Available online at www.sciencedirect.com
Acta Materialia 56 (2008) 1482–1490
www.elsevier.com/locate/actamat
Finite element simulation of quench distortion in a low-alloy
steel 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 Korea
b
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 2007
Available online 22 January 2008
Abstract
The uncontrolled distortion of steel parts has been a long-standing and serious problem for heat treatment processes, especially
quenching. To get a better understanding of distortion, the relationship between transformation kinetics and associated distortion
has been investigated using a low-alloy chromium steel. Because martensite is a major phase transformed during the quenching of steel
parts and is influential in the distortion, a new martensite start (Ms) temperature and a martensite kinetics equation are proposed. Oil
quenching 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 predictions
of the FEM simulation compare well with the measured data. The simulation results allow for a clear understanding of the relationship
between the transformation kinetics and distortion.
Ó 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 to
greatly enhance the mechanical properties of steel parts
such as bearings, gears, shafts, etc. Unfortunately, heat
treatments such as carburizing, quenching and tempering
often cause excessive and uncontrolled distortion. This
type of distortion is still a major issue in the production
of quality parts. Many research groups have examined
the causes of distortion and found that the phase transformations as well as thermal stresses that occur during the
heat treatment play an important role.
Denis et al. [1,2] have investigated the effects of stress on
the phase transformation kinetics and transformation plasticity. Inoue et al. have studied the relation between phase
transformations and residual stresses [3], as well as the
*
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 of
a carburized ring specimen [4]. Arimoto et al. [5] have
explained the origin of distortion and the stress distribution
in quenched cylinders by accounting for the phase transformation. Ju et al. [6] have studied the martensitic transformation plastic behavior during quenching.
Because martensite is the major phase produced during
the quenching of the steel parts, a reliable prediction of the
martensitic transformation kinetics is indispensable for the
computational simulators of the distortion such as
HEARTS [7], SYSWELD [8], DEFORM-HT [9], DANTE
[10] and COSMAP [11].
Koistinen and Marburger’s equation [12], dating from
1959, is still widely used for the prediction of martensite
kinetics. Their equation was obtained by fitting the martensite volume fraction, measured by X-ray diffraction, as
a function of temperature below the martensite start temperature (Ms) in various iron–carbon steels. Although the
equation was originally developed using iron–carbon steels,
many researchers have cited it without any modification
1359-6454/$34.00 Ó 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
doi:10.1016/j.actamat.2007.11.039
S.-J. Lee, Y.-K. Lee / Acta Materialia 56 (2008) 1482–1490
for low-alloy steels containing alloying elements such as
chromium, nickel and molybdenum. In addition, the
equation generates a C-curve shape for the martensite volume fraction plotted against the cooling temperature below
Ms. In contrast, for most low-alloys steels the martensitic
transformation kinetic curve exhibits a sigmoid shape.
Although many researchers [1–6] have attempted to
clarify the exact relationship between phase transformations and internal stress, few studies that clearly explain
the interaction between transformation kinetics and distortion have been conducted. Therefore, the purpose of the
present study was to investigate the relationship between
transformation kinetics, focussing on martensitic transformation and distortion using an AISI 5120 steel, which is
widely used for diverse automobile parts.
In the present work the Ms point and a martensite kinetics equation for steel are proposed. The equation considers
austenite grain size (AGS), chemistry and the shape of the
kinetic curve. The Ms point and the equation were validated
with experimental data from the literature. A finite element
method (FEM) analysis was performed, using thermal
and mechanical properties obtained from thermodynamic
calculations and the literature. Quenching experiments
using cut cylinders were conducted. The experimentally measured temperature and distortion data were used to explain
the relationship between the transformation kinetics and
distortion within the FEM simulations.
2. Transformation kinetics model
2.1. Diffusive transformation
Dilatometric specimens of AISI 5120 steel were
machined into small plates of 10 3 1 mm3 from a
hot-rolled bar. Table 1 lists the chemical composition of
AISI 5120 steel. The initial microstructure of the dilatometric specimen was a mixture of ferrite and pearlite produced
by furnace cooling. The specimens were austenitized at
900 °C with heating rates ranging from 1 to 50 °C s1,
and held for 10 min in a vacuum. The specimens were then
cooled to room temperature at cooling rates from 1 to
50 °C s1 by blowing nitrogen gas. A dilatometer was used
to measure contractions and expansions during the heating
and cooling. The sensor force needed to hold a dilatometric
specimen (7.9 kPa) was too small to produce plastic transformation phenomena. The cooled specimens were
mechanically polished and etched using 2% Nital.
