Finite Element Simulation of Quench

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Acta Materialia 56 (2008) 1482–1490

Finite element simulation of quench distortion in a low-alloysteel incorporating transformation kinetics

Seok-Jae Lee a, Young-Kook Lee b,*

a Research Institute of Iron and Steel Technology, Yonsei University, Seoul 120-749, Republic of Koreab Department of Metallurgical Engineering, Yonsei University, Seoul 120-749, Republic of Korea

Received 17 October 2007; received in revised form 22 November 2007; accepted 27 November 2007Available online 22 January 2008

Abstract

The uncontrolled distortion of steel parts has been a long-standing and serious problem for heat treatment processes, especiallyquenching. To get a better understanding of distortion, the relationship between transformation kinetics and associated distortionhas been investigated using a low-alloy chromium steel. Because martensite is a major phase transformed during the quenching of steelparts and is influential in the distortion, a new martensite start (Ms) temperature and a martensite kinetics equation are proposed. Oilquenching experiments with an asymmetrically cut cylinder were conducted to confirm the effect of phase transformations on distortion.ABAQUS and its user-defined subroutines UMAT and UMATHT were used for finite element method (FEM) analysis. The predictionsof the FEM simulation compare well with the measured data. The simulation results allow for a clear understanding of the relationshipbetween the transformation kinetics and distortion.� 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Finite element method; Martensitic transformation; Transformation kinetics; Distortion; Low-alloy steel

1. Introduction

Heat-treating processes have traditionally been used togreatly enhance the mechanical properties of steel partssuch as bearings, gears, shafts, etc. Unfortunately, heattreatments such as carburizing, quenching and temperingoften cause excessive and uncontrolled distortion. Thistype of distortion is still a major issue in the productionof quality parts. Many research groups have examinedthe causes of distortion and found that the phase transfor-mations as well as thermal stresses that occur during theheat treatment play an important role.

Denis et al. [1,2] have investigated the effects of stress onthe phase transformation kinetics and transformation plas-ticity. Inoue et al. have studied the relation between phasetransformations and residual stresses [3], as well as the

1359-6454/$34.00 � 2007 Acta Materialia Inc. Published by Elsevier Ltd. All

doi:10.1016/j.actamat.2007.11.039

* Corresponding author. Tel.: +82 2 2123 2831; fax: +82 2 312 5375.E-mail address: [email protected] (Y.-K. Lee).

influence of transformation plasticity on the distortion ofa carburized ring specimen [4]. Arimoto et al. [5] haveexplained the origin of distortion and the stress distributionin quenched cylinders by accounting for the phase transfor-mation. Ju et al. [6] have studied the martensitic transfor-mation plastic behavior during quenching.

Because martensite is the major phase produced duringthe quenching of the steel parts, a reliable prediction of themartensitic transformation kinetics is indispensable for thecomputational simulators of the distortion such asHEARTS [7], SYSWELD [8], DEFORM-HT [9], DANTE[10] and COSMAP [11].

Koistinen and Marburger’s equation [12], dating from1959, is still widely used for the prediction of martensitekinetics. Their equation was obtained by fitting the mar-tensite volume fraction, measured by X-ray diffraction, asa function of temperature below the martensite start tem-perature (Ms) in various iron–carbon steels. Although theequation was originally developed using iron–carbon steels,many researchers have cited it without any modification

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S.-J. Lee, Y.-K. Lee / Acta Materialia 56 (2008) 1482–1490 1483

for low-alloy steels containing alloying elements such aschromium, nickel and molybdenum. In addition, theequation generates a C-curve shape for the martensite vol-ume fraction plotted against the cooling temperature belowMs. In contrast, for most low-alloys steels the martensitictransformation kinetic curve exhibits a sigmoid shape.

Although many researchers [1–6] have attempted toclarify the exact relationship between phase transforma-tions and internal stress, few studies that clearly explainthe interaction between transformation kinetics and distor-tion have been conducted. Therefore, the purpose of thepresent study was to investigate the relationship betweentransformation kinetics, focussing on martensitic transfor-mation and distortion using an AISI 5120 steel, which iswidely used for diverse automobile parts.

In the present work the Ms point and a martensite kinet-ics equation for steel are proposed. The equation considersaustenite grain size (AGS), chemistry and the shape of thekinetic curve. The Ms point and the equation were validatedwith experimental data from the literature. A finite elementmethod (FEM) analysis was performed, using thermaland mechanical properties obtained from thermodynamiccalculations and the literature. Quenching experimentsusing cut cylinders were conducted. The experimentally mea-sured temperature and distortion data were used to explainthe relationship between the transformation kinetics anddistortion within the FEM simulations.

