationtest(thereisnoelasticphase) [29]. This kind of deformation has been assumed byinvestigatorsinmanymodelingsofgrinding, lappingorpolishingprocesses [21,29].Fundamental assumptionsmadeinthepresent workarethefollowing: The hardness of the chip is lower than the tools one andthe active abrasive particle is assumed embedded in the chip. Thecontact between an abrasive particle and the tool is considered tobeaslidingindentationof ahalf-spacebyahardindenter. Thecontact between abrasive particles and the chip is considered to beaquasi-staticindentationof half spacebyahardindenter. Asaconsequence, when deducing applied forces from the tool and thechip, a plastic zone with semi projected circle is considered for thesliding indentation (tool) and a fully projected circle is consideredfor the quasi-static indentation (chip). Adopting a tribological pointofview, thepressureappliedbytheabrasiveparticleonthetoolsurface(resp. chipsurface)isequaltothetoolhardnessHt(resp.chip hardness Hc). Denoting by F the force applied on the abrasiveparticle, theradiusacoftheprojectedcirclecontactbetweentheconical indenter and the chip surface is given by:acFpHc3Similarly, F and the radius atof the semi projected circlecontact betweentheconical indenter andthetool surfacearerelatedthroughtheequation:at2FpHt4Because of the conical shape of particle, a relation existsbetweentheradiusandthepenetrationdepth:dcacdtattan j 5R Ydcdt2ac2atFig.3. Schematicshowingparticleparametersandtherelationshipbetweenthedeformation Ddcdtintheneighborhoodofthebiggestparticle.Bottom ViewSideViewVcGrooveFrontal areaFront Viewatdt2atFig.4. Geometryofcontactbetweentheconicalabrasiveparticleandtheatcuttingtoolsurface.F.Halilaetal./Wear302(2013)11451157 1148andthen:dctan jFpHc6dttan j2FpHt7According to [21], the chip/tool contact pressure discontinuity(duetotheabrasive/toolcontactandabrasive/chipcontact)canbe neglected. Thus the force F applied on each particle (identiedby a size R and an apex anglej) may be approximated byF0.25p(R/tanj)2P, wherePistheappliedpressure(seeEq. (2)withc1).Eqs.(6)and(7)thenbecome:dcR2PHc8dtR22PHt93.1.2. SingleparticleabrasivewearAs previously mentioned high pressures are observed inmachiningandfullyplasticdeformationoccurs. Consequentlyagrooveisformedastheparticleismovingalongthetool (seeFig.4).The frontal surface of the cone, denoted by Af is depending onthepenetrationdepthdt,theapexangle jisgiven by:Af d2t =tan j 10The removed volume by a single abrasive particle, with size Aandanapexangle j,perunit timeisequalto:v1pxAfVc11whereVcisthechipvelocityand xisaparameterintroducedtodescribethefractionof removedmaterial convertedintoweardebris [30]. Here it is assumed that all removed material leads tomicro-chip formation,sothat x1andthen:v1pd2ttan jVc12UsingEq. (9)thevolumeremovedbyasingleactiveparticleperunittime isnally expressedas:v1pR22PHttan jVc133.2. StatisticaldescriptionAs mentionedinSection2.2, thevarious shapeandsizeofabrasive particles in the chip/tool contact is depicted by a statisticdistributionofRandangle j. Manytypesofprobabilitydensityfunction have been adopted in the literature to describe thevariationinsizesandshapesofinclusions(e.g.exponential[31],log-normal [32]regardinginclusionsinsteels)thatmightbeatthe origin of abrasive particles. Here, the two geometricalparametersRand jareassumedtofollowastatisticaldistribu-tion governed by a bell-shaped Gaussian probability densityfunctionfor its commonuseandeasetounderstand. Sinceatthisstageofinvestigation, nopreciseanalysishasbeendoneonthe identication of particles shape and size for a particularmaterial, thischoiceofaGaussiancurvemustbeseenasarstapproximation. A parametric study on the mean and the standarddeviationthat characterizetheGaussianlawis presentedinalater section in order to measure the effect of the adoptedstatisticallaw.Inthefollowing, onlythestochasticstudyforthesizeRofthe particlewillbedeveloped. Identicalcalculation wasdone(notgivenhere)forthesecondparameter j.Valueof thesize parameterisinarange [Rinf,Rsup]whereRinf(respRsup) stands