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See discussions, stats, and author profiles for this publication at: http://www.researchgate.net/publication/257713132Modeling the Effect of Carburization andQuenching on the Development of ResidualStresses and Bending Fatigue Resistance ofSteel GearsARTICLEinJOURNAL OF MATERIALS ENGINEERING AND PERFORMANCE MARCH 2013Impact Factor: 0.98 DOI: 10.1007/s11665-012-0306-0CITATION1DOWNLOADS32VIEWS3044 AUTHORS, INCLUDING:Zhichao LiDANTE Solutions, Inc.24 PUBLICATIONS 36 CITATIONS SEE PROFILEAndrew M. FreborgDANTE Solutions25 PUBLICATIONS 151 CITATIONS SEE PROFILET. S. SrivatsanUniversity of Akron385 PUBLICATIONS 2,520 CITATIONS SEE PROFILEAvailable from: Zhichao LiRetrieved on: 14 August 2015ModelingtheEffectofCarburizationandQuenchingontheDevelopmentofResidualStressesandBendingFatigueResistanceofSteelGearsZhichaoLi,AndrewM.Freborg,BruceD.Hansen,andT.S.Srivatsan(SubmittedJanuary7,2011;inrevisedformFebruary10,2012;publishedonlineJuly24,2012)Most steel gears are carburized and quenched prior to service to obtain the desired specic strength (r/q)andhardness requirements. Use of carburizationandquenchingof steel gears creates acompressiveresidual stress on the carburized surface, which is benecial for improving both bending and contact fatigueperformance. Also, higher carbon content in the carburized surface decreases the starting temperature forformation of the martensitic phase and delaying the martensitic transformation at the part surface duringthequenchinghardeningprocess. Duringthemartensitephaseformation, thematerial volumeexpands.Thedelayedmartensitictransformation, coupledwiththeassociateddelayedvolumeexpansion, inducesresidual compressive stress on the surface of the quenched part. The carburized case depth and distributionof carbonaffect boththemagnitudeandthedepthof theresultingresidual compressivestress. Inthisarticle, the effect of carbon distribution on the residual stress in a spur gear is presented and discussed usingniteelement modelingtounderstandtheintrinsicmaterial mechanics contributingtothepresenceofinternal stress. Inuence of the joint on thermal gradient and the inuence of phase transformation on thedevelopmentofinternal stressesarediscussedusingresultsobtainedfrommodeling. Theresidual stressarisingduetoheattreatmentisimportedintosingle-toothbendinganddynamiccontact stressanalysismodelstoinvestigatetheintrinsicinterplayamongcarboncasedepth, residualstress,bendingload, andtorsional loadonpotential fatigue life. Three carburizationprocesses, followedbyoil quenching, areexamined. A method for designing minimum case depth so as to achieve benecial residual stresses in gearssubjectedtobendingandcontactstressesissuggested.Keywords bending fatigue, carbon distribution, carburization,nite element modeling, gear, life, quenching, residualstress,steel1. IntroductionPartsmadefromlowcarbonsteel areoftencarburizedtoincreaseboththehardnessandstrengthof thesurface, whilemaintaining the core ina toughandductile condition. Thecarburization and quenching processes not only aids inenhancingbothsurfacehardness andstrengthbut alsotendsto introduce compressive residual stress in the carburized layer.This aid in increasing the fatigue life by counteracting thebending and contact stresses that are introduced during loading.Thedepthandmagnitudeofcompressiveresidualstressesarereadily inuenced by both part geometry and depth of thecarburizedcase. Agreater depthof theresidual compressivestress alonedoes not necessarilyequatetoimprovedfatigueresistance. This is because fatigue crack initiation is primarily asurface phenomenon, and high-cycle fatigue (HCF) life isprimarilycontrolledbycrackinitiation(Ref1).Withsustainedandnoticeableimprovements incomputerhardware and modeling technology, nite element analysis(FEA) is being increasingly used in the manufacturing industry.Inmorerecent