2. Transformation kinetics model

2.1. Diffusive transformation

Dilatometric specimens of AISI 5120 steel weremachined into small plates of 10 � 3 � 1 mm3 from ahot-rolled bar. Table 1 lists the chemical composition ofAISI 5120 steel. The initial microstructure of the dilatomet-ric specimen was a mixture of ferrite and pearlite producedby furnace cooling. The specimens were austenitized at900 �C with heating rates ranging from 1 to 50 �C s�1,and held for 10 min in a vacuum. The specimens were thencooled to room temperature at cooling rates from 1 to50 �C s�1 by blowing nitrogen gas. A dilatometer was usedto measure contractions and expansions during the heatingand cooling. The sensor force needed to hold a dilatometricspecimen (7.9 kPa) was too small to produce plastic trans-formation phenomena. The cooled specimens weremechanically polished and etched using 2% Nital.

A common differential formula to characterize the diffu-sive transformation was used in this study. Kirkaldy et al.

Table 1Chemical compositions of AISI 5120 steel (wt.%)

C Mn Si Cr P, S Fe

0.21 0.89 0.24 1.25 <0.01 Bal.

[13] first introduced this equation. It is based on the workof Zener [14] and Hillert [15].

dVdt¼ f ðchem; N ; Q; DT Þ � gðV Þ ð1Þ

where V is the volume fraction of the product phase at aprocess time t, chem means the effects of alloying elementson the diffusive mobility, N is the ASTM grain size num-ber, Q is the activation energy for the transformation andDT is the undercooling below the equilibrium transforma-tion temperature. g(V) is a function of V relating to theoverall kinetics rate. The differential form of Eq. (1) is con-venient, since it allows the combination of the kineticsmodel for phase transformations with a constitutive mate-rials model so that the stress–strain matrix can be calcu-lated within the finite element analysis.

The dimensional change of the dilatometric specimendue to the transformation during heat-up results from thecrystal structural change from body-centered cubic (bcc)ferrite and pearlite to face-centered cubic (fcc) austenite.This dimensional change, which is a transformation strain,can induce stresses within the specimen that could affectsubsequent transformations during the heating and coolingprocesses. Thus, the kinetic model of the transformationduring heating has to be considered in the heat treatmentsimulation for the accurate prediction of the final distor-tion. The austenite volume fraction is obtained by applyinga lever rule to the change in dilatometric curves assumingan isotropic transformation and insignificant cementiteeffect. According to the lever rule, the volume fraction oftransformed phase at a given temperature is calculated bythe ratio of the measured transformation strain to the totaltransformation strain, which is the gap between the extrap-olated linear thermal expansion lines of parent phase andfully transformed phase at that temperature. Based onEq. (1), the optimized kinetic equation for the diffusivetransformation on heating of AISI 5120 steel is given by

dV A

dt¼ 8932 � ðT � Ae1Þ4:45 � exp � 242742

RT

� �� V 0:14

A

� ð1� V AÞ3:07 ð2Þ

where Ae1 is an equilibrium eutectoid temperature, R is thegas constant (8.314 J mol�1 K�1) and VA is the volumefraction of austenite. The values for the parameters inEq. (2) were based on the austenite volume fractionobtained from an optimization program.

The phases formed by diffusive transformation duringcooling are classified as ferrite, pearlite and bainite, whilemartensite forms via a diffusionless transformation. Thus,it is impossible to apply a lever rule to obtain the productphase fractions in a cooling process. The volume fractionsof the product phases were obtained using a routine [16]that converts the transformation strain measured from adilatational curve to the volume fraction of each phase.This conversion routine calculates more reasonable volumefractions of product phases compared to the lever law, and

1484 S.-J. Lee, Y.-K. Lee / Acta Materialia 56 (2008) 1482–1490

is used in developing the kinetic models of both the diffu-sive and diffusionless transformations during cooling. Thekinetic equations of diffusive transformations wereobtained by optimization as follows:Ferrite transformation

dV F

dt¼ 91073 � ðAe3 � T Þ3:48 � exp � 59093

RT

� �� V 0:10

F

� ð1� V FÞ2:97: ð3Þ

Pearlite transformation

dV P

dt¼ 24647 � ðAe1 � T Þ2:12 � exp � 40384

RT

� �� V 0:42

P

� ð1� V PÞ1:46: ð4Þ

Bainite transformation

dV B

dt¼ 91111 � ðBs � T Þ3:10 � exp � 39538

RT

� �� V 0:53

B

� ð1� V BÞ3:68; ð5Þ

where Ae3 , Ae1 and Bs are the transformation start temper-atures of ferrite, pearlite and bainite, respectively. Vi is thevolume fraction of product phase i.