for thesmallest potentiallyabrasiveparticle(resplargest),theprobabilitytondaparticleoutsidetherange[Rinf, Rsup] beingnegligible. AccordingtotheGaussianlaw, theprobability densityfunctionisgivenby:GRR0 1sR2pp exp12R0RmoysR_ _2_ _14where sRmeansthestandarddeviationof thedistributionandRmoyisthemean.For computational purpose, theprobabilitydensityfunctionneedstobediscretized. Therangeofparticlesizesofinterestis[Rmin, Rsup]correspondingtothenumberof activeparticlesNactwhere Rmin is the size of the smallest active particle. To nd Rmin,itissupposedthatundertheappliedpressure, largestparticleswill be embedded in both chip and tool with a penetration depthinthetooldenotedbydsupt(givenbyEq. (9)withRRsup)andapenetrationdepthinthechipdenotedbydsupc(givenbyEq. (8)withRRsup). Thefreespaceleftbythelargestparticles(intheneighborhood), denotedby Y inFig. 3, caninvolve anactiveparticleofasizeRminatleastequaltoY.Thatleadsto:Y Rsupdsuptdsupc 15UsingEqs. (8), (9)and(15), Rmincanexpressintermsoftheappliedpressureasthefollowing:RminRsup1Pp22Ht1Hcp_ _ _ _16Note that for the second parameter j all the range [jinf,jsup]was discretized, where jsup denotes the biggest angle and jinfthesmallestone.AdoptedvaluesarelistedinTable1.The range of active particles [Rmin, Rsup] is divided into an oddnumbernit2k1of subintervalsof lengthL RsupRmin=nit.TheithintervalInt(i):Inti R01i,R02i R01iRminL i1 R02iR01iLiscenteredonthevalueR0iRminL i1=2. ThefamilyFRiisdenedasbeingthegroupofparticleswithsizeRbelongingtotheintervalInt(i),seeFig. 5.According to the discretization scheme, the probability to ndaparticlewithasizeR0ibelongingtothefamilyFRiof activeTable1Referenceparameters.sRmmRmoymmRsupmmRinfmmsjradjmoy1jsup1jinf1HcGPaHtGPaPGPaNbrm2nit1 5 9 1 0.15 45 80 10 3.34 14.6 1.5 J10551F.Halilaetal./Wear302(2013)11451157 1149particlesisgivenby:PrRiR0i PrRR01i,R02i _R02iR01iGRR0 dR012erfR02iRmoysR2p_ _erfR01iRmoysR2p_ _ _ _17whereerf x _x0 2=ppexpy2dyistheerrorfunction.Thesamestatisticaldescriptionisadoptedfortheapexanglej(notpresentedhere).3.3. OverallmaterialremovalAccordingtoexplanationsgiveninSections2.1and3.2, thenumber of activeparticlespresent inthetool/chipinterfaceisgivenby:NactNbr_RsupRminGRRdR NbrPrRRZRmin 18Thepart of activeparticleswithsizeR0i, apexanglej0iandbelonging tothefamilyFRiisgivenby:NiNbrPrR0i,j0i 19wherePrR0i,j0istandsfortheprobabilitytondaparticleofasize R0iandapexanglej0i. Intheproposeddescription, it isbelieved that any abrasive particle can have an apex anglecoveredbytheprobabilitydensityfunctionGj(j0)givenbyEq.(14)initsR-form. Inthatsense, itappearsthatthetwoeventsPrRR01i,R02i and Prjj01i,j02i are independent events. Theprobability to havea particleidentied by asizeR0i and anapexangle j0iisthereforeexpressedas:PrR0i,j0i PrRR01i,R02i:Prjj01i,j02i 20Thetotal volumeremoved, per unit timeandunit area, byparticles belongingtothesamefamilyFRi :vitNi:vi1p21where vi1pis the volume removed, per unit time, bya singleabrasiveparticlegivenbyEq.(13).If nointeractionissupposedbetweenparticlesandbetweenthe couple ((R0i,j0i),v1p(R0i,j0i)) for iA[1,nit], the total volume perunit time and unit area, removed by all active particles trapped inthecontacttool/chipisgivenby:vtotal

niti 0vit

niti 0Nbr:PrRR01i,R02i :Prjj01i,j02i_ _ R0i22PHttanj0iVc____224. Parametric analysisAparametricstudyhasbeenperformedinthissectionusingEq. (22) in which the total volume removed per unit time and unitarea is expressed as a function of several parameters. Theobjectiveistoanalyzetheinuenceoftheseparametersaswellastheeffect of varyingthestatistical description(throughthemeanandthestandarddeviationof theGaussianlaw). Table1summarizesparametersofthetoolmaterialkt{Ht}, ofthechipmaterial kc{Hc}, microstructural andgeometricparametersofabrasive ka{R,j}, parameters of the statistical distributionks{sR,sj,Rmoy,jmoy}andcuttingconditions(P,Vc).ValueslistedinTable1areconsideredasreferenceones.ThemeanvalueRmoyandthestandarddeviationsRof theGaussianlawaregivenaccordingtotheworkof [23,33]. Oneshould note that the choice of a particular value is only0.0E+005.0E-091.0E-081.5E-082.0E-082.5E-080 100 200 300Volume removal rate (m3/s.m2)Chip Velocity (m/min)Reference curveFig. 