Numerical analysis of constitutive coefficients effects on FE simulation of the 2D orthogonal cutting

22 Pages·2017·5 MB·English

Numerical analysis of constitutive coefficients effects on
FE simulation of the 2D orthogonal cutting process:
application to the Ti6Al4V
Mariem Yaich, Yessine Ayed, Z. Bouaziz, Guenael Germain
To cite this version:
Mariem Yaich, Yessine Ayed, Z. Bouaziz, Guenael Germain. Numerical analysis of constitutive coef-
ficients effects on FE simulation of the 2D orthogonal cutting process: application to the Ti6Al4V.
International Journal of Advanced Manufacturing Technology, 2016, pp.1-21. ￿10.1007/s00170-016-
8934-4￿. ￿hal-01361858￿
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IntJAdvManufTechnol
DOI10.1007/s00170-016-8934-4
ORIGINALARTICLE
Numerical analysis of constitutive coefficients effects
on FE simulation of the 2D orthogonal cutting process:
application to the Ti6Al4V
M.Yaich1,2&Y.Ayed1&Z.Bouaziz2&G.Germain1
Received:4February2016/Accepted:16May2016
#Springer-VerlagLondon2016
Abstract Inthispaper,adeepstudyofconstitutiveparame- interesting agreement between numerical and experimental
ters definition effect is done in order to guarantee sufficient results.
reliabilityofthefiniteelementmachiningmodeling.Thecase
ofaparticularbiphasictitaniumalloyTi6Al4Vknownbyits Keywords Shearbands .Strainevolution .Lagrangian
low machinability is investigated. The Johnson-Cook (JC) formulation .Chipserrationsensitivity.Finiteelements
elasto-thermo-visco-plastic-damage model combined with modeling .Orthogonalcuttingprocess
the energy-based ductile fracture criteria is used.
Segmentation frequency, chip curvature radius, shear band
spacing,chipserration sensitivity and intensity, accumulated Abbreviations
plasticstrainintheformedchipsegments,andcuttingforces JC Johnson-Cook
levelsaredeterminedwheretheirdependencytoeveryconsti- ASB Adiabaticshearband
tutive coefficient is examined and highlighted. It is demon- FEM Finiteelementsmodeling
stratedfromtheseparatevariationofeveryplasticanddamage FEA Finiteelementsanalysis
parametersthataninterestingfiniteelementmodeling(FEM) A Initialyieldstress(MPa)
relevanceisreachedwiththeadjustmentofJCstrainharden- B Hardeningmodulus
ing coefficients term, thermal softening parameter, exponent n Workhardeningexponent
fracture factor, and damage evolution energy. Moderate and C Strainratesensitivitycoefficient
highcuttingspeedsareappliedtothecuttingtoolintheaimto m Thermalsofteningcoefficient
testtheirimpactonshearlocalization,chipsegmentation,and T Referencetemperature(°K)
Ref
numerical forces levels as well as to approve previous T Melttemperature(°K)
melt
highlightedfindingsrelatedtoconstitutiveparametersdefini- ε Equivalentplasticstrain
:p
tion.Ingeneral,thisstudyfocusesonaprominentdecreasein ε Referenceplasticstrainrate
:0
identificationprocesscostwiththepreviousknowledgeofthe ε Actualizedplasticstrainrate
p
most affecting constitutive coefficients while keeping an Δε Incrementofupdatedplasticstrain
D Initialfailurestrain
1
D Exponentfactor
2
D Triaxialityfactor
3
D Strainratefactor
4
* M.Yaich D Temperaturefactor
5
[email protected];[email protected] D Johnson-Cookactualizedstatevariable
D Lineardamageevolution
ev.L
1 ArtsetMétiersParisTech,LAMPA,2bdduRonceray, Dev.Exp Exponentialdamageevolution
49035Angers,CEDEX,France L Characteristicmeshelementlength(mm)
2 EcoleNationaled_IngénieursdeSfax,MFAM,RoutedeSoukrakm uf Equivalentplasticdisplacementintotally
3.5,Sfax3035,Tunisia fracturedmaterial
IntJAdvManufTechnol
u Equivalentplasticdisplacement changesthattakeplaceinextremelythinzoneduringavery
p
G Fractureenergycorrespondingtotensile/shear short time period, as well as availability of many new and
f(III)
mode(Nm−1) pffiffiffiffi powerful software, are the origins of the wide use of finite
k Fracturetoughness(MPa m) elementmodeling(FEM)intheselastdecades.Thismethod
c
E Youngmodulus(GPa) presentsanirreplaceabletoolinmaterialmachiningmodeling
ν Poisson’sratio as well as in local and instantaneous information capturing.
σ Hydrostaticstress(MPa) Hence, it allows a deep comprehension of several dynamic
h
σ VonMissesstress(MPa) phenomena accompanyingthe cutting process and ofcourse
VM
σ Yieldstressofmachinedmaterial a best management of the contact conditions produced be-
y
σ* Stresstriaxiality(MPa) tween the cutting tool and the workpiece. In fact, the use of
σ~ Unrealstressstate(whennodamageispresent) thenumericalmethodgreatlyhelpsinreducingfrommachin-
μ Coulomb’sfrictioncoefficient ing cost while ameliorating from the comprehension of ma-
m Trescafactor chining phenomena [2]. Recently, finite element analysis
Tresca
k Shearflowstress(MPa) (FEA) has been increasingly used instead of the analytical
σ Normalstress(MPa) methodstofocusonthedifferentaspectsofmaterialsmachin-
n
τ Frictionstress(MPa) ing and to ameliorate its global control including the chip
f
η Fractionofenergyproducedbymaterialplastic formationprocedure[3],thecuttingforcesprediction[4],the
p(f)
(friction)work temperaturedetermination[4],thefinishedsurfacequalityin-
f Fractionofheattransmittedtothecuttingtool crease[5],andthetoolwearprevention[6].