Fig. 1 shows a dilatometric curve measured at the cool-ing rate of 50 �C s�1 and the volume fractions of productphases calculated by the conversion routine. The micro-structure of the sample was confirmed by opticalmicroscopy.

2.2. Martensitic transformation

A number of empirical formulae have been proposedto predict the Ms temperature as a function of the chem-ical composition of steels [17–20]. The effect of the alloy-ing element on the Ms temperature of iron-based binaryalloys has been investigated in many studies, and Liuet al. [21] have summarized the results. The measured

Fig. 1. Dilatometric curve of AISI 5120 steel measured at a cooling rate oconversion routine.

Ms temperature of Fe–1 at.% C steel by Izumiyamaet al. [22] is around 470 �C, while that of the same steelobtained by Ackert and Parr [23] is about 150 �C. Thisdifference in the Ms temperature of the same steel possi-bly comes from a difference in austenite grain size(AGS), which strongly affects the nucleation and growthof martensite.

Some experimental results regarding the relationshipbetween the AGS and the martensitic transformation havebeen reported in Fe–Ni and Fe–Ni–C alloys [24,25]. Theresults indicate that the AGS has a significant effect onmartensite formation. The Ms temperature rose withincreasing austenite grain size especially in Fe–Ni–C alloys.The relationship between the Ms temperature determinedfrom dilatational curves and the ASTM grain size numbersof low-alloy steels is investigated in this study, where it isfound that the Ms temperature increases with decreasingASTM grain size number.

In order to obtain the experimental data regarding Ms

temperature and martensitic kinetics, dilatometric tests of29 low-alloy steels were conducted. The specimens wereheated to austenitizing temperatures ranging between 850and 1050 �C and held for a maximum of 90 min. In orderto obtain only the martensite phase from austenite, thespecimens were quenched to room temperature by blowinghelium gas into the dilatometer chamber. The average cool-ing rate between the austenitizing temperature and the Ms

temperature was greater than 170 �C s�1. The cooling ratewas slowed below the Ms temperature due to the latentheat generated during the martensitic transformation.For the measurement of the AGS, the quenched dilatomet-ric specimens were etched in a saturated picric acid solutionafter mechanical polishing with a 1 lm diamond suspen-sion. Based on these data, the authors propose a new pre-dictive equation of Ms temperature as functions of bothchemical composition and the AGS of low-alloy steels asfollows:

f 50 �C s�1 and its predicted volume fractions of product phases by the

Fig. 2. Comparison between the Koistinen–Marburger equation and Eq. (7) from this study with the measured (a) M50 and (b) M90 temperatures wherethe martensite fractions are 50 and 90 vol.%, respectively.


M sð�CÞ ¼ 402� 797Cþ 14:4Mnþ 15:3Si� 31:1Ni

þ 345:6Crþ 434:6Moþ ð59:6Cþ 3:8Ni

� 41Cr� 53:8MoÞ � G ð6Þ

where each element is in weight per cent and G is theASTM grain size number.

The K–M equation [12] and some similar equations[26,27] have been previously proposed to predict martensitekinetics in steels. The Ms temperature is directly affected bythe AGS, indicating that the kinetics of martensite trans-formation is also influenced by the AGS. However, theseprevious kinetics equations, including the K–M equation,do not contain an AGS term or factor. The new kineticsequation for the martensitic transformation of low-alloysteels, which includes the effect of AGS, undercoolingbelow Ms temperature and chemical composition, wasmade based on the converted martensite fractions fromthe dilatational curves. The new kinetics equation is givenas

dV M

dT¼ K � V a

M � ð1� V MÞb

K ¼ G:240 � ðM s � T Þ:191

9:017þ 62:88 � Cþ 9:27 �Ni� 1:08 � Crþ :76 �Mo

a ¼ :420� :246 � Cþ :359 � C2

b ¼ :320þ :576 � Cþ :933 � C2

ð7Þwhere VM is the volume fraction of martensite, C is carboncontent in weight per cent and T is the temperature belowthe Ms temperature in degrees Celsius.