6. Inuence of the chip velocity on the volume removal rate per unit time andunitarea. Thiscurvestandsasareferencecurveinthecourseof theproposedparametricstudy.Gaussian probability distributionof particle size (1/m) Particle size (m)Range of active particles[Rmin,Rsup] Int(i)0.0010.0000.0030.0050.007FamilyRiFFig. 5. Gaussianprobabilitydistributionofparticlesizegiven byEq.(14).ParametersarelistedinTable1.0.0E+001.0E-082.0E-083.0E-084.0E-085.0E-086.0E-080 100 200 300Volume removal rate (m3/s.m2) Chip velocity (m/min)Reference curveP2=3 GPaP1= 0.75 GPaFig. 7. Evolution of the volume removal rate per unit time and unit area versus thechip velocityfortwovaluesofthecontactpressure.F.Halilaetal./Wear302(2013)11451157 1150meaningful for aspecicmaterial. Theupper limit isgivenbyRsupRmoy4sRandthelowerlimitisgivenbyRinf Rmoy4sR.Alargerangeisadoptedfortheinterval[jinf,jsup].Adopted values ofHc andHt correspondto theTi6Al4V astheworkpiece materialandtheWCCoasthecutting tool.It hastobenotedthat it isdifcult togivetheexact totalnumber of abrasives Nbr present in the contact (active andinactive) because of the different origins of particles (weardebris, non-metallicinclusions). Someauthorsconsiderthatallparticles areprovidedfromnon-metallic inclusions, referring,for example, to the work of Atkinson et al. [24] which also givesanoverviewof all experimental techniques tondthepara-meter Nbr When considering that all abrasive particlesare fromwear debris, the work of Soda [34] can give us an approximationofNbrbythefollowingequation:Nbr 0:026P1=4O2U 23whereP1=42isthepressureofoxygenandUistheslidingspeed.ButitshouldbenotedthatNbrgivenbySodasequationisperunittime.0.0E+001.0E-102.0E-103.0E-104.0E-105.0E-100 100 200 300Volume removal rate (m3/s.m2)Chip velocity(m/min)Reference curveR=0.5 mR=1.5 m=0.05 Rad0.0E+001.0E-102.0E-103.0E-104.0E-105.0E-100 100 200 300Volume removal rate (m3/s.m2)Chip velocity (m/min)Reference curveRmoy=3.5 mRmoy=7 mFig.9. (a)Inuenceoftherstgroupofparametersks1onthevolumeremovalrateperunittimeandarea. (b)Inuenceofthesecondgroupofparametersks2onthevolumeremovalrateperunit timeandarea.00.0020.0040.0060.0080.010.0120 1 2 3 4 5 6 7 8 9 10 Gaussian Probability Distribution of particles size (1/m)Particles size (m)R=1 mR=0.5 mRmin(R=0.5)=3.04mRmin(R=1)=3.94m Fig. 10. Gaussianprobabilitydensityfor twovaluesof thestandarddeviation.OtherparametersarelistedinTable1.0.0E+001.0E-102.0E-103.0E-104.0E-105.0E-106.0E-100 50 100 150 200 250 300Volume removal rate (m3/s.m2)Chip velocity (m/min)Reference curveHt1=2 x HtHt2 = 0.5 x HtHc1=2 x HcHc2=0.5 x HcFig. 11. Inuenceof HtandHconthevolumeremoval rateper unit timeandunitarea.1.0E-141.0E-121.0E-101.0E-081.0E-061.0E-040 50 100 150 200 250 300Volume removal rate (m3/s.m2)Chip Velocity (m/min)Reference curveNbr =10Nbr=1000Fig. 12. Inuence of the total particle number Nbr on the volume removal rate perunit timeandunitarea.0.0E+002.0E+044.0E+046.0E+048.0E+041.0E+051.2E+050.0 1.3 2.5 3.8 5.0 6.3 7.5Number of active abrasive particles (1/m2)Contact Pressure(GPa)9.9E+041.0E+052.0 3.0 4.0 5.0 6.0Contact Pressure(GPa)Number of active abrasive particles (1/m2)actN Nbr =satP 3.75GPa Fig.8. Evolution ofthenumberofactiveparticlesNactversusthe contactpressure.ParametersusedforcalculationsarelistedinTable1.F.Halilaetal./Wear302(2013)11451157 1151Inthepresent work, theparameter Nbr wasxedbasedonHolappaswork[35]. TheauthorproposedanumberofparticlesNV105corresponding to the number of alumina inclusionsestimatedin1 cm3of steel. This value, whichis avolumetricconcentration, is adopted as a rst approximation to identify Nbrbyusingthefollowingequation:Nbr Nv2=324Note that this number is just a magnitude; its inuence on thevolumeremovalrateisshownbytheparametricstudy.4.1. Effectofcuttingconditions:chipvelocityVcandcontactpressureP4.1.1. EffectofthechipvelocityVcFig. 