International Journal of Automotive Technology, Vol. 20, No. 4, pp. 813825 (2019)
DOI 10.1007/s122390190076x
Copyright © 2019 KSAE/ 10916
pISSN 12299138/ eISSN 19763832
THERMO-MECHANICAL COUPLED ANALYSIS OF HOT PRESS
FORMING WITH 22MnB5 STEEL
Hyung-gyu Kim1)#, Chanhee Won1)#, Seungho Choi1), Moon-gyu Gong2),
Joon-gyu Park2), Heejong Lee3) and Jonghun Yoon4)*
Department of Mechanical Design Engineering, Hanyang University, Seoul 04763, Korea
Research and Department, GNS Ltd., 19 Beomjigi-ro, Danwon-gu, Ansan-si, Gyeonggi 15597, Korea
3)
Research and Department, LG Electronics, 222 Lg-ro, Jinwi-myeon, Pyeongtack-si, Gyeonggi 17709, Korea
4)
Department of Mechanical Engineering, Hanyang University, Gyeonggi 15588, Korea
1)
2)
(Received 28 September 2018; Revised 7 December 2018; Accepted 18 January 2019)
ABSTRACTThis paper mainly concerns the thermo-mechanical analysis to evaluate the process parameters in the hot press
forming with the 22MnB5 sheet such as the austenitization temperature, transport and quenching time for enhancing the
efficiency in the production cycle. It is noted that the transport time is most influencing process parameter in the hot press
forming to increase production efficiency without sacrificing the strength of the final product. In addition, we newly proposed
a scheme to reproduce the flow curves of the hot stamped 22MnB5 sheet with respect to the martensite fraction by correlating
the numerical analyses and tensile test results. To take into consideration of the strength variation in the hot stamped door
impact beam, entire part is partitioned into several domains on which adaptive flow curves are assigned with respect to the
martensite fraction. It demonstrates a good agreement with experimental 3-point bending test with the hot stamped door
impact beam when applying the proposed method adopting adaptive flow curves with respect to the martensite fraction.
KEY WORDS : Hot press forming, Coupled analysis, Martensite, 22MnB5, 3-point bending
1. INTRODUCTION
There are extensive researches on numerical simulations
to optimize process parameters in the HPF process such as
cooling rate, quenching time, austenitization temperature,
and so on (Fan et al., 2010; Min et al., 2013; Nikravesh et
al., 2012). Wang et al. (2016) conducted non-isothermal
hot press forming analysis with coupling thermalmechanical-metallurgical characteristics, which were
validated with experimental results for a V-channel panel.
Cui et al. (2012) proposed a methodology to investigate
phase transformation by taking into account the effects of
cooling water and oxidation. Tekkaya et al. (2007)
evaluated efficiency of the fully coupled thermomechanical analysis for the HPF process in which they
suggested several simplifications and assumptions to
decrease computation time.
However, in the numerical simulation, it is quite difficult
to predict martensite fraction over entire domain of the
blank, precisely, since there are non-uniform contacts
between pre-heated blank and mold surface, which induces
different quenching conditions, locally. Furthermore, it is
hardly able to consider temperature variations in the mold
surface according to repetitive HPF process since there is
cooling channel in the die mold to maintain the quenching
rate, which causes temperature variations due to abrupt
heating and quenching. To overcome these issues,
Bardelcik et al. (2012) carried out the tensile and hardness
tests with 22MnB5 sheet according to the cooling rates in
With increasing demands for the light-weight design and
crashworthiness in autobody industries, ultra-high strength
and GPa-grade steels have been developed over the last
two decades. However, they exhibit low formability and
large amount of springback (Jha et al., 2013; Kuziak et al.,
2008; Liu et al., 2010; Won et al., 2018) during cold
stamping process although showing substantial ultimate
tensile strength (UTS) over 1 GPa. The hot press forming
(HPF) process using boron steels was developed in the late
1980s to resolve these issues in which the pre-heated initial
blank up to 850 °C is transported to a cold die-set and
stamped with quenching, simultaneously. In this process,
the austenitized microstructure of the initial blank is
transformed to the martensite one, which tends to enhance
the material properties such as the UTS over 1.0 GPa with
guaranteeing high formability due to elevated forming
temperature (Caron et al., 2014; Karbasian and Tekkaya,
2010; Merklein et al., 2016; Mori et al., 2017). Therefore,
it is essential to secure the thermo-mechanical properties of
the boron steels and forming conditions in the HPF (Cui et
al., 2015; Lim et al., 2014; Zhao et al., 2016) with which a
desired strength of the final product can be obtained.