years, engineeringanalysissoftwarefor heat-treatmentmodelinghavebeendevelopedandeffectivelyusedtopredict residual stresses andrelateddistortion(Ref 2, 3).Through numerical analysis, the response of a part to:(i)thermalstress, (ii)phasetransformation, and(iii)geometrycan be easily understood (Ref 4-7). The knowledge gained fromcalibrated modeling can be put to effective use towardimprovingbothpartdesignandtheheat-treatmentprocess.A deep carbon case tends to reduce the magnitude of residualcompressive stress on the surface resulting from quenchhardening. The reason for this will be explained in this article.Duringactiveservice, thecontact betweenthedriverandthedriven gears creates stresses that penetrate into the part surface.The magnitude and the depth of these contact stresses are key tounderstandingcontactfatigueperformance. Forservicecondi-tions, which create deeper contact stresses, a deeper carburizedcase is both essential and required. The heat-treatment process isthe primary means by which benecial compressive stresses areintroduced. Currently, there is limited information in thepublished literature quantifying the synergistic and/or mutuallyinteractive inuences of these effects.Dr.T.S.SrivatsanisaMemberofEditorialBoardofJMEP.Zhichao Li and AndrewM. Freborg, Deformation Control Technology,Inc., 7261 Engle Road, Suite 105, Cleveland, OH44130; BruceD. Hansen, Sikorsky Aircraft Corporation, 6900 Main Street, Stratford,CT06615; andT.S. Srivatsan, Divisionof Materials Science andEngineering, Department of Mechanical Engineering, The University ofAkron, Akron, OH 44325. Contact e-mails: zli@ DeformationControl.com, [email protected], [email protected], and [email protected](2013)22:664672 ASMInternationalDOI:10.1007/s11665-012-0306-0 1059-9495/$19.00664Volume22(3)March2013 JournalofMaterialsEngineeringandPerformanceIn this article, nite element models are developed to studyresidual stresses arising from three vacuum carburizationschedules, followed by a standard oil quench hardeningprocess. The objective of this study is to demonstrate thecompoundingandcontrollableeffectsofresidualstressdevel-oped during processing on the effective stress experiencedunderserviceloads. Todemonstratethisconcept, theresidualstresses predicted from the oil quench models are imported intosingle-toothbendingandcontact stress analysis models of aspurgearunderload.Theeffectof(a)carburization,(b)heat-treatment residual stresses, (c) bending stresses, and (d) relatedcontact stresses are then examined and appropriately discussed.Conclusionsarethendrawnconcerning(i) theinteractionofcarburization,quenching, and gear geometryon residualstressstate and (ii) their benet in response to service stressesintroducedduringsubsequentpartloading.2. TheFiniteElementModelThe geometry of the spur gear chosen for use in this study isshown in Fig.1. The tip diameter of the gear is 95mm, the innerdiameter is 30mm, and the gear face width is 6.35mm. The hubthickness is 19.05mm. The gear has a total of 28 teeth. The gearsteel chosenfor this studywas AMS6308(Pyrowear53),havinga chemicalcomposition (wt.%): 0.10C, 0.35Mn, 1.00Si, 1.00 Cr, 2.00 Ni, 3.25 Mo, 2.00 Cu, and 0.10 V.The single-tooth nite element model developed for the gearis also shown in Fig.1. Using boundary conditions with cyclicsymmetry, the single-tooth model can represent the whole gearwith an assumption that all teeth experience the sameconditions circumferentially during heat treatment. The sin-gle-toothniteelement model has 26,256nodes and22,854hexahedral linear elements. Fineelements were usedonthegeartoothsurfacewiththeprimarypurposeofidentifying:(i)thecarbongradient and(ii) thethermal gradient duringheattreatment.3. EffectofVacuumCarburizingCaseDepthVacuumcarburization is being increasingly used in heattreatment due to the benets of reduced furnace time andsuperior as-carburized product quality. The effect of threecarburizedcasedepthsonresidual stresswasexaminedusingthemodels:0.5,1.0,and1.5mm.Forthisstudy,casedepthwasdenedasthedistancefromthe outer surface to a depth having a carbon content of0.4wt.