6showstheevolutionof volumeremoval rateper unittimeandunit areavtotalfor chipvelocities rangingfrom0to300 m/minandusingreferencevalueslistedinTable1.ItcanbeeasilyseenfromFig. 6thatvtotalgivenbyEq. (22)increases linearly with the chip velocity without any stabilizationoftheabrasivewearprocess. OneshouldnotethatFig. 6repre-sents the inuence of chipvelocity (andat some extent, theinuence of thecutting speed)onvolume removalrate, but onlywhen solely abrasion is considered. At low chip velocity and highpressureandforsomerefractorymaterials, adhesioncanbethemainwear mechanismandbuilt upedgemayoccur for somerefractoryalloys.Thebuiltupedgewillaffectthewearmechan-ism, and also the contact pressure and temperature distributionsalongthetool/chipcontactlength. Asaconsequence, thislineartendency may be valid for higher velocities and it is expected thatforlowervaluesofVc, theresponsewouldbequitedifferent. Inthefollowing, resultsshowninFig. 6aretakenasareferencecurve foranalyzing nextparametersinuences.4.1.2. EffectofthecontactpressurePTheeffectof thecontactpressureisanalyzedinFig. 7. Twovalues of thecontact pressurewerechosen: P10.75 GPaandP23 GPa. As observed for the cutting speed inuence, vtotalincreases linearly with increasing the contact pressure. Thisgrowth is due to the direct and indirect role played by the contactpressure. The direct role can be seen through Eq. (13) where it canbe noticedthat the single particle abrasive wear v1pdependsdirectly inalinearwayonthecontactpressurePThe indirect effect of the contact pressure occurs in thenumberof activeparticlesNactaccordingtoEqs. (16) and(18).Indeed, whenthecontactpressurePtendstowardsasaturationpressuredenotedbyPsat, thesizeofthesmallestactiveparticleRminwill tend toward Rinf. Thus, accordingly _RsupRminGRRdR 1leadingtoNactNbr. WhenPissuchthatP4Psat, andsincethenumberofactiveparticlescannotbegreaterthanallpotentiallyactivated particles, it is observed a plateau (Fig. 8). The saturationpressure Psat is obtained from Eq. (16) considering RminRinfandcanthenbeexpressedas:Psat2RsupRinfRsup2Ht_1Hcp_ _________2254.2. EffectofthedistributionparameterThe effect of the statistical distribution is studied usingFig.9(a)and(b)whenvtotalversusthechipvelocityfordifferentset of distribution parameters. The statistical parameter kswas separated into two groups. First group contains three valuesCutting tool(WC-Co)ChipWork piece(Ti6Al4V)fFfFcfVFig. 13. Schematic representation of the orthogonal cutting process. (a) 3D representation, (b) 2D representation. f is the feed (mm), w is the width of cut (mm), a is therakeangle(1), Fistheshearangle(1)andLcisthecontactlength(mm).+Undeformed Deformed Tool/chip contact Fig. 14. Microstructureof the Ti6Al4V material.(a) Beforemachining (inthe workpiece)and (b)aftermachining (inthe chip),closeto the tool/chip contact(secondaryshearzone).Inthiszoneahighdeformationof bphasecanbeidentied.Table2ChemicalcompositionofTi6Al4V(mass%).Fe V Al C O N O2NMax0.25 3.54.5 5.56.75 Max0.8 Max0.2 Max0.3 Max0.25F.Halilaetal./Wear302(2013)11451157 1152of the standard deviation ks1{sR10.5 mm, sR21.5 mm,sj10.05 rad}. Secondgroupcontainstwovaluesof themeanvalue size ks2{Rmoy13.5 mm, Rmoy27 mm}. All other para-meters remain constant and are given in Table 1.Fig. 9(a)showstheinuenceoftherstgroupofparameteronvtotalwhileFig. 9(b)givestheinuenceofthesecondgrouponvtotal.When sRincreases, thevolumeremovalrateperunittimeand unit area decreases. Same conclusions can be obtainedregarding the inuence of sj. It is also observed that an increaseinRmoyleadstoanincreaseinvtotal.Size of particles has a direct effect on the single particleabrasivewearasindicatedinEq. (13). Anincreaseinthesizeofparticleswillleadtomorequantityofremovedmaterial.Thestandarddeviationhasadirecteffectonthenumberofparticles involved in the abrasion wear process. Indeed thevariationof thestandarddeviationleads toavariationintherange of active particles [Rmin, Rsup] and then more or less particleswillbeactivated asillustratedinFig.10.4.3. EffectofthehardnessofthetoolandthechipHt,HcThis inuence of chip and tool hardnesses on the worn volumeis illustrated in Fig. 11. Values of the tool hardness considered, incalculationsareHt12HtandHt20.5Ht. Sameratioswerechosen for the chip hardness Hc, such that Hc12HcandHc20.5Hc.Itiswellknownthatforlowvaluesofthetoolhardness, theremoval material process can be facilitated and more quantities ofmaterial will beremoved. Thiseffect of HtshowninFig. 