*Corresponding author. e-mail: jyoon@hanyang.ac.kr
#These authors contributed equally to this work.
813
814
Hyung-gyu Kim et al.
which they suggested a linear relationship between Vickers
hardness and area martensite fraction and bainite
investigated in the SEM experiments. Bok et al. (2015)
proposed a kinetics model concerning non-isothermal
phase transformation to examine the martensite fraction,
analytically, assuming that the diffusion controlled phase
transformation is highly dependent on the plastic
deformation before cooling.
Most researchers have mainly focused on optimizing
process parameters utilizing numerical analysis. However,
there have been insufficient studies on the correlation with
the HPF analysis and the crashworthiness test such as 3point bending test and crash test. Conventionally, the
material properties of full martensite or flow curves
obtained from the HPF part (Han et al., 2017; Omer et al.,
2017) are uniformly applied to the entire HPF part during
crashworthiness analysis for enhancing the analysis
efficiency although non-uniform strength is observed in
one part (Shapiro, 2009). However, it is possible to
overestimate the energy absorption of HPF part depending
on the the HPF processes and location of specimen in the
HPF part. For these reasons, it is highly required to take
consideration of the non-uniform strength of HPF part to
examine the energy absorption effectively.
In this paper, a thermo-mechanical finite element
analysis has been carried out for the HPF of the door
impact beam to predict the martensite fraction with respect
to the process parameters such as the austenitization
temperature, transport and quenching time. The punch and
die are treated with deformable bodies in the thermomechanical analysis to consider temperature variation in
the mold surface when the coolant flow through the
cooling channel during the HPF process. In order to
consider the strength variation in the hot-stamped door
impact beam during the 3-point bending test for evaluating
the energy absorption, we newly proposed a method to
predict the flow curves with respect to the martensite
fractions by correlating the numerical analyses and tensile
test results. Entire part is partitioned into several domains
according to the martensite fraction in the HPF analysis.
The adaptive flow curves are assigned to the partitioned
domains depending on the martensite fraction. The
proposed method is validated with the experimental 3-point
bending test in terms of reaction force.
22MnB5 sheet with the thickness of 1.4 mm, which is a
conventional quenchenable steel for the HPF process
(Merklein and Lechler, 2006). To obtain the thermomechanical properties of the 22MnB5 sheet with respect to
heating rates, soaking times, and cooling rates, the Gleeble
tests (Schicchi and Hunkel, 2016) were carried out based
on the continuous cooling transformation (CCT) diagram
(Valls et al., 2010) as shown in Figure 1. The initial
specimen is heated to 800 °C with a heating rate of 9 °C/
sec and continuously heated up to 950 °C with a slow
heating rate of 3 °C/sec to guarantee the homogeneous
austenite phase of tested specimen at elevated temperature
(Bardelcik et al., 2012; Fan et al., 2010). Then, it is
exposed to the soaking stage at 950 °C for 180 seconds (Li
et al., 2016) to obtain homogeneous austenite. The
austenitized specimens are cooled down to 500, 650, and
Figure 1. Continuous cooling transformation diagram of
22MnB5 sheet (Valls et al., 2010).
2. MATERIAL PROPERTIES OF 22MnB5
SHEET
Figure 2. Heating and cooling profile of the austenite and
martensite fraction in the Gleeble test.
Table 1 demonstrates chemical composition of the
Table 1. Chemical composition of 22MnB5 sheet.
Material
22MnB5
Chemical composition (wt.%)
C
Si
Mn
P
S
Cr
Ti
B
N
Al
0.21
0.22
1.23
0.022
0.002
0.2
0.028
0.0022
0.002
0.029
THERMO-MECHANICAL COUPLED ANALYSIS OF HOT PRESS FORMING WITH 22MnB5 STEEL
815
Figure 3. Stress-strain curves of 22MnB5 sheet with respect to various temperatures and strain rates for: (a) Austenite
phase; (b) Martensite phase.