:f
q Heatfluxcreatedbymaterialfriction(plastic) Producedchipresultedfrommachiningoperationscanbe
fðpÞ
work(Wm−2) qualitativelyclassifiedonfourdistinctcategories(continuous,
:
q Heatflowgoingtothecuttingtool(Wm−2) wavy, serrated, and discontinuous) depending on model ge-
→Tool
a Depthofcut(mm) ometry(rakeandflankangles,chamferlengthandangle,tool
p
f Feedrate(mm/rev) edge radius), cutting conditions (cutting speed, depth of the
V Cuttingspeed(m/min) cut,feedrate),materialproperties(thermomechanicalproper-
c
F Tangentialforce ties, failureinitiation),and contact conditions.Infact, repro-
c
F Feedforce ducingwithenoughprecisionthechipmorphologyiscrucial
f
f Segmentationfrequency sincethislatterpresentsasignificantindicatoraboutthewhole
seg
R Chipcurvatureradius(mm) cutting process stability and it deeply helps in well under-
c
L Shearbandspacing(mm) standing and improving from machined surface integrity. In
s
Handh Peakandvalleychipthickness(μm) theirstudy,Daviesetal.[7]haveconcludedthattheonsetof
G % Chipsegmentationdegree whateverchipmorphologystronglymodifyfromthereached
seg
S % Chipserrationsensitivityfactor levelsintermsoftemperatures,cuttingforces,toolwearevo-
seg
Δε Accumulatedplasticstraininasegment lution,andmachinedsurfacequality.Therefore,wellmaster-
p(in-out)
CSI Chipserrationintensity ingthecuttingprocessisbasedontheaccuratepredictionof
the chip formation mechanisms as well as of its specific
characteristics.
In this investigation, machining modeling of a particular
1Introduction titaniumalloy,theTi6Al4V,isstudied.Thismaterial,known
byitsinterestingstrengthtodensityratio,hasbeenusedina
Machiningprocesspresentsnowadaysoneofthemostuseful varietyofmechanicalcomponentssubjectedtosevereoperat-
manufacturingmethodswhichallowhavingafinishedprod- ing conditions like corrosion, mechanical chocks, and high
uctwithsuperiorsurfacequality.Mostofmechanicalcompo- temperatures. However, the most drawback of this material
nents, especially for those in titanium alloys, are produced isitslowthermalconductivitycombinedwithitshighchem-
with machining operation. This latter generally involves ical reactivity with the cutting tool generally resulting on its
coupledthermomechanicalconditionsaddedtothehighnon- acceleratedwear[8].Inadditiontoitspoormachinability,the
linearitycausedbytheinterestinglevelsofstrain,strainrate, drymachiningofsuchdifficulttocutmetalischaracterizedby
and temperature undergone by the machined material. thefrequentformationofaserratedchipevenunderlowcut-
Therefore,thetotalunderstandingofthecuttingprocessisstill ting conditions which is not the case of other materials [9].
untilnowagreatchallengethatcannotbeyetsolvedanalyti- Thischipsegmentationpresentsoneofthemostinvestigated
cally or experimentally [1]. Interaction between different as- phenomena that need to be accurately understood. Saw-
pectslikestrainhardening,viscosity,thermalsoftening,hard- toothedremovedmaterialresultsasreportedin[10]onahigh
ening softening, loading history, and material microstructure frequency of cutting forces oscillations as well as on an
IntJAdvManufTechnol
interesting fluctuation in the cutting tool-workpiece contact are asked to perfectly describe the elasto-thermo-visco-
length, which further accelerates the cutting tool wear thus plastic-damagebehaviorofthemachinedmaterial.
reduces fromthe machined surface quality. These recent de- Adiversityofconstitutivemodelshasbeendevelopedand
cades,manyinvestigationshavebeendoneinordertoaccu- usedbymanyauthorsinthecaseofmachiningmodeling.This
ratelyinsightthemajorfactorscontrollingthechipsegmenta- diversity is mainly due to the coupled effects taken into ac-
tion.Inliteraturereview,twotheoriesaboutchipserrationare countandthenumberofthecoefficientsthatneedtobeiden-
generallyfoundwheretheonsetofsuchmorphologyhasbeen tified.Meanwhile,theuseofonematerialconstitutivelawand
attributedeithertoadiabaticshearbands(ASBs)theory[8,11, not the others could be justified by how much of reliability
12]ortocrackinitiationandpropagation[13–15]. mightbecheekedthroughthedefinitionofonespecificmod-
ShawandVyas[14]havestudiedthecaseofhigh-strength el. Nonetheless, achieving interesting accuracy of FEM re-
steelsmachining.Theyhaveconcludedthatsegmentedeven mainsuntilnowagreatchallengethatneedstobeovercome.