A common differential formula to characterize the diffusive transformation was used in this study. Kirkaldy et al.
Table 1
Chemical compositions of AISI 5120 steel (wt.%)
C
Mn
Si
Cr
P, S
Fe
0.21
0.89
0.24
1.25
<0.01
Bal.
1483
[13] first introduced this equation. It is based on the work
of Zener [14] and Hillert [15].
dV
¼ f ðchem; N ; Q; DT Þ gðV Þ
dt
ð1Þ
where V is the volume fraction of the product phase at a
process time t, chem means the effects of alloying elements
on the diffusive mobility, N is the ASTM grain size number, Q is the activation energy for the transformation and
DT is the undercooling below the equilibrium transformation temperature. g(V) is a function of V relating to the
overall kinetics rate. The differential form of Eq. (1) is convenient, since it allows the combination of the kinetics
model for phase transformations with a constitutive materials model so that the stress–strain matrix can be calculated within the finite element analysis.
The dimensional change of the dilatometric specimen
due to the transformation during heat-up results from the
crystal 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 affect
subsequent transformations during the heating and cooling
processes. Thus, the kinetic model of the transformation
during heating has to be considered in the heat treatment
simulation for the accurate prediction of the final distortion. The austenite volume fraction is obtained by applying
a lever rule to the change in dilatometric curves assuming
an isotropic transformation and insignificant cementite
effect. According to the lever rule, the volume fraction of
transformed phase at a given temperature is calculated by
the ratio of the measured transformation strain to the total
transformation strain, which is the gap between the extrapolated linear thermal expansion lines of parent phase and
fully transformed phase at that temperature. Based on
Eq. (1), the optimized kinetic equation for the diffusive
transformation on heating of AISI 5120 steel is given by
dV A
242742
4:45
0:14
VA
¼ 8932 ðT Ae1 Þ exp RT
dt
ð1 V A Þ3:07
ð2Þ
where Ae1 is an equilibrium eutectoid temperature, R is the
gas constant (8.314 J mol1 K1) and VA is the volume
fraction of austenite. The values for the parameters in
Eq. (2) were based on the austenite volume fraction
obtained from an optimization program.
The phases formed by diffusive transformation during
cooling are classified as ferrite, pearlite and bainite, while
martensite forms via a diffusionless transformation. Thus,
it is impossible to apply a lever rule to obtain the product
phase fractions in a cooling process. The volume fractions
of the product phases were obtained using a routine [16]
that converts the transformation strain measured from a
dilatational curve to the volume fraction of each phase.
This conversion routine calculates more reasonable volume
fractions of product phases compared to the lever law, and
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S.-J. Lee, Y.-K. Lee / Acta Materialia 56 (2008) 1482–1490
is used in developing the kinetic models of both the diffusive and diffusionless transformations during cooling. The
kinetic equations of diffusive transformations were
obtained by optimization as follows:
Ferrite transformation
dV F
59093
3:48
¼ 91073 ðAe3 T Þ exp V 0:10
F
RT
dt
ð1 V F Þ
2:97
:
ð3Þ
Pearlite transformation
dV P
40384
2:12
¼ 24647 ðAe1 T Þ exp V 0:42
P
RT
dt
ð1 V P Þ
1:46
:
ð4Þ
Bainite transformation
dV B
39538
3:10
¼ 91111 ðBs T Þ exp V 0:53
B
RT
dt
ð1 V B Þ
3:68
;
ð5Þ
where Ae3 , Ae1 and Bs are the transformation start temperatures of ferrite, pearlite and bainite, respectively. Vi is the
volume fraction of product phase i.
Fig. 1 shows a dilatometric curve measured at the cooling rate of 50 °C s1 and the volume fractions of product
phases calculated by the conversion routine. The microstructure of the sample was confirmed by optical
microscopy.