800 °C, respectively, with a cooling rate of 30 °C/sec at
which tensile tests start to begin as depicted in Figure 2
since a conventional HPF takes place at these temperature
ranges (Merklein et al., 2016). The cooling profile for the
water-quenching is represented with blue line in the Figure
2 for obtaining the full martensite.
Figure 3 (a) demonstrates the experimental flow curves
of 22MnB5 sheet with respect to various temperatures and
strain rates such as 0.01, 0.1, and 1/sec for austenite phase.
In order to represent the inherent material properties of
austenite phase in Figure 3 (a), we eliminated the
experimental data after phase transformation in which
phase transformation to the bainite phase is observed after
0.03 of strain in experiment results of 500 °C at 0.01/s.
Figure 3 (b) shows the experimental flow curves of the
martensite obtained from the Gleeble tests at room
temperature with the strain rate of 0.001/sec since it does
not show the strain rate sensitivity. These experimental
flow curves are fitted with the Swift and Hockett-Sherby
hardening model depending on the strain rates, separately,
as expressed in Equation (1), which are applied to the
numerical simulation with the AutoFormplusR7 (2016),
where  and  denote the flow stress and combination
factor. 0 and pl indicate the strain at yield point and plastic
strain. i and sat represent the saturation stress and yield
stress. a and m are the work hardening exponents, and C
and P are material constants.
  (1   ){C ( pl   0 ) m }   { sat  ( sat   i )e
 plp
(1)
}
The specific material parameters for austenite and
martensite phases are listed in Table 2. The other thermomechanical flow curves for the other minor phases during
the HPF such as the pearlite and bainite are adopted by the
materials library supported by the AutoFormplusR7 (2016).
Table 2. Material parameters of austenite and martensite phases with respect to the temperatures and strain rates.
Phases
Austenite
Martensite
Temp.
(C)
Strain rate
(/sec)


m
C
i
sat
a
P
500
0.01
1
0.05
0.234
378.8
182.9
442.6
1.37
0.719
500
0.1
1
0.0109
0.436
741.7
131.3
650.8
2.79
0.912
500
1
1
0.00259
0.396
810.2
141.7
771.3
2.31
0.822
650
0.01
1
0.0195
0.219
275.4
115.9
200.7
8.18
0.875
650
0.1
1
0.0061
0.301
447.2
125.5
341.4
5.62
0.943
650
1
0.9
0.00767
0.299
526.8
143.4
434.7
3.91
0.836
800
0.01
0.4
0.001
0.104
132.9
66.57
137.5
2.09
0.433
800
0.1
1
0.05
0.289
264.5
111.5
252.5
2.51
0.861
800
1
0.8
0.0107
0.276
341.9
119.6
261.1
6.75
1.03
20
0.001
1
0.00259
0.396
810.2
141.7
771.3
2.31
0.822
816
Hyung-gyu Kim et al.
3. FINITE ELEMENT ANALYSIS OF HOT
PRESS FORMING
Table 3. Analysis conditions for HPF process.
It is quite difficult to carry out the forming analysis of the
HPF since there occurs severe phase transformation in
microstructure from the austenite to bainite and martensite
with respect to the heating temperature, quenching rate and
time, which tends to determine the distribution of the
strengths in the final product. Nonlinear computational
analysis requires complex conditions of high difficulty
considering both microstructure, mechanical properties and
thermal properties.
To calculate the volume fractions for each phase with
respect to the phase transformation, numerically, the
JMAK
(Johnson-Mehl-Avrami-Kolmogorov)
model
(Denis et al., 1985) has been adopted to the thermomechanical analysis as expressed in Equation (2) where X
indicates the phase fraction at time t, ξ and n are the
kinetics coefficients.