The M50 and M90 temperatures, where the martensitefractions are 50 and 90 vol.%, respectively, wereobtained from the published isothermal transformationdiagrams [28] of 37 low-alloy steels for more reliable

comparison between the K–M equation and Eq. (7).The chemical composition and the AGS of the selectedsteels from the published isothermal transformationdiagrams are quite different from the experimental con-ditions used to formulate Eq. (7). The comparisonbetween two kinetic equations with the measured M50

and M90 temperatures is shown in Fig. 2. For the M50

temperature, the two equations reveal insignificant differ-ences. However, for the M90 temperature, Eq. (7) showsa very good agreement with the measured M90 tempera-tures, while the values predicted by the K–M equationdiffer significantly.

3. Material properties

The thermal conductivity calculated by Miettinem’sformulae [29] is used in this study. He proposed equa-tions to predict the thermal conductivity of alloyed steelsat the liquidus temperature, at the austenite decomposi-tion temperature, and at 400, 200 and 25 �C. Heremarked that the thermal conductivity is usually notknown for each individual solid phase but rather forthe solid as a whole.

The values (J mol�1 K�1) for heat capacity (CP) werecalculated using Thermo-Calc [30], assuming the steel tobe in equilibrium. The heat capacities of austenite, ferriteand ferrite+cementite as a function of temperature forAISI 5120 steel are

austenite

CP ¼ 93:82þ 25:162T 0:5 � 0:378T þ 0:0000717T 2; ð8Þferrite

CP ¼ �8938:11þ 444417:483=T þ 786:886T 0:5

� 20:662T þ 0:00529T 2; ð9Þ

Fig. 3. Shape and dimension of the cut cylinder specimen of AISI 5120steel.


ferrite + cementite

CP ¼ �1091:734þ 3768:92=T þ 175:576T 0:5

� 5:742T þ 0:00227T 2 ð10Þwhere T is temperature in Kelvin. A simple rule of mixturesis applied to obtain the heat capacity for multiphaseconditions.

The enthalpy change due to a phase transformation, i.e.latent heat, causes heat absorption or heat generation ofthe system. In this study, the latent heat of the diffusivetransformations is calculated based on the thermodynamicsof the transformation. The latent heat for ferrite formationis calculated at the temperature at which the austenitedecomposition is thermodynamically complete, while thelatent heat of the pearlite formation is calculated by therule of mixtures between the latent heats of the cementiteand ferrite formation. Although bainite is composed offerrite and cementite-like pearlite, the latent heat of thebainite formation contains an additional shear energyvalue of 600 J mol�1, which was reported by Nanba et al.[31]. The calculated latent heats of ferrite, pearlite and bai-nite are: DHF = 5.95 � 108, DHP = 5.26 � 108 and DHB =5.12 � 108 (J m�3), respectively.

Only a few studies have reported the latent heat of mar-tensite formation. Recently, Cho et al. [32] suggested thefollowing equation to calculate the Gibbs free energychange as the latent heat of martensite transformation:

DG ¼ DGC 1� T �M s

T 0 �M s

� �ð11Þ

where DGC is the Gibbs free energy change between austen-ite and martensite at the Ms temperature. According toKunze and Beyer [33], DGC is 2100 J mol�1 for the forma-tion of plate martensite and (1200 + 3128yCr + 29260yMn +6470yNi + 21000yC) J mol�1 for lath martensite, where yi isthe site fraction of element i. T0 is a thermodynamic equi-librium temperature at which the chemical free energies ofaustenite and martensite are equal and is usually expressedas T0 = 1/2(Ms + As) [34]. As is the austenite start temper-ature from martensite and Andrews’ formula [19] is used tocalculate the As temperature of AISI 5120 steel. The latentheat of the martensite formation of AISI 5120 steel iscalculated using Eqs. (7) and (11). The value for the latentheat for martensite formation is DHM = 3.14 � 108 (J m�3).

The published stress–strain curves of AISI 5120 steelwith different microstructures are used for the stress anal-ysis [35]. The stress–strain curves were generated as afunction of temperature using Instron and Gleeblemachines. In addition, the hardness is also an importantmeans to assess the mechanical properties after heattreatment. In this study, the empirical formula proposedby Maynier et al. [36] was used to predict the hardnessafter cooling. The values of the phase transformationplasticity of AISI 5120 steel are taken from recentlymeasured data [37]. The thermal and transformationexpansions are calculated by the equations used in theprevious work [16].