2.2. Martensitic transformation
A number of empirical formulae have been proposed
to predict the Ms temperature as a function of the chemical composition of steels [17–20]. The effect of the alloying element on the Ms temperature of iron-based binary
alloys has been investigated in many studies, and Liu
et al. [21] have summarized the results. The measured
Ms temperature of Fe–1 at.% C steel by Izumiyama
et al. [22] is around 470 °C, while that of the same steel
obtained by Ackert and Parr [23] is about 150 °C. This
difference in the Ms temperature of the same steel possibly comes from a difference in austenite grain size
(AGS), which strongly affects the nucleation and growth
of martensite.
Some experimental results regarding the relationship
between the AGS and the martensitic transformation have
been reported in Fe–Ni and Fe–Ni–C alloys [24,25]. The
results indicate that the AGS has a significant effect on
martensite formation. The Ms temperature rose with
increasing austenite grain size especially in Fe–Ni–C alloys.
The relationship between the Ms temperature determined
from dilatational curves and the ASTM grain size numbers
of low-alloy steels is investigated in this study, where it is
found that the Ms temperature increases with decreasing
ASTM grain size number.
In order to obtain the experimental data regarding Ms
temperature and martensitic kinetics, dilatometric tests of
29 low-alloy steels were conducted. The specimens were
heated to austenitizing temperatures ranging between 850
and 1050 °C and held for a maximum of 90 min. In order
to obtain only the martensite phase from austenite, the
specimens were quenched to room temperature by blowing
helium gas into the dilatometer chamber. The average cooling rate between the austenitizing temperature and the Ms
temperature was greater than 170 °C s1. The cooling rate
was slowed below the Ms temperature due to the latent
heat generated during the martensitic transformation.
For the measurement of the AGS, the quenched dilatometric specimens were etched in a saturated picric acid solution
after mechanical polishing with a 1 lm diamond suspension. Based on these data, the authors propose a new predictive equation of Ms temperature as functions of both
chemical composition and the AGS of low-alloy steels as
follows:
Fig. 1. Dilatometric curve of AISI 5120 steel measured at a cooling rate of 50 °C s1 and its predicted volume fractions of product phases by the
conversion routine.
S.-J. Lee, Y.-K. Lee / Acta Materialia 56 (2008) 1482–1490
1485
Fig. 2. Comparison between the Koistinen–Marburger equation and Eq. (7) from this study with the measured (a) M50 and (b) M90 temperatures where
the martensite fractions are 50 and 90 vol.%, respectively.
M s ð CÞ ¼ 402 797C þ 14:4Mn þ 15:3Si 31:1Ni
þ 345:6Cr þ 434:6Mo þ ð59:6C þ 3:8Ni
41Cr 53:8MoÞ G
ð6Þ
where each element is in weight per cent and G is the
ASTM grain size number.
The K–M equation [12] and some similar equations
[26,27] have been previously proposed to predict martensite
kinetics in steels. The Ms temperature is directly affected by
the AGS, indicating that the kinetics of martensite transformation is also influenced by the AGS. However, these
previous kinetics equations, including the K–M equation,
do not contain an AGS term or factor. The new kinetics
equation for the martensitic transformation of low-alloy
steels, which includes the effect of AGS, undercooling
below Ms temperature and chemical composition, was
made based on the converted martensite fractions from
the dilatational curves. The new kinetics equation is given
as
dV M
¼ K V aM ð1 V M Þb
dT
:191
G:240 ðM s T Þ
K¼
9:017 þ 62:88 C þ 9:27 Ni 1:08 Cr þ :76 Mo
a ¼ :420 :246 C þ :359 C 2
b ¼ :320 þ :576 C þ :933 C2
ð7Þ
where VM is the volume fraction of martensite, C is carbon
content in weight per cent and T is the temperature below
the Ms temperature in degrees Celsius.
The M50 and M90 temperatures, where the martensite
fractions are 50 and 90 vol.%, respectively, were
obtained from the published isothermal transformation
diagrams [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 selected
steels from the published isothermal transformation
diagrams are quite different from the experimental conditions used to formulate Eq. (7). The comparison
between two kinetic equations with the measured M50
and M90 temperatures is shown in Fig. 2. For the M50
temperature, the two equations reveal insignificant differences. However, for the M90 temperature, Eq. (7) shows
a very good agreement with the measured M90 temperatures, while the values predicted by the K–M equation
differ significantly.