Sheet thickness (mm)
1.4
Initial sheet temperature (C)
900
Initial tool temperature (C)
20
Holding force in quenching (kN)
500
Friction coefficient
(Coulomb friction model)
0.2
X  1  exp(t n )
Sheet material
(2)
When the quenching profiles pass through the
transformed area as represented with red line in Figure 1,
the transformed bainite, ferrite, pearlite fractions from
austenite fraction are determined by the remaining time in
the transformed area. The remained austenite fraction is
transformed to the martensite fraction using the Koistinen
and Marburger equation (Koistinen, 1959) as expressed in
Equation (3),
Fm  Fa {1  exp[0.011( M s  T )]}
Young’s modulus (GPa)
(20 C / 950 C)
210 / 45
Ambient temperature
20.0
Heat Transfer Coefficient (HTC) to tool
(mW/mm2K)
1.0
Heat Transfer Coefficient (HTC) to water
(mW/mm2K)
10.0
Heat Transfer Coefficient (HTC) to air
(20 C / 950 C)
(mW/mm2K)
0.020 / 0.200
Volumetric heat capacity (mJ/mm3K)
4.37
Conductivity (mW/mmK)
32.0
Table 4. Process time with respect to the HPF stage in
numerical analysis.
TransDie close
Die
Loading
Quenching
porting
(Forming)
open
(3)
where Fm and Fa represents the martensite fraction and
remaining austenite fraction when the phase transformation
from austenite into martensite is start. Ms and T denote the
start temperature of martensitic transformation and the
actual time.
Furthermore, it is required to take into consideration of
temperature variations in mold surface induced by a
cooling channel and the number of strokes, simultaneously,
since they significantly influence on the process parameters
in the HPF. Under these circumstances, there are two kinds
of research approaches such as coupled and decoupled
analysis to conduct the numerical simulations for the HPF
analysis (Cui et al., 2012; Wang et al., 2016). The coupled
analysis is able to take into consideration of temperature
variation in the mold surface with the types of conduction
from the austenitized sheet to the mold surface and
convection from the austenitized sheet to the ambient by
considering it as a deformable body when the coolant flows
through the cooling channel, continuously. On the other
hand, decoupled analysis disregards temperature variation
in the mold surface since it treats the mold as rigid bodies
during the overall HPF process. Even though the decoupled
analysis tends to decrease computing time, tremendously, it
is not possible to predict the complicated side effects such
as the thermal concentration (Kim et al., 2015) and thermal
22MnB5
Time
(sec)
2, 4, 6,
8, 10
(5 cases)
1
3
1, 2, 3, 4,
5, 10
(6 cases)
3
fatigue due to inhomogeneous quenching rates over the
whole blank during the HPF. Then, it is highly
recommended to adopt the coupled analysis in the HPF for
optimizing the process parameters, precisely, under the
repetitive forming processes.
3.1. Comparison between Coupled and Decoupled
Analyses
The coupled and decoupled HPF analyses have been
carried out for the door impact beam as shown in Figure 4
(a) to examine the variation effects in the thermomechanical properties on the strength distribution in the
final product. Tables 3 and 4 summarize analysis condition
with material properties of 22MnB5 provided by the steel
supplier ArcelorMittal and process time for the HPF
process applied to the AutoFormplusR7 (2016) commercial
code by interpolating thermal properties to consider
various temperature conditions. To take into consideration
of the cooling channel effect during the HPF process, a set
of upper and lower dies has been prepared as shown in
THERMO-MECHANICAL COUPLED ANALYSIS OF HOT PRESS FORMING WITH 22MnB5 STEEL
Figure 4. Schematic modeling of a set of HPF dies: (a)
Dimension of door impact beam; (b) Sectional view of
upper and lower dies; (c) Cooling channels.
Figure 4 (b) in which an inlaying method was adopted to
achieve uniform cooling effect by dividing those into an
upper shell part and a lower core part (Escher and Wilzer,
2015), which were fabricated for HPF experiments to
compare the results of coupled analysis. Since it requires
tremendous efforts and times to make a 3D FE model
representing the cooling channel over the entire mold body,
it has been represented with the built-in modeling
technique in AutoFormplusR7 (2016) by importing core
profile of cooling channels and diameter, simply, as shown
in Figure 4 (c).
