Simulation of shot peening: From process parameters to residual stress fields in a structure

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Simulation of shot peening: From process parameters to residual stress fields in a structure

Donato Gallitelli, Vincent Boyer, Maxime Gelineau, Yann Colaitis, Emmanuelle Rouhaud, Delphine Retraint, Régis Kubler, Marc Desvignes,

Laurent Barralier

To cite this version:

Donato Gallitelli, Vincent Boyer, Maxime Gelineau, Yann Colaitis, Emmanuelle Rouhaud, et al.. Sim-

ulation of shot peening: From process parameters to residual stress fields in a structure. Comptes Ren-

dus Mécanique, Elsevier, 2016, 344 (4-5), pp.355-374. �10.1016/j.crme.2016.02.006�. �hal-01326264�

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Computational simulation of manufacturing processes

Simulation of shot peening: From process parameters to residual stress ﬁelds in a structure

Donato Gallitelli^a, Vincent Boyer^b, Maxime Gelineau^b,Yann Colaitis^a,

Emmanuelle Rouhaud^a^,^∗, Delphine Retraint^a, Régis Kubler^c, Marc Desvignes^c, Laurent Barrallier^c

aUniversitédetechnologiedeTroyes,ICDLASMIS,Troyes,France bIRTM2P,Metz,France

cENSAMParisTech,MSMP,Aix-en-Provence,France

a b s t r a c t

Keywords:

Shotpeening Model Residualstress Shotdynamics

Manufacturing industries perform mechanical surface treatments like shot peening at the endofthe manufacturing chaintoprotect important workingparts. Thistreatment modiﬁesthenearsurfaceofthetreatedpartwiththeintroductionofcompressiveresidual stressesduetotherepeatedimpactsoftheshot.Then,thetreatedpartexhibits,notonly alongerlife,butalsoabetterfrettingbehavior,animprovedresistancetocorrosion. . . The objectiveofthepresentpaperisﬁrsttostudytherelationbetweentheprocessparameters and the materialstate(residualstress and plastic variables. . . ) foracomplex geometry.

Next, anumerical tool is proposed,able to predict thismaterialstate ina timeframe thatisconsistentwithindustrialconstraints.Theoriginalityoftheproposedapproachthus consists in the chaining of the different steps. The first step is to choose the process parameters for the shot peening process considering conventional or ultrasonic shot peeningandmodeltheshotdynamicsforacomplexgeometry.Oncetheimpactvelocity fieldisknown,theobjectiveistocomputethelocalincompatibleplasticdeformationfield dueto the repeatedimpacts using analyticalmethods. Then, afinite elementmodel is used tocomputetheresidualand deformationfieldsinthe consideredmechanical part.

Thecompletemethodhasbeenperformedonthemodelofagear,amechanicalpartthat ismostoftenshotpeenedandexhibitsacomplexgeometry.

ThisisanopenaccessarticleundertheCCBY-NC-NDlicense (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction

Mostmanufacturingindustriesroutinelyperformmechanicalsurfacetreatments attheendofthemanufacturingchain to protectimportantworkingparts. Shotpeeningis probablythemostcommonoftheseprocesses.The pioneeringwork ofAlmen[1]hasindeeddemonstratedtheeﬃciencyofshotpeeningprocessestoincreasefatiguelife,andthis,foravery moderate cost. The treatedpart isin this casesubmitted to the impacts of many hard particles madeof glass, ceramic or metal, known as the shot. The motion of the shot is produced with the help of turbines or compressed air in the

* Correspondingauthor.

E-mailaddress:rouhaud@utt.fr(E. Rouhaud).

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Fig. 1.Principleofthemethodwiththechainingofdifferentstepsfromtheprocessparameterstotheresidualstressﬁeldinacomplexgeometrytaking intoaccountaninitialstatecomingfrompreviousmanufacturingprocesses.

case ofconventional shotpeening orthe vibrationsof a sonotrodein thecase ofultrasonicshotpeening. Thisfamily of manufacturingprocessesmodiﬁesthenearsurfaceofthetreatedpartwiththeintroductionofcompressiveresidualstresses andthe modiﬁcationofthestructureofthe materialduetotherepeatedimpacts. Withanappropriate choice ofprocess parameters,thetreatedpartcanexhibit,notonlyalongerlife,butalsoabetterfrettingbehavior,animprovedresistanceto corrosion. . .