11isotherwiseclearlycapturedinEq.(13).Concerning the chip hardness Hc, an increase in its values leadstoadecreaseinthevolumeremovalrateperunittimeandunitareavtotal. Thiscanbeexplainedbythefact that accordingtoEq. (16) Hc affects RminQUOTE and then, indirectly, inuences thenumberof activeparticlesNact. AssaidinSection3.2, abrasiveparticlesareembeddedinthechipbecauseHcQUOTEismuchlower than the particles one. As a consequence, for a chip with ahigherhardness, itwill bemoredifcultfortheabrasivetobeembeddedinthechip,reducingthusthetwo-body abrasion.4.4. EffectofthetotalnumberofparticlesNbrFor this study, two values of Nbr are considered:Nbr1l1Nbr and Nbr2l2Nbr with l10.1and l210.Theinuenceof Nbr onthevtotalisshowninFig. 12withtheY-axisgiveninlogarithmicscale.Increasing 10 times the number of particles induces anincreaseof100timesinthevolumeremoval rateperunittimeand unit area and vice versa. The gure shows the major impact ofNbronvtotal.5. Experimentalverication5.1. ExperimentalsetupMachining tests were carried out under dry and orthogonalcongurations, seeFig. 13, usingthe a-btitaniumalloyTi6Al4Vasthe workpiece material and a cemented carbide WCCo as thecutting tool.Tests wereperformedonaheavy-dutylathemachinewitha11 kW motor drive, which generates a maximum torque of 1411 Nm.The spindle rotational speed ranges from 18 to 1800 rpm. As shownin Fig. 14(a), the titanium alloy Ti6Al4V presents before machining aduplex microstructure a/ab with an average grain size of10 mm(rangingfrom5 mmto20 mm). Inclusionsof bgrainscanbeclearly seen inside the microstructure before machining in Fig. 14(a),and after machining in Fig. 14(b). Vickers tests have been performedonninedifferent specimens. Theaveragemicro-hardnessisabout340 HV0.2. The high level hardness depends on several strengtheningmechanisms such as grain size, solid solution atoms, and precipitationTable4Mechanicalandthermalpropertiesofchemicalcomponentsofthe cuttingtool.Toolmaterial Specications Thermalexpansioncoefcient (106/K) Density(g/cm3) Meltingpoint(1C) Hardness(Hv) Youngsmodulus(MPa)WC 69.8% 5.1 15.6 2900 2150 700 103Co 9.5% 12.3 8.9 1495 100180 103Table 5Mechanicalpropertiesthetoolsubstrate.Toolsubstrate WCCoHardness25 1C(HV10) 1485Hothardness800 oC(kg/mm2) 600Density(g/cm3) 11.4Thermalconductivity(W/mK) 45Thermalexpansion(106/K) 6.1Modulusofelasticity(GPa) 510Traverserupture(GPa) 2.2Co WC Fig. 15. Highmagnicationonthetool rakefacemicrostructureshowingtheshapeandthe sizeofWC grainsandbinderphaseCo.Table3MechanicalandthermalpropertiesofTi6Al4V.Tensilestrength(MPa)Limitofelasticity(MPa)Elongation(%)Young modulus(GPa)Hardness(HV)Density(g/cm3)Specicheat20100 1C(J/kgK)Thermal conductivityat20 1C(W/mK)931 862 10 110 340 4.43 580 7.3F.Halilaetal./Wear302(2013)11451157 1153hardening. It controls directly the level of obtained cutting forces, toolwear, andcuttingtemperatureandthenthemachinabilityof theconsidered material, see the work of Cle ment et al. [36].ThemicrographofFig. 14(b)clearlyexhibitsthemicrostruc-tureevolutionduringthechipformationprocesswithveryhighdeformation of b phase. A lamellar structure can easily be020040060080010001200140016001800Cutting force Fc (N)Cutting speed V (m/min)f=0.1 mm,=0 f=0.2 mm,=0 01002003004005006007000 20 40 60 0 20 40 60Cutting force Ff (N)Cutting speed V (m/min)f=0.1 mm,=0 f=0.2 mm,=0 Fig.16. Evolutionof(a) cuttingand(b)feedforceswithcuttingspeedforthreefeedsf 0.1 mm,0.2 mm.05001000150020002500Contact pressure P (MPa)Cutting speed V (m/min)f=0.1 mm,=0 050010001500200025000 20 40 60 0 0.1 0.2Contact pressure P (MPa)Feedf(mm)V=15m/min,=0 V=30m/min,=0 V=60m/min,=0f=0.2 mm,=0 Fig. 17. Evolutionof contact pressurewith(a) cuttingspeedforthreefeedsf 0.1 mm, 0.2 