Figure 5 demonstrates temperature profile on the mold
surface with increase of cycle times. When the austenitized
sheet contacts with mold surface during loading process,
the temperature of mold surface slightly increases by the
heat transfer from the austenitized sheet with the
conduction. During the forming and quenching process, the
mold temperature tends to increase dramatically since heat
transfer is accelerated by the full contact with mold surface
and excessive quenching force, which are calculated by
heat transfer coefficient as a function of the contact
pressure and distance between tool and sheet by
implementing the piecewise data supported by the
AutoFormplusR7 (2016).
At the unloading and transporting process, the peak
817
Figure 5. Comparison of coupled and decoupled analysis:
(a) Temperature distribution and measuring point; (b)
Temperature changes in mold surface with increase of
cycle numbers.
temperature starts to decrease by the convection from mold
surface to the ambient temperature and conductions from
the mold body to the cooling channels. However, the peak
temperature of the mold surface in each stage gradually
increases since the next stage forming immediately begins
without maintaining enough time to cool the previous mold
Figure 6. Comparison of martensite fraction between
decoupled and coupled analyses.
818
Hyung-gyu Kim et al.
temperature. The mean values of the fluctuating
temperature profile from minimum to maximum is
converged to 153 °C after 5 cycles in the coupled analysis
while the temperature on the mold surface is maintained
with 153 °C during the analysis cycles adopting the
decoupled analysis. As the result, decoupled analysis
demonstrates average 2.6 % of lower martensite fraction
than coupled analysis as depicted in Figure 6 since
maintained mold temperature with 153 °C significantly
decreases the cooling rate during quenching process. In the
coupled analysis, heat transfers of cooling channel to die
and die surface to air increase the cooling rates by
decreasing the temperature of mold surface.
3.2. Effect of Process Parameters
There are a lot of process parameters in the HPF process
influencing on the martensite fraction over the final
product. In this study, three process parameters such as the
austenitization temperatures ranged from 850 C to 950 °C
in the heating chamber, transport time for the pre-heated
blank from the heating chamber to a stamping mold, and
quenching time for holding the stamped blank are
evaluated with the coupled analysis in terms of martensite
distributions in the door impact beam.
To examine the effect of the austenitization temperatures
on the martensite fraction, the initial pre-heated blanks at
850, 875, 900, 925, and 950 °C are applied to the coupled
HPF analyses as shown in Figure 7. When applied the
austenitization temperature over 900 °C with fixing the
transport time of 6 sec and the quenching time of 5 sec, the
average martensite fraction becomes larger than 90 %,
which is able to guarantee enhanced ultimate tensile
strength greater than 1.4 GPa (Taylor and Clough, 2018).
Furthermore, difference between the minimum and
maximum martensite fraction is substantially reduced over
the austenitization temperature of 900 °C as shown in
Figure 7. In order to examine the phase formation with
CCT curve, quenching profile is measrued at the bottom of
Figure 7. Distribution of martensite fraction with respect
to austenitization temperature.
Figure 8. Quenching profiles of pre-heated initial blank in
CCT diagram with respect to austenitization temperatures:
(a) Measuring point; (b) Log-scale time domain; (c)
Linear-scale time domain.
HPF part as shown in Figure 8 (a). The austenitization
temperatures over 900 °C rapidly drop without passing
through the austenite and bainite (A+B) region as
represented with red solid line in Figure 8 (b). Since the
CCT diagram is significantly shifted to left direction as
represented with red dotted line in Figure 8 (c) when the
austenitization temperature decreases and the predeformation is induced, it is possible to remain in the
austenite and ferrite (A+F) region for a long time with
decrease of austenitization temperature. The reason for
shifting phenomenon is that pre-deformation increases
dislocation density inside the steel matrix, which
suppresses martensite transformation (Cai, 2011).
It is also supported by the previous literatures that CCT
THERMO-MECHANICAL COUPLED ANALYSIS OF HOT PRESS FORMING WITH 22MnB5 STEEL
819
Figure 9. Distribution of martensite fraction with respect to
transport time.
diagram tends to move to the left in the conventional CCT
diagram since the number of nucleation sites increases with
decrease of the austenitization temperature (Barcellona and
Palmeri, 2009; Taylor and Clough, 2018). As the result,
final products with the austenitization temperatures of 850
°C and 875 °C have small ferrite fraction average 4.7 to
10.2 % while they rarely show the ferrite fraction with the
austenitization temperatures over 900 °C.