3. Material properties
The thermal conductivity calculated by Miettinem’s
formulae [29] is used in this study. He proposed equations to predict the thermal conductivity of alloyed steels
at the liquidus temperature, at the austenite decomposition temperature, and at 400, 200 and 25 °C. He
remarked that the thermal conductivity is usually not
known for each individual solid phase but rather for
the solid as a whole.
The values (J mol1 K1) for heat capacity (CP) were
calculated using Thermo-Calc [30], assuming the steel to
be in equilibrium. The heat capacities of austenite, ferrite
and ferrite+cementite as a function of temperature for
AISI 5120 steel are
austenite
C P ¼ 93:82 þ 25:162T 0:5 0:378T þ 0:0000717T 2 ;
ð8Þ
ferrite
C P ¼ 8938:11 þ 444417:483=T þ 786:886T 0:5
20:662T þ 0:00529T 2 ;
ð9Þ
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S.-J. Lee, Y.-K. Lee / Acta Materialia 56 (2008) 1482–1490
ferrite + cementite
C P ¼ 1091:734 þ 3768:92=T þ 175:576T
0:5
5:742T þ 0:00227T 2
ð10Þ
where T is temperature in Kelvin. A simple rule of mixtures
is applied to obtain the heat capacity for multiphase
conditions.
The enthalpy change due to a phase transformation, i.e.
latent heat, causes heat absorption or heat generation of
the system. In this study, the latent heat of the diffusive
transformations is calculated based on the thermodynamics
of the transformation. The latent heat for ferrite formation
is calculated at the temperature at which the austenite
decomposition is thermodynamically complete, while the
latent heat of the pearlite formation is calculated by the
rule of mixtures between the latent heats of the cementite
and ferrite formation. Although bainite is composed of
ferrite and cementite-like pearlite, the latent heat of the
bainite formation contains an additional shear energy
value of 600 J mol1, which was reported by Nanba et al.
[31]. The calculated latent heats of ferrite, pearlite and bainite are: DHF = 5.95 108, DHP = 5.26 108 and DHB =
5.12 108 (J m3), respectively.
Only a few studies have reported the latent heat of martensite formation. Recently, Cho et al. [32] suggested the
following equation to calculate the Gibbs free energy
change as the latent heat of martensite transformation:
T Ms
C
DG ¼ DG 1 ð11Þ
T 0 Ms
where DGC is the Gibbs free energy change between austenite and martensite at the Ms temperature. According to
Kunze and Beyer [33], DGC is 2100 J mol1 for the formation of plate martensite and (1200 + 3128yCr + 29260yMn +
6470yNi + 21000yC) J mol1 for lath martensite, where yi is
the site fraction of element i. T0 is a thermodynamic equilibrium temperature at which the chemical free energies of
austenite and martensite are equal and is usually expressed
as T0 = 1/2(Ms + As) [34]. As is the austenite start temperature from martensite and Andrews’ formula [19] is used to
calculate the As temperature of AISI 5120 steel. The latent
heat of the martensite formation of AISI 5120 steel is
calculated using Eqs. (7) and (11). The value for the latent
heat for martensite formation is DHM = 3.14 108 (J m3).
The published stress–strain curves of AISI 5120 steel
with different microstructures are used for the stress analysis [35]. The stress–strain curves were generated as a
function of temperature using Instron and Gleeble
machines. In addition, the hardness is also an important
means to assess the mechanical properties after heat
treatment. In this study, the empirical formula proposed
by Maynier et al. [36] was used to predict the hardness
after cooling. The values of the phase transformation
plasticity of AISI 5120 steel are taken from recently
measured data [37]. The thermal and transformation
expansions are calculated by the equations used in the
previous work [16].
4. Experiments and FEM simulation of an asymmetrically
cut cylinder
Fig. 3 shows the shape and dimensions of an asymmetrically cut cylinder of AISI 5120 steel. The asymmetric design is helpful for the investigation of the
relationship between transformation kinetics and distortion during quenching. The asymmetrically cut cylinder
was austenitized at 860 °C for 10 min and quenched in
oil at 17 °C. K-type thermocouples and a multichannel
recorder were used to measure surface temperatures during the heat treatment. To obtain a heat transfer (convection) coefficient during oil quenching, a cylinder of AISI
304 stainless steel (10 mm diameter 100 mm long) was
austenitized at 860 °C for 10 min and quenched in the
same oil. 304 stainless steel was selected because no
latent heat is generated by phase transformation during
the heat treatment. The published thermal properties of
AISI 304 stainless steel [38] and the measured surface
temperatures were used to determine the convection coefficient. The convection coefficient was calculated as a
function of temperature by the inverse algorithm shown
in Fig. 4.