mmand(b) feedrateforthreecuttingspeedsV15 m/min, 30 m/min,60 m/min.Chipping Built-up-layer (BUL) Tool rake face Worn contact area Fig. 18. Worn tool with rake angle a01 (test with V60 m/min and f 0.2 mm). (a) Worn contact area (b) Chipping wear and build up layer formed on the tool rake face.Table6Datarecordedfromcuttingtests.Frictioncoefcients,shearanglesandchipvelocitieswerecalculatedusingMerchantModel[37]andcontactpressurewascalculatedusingMoufkietal.model[38].CuttingspeedV(m/min)Feedf(mm)Rakeanglea(1)CuttingforceFc(N)(start1stpass)CuttingforceFc(N)(end5thpass)CuttingforceFc(N)(ave.)FeedforceFf(N)(start1stpass)FeedforceFf(N)(end5thpass)FeedforceFf(N)(ave.)WornlengthLw(mm)Apparentfrictioncoefcient mContactpressureP(MPa)ShearangleF(1)Chipvelocity(m/min)15 0.1 0 900 1100 1000 400 480 440 0.33 0.44 2240 33.13 9.8015 0.2 0 1500 1875 1688 520 600 560 0.58 0.33 2168 35.82 10.9430 0.1 0 970 1200 1085 450 550 500 0.34 0.46 2366 32.63 19.2030 0.2 0 1250 1420 1335 580 650 615 0.69 0.46 1456 32.63 19.2060 0.1 0 800 1000 900 300 600 450 0.36 0.50 1866 31.72 37.0460 0.2 0 900 1100 1000 580 710 645 0.87 0.65 859 28.59 32.5330 0.1 15 1000 900 950 560 600 580 0.52 1.05 1114 29.30 15.1330 0.2 15 1000 1100 1050 700 1000 850 1.43 1.38 418 25.50 13.0115 0.1 30 450 600 525 60 50 55 0.27 0.73 1168 42.01 10.24F.Halilaetal./Wear302(2013)11451157 1154observedinthemachinedmaterial. OnFig. 14(b) whitespotscorrespondtoundeformedbphase. Theinitial equiaxedmicro-structure in Fig. 14(a) gives to the material a good combination ofstrength and ductility. It is well known that the lamellar structurein titaniumalloys possesses higher creep resistance, fracturetoughness and crack propagation resistance. This means thatmachining process plays a very important role in the mechanicalpropertiesof alloysbyaffectingtheirmicrostructure. Thecom-plex microstructure of titanium alloys provides during machininga variety of microstructures ranging fromthe equiaxed a-bmicrostructure to the b-transformed (martensitic or lamellar)and poses many challenges in microstructural control duringthermo-mechanical processingtomeet nal machinedcompo-nent properties. Also, the exhibited deformation process shows anextreme thermomechanical loading (high pressure and hightemperature) appliedtotheworkpiecebythecuttingtool. Theexaminationof thedeformedmicrostructureina, bandabphases reveals ne sizes of b grains and two localized shear zones.Therstoneiscalledtheprimaryshearzone andthesecondonethesecondary shearzone.Tables25present asummaryof thechemical composition(mass%),mechanical andthermalpropertiesofthealloy.Uncoated cemented carbide inserts were employed formachiningTi-6Al4Vspecimens. Eachtool consistedof tungstencarbide (WC) with cobalt as the binder phase. The surfaceroughnessRaoftherakefaceisabout0.5 mmandtheRtabout5 mm. The chemical analysis on a polished surface inside the toolgives acompositionof 69.8 wt%of WC, 9.5 wt%of cobalt and20.7 wt%of Ti/Ta/Nb, see Tables 4and5. Tool micrographinFig. 15 shows that the Co binder is uniformly distributed and WCgrainshavesizesvaryingfrom 1to5 mm.Cutting conditions (cutting speed and feed) and tool geometry(rakeangle)wereconsideredasthemainfactorstoinvestigatethe correlation between tool wear, sliding chip velocity andpressure. As showninTable 6, experiments were carriedoutkeepingcuttingspeed, feedandrakeangleatvariouslevels.Therangeofeachfactorwasselectedbasedonindustrialrequirements.Thecuttinglengthallowedbythemachinecapacity(about1.5 m)providesasufcientcuttingtimetoreachthestationaryregimeof thecuttingprocess (1.6 s for acuttingspeedof 60 m/min).ThecuttingspeedVhasbeenvariedbetween15and60 m/min,feeds f between 0.1 and 0.2 mm and rake angle between 01 and 301.For all experiments, thewidthof cut wwas kept constant to4 mmtosatisfyconditionsof orthogonal machining. Theothervariables suchas machinecondition, variabilityinset up, etc.,havebeenmaintained constant throughout theexperimentation.AthreecomponentsKistlersdynamometerwereemployedforcuttingforcemeasurements. Theforces