4. Experiments and FEM simulation of an asymmetrically

cut cylinder

Fig. 3 shows the shape and dimensions of an asym-metrically cut cylinder of AISI 5120 steel. The asymmet-ric design is helpful for the investigation of therelationship between transformation kinetics and distor-tion during quenching. The asymmetrically cut cylinderwas austenitized at 860 �C for 10 min and quenched inoil at 17 �C. K-type thermocouples and a multichannelrecorder were used to measure surface temperatures dur-ing the heat treatment. To obtain a heat transfer (convec-tion) coefficient during oil quenching, a cylinder of AISI304 stainless steel (10 mm diameter � 100 mm long) wasaustenitized at 860 �C for 10 min and quenched in thesame oil. 304 stainless steel was selected because nolatent heat is generated by phase transformation duringthe heat treatment. The published thermal properties ofAISI 304 stainless steel [38] and the measured surfacetemperatures were used to determine the convection coef-ficient. The convection coefficient was calculated as afunction of temperature by the inverse algorithm shownin Fig. 4.

The FEM simulation was performed using ABAQUS[39] and its user-defined subroutines UMAT andUMATHT. The hexahedral element (C3D8T) was usedand the total numbers of nodes and elements were 2205and 1632, respectively. Two-step conditions were specifiedfor the simulation: the heating process of the asymmetri-cally cut cylinder from room temperature to 860 �C wassimulated by convectional heat transfer (300 W m�2 K�1)for 15 min followed by quenching simulation for 5 minusing the convection coefficient obtained from the AISI304 stainless cylinder.

Fig. 4. Calculated convection coefficient of oil quenching using AISI 304stainless steel.

Fig. 6. Phase fractions predicted at two different positions of the sampleand the predicted and measured hardness values at the central cross-section of the quenched cut cylinder.


5. Results and discussion

Fig. 5 shows the comparison between the surface tem-peratures obtained by the simulation and the measuredtemperatures at different positions of the asymmetricallycut cylinder during oil quenching. During this quenching,the measured temperature changes at four different pointsare similar. The predicted cooling profiles show goodagreement with the measured ones. Unfortunately, how-ever, the latent heat, which occurs during oil quenching,is too small to cause a significant temperature changebecause of both the low carbon content of the steel andthe relatively small volume of the cylindrical specimen.

Fig. 6 shows the predicted microstructural changes onthe edge and in the center of the asymmetrically cut cylin-der during oil quenching. Within 2 or 3 s of the start of

Fig. 5. Comparison between the predicted and measured surface temper-atures at each different position of the cut cylinder during oil quenching.

cooling, the bainitic transformation occurs and is followedby the martensite transformation. The predicted relativeamount of martensite is 77% on the edge and 71% in thecenter. This difference is due to the different cooling ratesthroughout the thickness of the sample producing differentbainite fractions prior to the start of martensite formation.The measured average hardness of the central cross-sectionof the quenched asymmetrically cut cylinder is about 42HRC. The predicted hardness based on the Maynier’s for-mula at the same position is within ±2.2% of the measuredhardness.

Distortion of the asymmetrically cut cylinder before andafter oil quenching was quantitatively measured at nine dif-ferent points along the longitudinal direction at the centerof the outside surface of the cylinder using a coordinatemeasuring machine with a minimum resolution of100 nm. Fig. 7 shows the predicted distortion to have verygood agreement with the measured distortion. The maxi-

Fig. 7. Predicted and measured distortions of the asymmetrically cutcylinder, which was bent in the opposite direction of the cutting plane (axis1 direction) after quenching.


mum distortion is approximately 500 lm, which could posea problem in terms of dimensional stability during a com-mercial heat treatment process.

Fig. 8. Relationship between the distortion and microstructure changes in the(b) martensite.

Fig. 9. Effect of phase transformations on the distortion of the cut cylinder duwithout transformations.

Fig. 8 shows the relationship between distortion andmicrostructural change in the vertical section during oilquenching. The specimen was bent in the normal direction

asymmetrically cut cylinder specimen during oil quenching: (a) bainite and

ring oil quenching: (a) distortion with transformations and (b) distortion

Fig. 10. Variations in the axial stress (rz), radial stress (rr) and hoop stress (rh) during oil quenching of the cut cylinder: (a) without phase transformationsand (b) with phase transformations. The subscripts (C, S and cut S) indicate the node positions of the cut cylinder at which the stresses were calculated.