Many parts in the aeronautical and automobileindustries are shot peened. In most cases, the treatment is used to improve safetycoeﬃcients, but isnot accountedforin design analyses. Forthe process to be takeninto account atthe design stage, the exact consequences of the parameters on the treatedpart have to be better mastered. This is further necessaryforaccreditationpurposesinmanyindustries.Thehopeisthentobeabletoreducetheweightofthemechanical parts,ofcrucialimportancenowadaysintransportindustries.Arenewedinterestforpre-stressingprocesseshasthusbeen observedrecently.Oneoftheobjectivesoftherelatedmodelingactivityistoproducemodelsthatare eﬃcientenough to enter designtools.It isthusimportantto understandthedetails ofthe physicsatplay. Then, themodelsshould capture the essential phenomenaat handintheprocess anddirectlycorrelate processparameters withthe consequenceson the product.Furthermore,thetimethatisnecessarytoreachasolutionhastobeconsistentwithindustrialconstraints.Finally, indevelopingthemodels,one shouldkeepinmindthefactthattheresultsoftheshotpeeningmodelsaretobeusedas initialconditionsforresistanceorfatiguemodelsandhavetosupplytheappropriatedata.

Proposedshotpeeningmodelsarenumerousintheliteratureandreviewedin[2–5].Mostofthesemodelsconcentrate on thepredictionofresidual stressandplasticdeformation fieldsandusetheimpact velocityasan initialcondition and nottheprocessparametersthemselves.Moreover,thegeometryofthetreatedpartismostoftenreducedtoasemi-infinite massif ortosufficientlythickplates.Nevertheless,itisclearlythat thegeometryofthepartinfluencesthetreatmentdue to,forexample,variationsinthecoverageoftheimpactsortheinfluenceofboundariesonthemechanicalfields.

The objectiveofthepresentpaperistoproposemethodologiesabletoproducearelationbetweentheprocessparam- eters andthestateofthetreatedpart(stressﬁeld,hardening. . . ) consideringacomplexgeometryandincludinganinitial state comingfrom previous manufacturing processes, this, in a time frame that is consistent withindustrial constraints.

Second-order phenomena will thus be neglected to simplify the model and analytical models preferredwhen possible.

The existingmethodologiesproposed intheliterature andsuitedtothisspecific objectivearereviewedinthiswork. The originality ofthe proposed approach isthus to chaindifferentsteps, asdetailedin Fig. 1,to relate the final state ofthe mechanicalpartaftershotpeening totheprocessparameters andthisfora partwithcomplexgeometry.Thefirststepis tochoosetheparametersconsideringconventionalorultrasonicshotpeeningandmodeltheshotdynamicsforacomplex geometry.Oncethevelocityfieldoftheimpactsisknownonthepart,theobjectiveistocomputetheincompatibleplastic deformation field dueto therepeated impacts usingnumerical oranalytical methods. Incompatibledeformationsdue to other previousmanufacturingprocessesmayalsobetakenintoaccount.Then,afiniteelementmodelisusedtointroduce the residualstress anddeformation fieldsin amodelof themechanicalpart.The complete methodisapplied tothe ultrasonic shotpeeningof agear,a mechanicalpartthat exhibitsacomplex geometry.Realistic(in other wordsindustrial) conditionshavebeenchosenfortheprocessparameterstocreateademonstratorforthismethodology.

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2. Mechanicalstateaftershotpeening

Wewish ﬁrstto concentrateonthe mechanicalstateafter shotpeeningwitha reviewofthe physicalconstraintsand thetechnologicaldataavailableintheliterature.Thisanalysisenablestoselectthepreponderantphenomenatobeselected andmodeledinthenextstage.Inthissection,wethusproposetoreviewseveralhypothesesthatcanbemadeinthecase ofshotpeeningtreatmentstakingthehistoryofthepartintoaccount.

2.1. Mechanicalproblem

Aresidualstressfieldisastressfieldthatexistsinsideapartwhennoexternalloadisappliedtothesystem.Theelastic strainsarethesourcesofresidualstressesinthepart.Itisheresupposed thatthematerialisisotropicandhomogeneous andthereisnoplasticityinducedbyphasetransformationsatconstanttemperature.Theresidualstresstensor σ inashot peenedpartofvolume V andsurface S ofnormalnverifies:

⎧⎪

⎨

⎪⎩

div(σ)=⁰ ôn^V σn=⁰ ôn^S σ=Ê

ε−ε^p

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assuming thatthe elasticbehaviorofthe materialisrepresentedby thetensormodulus E representingHooke’slaw;the total strain ε hasbeenadditively decomposedbetweenan incompatible strain ε^p andan elasticstrain ε^e (ε=ε^e+ε^p) within a small strain framework. Residual stresses are dueto strain heterogeneities introduced at anyscale (macro- or microscopicscale).Themainoriginofresidualstressesduring mechanicaltreatments (shotpeening,rolling)istheincom- patibilityof plasticstrains[6].Inthe caseof nitriding,residualstresses aredueto volumestrainsincompatibility caused bythe diffusion/precipitationphenomena:insertion ofnitrogenandcarbonintheferritic matrixaswell astheformation ofnitridesandcarbides[7–9].Inthecaseofcarburizingorcarbonitriding,thediffusionandplasticstrainsincompatibility duetothedifferentialexpansionandthenon-simultaneousnessofphasetransformationsduringthemartensiticquenching activelycontributetothegenerationofresidualstresses[10].