Figure 9 demonstrates distribution of the martensite
fraction with respect to the transport times with applying
the austenitization temperature of 900 °C. It is noted that
the rapid transport from the heating chamber to the forming
mold is able to guarantee high martensite fraction,
substantially. Especially, when the transport is
accomplished less than 6 sec, average martensite fraction
reaches 90 % over the entire domain in the door impact
beam. It is crucial to minimize the transport time during the
HPF process in order to guarantee a target martensite
fraction since the rapid transport time secure sufficient time
for the subsequent forming and quenching processes as
shown in Figures 10 (a) and (b). Otherwise, owing to the
narrow quenching window in the CCT diagram, it tends to
reduce the strength of the final product due to increased
bainite fraction. The austenitization temperature and
quenching time have a problem in that the cycle time
increases to develop the martensite fraction, while the
transport time is the only process variable that can increase
the martensite fraction with shortening the overall cycle
time.
The effect of the quenching time on the martensite
fraction is evaluated in Figure 11 by varying it from 1 sec
to 10 sec. The average martensite fraction becomes larger
than 90 % over the entire door impact beam when the
quenching times are maintained more than 3 sec. The
cooling rate was measured using an infrared laser
thermometer to validate the cooling rate of the analysis
Figure 10. Quenching profiles of pre-heated initial blank
according to transport times in CCT diagram: (a) Logscale time domain; (b) Linear-scale time domain.
Figure 11. Distribution of martensite fraction with
increase of quenching time.
results with applying the austenitization temperature of
900 °C, transport time of 5 sec, and quenching time of 10
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Hyung-gyu Kim et al.
Figure 14. Experimental HPF set: (a) Heating furnace and
die set for the HPF experiment; (b) Formed part and
dimension of tensile test specimen.
right after the quenching process is abruptly reduced, the
temperature profile is subjected to pass through the
boundary line for the austenite and bainite (A+B) region
without guaranteeing sufficient quenching time as depicted
in Figures 12 (a) and (b).
4. EXPERIMENTAL VALIDATIONS
Figure 12. Final product temperatures with increase of
quenching times in CCT diagram: (a) Log-scale time
domain; (b) Linear-scale time domain.
Figure 13. Temperature history comparison between
experiment and FEM analysis results according to process
stage.
sec in the HPF analysis. The average quenching rates are
calculated as 47.15 °C/sec in the experiment and 43.04 °C/
sec in the HPF analysis as shown in Figure 13. We
concluded that the quenching rate of numerical analysis
conforms with the HPF experiment. Since the cooling rate
To validate the coupled analysis results with respect to the
various process parameters, the HPF experiments for the
door impact beam have been carried out with 22MnB5
sheet having the initial thickness of 1.4 mm in the
hydraulic press shop with a capacity of 500-tonf as shown
in Figure 14 (a) where the heating furnace is set up for the
austenization of the initial blank. The pre-heated initial
blanks up to 900 °C in the heating furnace are transported
to the stamping die by manipulating a robot arm (ABB
IRB-660) with the transporting times of 6, 8, and 10 sec.
After the die closing, it maintains the quenching times of 5
or 10 sec to evaluate the martensite fraction according to
variations in transporting and quenching times. The tensile
test specimens were extracted based on the ASTM-A380 as
shown in Figure 14 (b) from the side wall of the door
impact beam where the uniform thickness is guaranteed,
which are applied to the quasi-static tensile tests at the
strain rate of 0.001/sec and the Vickers hardness tests after
the HPF. Microstructures are evaluated by utilizing the
optical microscope as shown in Figure 15, which are
quantitatively compared with numerical analyses by
utilizing image processing technique (Bardelcik et al.,
2012).
As reported in the previous literature (Bardelcik et al.,
2012), the Vickers hardness of the hot stamped parts has a
THERMO-MECHANICAL COUPLED ANALYSIS OF HOT PRESS FORMING WITH 22MnB5 STEEL
821
Figure 17. Comparison of tensile test results according to
transport and quenching times.