%. The expected carbon content on the surface is0.8wt.%. DANTE-VCARBsoftwarewasusedtodesigntheboost and diffuse schedule for the vacuumcarburizationprocess to meet requirements for: (i) 0.8wt.%carbon and(ii) thethreedenedcasedepths. Acetylenewasusedasthecarburizing gas, with only the tooth surface being carburized tobeconsistent withstandardaerospacegearpractice. All othersurfaces, toincludethegear tip, wereconsideredmaskedtocarbon diffusion, which is typically accomplished throughcopper-platingduringthephysical processingof theseparts.This is done to avoid the potential for localized areas at the tipof theteethandanyother sectionsizechangesfromhavingexcessive carbon concentrations that could result in theformation and the presence of deleterious carbides both onthesurfaceandtheinterior.Thefurnaceprocessingtimesfor thethreevacuumcarbu-rizationschedulesareshowninTable1. Itistobenotedthatindividual boost times, aswell asoverall furnaceprocessingtimes, increasewithcasedepth. Thisisprimarilybecausethecarbon gradient drops signicantly as diffusion from the surfaceoccurs. To minimize the total carburization time, additionalboostcycleswereusedtofacilitatecontinuousdiffusions.Figure2 shows the predicted carbon distribution for aneffectivecasedepthof1.5mmsubsequent tovacuumcarbu-rization. The carbon content at the root surface is about0.68%, which is lower than the 0.8% carbon at the tooth anksurface. This is an important illustration of how geometry doesaffect the local carburizationresponse, whichwill subse-quentlyinuencethelocal quenchhardeningandresidualstress response. A cross section through the middle thickness ofthegearisshowninFig.3.Twodirections,shownasstraightlinesinthecutsection, canbeusedtoexaminethefollowingeffects:(i) Acomparisonofcarbondistributionforthethreecarbu-rizationschedules.(ii) The temperature, phase, and stress evolutions duringquenching.Fig.1 Gear geometry and nite element mesh of single toothmodelTable1 Comparisonoffurnacetimesofthree vacuumcarburizationschedulesCasedepth 0.5mm 1.0mm 1.5mmBoosttime,s 848.0 1668.0 2460.0Diffusetime,s 3608.0 17256.0 40930.0Furnacetime,s 4456.0 18924.0 43390.0Rvalue 4.25 10.35 16.64JournalofMaterialsEngineeringandPerformance Volume22(3)March2013665The inuenceof geometryoncarbondistributioncanbenoticeablysignicant. Withanincreaseincarburizationtimeanddepthof thecarboncase, theeffect and/or inuenceofgeometryalsoincreases. The gear toothankhas aconvexshape,whichis closeto beingat. However, theroot areahassignicant geometric curvature, resulting in localized radialdilution of the diffusing carbon. The difference in carboncontent betweentheat ankandcurvedroot increaseswithcase depth. This is shown in Fig.4. For the three different casedepths examined in this article, the differences in localcarboncontentbetweentheankandthe rootare0.06%foracarburizedcaseof 0.05mm, 0.10%for acarburizedcaseof0.10mm, and 0.13%for a carburized case of 0.15mm.Therefore, theinuenceoflocalgeartoothgeometrymustbe considered during the vacuum carburization process so as tobe able to both guarantee sufcient carbon content on thesurface, while concurrently ensuring case depth and the carboncontent neededtopromoterequiredmartensiteformationandconsequent residual stressformation. Furthermore, useof theone-dimensional analytical modeling approach provides aviable basis for the rst stepindesigningthe carburizationprocess.4. ModelingtheQuenchingProcessUponcarburization, thegearis(a)quenchhardenedinoil,(b) cryogenicallytreatedtominimizetheamount of retainedaustenite, and then (c) double tempered. Finite element processmodelsfor thethreecarburizationscenariosexaminedprevi-ously were extended to include the quench hardening