reportedarethosefortheprocessinastablestatewithalmoststeadypulses. Thetoolwear length was collected using a toolmakers microscope(1 mm resolution) at 30 magnication. Thewearsurfaces wereexamined under a scanning electron microscope (SEM) equippedwithenergy X-rayspectrometer(EDS).5.2. ResultsThe data recordedfromthe experiment andthe results ofcalculation based on Merchant model [37] and Moufki et al.model [38] are listed in Table 6. More precisely, merchant modelwas used to calculate the shear angle F, the friction coefcient mand the chip velocity Vc. Moufki et al. model was used to calculatethecontactpressureP.5.3. CuttingforcesandcontactpressureDuringthecuttingprocess, thetool removes a part of theworkpiecebyaprocess of intenseplastic deformationat highstrainratewithintheprimaryandsecondaryshearzones. Thus,thecuttingtool is subjectedtoa hightemperature andgreatpressure.The value of the cutting force of each cutting test is an averagevalueof forcesrecordedwhenstartingtherstmachiningpassandattheendforthelastmachiningpass(5thpass). ItcanbeobservedfromFig. 16(a) thatcuttingforcedecreaseswhenthecuttingspeedincreases. It iscommonlystatedintheliteraturethat increasing the cutting speed leads to a decrease in the cuttingforcelevel. Muller et al. [39] havedonea workonthesamematerial andunder thesamecuttingconditions. Theyshowedthat the measuredcutting temperature increases from550 1Cwith a cutting speed of V15 m/min to 700 1C with V60 m/min.It meansthat thethermal softeningof thematerial makesthecutting forces lower and then pressure decreases too, seeFig. 16(a). Indeed, whenmachining titaniumalloys, the toolchip interface is controlled by the contact temperature which canattain large values and affects drastically the mechanical proper-ties themachinedmaterial. Consequentlythecontact pressureand cutting forces decrease.In the sametime, the hightempera-ture (especially with low thermal conductivity of titanium alloys)Chipping wear Excessive chipping Fig.19. Worntoolwithrakeangle a151 (testwithV60 m/minandf 0.2 mm).(a) and(b)showexcessivechippingwearprocessonthetoolsurface.00.10.20.30.40.50.60.70.80.90 10 20 30 40Worn Length (mm)Rake angle ()V=30 m/min, f=0.1 mmFig.20. Worn lengthLwvs.rakeangle.F.Halilaetal./Wear302(2013)11451157 1155affects signicantly the wear behavior of cutting tools [40]. FromFig. 16(b), it can be observed that the feed force increases with theincreaseinthefeed.Fig. 17(a) and (b) represents the inuence of the cutting speedV,feedfonthecontactpressure.5.4. ToolwearForobservationsandqualitativeanalysis, ascanningelectronmicroscopy(SEM) coupledtoEnergyDispersiveX-raySpectro-scopy(EDS)wasperformedonwornspecimenof cuttingtools.For a quantitative analysis and measuring the worn contactlength, a Prolometer was used. Eachspecimenwas analyzedafterobtainingstablecutting forces.5.4.1. EffectoftherakeAngleResults on the examination of cutting tool with rake angle of 01showthatthetoolfailureisduetoadhesionandabrasionwear.ThesampleofevidenceispresentedinFig. 18. InFig. 18(a), therake surface exhibits two worn areas. The rst area is covered bytheBuiltUpLayer(BUL)oftheworkpiecematerial(Ti6Al4V).From results of our previous work [41], this worn area can beclassiedastheareawithadhesiveweararea. Theexaminationunder SEMEDSshowsthat thisareaiscoveredwithtitaniumalloy layer with a thickness of 5 mm. On the second area, chippingwearcanbeobserved(about17 mmindepth).Thisisduetothedetachment of BUL which is pulled away by the chip ow on thetool rakeface. Sincetheadhesivewear mechanismbondsBULstronglyonthisarea, thedetachmentofBULisalsopinchedoutthetoolsubstrate.When the rake angle increases from 01 (Fig. 18) to 151 (Fig. 19),the cutting tool shows chipping wear and excessive chipping. Thechipping wear area is about (750 13080) mm3(length x widthx depth). Chipping on the tool rake face with a rake angle of 151 ismore excessive thanthe tool with01. The SEMmeasurementrecorded that the depths of chipping along the cutting edge variesfrom100to220 mm.Itcanbeconcludedfromtheseresultsthattheweariswideranddeeperwhentherakeangleincreases. Toprove that, the worn length along the cutting edge, denoted by Lw,wasmeasuredandpresentedvs.therakeangleinFig.20.The evolution of the worn length shows an increasing functionfrom01to151andaplateauforlargervaluesoftherakeangle(here from151 to301).ResultsshowninFig. 