SEMI-EMPIRICAL METHOD TO PREDICT HARDNESS DURING FAST INDUCTION HEATING OF A TEMPERED MARTENSITIC AMS6414 STEEL*C. Ducassy1, F. Bridier1, P. Bocher1, P. Arkinson2 1cole de technologie suprieure 1100 rue Notre Dame ouest Montral, Qc Canada H3C 1K3 (Corresponding author: philippe.bocher@etsmtl.ca) 2Pratt&Whitney Canada 1000 boulevard Marie Victorin Longueuil, Qc Canada J4G 1A1 ABSTRACT Duringsuperficialinductionheatingofaquenched-temperedgear,thesurfaceexperiencevery high temperature gradients in a very short time, resulting in beneficial hard layer of martensite and strong compressiveresidualstressatthesurfaceofthegear.Acommonlycalledover-temperingregionis observedbetweenthehardenedsurfacelayerandthecoreofthepart.Inthisarea,thehardnesscanbe significantly lower than the bulk hardness before the induction treatment. In order to quantify the size and amountofhardnessdropinthisregion,thetemperingkineticswerestudiedfortheveryparticular conditionsexperiencedduringinductionheattreatment,i.e.,veryshorttimesand hightemperatures.The specific influences of time and temperature on the alloy tempering kinetic were investigated and analyzed with regards to the over-tempering phenomenon. The present work proposes to quantify the hardness drop for parts made of AMS6414 steel. INTRODUCTION General Inductionheatingprocessiswidelyusedinindustrytohardengearssuperficially.Thesurface regionisrapidlyheateduptotheausteniticphase(coremartensite'austenitic)bystrongmagnetic fieldsandquicklyquenchedtoobtainahardmartensitelayer(austeniticmartensite').Inthe induction hardening application that is under development in our research groupe, the heating rate is very fast (about 1000 C/s) and the heat cycle small (less than a second). This thermal cycle affects only a very smalllayerofmaterialincludingtheregionofphasechangeandthesub-surfacelayerthatundergoesa temperingcycle(coremartensite'tempermartensite).Thistemperingresultsintoaso-calledover-temperedregionwherethehardnesscanbesignificantlylowerthanthecorematerial.Theinfluenceof thissizeandminimumhardnessofthisregiononthepartperformanceisnotwelldocumentedinthe literature, and is a concern for industrial applications such as aerospace gears. Atypicalhardness profile obtained by induction heating is depicted in Fig. 1. As it can beseen, thematerialusedinthepresentstudyisquenchedandtemperedtoreacharelativelyhighcorehardness varying between 400 HV and 450 HV, i.e., the microstructure is in an unstable martensitic state. At the top ofFigure1,thetypicalrangeoftemperaturesreachedduringtheinductionheatingprocessisdisplayed (Ac1 is the beginning of austenitization and Ac3 the end): -z1correspondstothehardenedregion.ItwasheatedabovetheAc3temperature(total austenitization) and then quickly cooled. Its hardness is higher than the rest of the part; -z2regioniscomposedofamixtureoffresh(hard)andtemperedmartensite(asthe temperature only reached values between Ac1 and Ac3); -z3 region is the over-tempered area. During the treatment, this region is heated up significant temperatures (but lower than Ac1) that do affect hardness due to the tempering effect of this heat flow; -finally,z4regioncorrespondstothecoreandisnotaffectedbythethermalflow(toolow temperature and too short time). Figure 1 A typical hardness profile obtained after induction hardeningInvariousstudies,thefinalhardnessafterheattreatmentfromaustenitetomartensitehasbeen predicted[1,2,3].Ontheotherhand,thehardnesspredictionofthermallyaffectedzonehasonlybeen sparsely addressed and mainly for the case of welding [4, 5]. In both cases, the hardness of the transformed regions and the tempering of the heat affected zone are usually described based on Johnson-Mehl-Avrami equations.TheseequationshavetheadvantagetowelldescribethetypicalSshapecurveofphase transformation, i.e., the kinetics of tempering.In the present study, an other approach is proposed: a parameter of equivalence, i.e., the Hollomon and Jaffe parameter PT [6]. By assuming that tempering obeys to the laws of diffusion, the Hollomon and Jaffe tempering parameter express the effect of time and temperature with a single parameter PT given as:

(1) Thisparameterwill beusedtopredict the hardness lost in the subsurfaceregionaffectedbythe fastheatingcycleofinductionheating.Thefullthermalcycleseenbyagivenpointofthepart(seean exampleinFig.2)canbedescretizedintosmalltemperingcyclesandthelocalhardnesslostcanbe calculated. The main interest of this method is its simplicity since it does not require any calculations of the apparentactivationenergy.Thepresentmethoddoesnotimplytheinputoftemperaturedependent parameters or metallurgical calculations of the phases in presence. It can be implemented in a routine of a numericalsimulationandfromathermalhistoryprofileprovidesthelocalhardnessatanypointofthe over-tempering zone. Figure 2- Discretization of anisothermal heating cycle EXPERIMENTAL TheAMS6414steelinvestigatedinthisstudyisalow-alloyedmartensiticsteelusedintheaeronautic industry. It combines a good ductility and good mechanical strength (including fatigue) when heat treated. The ranges of composition are reported in Table 1. The as-received 56 samples were in a quenched state. The hardness of the samples after quench is 635 HV (11 HV) and was kept at this hardness in order to see bettertheeffectoftempering.Samplesizeis10mmx2mmx1mmtobesmallenoughtoreachthe tempering temperature rapidely. Table 1 - Composition of the AMS 6414 steel [7] Element Content (wt %) C0.38 0.43 Cr0.70 0.90 Cu Mn 0.35 0.65 0.90 Mo0.20 0.30 Ni1.65 2.00 P 0.01 Si0.15 0.35 SFe 0.010 bal. t Temperinginasaltbathfurnacehasbeenappliedtosmallsamples(about20mm3big).Four temperatures were tested (250 C, 350 C, 450 C, and 550 C) for 14 various tempering times (from 1 s to 2h).Temperaturesabove550Ccouldnotbereachedbythesaltbathfurnaceusedforthepresent investigation. Micro-hardness measurements were performed beforeandafter treatments according to the HV0,2 standard [8]. The average of 3 measurements of microhardness per sample was taken into account. RESULTS AND DISCUSSION History of the part In its initial state, before induction heat treatment, the hardness is uniform among the part. Indeed, the history of heat treatments as seen by the workpiece is described in Fig. 3a. Zones (z1), (z3) and (z4) are simultaneously quenched after heating 45 min at 850 C, the hardness is 635 HV. They are then tempered (R1 in the Fig. 3) at a temperature of about 400 C for 2 h to achieve a hardness of 450 HV (as illustrated in Fig. 4). Finally, the piece undergoes induction hardening. Due to the austenitization and fast cooling of the surface layer during the induction process, its local hardness increases (Fig. 3b) while the core hardness will not be affected as it does not see any significant temperature variations (Fig 3d). On the other hand, in the over-tempering area (Fig. 3c), there is a continuous loss of hardness in addition to the usual furnace tempering (R1), i.e., from the tempering of the sub-surface layer during the induction (R2). To predict the loss of hardness during (R2), we must study the softening kinetics of the martensite from the as-quenched statebefore(R1).Itisnotedthatothersofteningkineticsmayappearsforveryshorttimeandhigh temperature exposure this will be investigated in further work. Figure 3 - Hardness history of different layers of the part: a) heat treatment history; b) Hardened region (z1); c) over-tempering region (z3); d) core region (z4) The effect of tempering time and temperature on hardness The loss of hardness is associated with a partial return to the equilibrium state of martensite which isathermallyactivatedphenomenon.Indeed,itcanbeobservedinFig.4thatthedropinhardnessis functionof temperatureandlesssignificantlyoftime.Thelinear behaviorof thishardnessdropwith the logarithm of time can be observed. Figure 4 - Hardness during tempering treatment of AMS 6414 The Hollomon-Jaffe tempering parameter For the same kinetic of tempering, the curve HV = f (PT) should describe a straight line regardless ofthetimeandthetemperatureofthetreatment[10].Thisrelationshipiswellverifiedforthe measurements displayed in Fig. 4, the data can be grouped as the data fall in a single line when using the Hollomon-Jaffe parameter (see Fig. 5). Theregressionof thelinearcurveofFig.5allowspredictingthehardnessasafunctionoftime and temperature treatment thanks to the equation: (2) whereaandbareconstantsthatdependonthesteeland itspreviousheat treatmenthistory.Thepresent data give a = -0.031 and b = 838.As specified above, the hardness loss has been measured for temperatures ranging from 250 C to 550 