andcryogenictreatmentprescribedforAMS6308.Thiswasdonetofurther assess the residual stress effects arising fromthegeometry-induced, variable carburization response. The DANTEnite element software was used for these models. DANTE usesaninternalstatevariable(ISV)materialmodel,linkingtemper-atureandtime-dependent phasetransformationkineticswithamaterial mechanics(stress) model describingbothtemperatureand material strain rate dependencies (Ref 8) The softwareprovidesaccuratepredictionsofmicrostructural,residualstress,anddistortionresponse, andisespeciallyuseful inevaluatingprocess sensitivities by facilitating an examination of the in situmaterial response during heat-treatment processing.Theminimumprincipalresidualstressespredictedforeachconditionfollowingcryogenictreatment areshowninFig.5.The carburized tooth surface shows compressive residualstresses, with depth of compressive stress increasing withincreasingcasedepth.Themagnitudeofresidualcompressivestress in the llet area of the root is noticeably higher than thatFig.2 Carbondistributioncontourwithcasedepthof1.5mmFig.3 Cross sectionandtwostraight lines selectedfor modelingresultanalysisFig.4 Carbon distributions in terms of depth and increased geometryeffect with case depth666Volume22(3)March2013 JournalofMaterialsEngineeringandPerformanceinthe ankareaofthe root.This canbe ascribedto bedue tothegeometryeffect.4.1 StressEvolutionDuringQuenchingDilatometryexperimentswereconductedwiththeprimarypurposeofcharacterizingthephasetransformationkineticsofAMS6307 alloy steel for use in process modeling. No diffusivephases(i.e.,ferrite,pearlite,orbainite)wereobservedtoformduringcooling(Ref 8). Theonlysecond-phasemicroconstit-uent present inthemicrostructuresubsequent toquenchingismartensite.The martensite transformation start temperature (Ms)decreases with an increase in carbon content. The MsforAMS 6307 having 0.1wt.% carbon is 437 C; while the Ms ofthesamesteelcarburizedto0.8wt.%carbonis135 C. Withthissurfacecarbongradient, themartensitephasetransforma-tionduringoil quenchingstartsfromunderthesurfaceat thecase-coreinterface, even though the temperature atthe surfaceis signicantly lower than the temperature in the interior. Also,there is a volumetric expansion associated with martensitetransformation. Thedelayedtransformationof thecarburizedcase relative to interior of the gear results in compressiveresidual stresses on the surface, as shown in Fig.5. For adeeper carboncase, theresidual compressivestresseswill bedeeper. It should also be noted that for all the three case depthsexamined, the root llet region reveals a higher residualcompressivestressthantheadjacentankregion.Evolution of residual stress development during oil quench isshowninFig.6forboththegearankandrootlletregions,using the gear carburized to a case depth of 1.0mm as the basis.Stressevolutioninthealloysteel gearduringquenchingisacombinationof thermal, phasetransformation, andgeometryeffects. The process modeled for this study was furnacere-heatingofthecarburizedandcooled gearto900 C,a10stransfer through air to the quench station, and subsequentimmersion and holding in agitated oil.During the early stages of quenching prior to the initiation ofphase transformation, the thermal shrinkage on the surfacecreates a tensile stress on the surface. Upon further cooling, themartensitictransformationstartsimmediatelybelow thecarbu-rizedsurface, atthecase-coreinterface, whenthetemperaturedrops below the local Ms. A compressive stress is thengenerated immediately below the surface by this phasetransformation. To balance the sub-surface compressivestresses, the surface with high carbon content goes into tension.At thispoint, the high carboncontent onthe surfaceis stillaustenitic and has a low yield stress relative to the transformedsubsurfacematerial.Tensilestressesonthesurfacearecondu-civefor plasticdeformation. Uponfurther cooling, thephasetransformationfrontmovestowardthegeartoothsurface.Thehigh carbon content surface nally transforms to martensite, asFig.5 Cutviewofresidualstressdistributionsforthreecarboncases.