Fig. 11. Effect of martensite kinetics on the final distortion after oilquenching. Two different kinetic equations were compared: the Koistinen–Marburger equation and Eq. (7) proposed in this study. The measuredvalues at P1–P9 were referred to previously in Fig. 7.


of the cutting plane (axis 1 direction) at the beginning ofthe oil quench and shortened in the longitudinal directiondue to thermal contraction. When the bainite and martens-ite transformations started, the additional transforma-tional strain and the strain due to thermal expansionaffected the distortion of the asymmetrically cut cylinder.Additionally, the position-dependent transformations havean influence on the distortion direction. Finally, the distor-tion changed to the direction opposite to the cutting plane(opposite to axis 1 direction) due to the transformation.The original causes of the distortion are not only the asym-metric shape of the cut cylinder but also the additionaltransformation strains.

Fig. 9 shows the effect of the transformation strain onthe distortion, which was investigated by computer simula-tions. The distortion simulations were performed with thesame initial and boundary conditions but different trans-formation strains. Fig. 9b shows the quenching distortionwithout transformation strains, indicating the distortiondue to the continuous contraction of austenite in the direc-tion normal to the cutting plane (axis 1 direction).

Fig. 10 provides a comparison of the variations in theaxial stress component (rz), radial stress component (rr)and hoop stress component (rh) during oil quenching ofthe cut cylinder with the phase transformation effect beingconsidered. Without consideration of the transformationstrains, as shown in Fig. 10a, the tensile stress at surfaceand the compressive stress at the center of an austeniticspecimen are generated at the beginning of oil quenchingbecause the surface temperature drops faster than the innertemperature. With continued cooling, the cooling rate atthe surface is decreased while that at the center is increased,and the temperature difference between these two tempera-tures is reduced by a few degrees. The compressed stress atthe surface and the tensile stress at center are generatedwhen the cooling rate at the center becomes greater thanthat at the surface. However, when considering the trans-formation strains, the stress variation is more complicatedand the amounts of the maximum compressive and tensile

stresses become greater as shown in Fig. 10b. The increasedstress variation is related to the bainite and martensitetransformations combined with thermal contraction ofthe asymmetrically shaped cylinder (Fig. 8).

Fig. 11 compares the effect of the martensite kinetics onquenching distortion using two different kinetic equations:the K–M equation and Eq. (7). The same material proper-ties and initial and boundary conditions were used for thedistortion simulation. Even if the predicted distortion wasin the same direction (opposite to axis 1) after quenching,the relative amount of distortion of the quenched cut cylin-der would be quite different. The predicted distortion calcu-lated using the K–M equation does not reach 200 lm,while the distortion predicted using Eq. (7) is greater than500 lm. The accuracy of the martensite kinetic equation,


Eq. (7), proposed in this study, demonstrates the need tohave a reliable kinetics model for phase transformationsif accurate distortion is to be predicted.

6. Conclusion

The relationship between transformation kinetics anddistortion during oil quenching of AISI 5120 steel has beeninvestigated. Experimental results were compared withcomputational simulations using ABAQUS with its user-defined subroutines UMAT and UMATHT. To predictaccurate martensite volume fraction during quenching, anew Ms temperature and kinetics equations of diffusiveand diffusionless transformations are suggested. Theseequations consider the influences of austenite grain size,alloy elements and the shape of the kinetics curve. The tem-perature change during oil quenching and distortion of anasymmetrical shaped AISI 5120 cut cylinder were mea-sured. FEM simulations were performed to predict themicrostructure, temperature, distortion and hardness ofAISI 5120 steel during heat treatment. These simulationsused the thermal and mechanical properties obtained fromthermodynamic calculations, literature and transformationkinetics measured by a dilatometer. The predicted resultswere successfully validated with experimentally measuredand observed results.

The effects of transformations on the distortion of thecut cylinder (i.e. the transformation strain, phase-depen-dent thermal expansion coefficients and flow stresses) areclearly verified by comparing the simulated results with/without phase transformations. The phase transformationsas well as the thermal contraction of the asymmetrically cutcylinder upon cooling cause high stress values. The impor-tance of an accurate martensite kinetics for better predic-tion of quenching distortion was verified by using twodifferent martensite kinetic equations: the K–M equationand the new kinetic equation proposed in this study. Thefinal distortion of the quenched asymmetrically cut cylindershows excellent correlation with the new martensite kinet-ics equation.

Acknowledgment

This research was supported by the National CoreResearch Center (NCRC) program from MOST andKOSEF (No. R15-2006-022-01002-0). The authors aregrateful to Professor C.J. Van Tyne at the Colorado Schoolof Mines for helpful discussions.

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Finite Element Simulation of Quench