fragmented chip is respectively the result of partial or total Effectively, in order to guarantee much correlation with ex-
crack propagation within the primary shear zone depending perimentalresults,itisimportantwhendeterminingconstitu-
ontheappliedcuttingconditions.Theauthorshaveconcluded tiveparametersandforwhatevertheflowstressexpressionto
a particular damagepropagation sense which startsfrom the reproduceassameaspossibletheencounteredsevereloading
freechipsurfaceanddisseminatestoitsinteriorsideincontact conditionsaccompanyingthemetalcuttingprocessandespe-
withthecuttingtooltip.LinandLin[15]haveasserted,when ciallyfortheTi6Al4V.Inthiscase,extremelyhighstrainsare
modelingthe3Dorthogonalcuttingprocessofthe6-4brass, involved, causing an interesting strain rate and temperature
thesameoriginofchipsegmentationbutwithoppositesense rise within the machined material (in the range of 102–
ofdamagepropagation.Theyhavesignaledthatmaterialfail- 106s−1andupto1000°C,respectively).
ure initially appears in the bottom chip side just above the TheJohnson-Cook(JC)constitutivelaw[16]appearsvery
cuttingtooledgeandprogressivelypropagatesalongthechip interestingtobeusedinmetalmachiningsimulationsinceit
thicknessuntilachievingitsfreesurface. allows the coupling between different effects (hardening,
Contrariwise,otherstudieshaveexplainedchipsegmenta- strain hardening, and thermal softening) with a minimum
tion phenomenon by the thermoplastic shear instability pro- number of coefficients (only five). Its common use in many
duced within the chip thickness. This instability is mainly investigations of hard machining modeling is explained also
produced when the thermal softening effect becomes more by its implementation indifferentFEcommercialsoftwares.
pronounced than the strain hardening one. High strains pro- Additionally,thewideavailabilityofJCparametersvaluesin
ducedinnarrowregionsofthemachinedmaterialleadstoits literature review corresponding to a variety of materials en-
softeningbecauseoftheheatriseconcentrationwithin.Inthis couragesitsgrowinguse.However,thepossibilityoffinding
regard,AmbatiandYuan[12]havesuggestedthatASBsfor- more than one JC parameter sets determined for the same
mation presents the most significant phenomena responsible material (see Table 1) presents one of this model drawback
ofthechipsegmentationwheresoftenedmaterialischaracter- thatcannotbeignoredsinceitstronglyinfluencesonprediction
izedbyitshighsusceptibilitytobeplasticallydeformeddueto qualityintermsofmaterialflowdescription,chipmorphology,
itsmechanicalcharacteristicsdropthatcontributestoapartial cutting forces, and temperature distribution once they are
upward motion of the removed material above the formed not suitably selected. This distinction is essentially due to
band. thedifferentthermalheattreatmentsappliedtothemachined
In fact, whatever the chip segmentation origin (ASB for- materialaswellastotheadoptedmethodusedinparameters
mation,fractureinitiationandpropagation,oreventhecom- identification.
binationbetweenthem),theFEmodelisrequestedtoperfectly Since this distinction in constitutive coefficients heavily
reproducematerialseparationprocess,shearstresseslocaliza- affectsnumericalmodelaccuracy,precisioninJCcoefficients
tion,andchipsegmentationinthecaseofmachiningmodel- identificationisstillfocusedintheaimtoachieveinteresting
ing. It is also asked to simulate plastic strain increase and correlation between numerical and experimental results.
temperature rise in the removed material coupled with its LiteraturereviewillustratesthatJCconstantshavebeeniden-
strength drop in order to accurately predict cutting forces, tified experimentally and/or numerically. Even if the first
temperature levels, and residual stresses distribution. That is method is frequently used, its principal limitation is that the
why in the lastdecades,manyefforts havebeendoneinthe testedconditionsareextremelyfarfromthosereallyreached
aim to increase the effectiveness of numerical models in re- incuttingoperations.Strainandstrainratelevelsachievedin
producing the cutting process. However, FEM has demon- simpletensile,compression,orsheartestsaremuchlowerthan
stratedtheparticularattentionthatshouldbeattachednotonly thoseencounteredinthemachiningtests(upto0.5and103s−1,
totheaccurateimplementationofnumericalparameters(such respectively)[9,19].Theinabilityoftheseexperimentaltests
temporalintegration,formulationtype,meshdensity)butalso to reproduce important loading conditions similar to those
to the right definition of material constitutive models which encountered during real cutting tests recommends usually
IntJAdvManufTechnol
Table1 DifferentJCconstants
valuesoftheTi6Al4V References [8] [9] [17] [9] [18] [17]
Designation JC-a JC-b JC-c JC-d JC-e JC-f
Initialyieldstress(MPa) A 782.7 870 884 968 983 1119
Hardeningmodulus(MPa) B 498.4 990 599 380 348 838.6
Workhardeningexponent n 0.28 0.25 0.362 0.421 0.32 0.473
Strainratedependencycoefficient(MPa) C 0.028 0.011 0.034 0.0197 0.024 0.019
Thermalsofteningcoefficient m 1 1 1.04 0.577 0.69 0.643
Initialstrainrate(s−1) έ – – 1 0.1 0.1 1
0
theextrapolationoftheflowstresscurvesprecedingthefinal tohighlightthemajorroleofappropriatematerialcoefficients
determination of the constitutive parameters as reported by choiceinnumericalmodelreliabilityincrease[9,23,24].On
Chenand al[20].Even ifthisfitting step israndomlydone, the other hand, it is important to note that the JC model ap-
ithelpshoweverinovercomingthequitedifferencebetween pearsunabletoreproducealonechipformationandsegmen-
thestatementstressstatesinspecimenandtheinducedonesin tation [25, 26] due to the fact that its expression exhibits a
simulated machined workpiece. In fact, constitutive coeffi- continuous increase of the flow stress-strain curve for what-
cientsvalidityshouldbequestionedoutsidethoseexperimen- everthestrainandthetemperaturelevelswhichdoesnotrep-
taltestedrangessincetheflowstressextrapolationcannottake resenttherealworkpiecematerialbehavior.Hence,addition-
intoaccounttheactualizedbehaviorofthemachinedmaterial. allytoplasticmodelimplementation,failureneedstobealso
Another problem generally encountered with experimental definedespeciallywhenusingtheLagrangian-basedanalysis.