The FEM simulation was performed using ABAQUS
[39] and its user-defined subroutines UMAT and
UMATHT. The hexahedral element (C3D8T) was used
and the total numbers of nodes and elements were 2205
and 1632, respectively. Two-step conditions were specified
for the simulation: the heating process of the asymmetrically cut cylinder from room temperature to 860 °C was
simulated by convectional heat transfer (300 W m2 K1)
for 15 min followed by quenching simulation for 5 min
using the convection coefficient obtained from the AISI
304 stainless cylinder.
Fig. 3. Shape and dimension of the cut cylinder specimen of AISI 5120
steel.
S.-J. Lee, Y.-K. Lee / Acta Materialia 56 (2008) 1482–1490
1487
Fig. 6. Phase fractions predicted at two different positions of the sample
and the predicted and measured hardness values at the central crosssection of the quenched cut cylinder.
Fig. 4. Calculated convection coefficient of oil quenching using AISI 304
stainless steel.
5. Results and discussion
Fig. 5 shows the comparison between the surface temperatures obtained by the simulation and the measured
temperatures at different positions of the asymmetrically
cut cylinder during oil quenching. During this quenching,
the measured temperature changes at four different points
are similar. The predicted cooling profiles show good
agreement with the measured ones. Unfortunately, however, the latent heat, which occurs during oil quenching,
is too small to cause a significant temperature change
because of both the low carbon content of the steel and
the relatively small volume of the cylindrical specimen.
Fig. 6 shows the predicted microstructural changes on
the edge and in the center of the asymmetrically cut cylinder during oil quenching. Within 2 or 3 s of the start of
Fig. 5. Comparison between the predicted and measured surface temperatures at each different position of the cut cylinder during oil quenching.
cooling, the bainitic transformation occurs and is followed
by the martensite transformation. The predicted relative
amount of martensite is 77% on the edge and 71% in the
center. This difference is due to the different cooling rates
throughout the thickness of the sample producing different
bainite fractions prior to the start of martensite formation.
The measured average hardness of the central cross-section
of the quenched asymmetrically cut cylinder is about 42
HRC. The predicted hardness based on the Maynier’s formula at the same position is within ±2.2% of the measured
hardness.
Distortion of the asymmetrically cut cylinder before and
after oil quenching was quantitatively measured at nine different points along the longitudinal direction at the center
of the outside surface of the cylinder using a coordinate
measuring machine with a minimum resolution of
100 nm. Fig. 7 shows the predicted distortion to have very
good agreement with the measured distortion. The maxi-
Fig. 7. Predicted and measured distortions of the asymmetrically cut
cylinder, which was bent in the opposite direction of the cutting plane (axis
1 direction) after quenching.
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S.-J. Lee, Y.-K. Lee / Acta Materialia 56 (2008) 1482–1490
mum distortion is approximately 500 lm, which could pose
a problem in terms of dimensional stability during a commercial heat treatment process.
Fig. 8 shows the relationship between distortion and
microstructural change in the vertical section during oil
quenching. The specimen was bent in the normal direction
Fig. 8. Relationship between the distortion and microstructure changes in the asymmetrically cut cylinder specimen during oil quenching: (a) bainite and
(b) martensite.
Fig. 9. Effect of phase transformations on the distortion of the cut cylinder during oil quenching: (a) distortion with transformations and (b) distortion
without transformations.
S.-J. Lee, Y.-K. Lee / Acta Materialia 56 (2008) 1482–1490
1489
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 transformations
and (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.
of the cutting plane (axis 1 direction) at the beginning of
the oil quench and shortened in the longitudinal direction
due to thermal contraction. When the bainite and martensite transformations started, the additional transformational strain and the strain due to thermal expansion
affected the distortion of the asymmetrically cut cylinder.