C, however, the temperatures seen by the region in the over-tempering zone varies beyond this range. For the presentattenttodescribetheover-temperingeffect,theHollomon-Jaffeparameterhasbeenusedto extrapolate hardness loss for temperatures above 550 C. Figure 5 - Hardness vs. Holloman tempering parameter Application for anisothermal heating cycle In the case of rapid induction heating, the thermal history at each point of the part is not isotherm. Thethermal pathof each point of the part isdescretized into small part-time,as shown in Fig. 2.For the present work, the time increment t was 0.02 s.Thecalculationofeachhardnessloss,i.e.,HVi,isexplainedbelowandillustratedinFig.6. Temperatures for a given time ti were calculated as i, the average of the temperature of Ti-1 and Ti. For eachtemperingstepsanequivalenttimetequiiscalculatedusingtheprevioushardnessofthesample HVi-1 and the equation obtained from the HVT(t) curve in Fig. 4: (3) Thisisrepresentedbythearrows1and2inFig.6.Onceobtained,atimeincrementtisaddedtotequi (arrow3inFig.6tobetterillustratethemethod,alargetwastakenmuchlargerthantheincrement used in the present method) and the new hardness HVi is calculated using the equation 4 (arrows 4 and 5 in Fig. 6): (4) Figure 6 Method of calculation of HVi VALIDATION OF THE APPROACH In order to validate this approach in the case of very fast heating by induction, a multiphysic finite element simulation has been run and the equivalent geometry and heating recipe have been perform on our inductionheatingfacility.Asimplegeometrywaschosen(a106mmcylinderanda109mm induction coil), and the axi-symmetrical mesh of the 2404 triangular finite elements can be seen in Figure 7. The heating duration is 0.5 s with at a frequency of 150 kHz, the power of the machine was adjusted in order to obtain a hardened surface layer of 1 mm at the center of the cylinder. The current of the simulation model was adjusted to obtain the same case depth. The parameters of materials (, Cp, ) are those of the AMS4340 and were chosen to vary according to the temperature [11]. The initial hardness of the part was 425 HV. Figure 7 - Simulation of induction heating of the cylinder t CylinderCoil Figure 8 - Thermal history obtained by simulation The Fig. 8 represents 6 temperatures cycles calculated at different depths below the surface at the center of the part displayed in Fig. 7 (1 mm, 1.2 mm, 1.4 mm, 1.6 mm, 1.8 mm and 2 mm). It is noted that the surface layer from 0 mm to 1 mm is not taking into account since the calculus of the hardened zone is not concerned by the present article. Onecannotethatsometemperaturesexceed710C,whichisthetheoreticphasechanging temperature at equilibrium thermodynamics [12]. Even if the finite element calculation were done with the thermodynamic Ac1 value of 710 C, the results will be analyzed using a higher temperature of Ac1, since this value depends of the heating rate [13] and is of the order of 800 C/s in the case of the region at 1 mm below the surface. In this condition, the phase transformation occurs at 790 C. Resultsof thecalculated hardness with thismethod and results fromhardness measurements are reported in Fig. 9 and Table 2. The error percentin thefourthcolumn shows a good correlationbetween thetheoryandtheexperiment,evenifonlylowtemperaturetempering(lessthan550C)wereusedto calculate the over-tempering effect. Figure 9 Over-tempering hardness calculated from thermal history Table 2 Theoretical vs. experimental hardness Depth (mm) Hardness measured (HV0.2) Hardness calculated (HV) Error percent (%) 1.03673711.1 1.23893900.3 1.44124041.9 1.64074152.0 1.84444215.2 2.04184231.2 2.24354252.3 2.44474254.9 2.64234250.5 2.84284250.7 3.04234250.5 CONCLUSIONS This semi-empirical method presented here for predicting the hardness in the over-tempering area seemsappropriateforfastinductionheating.Itremainstovalidatetheseresultsforavarietyofinitial hardness and with real temperature measurements and on more complex thermal cycle.Moreover,afterinductionheating,partshavetoundergoalowtemperaturestressreliefthermal cycle that may affect the superficial hardness in the fresh martensite. It is then relevant to predict the loss of hardness in the surface layer during such low temperature tempering. 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