identification even if high strain rates tests are performed In examining literature review, we note that distinct fracture
(thankstoGleeblesimulatoruse)ishowtoguaranteethesame models have been developed in the purpose to precisely de-
material treatment for both the specimen and the machined scribe the damage produced during the machining process.
workpiece.Nonetheless,experimentalmethodsusuallysuffer However, the effect of the right definition of failure coeffi-
from cost because of the need to acquisition posts treatment cients on the FE model reliability is still until now ignored
withhighprecision. and weakly understood by the majority of cutting modeling
Doubts related to the convenience of using constitutive investigations.
parameters experimentally determined in the cutting process In this study, the JC damage model coupled with the
simulationshaveencouragedthedevelopmentofdifferental- energy-based ductile criterion is defined to reproduce the
gorithms like Levenberg-Marquardt and Kalman filter dedi- Ti6Al4Vbehaviorwhenfailureisinitiatedinthematerialuntil
cated to the constitutive parameters identification [21, 22]. its total fracture. These criteria already implemented in
These algorithms consist essentially on minimizing the mis- Abaqus/ExplicitFEcodehavebeenwidelyusedinconjunc-
matchbetweennumericalandexperimentalresultsessentially tion with the JC plastic model. The main objective of this
duetothewrongdefinitionofthematerialbehavior.Theyare investigation is to increase as possible and with a minimum
basedontheuseoftheinitialconstitutivecoefficientsexper- effort from the FE model reliability while studying the ma-
imentallydeterminedforthesametestedmaterialorevenfor chiningprocessoftheTi6Al4Valloy.Theprincipalchallenge
anotheronefromthesamefamily[21,22]inthedefinitionof ofthepresentworkistoimprovefromnumericalsimulation
more accurate and suitable parameters well describing the qualitybyonlydeterminingthemostaffectingJCparameters
material behavior and giving appropriate predictions. These insteadofmodifyingordefiningnewconstitutivemodelswith
involvedinverseidentificationmethodsappearmoreinterest- more coefficients number. To emphasize and point out the
ingandreliablethantheformeroneduetothefactthatthey majorimpactofaccuraterheologicalanddamageparameters
allowreachingabettercorrelationwithlesscost.However,it definition on the FE model reliability rise, a 2D orthogonal
isofmajorimportancetonotethatinversemethodsgenerally cutting model based on Lagrangian formulation is used.
causethetimeincreasewiththenumberoftheidentifiedpa- Careful comparisons between FE numerical predictions and
rameters added to problems related to solution diversity experimental results taken directly from previous work [27]
resultingthusonagreatdistinctionintermsofchipmorphol- are made. Dependency of chip morphology, average cutting
ogy,temperaturedistribution,andshearangle[1]. forcesandtemperaturedistributiontoeachrheological(A,B,
Infact,availabilityofmanyidentificationtechniquespre- n,Candm)anddamage(D1–5andGf)materialparametersas
sents the principle origin of this distinction in JC plastic pa- wellastocuttingspeeddefinitionisstudied.Fromascientific
rameterscorrespondingtothesamematerial.Tocutwiththis pointofview,quantitativedescriptionofthepredictedchipis
problem,manyinvestigationshavebeendoneinthepurpose required to improve the cutting process modeling while
IntJAdvManufTechnol
highlightingitsdependencytomaterialconstitutivelawsdef- of the material separation through the deletion of its totally
inition. That is why segmentation frequency (f ), chip cur- damagedelements.Cuttingtoolmotionresultsonthematerial
seg
vature radius (R ), shear band spacing (Ls), chip serration separation where the upper part of the workpiece is trans-
c
sensitivity(S %),accumulatedplasticstrainswithinoneseg- formed into chip while the bottom one corresponds to the
seg
ment of the numerical chip (Δε ), and its serration in- finished material. In this study, an elasto-thermo-visco-
p(in-out)
tensity(CSI)aredefinedandcarefullyexaminedtoenableand plastic-damagebehaviorisdefinedtoparts1and2ofFig.1
furtherathoroughparametricstudyofalltheconstitutivepa- while no damage is applied to part 3 located below the ma-
rameters.Numericalcuttingforcesarealsocomparedwiththe chined surface.Numericalcutting toolintungstencarbide is
experimental ones in order to get a benchmark model. This considered as a rigid body where its thermal properties are
paper concludes that the adjustment of JC strain hardening implemented.