21(b) aregivenbyour abrasivewearmodel. Thelattercangivetheevolutionofthewornvolumevs.cutting speed for different feed rates. However, as in experiments,the worn length cannot be given directly by the modeling.Consequently, only a qualitative comparison has to be donebetweenour model andexperiments tovalidatetheproposedapproach.AsseenfromFig. 21, thecomparisonbetweentheproposedmodel andexperiments(underthesameconditions)showsthesametendencyintermsofincreasingtoolwear(abrasionwear)withcuttingspeed. However, thecomparisoncannot beeasilyextended to the inuence of the feed. Fig. 21(b), corresponding tothe proposed model, shows a higher level of the volume removalrate for the lowest feed. This can be explained by Fig. 17(a) wherethe contact pressure deduced from experiments decreases with f.Since our model strongly depends on the contact pressure wherepredictedwearvolumeincreasesasthepressureincreases(seeFig. 7),theresultsgiveninFig.21(b)arenotsosurprising.Onthecounterpart, Fig. 21(a)revealsthatanincreaseofthefeedfleadstoadecreaseintheexperimentalwornlength. Thisresultmustbereadwithcautionbecausethewornlengthisaresult of many other wear modes (diffusion, adhesiony) that arenotaccountedforinthiswork.6. ConclusionInthiswork, abrasionwearhasbeeninvestigated. Themaincontribution of the study concerns physical understanding ofwearphenomenathatoccurduringmachiningtheusual refrac-torytitaniumalloyTi6Al4V.Thelatterisextensivelyusedintheaerospace industry for structural components. Tool wear andinuenceofdifferentparameterssuchastoolgeometry, cuttingspeed, feed, pressure, etc. are some of the most important pointsdiscussedinthiswork. Theoriginalpointofthisresearchpaperconcerns the proposal of a new stochastic modeling in the eld ofmachining metallicalloys.Theworkwasorganizedinthree parts:(1) Therst part was dedicatedtothedevelopment of themodel based on the concept of a RVE including a statisticaldescription of potentially abrasive particles trapped in thetool/chip contact area. In the present approach, thevolumeremoval rateduringmachiningisobtainedfroman analytical relationship (see Eq. 22). This variable is seenas representativeof abrasivewear. Themost importantparameters affecting tool wear by abrasion were shown tobe the cutting conditions parameters (chip velocity Vc andcontact pressure P) aswell asmicrostructure heterogene-ities(describedbythedistribution insize andapexangleofabrasiveparticles)andcontactingbodiesproperties. Itappearsthattheabrasivesizeisofparticularimportancesince it is squared in the relation giving the volumeremovalrate.(2) Thesecondpartwasfocusedonaparametricanalysisofthe inuence of material and cutting condition parametersaswell asthe effectof the statistical lawon abrasivetoolwear. Cuttingconditionparameters(P, Vc), tool hardness00.10.20.30.40.50.60.70.80.910 20 40 60Worn Length Lw (mm)Cutting speed V (m/min)f=0.1 mm, =0 f=0.2 mm, =0 0.00E+001.00E-102.00E-103.00E-104.00E-105.00E-106.00E-107.00E-108.00E-109.00E-101.00E-090 20 40 60 80Volume Removal Rate (m3/sm2))Cutting speed V (m/min)f=0.1 mm, =0 f=0.2 mm, =0 Fig.21. (a)Worn lengthLwvs.cuttingspeed,and(b)Theoreticalwornvolume vs.cuttingspeedandfeed.F.Halilaetal./Wear302(2013)11451157 1156Htandthetotal number Nbr of particles haveamajorinuence on the volume removal rate. An increase of theirvaluesleadstoanincreaseof thevolumeremoval rate.The chiphardness Hchas anindirect inuence onthevolume removal rate. It appears that the softer the chip is,themorethevolumeremovalrateis. Fromtheproposedanalysis, abrasive particles are responsible for the amountof wear, rather than the chip. Lower chip hardness allowslarger embedding of particles within the chip, which limitsthe particle abrasive capabilities. 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