Additionally, the position-dependent transformations have
an influence on the distortion direction. Finally, the distortion 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 asymmetric shape of the cut cylinder but also the additional
transformation strains.
Fig. 9 shows the effect of the transformation strain on
the distortion, which was investigated by computer simulations. The distortion simulations were performed with the
same initial and boundary conditions but different transformation strains. Fig. 9b shows the quenching distortion
without transformation strains, indicating the distortion
due to the continuous contraction of austenite in the direction normal to the cutting plane (axis 1 direction).
Fig. 10 provides a comparison of the variations in the
axial stress component (rz), radial stress component (rr)
and hoop stress component (rh) during oil quenching of
the cut cylinder with the phase transformation effect being
considered. Without consideration of the transformation
strains, as shown in Fig. 10a, the tensile stress at surface
and the compressive stress at the center of an austenitic
specimen are generated at the beginning of oil quenching
because the surface temperature drops faster than the inner
temperature. With continued cooling, the cooling rate at
the surface is decreased while that at the center is increased,
and the temperature difference between these two temperatures is reduced by a few degrees. The compressed stress at
the surface and the tensile stress at center are generated
when the cooling rate at the center becomes greater than
that at the surface. However, when considering the transformation strains, the stress variation is more complicated
and the amounts of the maximum compressive and tensile
stresses become greater as shown in Fig. 10b. The increased
stress variation is related to the bainite and martensite
transformations combined with thermal contraction of
the asymmetrically shaped cylinder (Fig. 8).
Fig. 11 compares the effect of the martensite kinetics on
quenching distortion using two different kinetic equations:
the K–M equation and Eq. (7). The same material properties and initial and boundary conditions were used for the
distortion simulation. Even if the predicted distortion was
in the same direction (opposite to axis 1) after quenching,
the relative amount of distortion of the quenched cut cylinder would be quite different. The predicted distortion calculated using the K–M equation does not reach 200 lm,
while the distortion predicted using Eq. (7) is greater than
500 lm. The accuracy of the martensite kinetic equation,
Fig. 11. Effect of martensite kinetics on the final distortion after oil
quenching. Two different kinetic equations were compared: the Koistinen–
Marburger equation and Eq. (7) proposed in this study. The measured
values at P1–P9 were referred to previously in Fig. 7.
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S.-J. Lee, Y.-K. Lee / Acta Materialia 56 (2008) 1482–1490
Eq. (7), proposed in this study, demonstrates the need to
have a reliable kinetics model for phase transformations
if accurate distortion is to be predicted.
6. Conclusion
The relationship between transformation kinetics and
distortion during oil quenching of AISI 5120 steel has been
investigated. Experimental results were compared with
computational simulations using ABAQUS with its userdefined subroutines UMAT and UMATHT. To predict
accurate martensite volume fraction during quenching, a
new Ms temperature and kinetics equations of diffusive
and diffusionless transformations are suggested. These
equations consider the influences of austenite grain size,
alloy elements and the shape of the kinetics curve. The temperature change during oil quenching and distortion of an
asymmetrical shaped AISI 5120 cut cylinder were measured. FEM simulations were performed to predict the
microstructure, temperature, distortion and hardness of
AISI 5120 steel during heat treatment. These simulations
used the thermal and mechanical properties obtained from
thermodynamic calculations, literature and transformation
kinetics measured by a dilatometer. The predicted results
were successfully validated with experimentally measured
and observed results.
The effects of transformations on the distortion of the
cut cylinder (i.e. the transformation strain, phase-dependent thermal expansion coefficients and flow stresses) are
clearly verified by comparing the simulated results with/
without phase transformations. The phase transformations
as well as the thermal contraction of the asymmetrically cut
cylinder upon cooling cause high stress values. The importance of an accurate martensite kinetics for better prediction of quenching distortion was verified by using two
different martensite kinetic equations: the K–M equation
and the new kinetic equation proposed in this study. The
final distortion of the quenched asymmetrically cut cylinder
shows excellent correlation with the new martensite kinetics equation.
Acknowledgment
This research was supported by the National Core
Research Center (NCRC) program from MOST and
KOSEF (No. R15-2006-022-01002-0). The authors are
grateful to Professor C.J. Van Tyne at the Colorado School
of Mines for helpful discussions.
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