coefficients (A, B, and n), thermal softening parameter (m), Achieving a sufficient accuracy of the cutting process
exponent fracture factor (D ), and damage evolution energy modelingwithreasonabletimecostisgenerallyrequired,that
2
(G) leads to interesting reduction in numerical model dis- iswhyameshrefinementislocallyappliedinordertoprop-
f
agreement,whilealltheotherconstitutiveparametersdemon- erlyreproduceshearbandsformation,saw-toothedchipchar-
stratealmostaminoreffect.Thisprecisionindeterminingthe acteristics,andtoolgeometryspecificationswhilereducingas
maincausesofFEaccuracydecreaseisofvitalinterestsince possiblefromthecomputationaltime.Meshelementlengths
requiredtimeinparametersidentificationisdeeplyminimized about5and10μmarerespectivelydefinedaroundthecutting
thanks to the reduction in requested experimental tests and tool tip and in the intermediate-superior workpiece parts.
numericaliterationnumbers. These values are chosen after many mesh convergence tests
whichhavebeenpreliminarydoneinthepurposetoguarantee
both:(a)aninterestingsimilaritybetweennumericalandex-
2Orthogonalcuttingmodel perimentalchipmorphologyand(b)areasonablecomputing
time.
2.1Numericalmodeldefinition Thebasicmodeldimensions,geometry,andboundarycon-
ditions defined inthisstudy are illustrated inFig.1. Cutting
Inordertoanalyzetheeffectofconstitutiveparametersdefi- tooledgeradius,rake,andflankanglesarerespectivelyequal
nition on the cutting process, eventually on material separa- to20μm,2°,and7°.Theworkpieceissupposedtobefixedin
tionandchipformation,a2Dorthogonalcuttingmodelofthe itsbottomandbothsideswhilethecuttingspeedisappliedto
Ti6Al4Vwithassumptionofplanestrainconditionsisdevel- therigidtoolwhichisconstrainedtomoveonlyinthevertical
opedwiththeFEsoftwareAbaqus/Explicit®.Explicitintegra- direction.Testedcuttingspeed,feedrate,anduncutchipthick-
tion with fully coupled temperature-displacement conditions nessarethesameappliedbyCalamazinherexperimentaltests
isassumedinallsimulationsbecauseofitsadequacytohigh [27]. In addition to mechanical cutting conditions, a room
nonlinearproblemslikethosefacedinmetalmachiningoper- temperature of 293°K is initially applied to the cutting tool
ation.Interactionbetweenthecuttingtoolandtheworkpiece, and the workpiece. Along the machining process, it is yet
modelgeometrychangesaddedtomaterialpropertiesdepen- Eqs.8and10whichcontrolthecreatedandexchangedheat
dencytotheloadingconditionspresentthemainoriginofthis evolutionintheworkpieceandinthematerialscontactinter-
encounterednonlinearity.Four-nodeelementsmeshwithlin- faces.Heatradiationandconvectiontothevicinityisignored
ear interpolation, reduced integration, and automatic hour- in this investigation due to the fact that they present a weak
glass mode control (CPE4RT) are used in the discretization effectonnumericalpredictionssinceaveryshortcuttingtime
of both the cutting tool and the workpiece. These coupled simulation (about at maximum one millisecond) is defined
elements take into consideration the effects of temperature which is not sufficient to obtain interesting heat exchange
and displacement variation during machining modeling. betweentheworkpieceandtheenvironment.
Relax stiffness hourglass control features is defined based Notethatthesamematerialpropertiesoftheuncoatedcar-
ontheresultsofBargeetal.[28]inordertocontrolthenon- bide tungsten cutting tool and the Ti6Al4Valloy workpiece
physicaldeformationmodesgenerallyrelatedtoGausspoint than those defined by Calamaz in her investigation [27] are
definition. Similar to the experimental test conditions, no usedwheredependencytotemperaturevariationisignored.
cooling liquid is applied during Ti6Al4V machining
modeling. 2.2Workpiecematerialmodeling
Lagrangianformulationisadoptedwhereamultipartmod-
elisdefinedandtheworkpieceisdividedintothreetiedparts Theelasto-thermo-visco-plasticbehaviorofthemachinedma-
asshowninFig.1intheaimtoallowchipgenerationwitha terial is described with the JC plastic law [29] which flow
maximumcontroloftheelementsmeshdistortionproblems. stress expression is given by Eq. 1. This model has been fre-
Definitionofanintermediatethinlayerpermitsawellcontrol quently used in metal machining modeling because of its
IntJAdvManufTechnol
Fig.1 Numerical2Dorthogonal α
modelgeometry,boundary Fixed
conditions,andheatexchange 1
definition No Y displacement f
R
2
No thermal exchange Tool
3 γ
Thermal exchange Vc
permitted
ap
Workpiece Y
X
Z
adequacytohighnon-linearproblemslikethoseaccompanying expressedbyEq.3.Itisgivenasafunctionofstresstriaxiality
thechipformationinadditiontoitsreducednumberofcoeffi- σ*(equalstotheratioofhydrostatictoVonMisesstressesσ /
: h
cients. σ ),strainratesε ,andtemperaturesT.Notethatfailureis
VM p
" !# initiatedinthematerialwhentheactualizedstatevariableDis
h i : (cid:5) (cid:3) (cid:4) (cid:6)
n ε T−T m equaltotheunity.