Thepossibleevolutionofresidualstressesaftermechanicalloadingisduetoare-plasticizationofthematerial.Aslongas thestructureremainsintheelasticdomain,neithertheincompatiblestrainsnortheexistingresidualstressstatearemod- iﬁed. Asa whole,residualstressesare duetoincompatibilitiesinthe deformationﬁeld. Theseincompatibledeformations arealsoreferredtoas“stress-freestrains”or“eigenstrains”followingtheworkofKorsunsky[11].

2.2. Typicalresidualstressﬁeldaftershotpeening

Itispossibletoevaluateresidualstressesaftershotpeeningusingdifferentexperimentalmethodssuchasincremental holedrillingmethodsorX-raydiffraction[12].Whenthetreatmenthasbeenhomogeneousonaregular surfaceforwhich thelocalradiusofcurvatureislargecomparedtotheradiusoftheshot,thestresstensorcanbeapproximatedtotakethe followinggeneralform[3,13]:

σ→

⎛

⎝σ(z) 0 0 0 σ(z) 0

0 0 0

⎞

⎠ ₍₂₎

This tensor is expressed in the local coordinate system deﬁnedwith the normal to the surface as presented in Fig. 2.

A typicalresidual stressproﬁle σ(z)asit canbe measured inshotpeened parts ispresented inFig. 2. Thevalue ofthe maximalcompressivestress σCOMP isusuallyobservedtobebelowtheyieldstress σyofthematerial,butcanreachhigher valuesinthecaseofintensiveshotpeeningtreatments;inmostcases,onehas0.8σy<σCOMP<1.2σy.Thedepthaffected bythetreatment, zAFF,correspondingtothedepthforwhichcompressivestressesare observed,isusually oftheorderof 100 μmandismostoftenbelow1 mm.

2.3. Relationbetweenresidualstressesandstressfreestrainsforsemi-inﬁnitebodies

Fora semi-inﬁnite body,itis possibleto establishan analytical relationship betweenresidual stressesandstress-free strainskeepingthesamehypothesesasinSection3.2.Inthiscase,thetotalstraintensortakesthegeneralform:

ε_→

⎛

⎝^{0 0}0 0 ⁰0 0 0 εzz(z)

⎞

⎠

ThisisestablishedwiththehypothesesmadefortheresidualstressesinSection3.2,addedtothefactthat,inasemi-inﬁnite body,thereisnopossiblein-planedisplacements.Thestress-freestraintensorthentakestheform:

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Fig. 2.Typical residual stress proﬁle induced by shot peening.

ε^p→

⎛

⎝ε^p(z) 0 0 0 ε^p(z) 0 0 0 −²ε^p(z)

⎞

⎠

assumingherethattheplasticdeformations,andthusthestress-freestrainsareisochoric.Theelasticstrainsarethesources ofresidualstressesinthepart.UsingHooke’slaw(EisYoung’smodulusand νPoisson’sratio),andthefactthat ε^e+ε^p₌0, itcomes:

ε^p(z)=^v−1

E σ(z) (3)

Theanalysisaboveisuseful, becausethehypothesesofasemi-infinitebodycanbemadeformostshotpeened partsona localbasis. Indeed,inmostcases,thetreatmentishomogeneous,thetreatedsurface isregularandthedepthaffectedby the treatmentissmallcomparedtothedimensionsofthepart.Thiscanbe verifiedbyan experimentalevaluationofthe residualstressfield.Eq.(3),firstproposedbyZarka[14],isthenusefulinordertoestimatethestress-freestrainwhenthe residualstressprofilesareexperimentallydetermined.

3. Fromprocessparameterstoimpactvelocityﬁeld 3.1. Descriptionofthemodel

Oncetheshotpeeningparameters aresetusingdesignandtechnological constraints,theﬁrststepistodeterminethe coverage and velocity of the impacts. It becomes important to predict the coverage in the caseof complex geometries because the coverage may vary andthis mayeventually affect fatigue life [15].The simulation of the shotdynamics as a function of theprocess parameters offers an answerto thisproblem. Three main methods havebeen proposed inthe literature toreach thisgoal: theuseofdiscreteelements software[16–20],theuseofﬂuidsimulation software[21],and the constructionof adedicatedsoftware [22–25].Inthecaseofshotdynamics,usingan existing pieceofsoftware saves a lotofdevelopment time, butenablesto reach,indeed,realistic solutions,withvery longcomputation time. Thisisnot compatiblewithindustrialneeds.Further,itisthusnotpossibletoconsidertheshotdynamicsaroundcomplexgeometries, whichisouroriginalpurpose.Therefore,weproposetoconsideradedicatedsoftware.