(a)0.5mm,(b)1.0mm,and(c)1.5mmJournalofMaterialsEngineeringandPerformance Volume22(3)March2013667shown in Fig.6(a), the surface has a compressive residualstress at the end of the oil quench. However, at 0.8wt.%carbon, thesurfaceof theAMS6307gear has amartensitenishtemperature (Mf) lower thanthe oil temperature. Thistypically results in 20-25% retained austenite for the carburizedalloy subsequent to oil quenching. AMS 6307 is thereforetypicallycryogenicallytreatedfollowingquenchingtoreducetheretainedaustenitecontent tobelow3%. Duringcryogenictreatment, the additional martensite formation that occurs on thecarburized surface will tend to further increase the magnitude ofcompressivestressonthesurface.The variation of in-process stress evolution in the gear ankand root llet is shown in Fig.6(a) and (b), respectively.Differencesinstressdistributionarisemainlyfromgeometry.Thegearankhasarelativelyatsurface,anditsresponsetoquenching is quite similar to that experienced by a simplecylinder. Responseofthealloysteel toboththermal gradientandphasetransformationisprimarilyone-dimensional at thislocation. In contrast, the root llet region shows a higherconcentration of stress caused by the local radius. The residualcompressivestressat theroot llet regionisover1000MPa,whichissignicantlyhigherthanthatofthegearank.Both the thermal gradient and the phase transformation alsocontribute to local stress concentration at and around the rootllet regionduringquenching. The temperature of the gearank is noticeably lower than temperature of the gear root andllet regions during the entire quenching process primarilybecauseoflocalsurfaceareatomassdifferences.Thecoolingrateexperiencedbythegear ankismuchhigherduringtheearlystages of quenching. Thecoolingrateat thegear rootgraduallycatchesupandevenexceedsthecoolingrateat thegear ankasthecoolinggraduallyprogresses. Theobservednon-uniform cooling arising from gear geometry contributes tothepresenceoflocal stressconcentrationinthellet.A third factor contributing to the presence of stressconcentration inthe root llet is phase transformation. Themartensiteandstressdistributionsinthegearfollowing3.6sinto the quench process are shown in Fig.7(a) and (b),respectively.Thestresscontourmaprevealsthestressestobetangential to the gear tooth surface. Figure7(a) shows themartensiteformationtoinitiateunderthehighcarbonsurface.The volume expansion occurring at the core of the toothgenerates about 300MPa of compressive stress at this stage, asshown in Fig.7(b). To balance the compressive stress, the gearankrespondswithastressof 200MPaintension. Interest-ingly, the volume expansion of the gear tooth creates a bendingeffect aroundtheregionoftheroot llet, therebyplacingthellet regionundercompression. Thisisthekeyfactor, whichcauses a signicant difference in the residual stress between thegearankandtherootllet,asshownpreviouslyinFig.6(a)and(b),respectively.The response of the material at the gear ank duringquenching is similar to that experienced by a generalizedcylindrical part. Toillustrate this point, Fig.8(a) shows thetangential residual stresses as a function of depth from the anksurface, for all the three examined carburization scenarios. Themodels reveal the depth of residual compressive stress toincrease with depth of the carbon case. However, magnitude oftheresidual compressivestressonthesurfacedecreaseswithdepth of the carbon case. The predicted tangential residualcompressivestressesat thesurfaceof thegear ankfor casedepthsof 0.5, 1.0, and1.5mmare570, 500, and400MPa,respectively. Such a response may not be intuitively obvious tosteel heat-treatingprocessors. The results fromthe DANTEprocess models provide a reasonable explanation