σ¼ AþBεp (cid:2) 1þCln ε:p0 (cid:2) 1− Tmelt−Trerfef (cid:9) (cid:7) (cid:8)(cid:10) " ε: !#
ð1Þ εf ¼ D1þD2exp D3σ* (cid:2) 1þD4ln :p
ε
0
: : (cid:5) (cid:3) (cid:4)(cid:6)
whereεp,ε0,εp,TrefandTmeltarerespectivelytheequivalent (cid:2) 1þD T−Tref ð3Þ
plastic strain, the reference plastic strain rate, the actualized 5 T −T
melt ref
plasticstrainrate,thereferencetemperature,andthemeltone
oftheworkpiece.A,B,n,C,andm aretheJCplasticmodel whereD (i=1,2,3,4,5)aretheJCmaterialfractureparam-
i
parameterswhichcorrespondingvaluestotheTi6Al4Valloy eters and its corresponding values to Ti6Al4Valloy are pre-
aregivenbyTable1. sentedinTable2.
In order to model the material machining process with Inthispaper,damageevolutionD isintroducedintheaim
ev
accurate prediction of the chip morphology, different strate- toreproducetheprogressivedegradationofmaterialstiffness.
gies can be used. Either damage model definition [13, 15, The implementation of this criterion allows avoiding mesh
30–32]orstrainsofteningconsideration[9,33–36]hasbeen dependency problems [40] due to the fact that it describes
adoptedinmanyinvestigationstoreproducematerialsepara- material failure behavior no more as a stress-strain response
tionandshearbandslocalizationwithinthechipthickness.In but as a stress-displacement one. It is recommended to ade-
thispaperandfurthertotheJCplasticmodeldefinition,two quatelydefinethedamageevolutionmodessinceforthecase
distinct failure criteria are implemented is adopted where of2Dandplanestrainorthogonalcuttingconditions(whichis
damage in the machined material is assumed to undergo thecaseofthisinvestigation),onlytwo fracturemodesexist
two steps: (a) a failure initiation step (b) followed by its accordingto[30,41]:(1)theopeningmodeand(2)thesliding
propagation up to the total fracture occurrence. For the first onewhichcorrespondrespectivelytothetensileandtheshear
mode,theJCdamagemodel[37]isusedwhileforthesecond
one,energyductile failure criterion[38] isdefined.Thecor-
responding expressions of these two models are given by Table2 JCdamage
Eqs.2–5. coefficientsvalues JCdamagecoefficients Value
correspondingtothe
X Δε Ti6Al4V[20,39] Initialfailurestrain D1 −0.09
D¼ ð2Þ Exponentfactor D2 0.25
εf Triaxialityfactor D3 −0.5
Strainratefactor D 0.014
whereΔεpresentstheincrementofupdatedplasticstrainand 4
Temperaturefactor D 3.87
ε is the equivalent plastic strain in the damaged element 5
p
IntJAdvManufTechnol
modes.Thiswell explains,according to Miguelezetal[42], 2.3Workpiece-cuttingtoolinteractiondefinition
the noted differentiation in material triaxiality, and conse-
quently in failure levels, between the chip (part 1) and the Inadditiontonumericalmodeldefinitionandmaterialbehav-
passagetoolzone(part2).Forthisreason,exponentialdam- ior description,bothmechanicaland thermalcontact proper-
age evolution (Eq.5) withhigherfailure energyvalue is ap- tiesneedtobecarefullyimplementedduetothefactthatthey
pliedtotheupperpartoftheworkpiecetransformedintochip. heavilyinfluenceontheFEMresultsaccordingtoÖzel[45].
However, a linear damage evolution (Eq. 4) with less pro- Infact,anaccuratedefinitionofthefrictiontakingplacebe-
nounced energy value is defined to part 2 since it is not the tweenthecuttingtoolandthemachinedmaterialiscrucialin
same mechanical phenomena involved when modeling the machining modeling due to the fact that it controls the heat
materialseparationanditspartialslideawayabovetheformed distribution,thetemperaturelevels,thematerialflow,andthe
ASBs. cutting tool wear mechanisms. Despite the availability of
many friction models in literature review [45, 46] varying
Dev:L ¼ up ¼ Lεp ð4Þ fterorimalfceowntatoctviesrsytilcloumnptillincaotweda,mthaeinaccchuarlalteengpereadciccotimonpaonfyminag-
u u
f f
0 1 thatmetalcuttingprocess.Frictioninvolvedbetweenthecut-
Z
B up σ C ting tool and the workpiece are not yet totally understood
Dev:exp ¼1−exp@− G dupA ð5Þ since it isgreatly dependent onmultiplevariables (like tem-
f
peratureandchipslidingspeed).Accordingtopreviousinves-
0
tigations[9,46],excepttemperaturedistribution,alltheother
where ūp and εp are respectively the equivalent plastic dis- numerical outputs are weakly affected by friction definition.