Figure 15. OM images of hot stamped door impact beam
with respect to the transport time of: (a) 6 sec; (b) 8 sec;
(c) 10 sec.
linear relationship with the martensite fraction as shown in
Equation (4) where HV indicates the Vickers hardness, and
Msexp[%] denotes the martensite fraction. However, since
the experimental martensite fraction through the image
processing has a wide variation depending on which the
tested sample is selected, it is hard to correlate the
martensite fraction with the hardness as shown in Figure
16. Therefore, in this research, the experimental martensite
fraction is replaced with the simulated one for control point
as represented in red symbol in Figure 16 to construct the
relationship between the average Vickers hardness and
simulated martensite fraction as expressed in Equation (5)
where Mssim[%] indicates simulated martensite fraction.
(4)
HV  217.85  ( Msexp [%]  263.15
curves according to various hot stamping conditions where
each legend is designated with the process combinations of
the transporting and quenching times, respectively. It is
noteworthy that the strengths of the hot stamped parts are
more sensitively influenced by the transporting time rather
than the quenching time as shown in Figure 17.
With adopting the similar method in Equation (5), it is
possible to provide appropriate the stress-strain curves
depending on the martensite fraction in the hot stamped
part by scaling the full martensite curve with the ratio of
tensile strength based on the relationship as shown in
Equation (6) between the martensite fraction and ultimate
tensile strength (TS) as depicted in Figure 18, since little
sensitivity of hardening exponent is evaluated regardless of
the martensite fraction.
TS  0.00115  ( Mssim [%])3  0.1622  ( Mssim [%]) 2
 12.153  ( Mssim [%])  297.19
(6)
Figure 17 demonstrates comparison of the stress-strain
Since the hot stamped part has local variation in the
martensite fraction over the entire domain with respect to
the forming conditions, it is essential to take into
consideration of the strength variation, adaptively, with the
Figure 16. Relation between Vickers hardness and
martensite fraction.
Figure 18. Relation between ultimate tensile strength and
martensite fraction.
3
HV  0.0038  ( Mssim [%])  0.0528  ( Mssim [%])
 3.9601  ( Mssim [%])  263.15
2
(5)
822
Hyung-gyu Kim et al.
Figure 19. 3-point bending test: (a) Test conditions; (b)
Experimental device.
proposed Equation (6), for conducting subsequent
deformation tests such as the 3-point bending. In order to
examine the performance of the proposed Equation (6), the
3-point bending tests as shown in Figure 19 have been
conducted, experimentally, under the punch speed of 22
mm/sec and compared with simulation results in terms of
the reaction forces.
In order to consider the strength variation in the hot
stamped door impact beam, entire domain needs to be
partitioned depending on the martensite fraction where the
adaptive flow curves are assigned to each partitioned
domain, which is named after the partitioning method in
this research. Figure 20 (a) demonstrates distribution of the
martensite fraction in the hot stamped door impact beam,
which can be partitioned into 6 regions as shown in Figure
20 (b) in which purple region represents the separated
section deviating from the standard deviation of the
average of Section 1. In order to increase the analysis
efficiency, we neglect the effect of the local minimum
region at the both side of door impact beam since it is not
influence on the bending strength due to the fixed boundary
condition. Figure 20 (c) demonstrates the numerical model
for 3-point bending analysis.
Since the average martensite fraction at the
representative 6 sections are placed on the proposed
Equation (6) as depicted in Figure 21 (a), adaptable stressstrain curves are produced by scaling the full martensite
curve with the ratio of estimated tensile strength to full
martensite one depending on the martensite fraction of the
hot stamped as shown in Figure 21 (b). The fitted
hardening curves by Holloman’s equation with same
Figure 20. Partitioned model for 3-point bending analysis:
(a) Distribution of the martensite fraction; (b) Partitioned
into 6 sections; (c) Numerical model.
hardening exponent are applied to the 3-point bending
analyses by assigning the estimated hardening curves to
each section, differently. Figure 22 demonstrates
comparison of the reaction forces of the 3-point bending
tests between experimental and FE analyses in which the
conventional method 1 and 2 indicate the analyses results
by applying the stress-strain curves from the uniaxial
tension tests with specimens consisting of full martensite
and martensite fraction of 82 %, respectively. It is noted
that the first peak of the reaction force when applied the
partitioning method exhibits good agreement with
experimental one compared with the other numerical
results such as the conventional method 1 and 2.