for this effectprimarilybecause theyillustrate the evolutionhistorycorre-sponding to the distribution of carbon for each carburizingdepth.Figure8(b) shows the tangential residual stresses plotted interms of depth from the root llet surface. Here, a greater depthof carbonincreasesboththemagnitudeandthedepthof theresidual compressive stresses. However, the residual stressdifference between case depths of 0.5 and 1.0mm is noticeablymore than the residual stress difference between case depths of1.0 and 1.5mm. Also, the carburization furnace time of a1.5mm case depth is 2.3 times more than that of a 1.0mm casedepth,asshowninTable1.Selectionofcasedepthofcarbonshouldbe, therefore, basedonbothcost considerations andserviceloadingconditionsexperiencedbythegear.5. GearLoadingModelsThe ultimate importance of residual stresses lies intheirabilitytoeithermitigateorexacerbatestressesinducedinthepart fromserviceloads. Toevaluatethecompositeeffectsofresidual andloadingstresses onthetest gear, thequenchingstresses predictedfromheat-treatment models wereimportedFig.6 Stress evolution due to thermal gradient and phase trans-formation(a)gearankand(b)rootllet668Volume22(3)March2013 JournalofMaterialsEngineeringandPerformanceinto single-tooth bending and dynamic contact models. Todetermine the specic inuence of residual stress, loadingmodels without heat-treatment residual stress were concurrentlyevaluatedtounderstandthesignicanceoftheheat-treatmentprocessonloadingresponse.5.1 Single-ToothBendingLoadModelAs described, the spur gear used in this study had 28 teeth.The single-tooth bending load model included all 28 teeth,using the single-tooth DANTE heat-treatment model as a basisandusingcyclicsymmetrytobuildthefullgear.Theresidualstresses from the heat-treatment model with the 1.0mmcarburizedcaseweremappedintothe28teethofthebendingmodel. A bending load was then applied to an area close to thetooth tip, as shown in Fig.9(a). The maximum applied force inthe bending fatigue experiment was 11,250 Newtons(2925lbf), with the resulting stress distribution contour forthe loaded and heat-treated gear shown in Fig.9(a). ThestressesplottedinFig.9(a) aretheradial stresses, whichare(a) close to the tangential direction along the regions of both theroot llet andgear ankand(b) close inmagnitude tothemaximumprincipal stressintheseareas. Thetensilestressinthe root llet region is about 980MPa. The opposite root lletis under compressive stress, having a magnitude of about1800MPa. Increasing the bending load causes the higheststress location at the root llet to move away from the root andtowardthetoothtipalongthegearank.Bytakingtheresidual stressesarisingfromthequenchingprocess for the three carbon case depths and applying themaximum bending load, one can safely estimate the stresses inthe root llet. The stresses in the root llet region are plotted asafunctionofdepthfromtheroot llet surfaceandshowninFig.9(b). A bending model was also conducted withoutincluding the heat-treatment residual stresses, and is alsoshowninFig.9(b). The tensile stress onthe surface underFig.7 Cutviewof(a)martensitedistributionand(b)stressdistribution,at3.6sduringquenchusingthe1.0mmeffectivecasedepthstudyFig.8 Predicted residual stresses in terms of depth fromthreecarburizationcasedepthsat(a)rootlletand(b)gearankregionsJournalofMaterialsEngineeringandPerformance Volume22(3)March2013669bending is about 1800MPa, which is close to the yield stress ofhigh carbon tempered martensite. By adding the residualcompressive stress arising due to carburization and quenching,the effective tensile stresses at the root llet drop to 1000MPaundertheinuenceofabendingload. Therefore, theresidualcompressivestresses canhaveanimportant inuenceonthemagnitudeofeffectivestressexperiencedlocallybyagearinservice.Linear elastic material properties were assumed for theloading models, and the yield stress for the