placement and strain. L presents the characteristic length of Consequently,formoresimplicityandbasingonrecentstud-
the quadrangular element mesh edge and its introduction in ies[9,25,41],CoulombandTrescamodelsarecoupledand
plastic displacement definition causes a mesh element size usedinthispaper.Thissimultaneousdependencytobothnor-
dependency reduction. ū =2G/σ is the equivalent plastic malandshearfrictionstresses(asexpressedbyEq.9)permits
f f y
displacement in totally fractured material where G presents the reproduction, with more simplicity, of the sticking and
f
thefractureenergygivenbyEq.6.Itsexpressioninthecaseof sliding contact conditions taking place between the cutting
2Dstrainplaneconditionsisgivenasafunctionofthefracture tool and the machined material. Around the cutting tool tip,
toughness(K ),thePoisson’sratio(γ),andtheYoung’smod- astrongmaterialadhesionoccursresultingonveryinteresting
c
ulus(E)ofthemachinedmaterialaccordingtoMabroukietal. pressurelevelswhilefarawaythetooltip,machinedmaterial
[30].σ istheyieldstressofthemachinedmaterial. easilyslidesinfrontofthetoolfaces.Thisdistinctionincon-
y
tact types is followed by various pressure levels, from the
ðG Þ ¼ ð1−ν2Þ(cid:7)k 2(cid:8) ð6Þ cutting tool edge to the point where no more contact takes
f I;II E c I;II place,asjustifiedin[47].
ThesubscriptsIandIIcorrespondrespectivelytotheopen- If μ(cid:2)σ < τ Then τ ¼μ(cid:2)σ
n max f n ð9Þ
ingandtheshearingmodes.Whateverthedamageevolution If μ(cid:2)σ ≥τ Then τ ¼τ ¼m (cid:2)k
n max f max Tresca
mode,flowstresstensorinfailedelementσisdescribedbythe
followingEq.whereσ~correspondstothestressstatewhenno where μ, σn, mTresca, and k are respectively the Coulomb’s
friction coefficient, the normal stress, the Tresca factor, and
damageoccursinthesolicitedmaterial[43].
theshearflowstress.
σ¼ð1−D Þσ~ ð7Þ DuringTi6Al4Valloymachining,interactionbetweenthe
ev
cutting tool and the workpiece leads to the generation of an
:
Asmaterialremovalmechanismisgenerallyaccompanied interestingheat.Heatflowcreatedbymaterialsfriction(q )is
f
by a heat generation because of the interesting levels of in- describedbythefollowingrelation(Eq.10).Allthisenergyis
volvedfriction(Eq.10)andmechanicalplasticdeformationof assumedtobeconvertedintoheatandequallyabsorbedbythe
thesolicitedmaterial(Eq.8),thisgeneratedheatisaccompa- materialsincontact.Heatconductionfluxisneglectedinthis
niedbyanimportanttemperatureraisewithintheworkpiece investigation because the lack of experimental value corre-
andthecuttingtool.Fractionofenergyproducedinthecaseof spondingtothetestedmaterialscoupleandcuttingconditions
difficult-to-cutmaterialbyitsplasticworkη isusuallyranged in[27].
p
from 0.85 to 0.95 according to Shet and Deng [44] and is : : :
q ¼η (cid:2)τ (cid:2)V and q ¼ f q ð10Þ
assumedtobeequalto0.9inthecurrentwork. f f f s →Tool f f
: : whereη,τ,V,andf arerespectivelyfractionoftheenergy
q ¼η σ:ε ð8Þ f f s f
p p p generated by friction work and converted into heat, friction
IntJAdvManufTechnol
stress,materialslidingvelocity,andfractionoftheheattrans- reduced with whatever the cutting speed value. This result
:
mitted to the cutting tool. q is the heat flux created by emphasis that R depends not only on the cutting tool rake
→Tool c
materialfrictionandgonetothecuttingtool. angle as concluded by Atlati et al. [48], or on mesh density
andFEformulationdefinitionlikestatedin[49],butalsoon
materialbehaviordescription.AcombinationofFigs.2and3
3Numericalresultsanddiscussions confirmsthatflowstressdefinitionaffectsthechipmorphol-
ogywhichbecomesmoresaw-toothedasreachedlevelsofthe
3.1Chipmorphologyandcuttingforcesdependency flowstressesarehigher.Ontheotherhand,alowchipserra-
totheJCplasticparametersdefinition tionhasbeenobtainedwithJC-dandJC-esetswhichisdueto
thereductioninthehardeningmodulusvalueasdemonstrated
As already demonstrated in previous investigation [27], ma- in the next section. However, with a cutting speed equal to
chining process of the biphasic Ti6Al4V titanium alloy is 180m/min,numericalchiphasexhibitedlessdistinctioninits
generally resulting on a segmented chip formation, even at formed saw-teeth for different JC sets as shown in Fig. 4.
relativelylowcuttingspeeds.Meanwhile,itisofhighimpor- Almost no change has been noted in the chip segmentation
tancethatthenumericalmodelaccuratelyreproducesthisspe- frequencyaswellasintheshearbandspacingforthisV .This
c
cificchipmorphologyduetothefactthatitgreatlyaffectsthe resultcanbeattributedtothedominanteffectofcuttingcon-
wholecuttingprocess.However,toachieveabestagreement ditions on chip serration in regard to plastic parameters
betweennumericalandexperimentalresults,anadequatedef- definition.
