Int J Adv Manuf Technol DOI 10.1007/s00170-016-8678-1
ORIGINAL ARTICLE
Inverse evaluation of equivalent contact heat transfer coefficient in hot stamping of boron steel Min Wang 1,2 & Chun Zhang 1 & Haifeng Xiao 1 & Bing Li 1
Received: 2 December 2015 / Accepted: 23 March 2016 # Springer-Verlag London 2016
Abstract It is of significance to evaluate the equivalent contact heat transfer coefficient (ECHTC) at the sheet-die interface in hot stamping of boron steel (HSBS) for controlling the local cooling rate of the sheet and hence obtaining components with tailored microstructure and properties. Moreover, accurate evaluation of the ECHTC can provide a reliable thermal boundary condition for numerical simulation of the HSBS process. In the study, a simple and effective physical simulation setup for die quenching of boron steel (DQBS) was developed, where the temperatures at measurement points are related only to the ECHTC so as to improve the evaluation accuracy. A FE-based optimization model for inverse evaluating the ECHTC was established. The ECHTCs at the B1500HS sheet-H13 die steel interface were identified under various contact pressures, and it was found that the ECHTC increases exponentially with the pressure increasing. Both the physical simulation of DQBS and the HSBS experiment were performed to verify the ECHTC evaluated, and the maximum relative errors of 9.6 and 19.7 % were observed, respectively, between the predicted and measured temperature histories.
Keywords Boron steel . Hot stamping . Contact heat transfer coefficient . Inverse evaluation . Finite element
* Min Wang
[email protected]
1
College of Materials Science and Engineering, Hubei University of Automotive Technology, Shiyan 442002, China
2
Material Forming and Mould Technology Open State Key Laboratory, Huazhong University of Science and Technology, Wuhan 430074, China
1 Introduction Hot stamping of boron steel (HSBS) is an effective way to reduce the weight of car body and ensure the car crash safety [1, 2]. It is mainly used to manufacture crash-relevant components such as bumpers, A- and B-pillars, side-impact reinforcements, and tunnels. During the process, the boron steel sheet is heated to the austenitic state and held for several minutes, and then it is formed rapidly and quenched in the dies with cooling system to obtain the high strength component with microstructure of lath martensite. HSBS is a high nonlinear process under coupled effects of thermal-mechanical-metallurgical fields, in which the contact heat transfer coefficient (CHTC) at the sheet-die interface controls the local cooling rate of the sheet and hence determines the final microstructure and mechanical properties of the component. Particularly, the component having different mechanical properties in different regions is an urgent demand for the modern car applications [1]. Furthermore, the accurate prediction of the CHTC can provide a reliable thermal boundary condition for numerical simulation of the HSBS process. Therefore, how to accurately evaluate the CHTC is a key problem in the development of the HSBS technology. Up to now, there has been some published work on the CHTC in HSBS. Merklein et al. [3] evaluated the CHTC between the Al-Si-coated 22MnB5 sheet and die using the Newton cooling theory and revealed its association with the pressure, gap, and initial temperature of dies. Hung et al. [4] adopted the same method to identify the CHTCs under different pressures in hot stamping of 22MnB5 sheet. Although the method based on the traditional Newton cooling theory is simple, it is suitable for evaluating the CHTC under constant die temperature which is not true in HSBS. In view of this, Abdulhay et al. [5] used the heat conduction inversion method to calculate the CHTC at the Usibor1500P sheet-die interface
Int J Adv Manuf Technol Fig. 1 Schematic diagram and photo of physical simulation setup
and researched its variation with the pressure. Caron et al. [6] also employed the method to estimate the CHTC and analyzed its change with the pressure and the initial temperatures of the Usibor1500P sheet and dies. The heat conduction inversion method can effectively evaluate the CHTC with changing die temperature, but its ill-posed nature tends to result in the stability and convergence problems [7]. Thus, the FE-based optimization method for inverse evaluating the CHTC has achieved rapid development recently. Tondini et al. [8] predicted the CHTC at the Usibor1500P sheet-die interface using the method and investigated its variations with the pressure and die material. Hu et al. [9] adopted the method to identify the CHTC at the Usibor1500P sheet-die interface and revealed the impacts of the pressure, average interface temperature, and oxide scale thickness on the CHTC. Li et al. [10] estimated the CHTCs at the B1500HS sheet-die interface under various pressures by using the independently developed FE-based optimization software. In the procedure of the FE-based optimization method, an experimental setup generally needs to be designed for measuring temperatures of the sheet and/or dies. However, in the experimental setups developed by the above studies, besides the CHTC, the temperatures at measurement points are influenced in different extents by the heat transfer at the water-die, air-die, or worktable-die interfaces. The heat transfer at these interfaces is usually set in terms of experience in FE modeling of the experiments, which probably reduces the evaluation accuracy of the CHTC. So, Salomonsson et al. [11] developed an experimental setup, where the heat transfer is related only to the CHTC, to measure the surface temperatures of the sheet and dies, and used the FE-based optimization method to identify the CHTCs under various pressures. Table 1