gear steel isassumedtobe1800MPawithhardening. Furthermore, it isassumed that single-tooth bending is a geometrically andmateriallylinearproblembelowmaterial yielding. Byaddingtheheat-treatment residual stressesandpurebendingstresses,the combined stress matcheswith the predictedstress distribu-tion, asshowninFig.9(b). Thesecomparisonsclearlyrevealthe residual stress fromheat treatment to be critical to thebendingfatigueperformanceofthegear.The inuence of depthof residual compressive stress onsingle-tooth bending fatigue performance is not conclusive(Ref 9). Thereisasyet noproof that a0.5mmcarboncasewould have an inferior bending fatigue performance whencomparedwiththeothertwocases.5.2 DynamicContactStressAnalysisFinally,contactstressanalyseswereconductedusinggearsthat were initially stress free or gears that contained the residualstress state due to quench hardening. This was done to illustratethe effect of residual stress on contact fatigue performance. Theapplied torquewasadjustedsuchthatthe effect ofbending onthe root llet region matched the maximum single-toothbending load. The torque applied in this model was noticeablyhigherthanthetorquetypicalofserviceconditions.However,this exercisewasdone withthe objective ofunderstandingtheeffectsofheat-treatment processingoncarburizedcasedepth.The same material properties were used in this model as in thecaseofthesingle-toothbendingmodel(s).The contact Mises stresses, without the effects of heat-treatmentresidualstressesisshowninFig.10(a).Thehighestcontact stress occurs immediatelybelowthecontact surface,andplasticdeformationispredictedtooccur. Inthiscase, thegear would be expected to experience a low contact fatigue life,andfail byspalling. However, withtheresidual stressesfromheat treatment, the combined stresses under the contact surfacearereduced,asshowninFig.10(b).MisesstressdistributionsalonglineareplottedinFig.11for several different case depths. The Mises stress requiresdenition of orientation, and in Fig.11 the X-axis represents thedistance from surface point A, where X=0.0. The left Y-axis istheMisesstress, andtheright Y-axisisthecarboncontent inweight fraction. The curve with solid triangle marks representsthe contact stresses without the heat-treatment residual stresses.Plasticdeformationisshownbetweenthedepthsof0.20and0.55mm by the plateau of the curve with stress values of about1800MPa. Ahighstrengthmaterial is requireddeeper than0.5mm, sothat thecarburizedcasecanextenddeeper than0.5mm. TheMises stress onthesurfacedrops from950to625MPa. The highest stress occurs at a depth of 0.4mm,having a stress magnitude of about 1500MPa, which isreducedsignicantlyfromtheconditionwithout consideringtheheat-treatmentresidualstresses.Both the materials strength and the quenching residualstresses in the region of high contact stresses should beconsideredtorealizeimprovedcontactfatiguebehaviorofthegear. As mentioned in a previous section, a deeper carbon casedoes not necessarilyproduceahigher magnitudeof residualcompression. The magnitude of the residual compression at thegearankregionishigherforthe1.0mmcarbondepththanthat of 1.5mm carbon between the ank surfaces to a depth of0.75mm. A carbon case deeper than 1.0mm does notcontribute to contact fatigue behavior. As shown by the shadedareainFig.11, acarburizationcasedepthbetween0.75and1.0mmispreferredforacombinationofbendingfatigueandcontactfatiguebehavior,asalsoreducedcarburizationcost.6. ConclusionsInvestigationof the effects of geometryandheat-treatingprocess variables on residual stress and effective stressFig.9 Single-toothbendingstressdistribution. (a)Contourplot for1.0mmcarbon case depth and (b) stress distribution in terms ofdepth670Volume22(3)March2013 JournalofMaterialsEngineeringandPerformanceencountered in bending and dynamic service loads revealed thefollowing:1. Process simulation of the vacuumcarburizing processwith the