inition of thermo-elasto-visco-plastic behavior of the ma- Figure5showsawellcorrelationbetweentheonsetofthe
chined material is required. Due to the availability of many ASB and its total formation, in one hand, and the cutting
JC plastic parameters corresponding all to the same tested forcesminimumandmaximum,ontheotherhand.Ithasbeen
material(asreportedinTable1),apreliminarystudyfocusing highlightedthattheonsetofanewASBisaccompaniedbya
on determining the most suitable parameters set well repro- pronounced load applied to the cutting tool. However, this
ducingthemachinedmaterialbehaviorisdone.Inthissection, latter is subjected to less pronounced forces when the ma-
only JC parameters sets with a value of A approximately chined material partially slides away from the upper surface
(±25 %) equal to the initial yield stress of the studied of the workpiece within the totally formed shear band and
Ti6Al4V alloy determined in ambient temperature leadsconsequentlytoafewmaterialsincontactwiththecut-
(A=±25%σ )arecompared.Themostsuitablesetabletogive ting tool. This means that every cutting forces drop corre-
y
a bestagreement with the experimentallisted[27] iskeptin spondstoacompletelyformedASBandviceversa.Another
thenextparts. resultrelatedtoplasticmodeldefinitionhasbeennotedwhere
Itisworthnotingthatforthesamestrainrate,flowstress forthesamecuttingconditions,averageshearbandsspacing
curvedescribedasafunctionofthestrainandthetemperature correspondingtothedistancebetweentwoconsecutiveASBs,
exhibits a clear distinction in its evolution where reached isweaklyvariedfromoneJCsettoanother,exceptwithJC-d
levels strongly differ from one JC plastic parameters set to set.Withtheapplicationofthislatter,onemoresaw-toothhas
another (see Fig. 2). In fact, the effect of this diversity on been formed for the same machined materiallength and has
machiningprocessintermsofmaterialseparationmechanism, contributedtoadropintheaverageL value,sotoanincrease
s
chipmorphology,andcuttingforcesobtainedunderthesame in the chip serration frequency (see Fig. 6). Even with the
cuttingconditionsneedstobeclarified. same simulation, a slight modification in L value has been
s
A first correlation between numerical chip serration char- pointedout.Itispresentedbythedelay(oranacceleration)in
acteristicsandcuttingforceslevelshasbeenestablishedinthe tangentialforcesdropandconsequentlyinanewASBforma-
current section. The effect of JC coefficients definition on tionasstatedbyFig.5.
thesetwoparametershasbeenexaminedduetothefactthat Furthermore,itispossibletolinkbetweenaveragecutting
they greatly carried the aptitude of the FE model in well re- forces disagreement and chip morphology mismatch. For a
producing the cutting process phenomena. When comparing cutting speed equal to 75 m/min, a well saw-toothed chip
predicted chip morphology resulted from the definition of comparedtotheexperimentaloneisaccompaniedbyanegli-
different JC plastic sets and obtained under moderate even giblemismatchintangentialforcesprediction(seeFigs.3(b,
high cutting speeds, a serrated chip with obvious difference c,andf)and7).Infact,therightdefinitionofJCconstitutive
initscurvatureradius(R ),shearbandsspacing(L),andseg- coefficients leads not only to a high accuracy in numerical
c s
mentation frequency (f =V /L) has been simulated. The chip morphology but also to a well correlation in term of
seg c s
choicetoquantifychipserrationthroughthecheckofitschar- tangential forces F prediction. Moreover, it isdemonstrated
c
acteristics is justified by the fact that they give a clear idea thatsimulatedcuttingforcesfollowthesametrendoftheshear
about its morphology. Figures 3 and 4 highlight that a more bands spacing where a decrease in L is accompanied by a
s
curvedchipisformedwhenJChardeningmodulusBhasbeen reduction in the average simulated F (as highlighted in
c
IntJAdvManufTechnol
JC-a JC-b JC-c
JC-d JC-e JC-f
Fig.2 FlowstressevolutionwiththetemperatureandthestrainratecorrespondingtodifferentplasticJCsets(έ=104s−1)
Figs.6and7a).However,anunderestimationinfeedforcesF especiallyathighcuttingspeeds.Thisdisagreementisrelated
f
hasbeenobtainedespeciallywhenthecuttingspeedisraised tothedeletionofdamagedelementsmeshlocatedjustaround
from 75 to 180 m/min. In this regard, we can cite that an thecuttingtooledgeandsubjectedtoextremelyhighloading
increase in V has contributed to a negligible rise just of conditions.ThismethodisassociatedtoLagrangianformula-
c
20 N in simulated F contrarily to the experimental results tion assumption initially made which requires the use of a
f
[27] where a difference nearly about 120 N has been noted. specific failure model and the predefinition of an adequate
Moreover,withwhatevermoderateorhighcuttingspeed,F is criticaldamagevalue.However,withrealcuttingtests,crack
f
generally in bad agreement with the experimental one takes place in the machined material and results on micro-
Ls
JC-a JC-b JC-c
JC-d JC-e JC-f
Fig.3 ChipmorphologyandstrainevolutiondependencytoJCplasticparameters(V =75m/min,a =3mm,andf=0.1mm/rev)
c p