However, there is a slight deviation in reaction forces
between experiment and analysis after the first peak. It is
THERMO-MECHANICAL COUPLED ANALYSIS OF HOT PRESS FORMING WITH 22MnB5 STEEL
823
Figure 23. Variation of Rockwell hardness along the
thickness.
Figure 21. Predicted material properties of each part: (a)
Calculated results of predicted tensile strength; (b) Fitted
hardening curves.
Figure 22. Comparison of reaction forces of the 3-point
bending between experiment and FE analyses.
noted that there is a hardness variation along the thickness
direction of the 22MnB5 sheet as shown in Figure 23. The
hardness at the top and bottom surface exhibits average 5.5
HR of higher value compared with that at the middle
surface. It is also supported by previous literature (Choi
and De Cooman, 2014) that hardness variation along the
thickness direction occurs due to the decarburized layer at
the outer surface of HPF part, which influences on the
bending characteristics such that the collapse rate in the
experiment is faster than the analysis results assuming
uniform hardness along the thickness direction. Therefore,
it is concluded that the proposed partitioning method
linking with the Equation (6) does not only demonstrate the
material behaviors of the hot stamped part with high
accuracy, but also enhance the analysis efficiency since it
does not require to obtain the stress-strain curves,
experimentally, from the hot stamped part.
5. CONCLUSION
This paper mainly concerns the thermo-mechanical
coupled analysis for the HPF of the door impact beam,
which is not only applied to predict the distribution of the
martensite fraction with respect to the process parameters
such as the austenitization temperature, transport and
quenching times, but also utilized in a subsequent analysis
such as the 3-point bending test for evaluating the
crashworthiness of the hot stamped door impact beam,
simultaneously. The thermo-mechanical properties of the
22MnB5 sheet were directly obtained by the Gleeble tests
for the austenite and martensite phases with respect to the
temperatures and strain rates. The analysis results
concerning the distribution of the martensite fraction have
been validated with experimental data obtained from the
HPF for the door impact beam. To take into consideration
of variation of martensite distribution over the entire door
impact beam, the partitioning method has been proposed to
apply appropriate flow curves, adaptively, depending on
the martensite fractions, which are validated with the 3point bending test with the hot stamped door impact beam.
Based on these analyses of the HPF for the door impact
beam, the following conclusions can be drawn:
(1) Compared with the decoupled analysis, the coupled
analysis is not only able to consider the convergence in
824
Hyung-gyu Kim et al.
operating temperatures with respect to the number of
cycle times, but also take into account the temperature
variations in the mold surface depending on the
complex contact conditions and cooling channel effects
during the HPF, which enable precise prediction in the
distribution of the martensite fraction over the entire
door impact beam.
(2) Appropriate process parameters in the HPF have been
proposed the thermo-mechanical coupled analysis
when the austenitization temperature of 900 °C,
transport time of 6 sec, and the quenching time of 5
sec, which are able to guarantee sufficient martensite
fraction over 90 %. In terms of the total cycle times for
a single product, the transport time is most influencing
process parameter to reduce the cycle times without
sacrificing the strength of the final product.
(3) In order to take into consideration of the effect of the
martensite distribution over the hot stamped door
impact beam, the proposed partitioning method applies
the appropriate flow curves to each section, adaptively,
depending on the forming conditions in the HPF. Since
it shows good agreement with experimental 3-point
bending test with the hot stamped door impact beam, it
is highly recommended to adopt proposed partitioning
method for analyzing the hot stamped part without
additional experiments for hardness and tensile tests.
ACKNOWLEDGEMENTThis work was supported by the
National Research Foundation of Korea (NRF) grant funded by
the Korean government (2016R1C1B1006875). This work was
also supported by the “Human Resources Program in Energy
Technology” of the Korean Institute of Energy Technology
Evaluation and Planning (KETEP), granted by the Ministry of
Trade, Industry & Energy, Republic of Korea (no.
20174010201310).
The authors declare that they have no conflicts of interest.
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