DANTE VCARB mass diffusion modelshowed that gear tooth geometry affects local carbondistribution by dispersing carbon more widely in thegear root. Thisreducesthelocal carboncontent, result-inginahigher local martensiteformationtemperature.The change in martensite formation timing in turnaffectsresidual stressbyreducingthemagnitudeof thenalresidualcompression.2. For this spur gear, the residual compressive stresses fromquench hardening are greatest in the gear tooth llet area.3. Carburizationincreases the magnitude of surface com-pression achieved fromquench hardening by delayingthesurfacemartensitictransformation.4. Process simulationshows that residual stress evolutionisaffectedbygeometry, localthermalgradients, andthesurfacecarbonprole.Allacttoincreaselocalcompres-sive residual stresses fromcarburization and quenchhardeningofgeargeometries.5. Thedepthofresidualcompressivestressesincreasewithdepthofthecarburizedcase.6. The magnitude of the surface residual compressiondecreases nonlinearly with increased case depth.Maximum case depth examined in this study was1.5mm.7. Single-toothbendingloadmodelsshowsurfacetensionfromloadingtobedecreasedbythepresenceofsurfaceresidual compression. Theoretically, this shouldreducethedrivingforcefor crackinitiationinHCF. FailureinHCF is principally dominated by crack initiation asopposedtopropagation. Thus, decreasingthecrackini-tiationdrivingforcebyincreasingthestresses requiredto initiating a crack will theoretically increase theendurancelimitinHCF.8. Residual surface compression fromcarburization andquench hardening also reduces the effect of contactstressesduringgeartoothdynamicloading.9. Deeper carburized case depth with associated deeperresidual compression does not necessarily decreasedynamic loading effective stress. Gear geometry andheat-treatment responsedeterminetheoptimal depthofcompression. For this spur gear, an ECDof 0.7mmappearstobetheoptimumECDanddeeperECDsoffernofurtherbenet.10. Process simulation represents an important analyticaltool toinvestigatethecompoundingeffects of process,material, andpartgeometryinuencesonresidualstressresponse from heat treatment, and subsequent partresponsefromserviceloads.AcknowledgmentsTheauthorsgracefullyacknowledgetheUSArmyAATDfortheir generous support of this researchendeavor under ContractFig.10 Stressdistributionsfromthedynamiccontact analyses. (a)Without heat-treatment residual stresses and(b) withheat treatmentresidualstressesinonetoothFig.11 Relation between contact stresses and design of carboncasedepthJournalofMaterialsEngineeringandPerformance Volume22(3)March2013671Number W911W609D0016(ProgramManager: E. ClayAmes).DiscussionswithMr. E.Clay AmesoftheUS ArmyAATDwerealsohelpfulandinsightfulforthisstudy.References1. S. Suresh, Fatigue of Materials, Cambridge University Press,Cambridge,19982. B. FergusonandW. Dowling, PredictiveModel andMethodologyforHeatTreatmentDistortion,NCMSReport#0383RE97,19973. D. Bammann, et al., Development of a CarburizingandQuenchingSimulationTool:AMaterialModelforCarburizingSteelsUndergoingPhase Transformations, 2nd International Conference on Quenching andControl of Distortion, ASMInternational, Materials Park, OH, 1996,p3673754. Z. Li, B. Ferguson, andA. Freborg, DataNeeds for ModelingHeatTreatmentofSteelParts,ProceedingsofMaterialsScience&Technol-ogyConference,2004,p2192265. B.Ferguson,Z.Li,andA.Freborg,ModelingHeatTreatmentofSteelParts,Comput. Mater.Sci.,2005,34,p2742816. V. Warke, S.Sisson, andM. Makhlouf,FEAModelforPredictingtheResponseofPowderMetallurgySteelComponentstoHeatTreatment,Mater.Sci.Eng.,A,2009, 518(12),p7157. B. Ferguson, A. Freborg, and Z. Li, Residual Stress and HeatTreatmentProcess Design for Bending Fatigue Strength Improvementof Carburized Aerospace Gears Proceeding of 5thInternational Confer-ence on Quenching and Control Distortion. 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