Thesoftwareproposedtomodelshotdynamicsisabletoconsiderindustrialcomplex3Dgeometrieswiththepossibility touseaCADsoftwaretoconstructthegeometryofthepartandprocessenvironment[23–25].Themotionofthepartand avisualizationoftheshotmotionaroundthepartispossible(seeFig. 3).Themodelisbasedonmodelsthathavebeenini- tiallycreatedforgranulargases[22].Themodelpredictsthecompletetrajectoryofeachindividualsphereandinparticular thedatarelatedtotheimpactsonthetreatedpart.Allcollisionsaredetected,includingthecollisionsbetweenspheresand withthesurroundingenvironment.Normalandtangentialrestitutioncoefficients,specifictoeachpairofcollidingmaterials, enable ustotake the behaviorof thematerials into account.It hasbeendeveloped forultrasonicandconventional shot peening.Forconventionalshotpeening,Fig. 3presentstheshotflowanditslocalimpactsonthepart(locatedonthetop ofthefigure,butnotrepresented).Afictionalboxhasbeencreatedaroundtheimpacted surface;outsideofthisbox,the shotisrecycled.Forultrasonicshotpeening,Fig. 3presentstheshotaroundagear.Thesonotrodeisrepresentedingreen atthebottomofthestructure.Theoutsidemeshrepresentstheexternalwalloftheultrasonicchamber.

Forbothcases,itisthen possibletopredictandtovalidatethe coverageandthelocationandimpactvelocityofeach collision isknown. Statistical studies may be performedto optimize the design ofthe process. The results are obtained in a reasonable time frame: forsimple geometries, thecomputation isfaster than the actual process itself.For complex geometries andalargeamountofshot,whentheactualprocesscorresponds toseveralminutes,thecomputationcanlast forafewhoursonatypicallaptopcomputerandforverycomplexgeometrieslikeanentireturbine.

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Fig. 3.Typical visuals obtained with the models for shot dynamics of conventional shot peening (left) and ultrasonic shot peening (right).

Fig. 4.Maximum impact speeds on a spur gear estimated by the shot dynamics model.

3.2. Casestudyandresults

Tovalidate theapproach,wepropose acasestudyandconsidertheultrasonicshotpeeningofan aluminum(Al7075 T7051)spurgearpresentedinFig. 3andapply thedifferentmodelstoobtaintheresidualstressﬁeldinthegearfromthe processparameters.

Thefollowingprocessparametershavebeenchosen:

• ^rotationôf^the^gear^withâ^speedôf^{10 rpm,}

• ^shot:^100Cr6^steel^beads^(number^of^shots:^73;^radius^R=¹.5mm,density ρshot=⁷⁸⁰⁰^kg/m³).

• ^Sonotrode:^titanium(amplitude:50 μm;frequency:20 kHz).

• ^Duration^of^the^treatment:^{150 s.}

The parameterofthe materialofthe gearare: Youngmodulus E=⁷⁰,000MPa, densityρmat=²⁷⁰⁰^kg/m³, yieldstress

σy=²⁶⁰^MPa,^and^Poisson^coeﬃcient ν=⁰.3.

Thecomputationoftheshotdynamicstakesafewminutesonapersonallaptopcomputer.Formthesaveddatafile,the localmaximalnormalimpactspeedhasbeenextractedandispresentedinFig. 4.Asafirstapproximation,itisconsidered that the maximal normal impact speed is mostinfluent in terms ofresidual stress because these typesof impacts lead tothemostimportantlocalhardeningandplasticdeformation.Ontheexternalsurfaces,theimpactvelocity fieldisquite homogeneousandcanbe consideredconstantwithavalue loseto V=¹⁰^m/s.Onthesidesofthegear,forthesurfaces that are always perpendicular tothe sonotrode, themaximal normalimpact speed issmaller andis consideredequal to zerointhepresentstudy.

4. Simulationofshotpeeningforsimplegeometries

Modelsofshotpeeningarenumerousintheliterature.Theyareofthreetypes:numerical,semi-analytical,andanalytical.

As far asnumerical models ofshot peening are concerned, thepower of computersnow enables usto reach a realistic solution in an acceptable amount of CPU time (several hours to a few days). Numerical models use ﬁnite elements to predictthestateofasemi-inﬁnitebodyaftershotpeening.Manymodelshavebeenrecentlyproposedconsideringarealistic numberof impacts[26–29].Variousphenomena have beenstudied,like, forexample,the microstructureof thematerial