Unfortunately, the experimental setup is complex in structure and high in cost. In fact, the heat transfer at the sheet-die interface consists of the heat conduction at real contact points, the heat conduction of air in contact gap, and the thermal radiation. Besides, the oxide scale with lower thermal conductivity exists on the surface of the sheet without coating [11]. The above three methods for evaluating the CHTC commonly need to measure the temperature of the sheet and/or dies through experiments. Therefore, the CHTCs evaluated by these methods are equivalent, considering the integrated effects of the above three heat conduction mechanisms and oxide scale. The HSBS process includes the stamping and the die quenching stages. Usually, the former is conducted in less than 2 s, but the time for the latter is greater than 10 s. As a result, the contact heat transfer mostly occurs in the die quenching stage, in which the equivalent contact heat transfer coefficient (ECHTC) is affected by many factors, such as the contact pressure, the material of the sheet and dies, and the gap between the sheet and dies [9]. Research reported that the contact
Chemical composition of B1500HS (mass fraction, %)
C
Mn
B
Si
Cr
S
P
Fe
0.21
1.35
0.003
0.28
0.23
0.04
0.0055
97.9 Fig. 2 Specimen instrumented with thermocouple
Int J Adv Manuf Technol Fig. 3 Schematic diagram of positions of temperature measurement points
pressure is the most dominant factor influencing the ECHTC [4, 8–10]. In the study, a simple and effective physical simulation setup for die quenching of boron steel (DQBS) was developed, in which the temperatures at measurement points are related only to the ECHTC for enhancing the evaluation accuracy. The FE-based optimization method was used to inversely evaluate the ECHTC. The ECHTCs at the B1500HS sheet-H13 die steel interface under different pressures were identified and analytically modeled. Both the physical simulation of DQBS and the HSBS experiment were carried out to prove the reliability of the ECHTC evaluated.
2 Methodology 2.1 Physical simulation setup for DQBS The physical simulation setup for DQBS developed by the study is illustrated in Fig. 1. The specimen is pressed between the upper and lower quenching dies to physically simulate the actual state in DQBS. There are insulation boards synthesized by glass fiber and high heat-resistant composite between the quenching dies and worktables for preventing heat from transferring to the equipment. The insulation boards are connected to the worktables by joint plates and screws. The material of Fig. 4 Control system of nitrogen-based protective atmosphere
specimen is B1500HS, and its chemical composition is listed in Table 1. The specimen is 1.8 mm in thickness and 80 mm in diameter, as shown in Fig. 2. The quenching dies made of H13 steel have a thickness of 10 mm and a diameter of 80 mm. Figure 3 is the schematic diagram of positions of temperature measurement points. The temperature at P1 is used to evaluate the ECHTC, which is verified by the temperatures at P2 and P3. The K-thermocouples welded onto the measurement points are connected to the dynamical data acquisition system DDS16-32 to measure and collect temperature, with the sampling frequency of 10 HZ. In the setup, the heat transfer at measurement points can be simplified as a transient one-dimensional problem in the contact heat transfer direction, i.e., the temperatures at measurement points are related only to the ECHTC, so as to improve the evaluation accuracy. This is justified by three respects. First, considering the thin thicknesses, both the specimen and quenching dies can be viewed as large plates, where all the measurement points locate at the circumference center, far from the boundary, so that the air convection and thermal radiation have little effects on the temperatures at measurement points. Second, the insulation boards between the quenching dies and worktables can prevent heat from transferring to the equipment. Finally, the sheet does not deform in experiments to eliminate the impacts of deformation heat and frictional heat on heat transfer.
Int J Adv Manuf Technol Fig. 5 A FE model for physical simulation of DQBS
2.2 Inverse evaluation of ECHTC
rotating body. The transient heat transfer analysis was conducted because the sheet did not deform in experiments. The symmetry axis and boundary of the model were set as be adiabatic. The sheet had a density of 7850 kg/m3 [9], and its thermophysical properties were from literature [12]. The density and thermophysical properties of the die material were obtained from literature [10]. The quadrilateral solid element was chosen to discretize the model. Then, a FE-based optimization model was developed to inversely evaluate the ECHTC. The design variable is the ECHTC, and the objective function is the maximum relative error between the simulation and measured values of temperature history at P1. The optimization objective is expressed by: e s N T i; j −T j f ðxÞ ¼ max ð1Þ ≤ δ i ¼ 1; 2; ⋯; M j¼1 T ej
A FE model for physical simulation of DQBS was established based on ANSYS, as illustrated in Fig. 5. The model can be simplified as an axisymmetric problem since its geometry is a
where x is the value of the ECHTC, j the times of temperature acquisition in each experiment, i the optimization iteration s times, Ti,j the simulation value of temperature at jth acquisition
The experiments were carried out on the electronic universal testing machine CMT5305. In order to form the oxide scale comparable to the practical one on the sheet surface, the specimen was heated to 950 °C and held for 5 min in the box type resistance furnace filled with nitrogen-based protective atmosphere through the self-developed control system (Fig. 4). Then, the specimen was quickly transferred to the quenching dies to be cooled for 30 s. For ensuring the same initial condition, the initial quenching temperatures of the specimen and dies were set as 800 and 65 °C, respectively. Five pressure levels (5, 10, 20, 30, 40 MPa) were selected within the range involved in practical hot stamping applications. Under each pressure, the experiment was performed for three times and the average values were adopted.
Fig. 6 Flow chart of inverse evaluation of ECHTC
Start Set initial value of ECHTC FE solution of transient heat transfer problem
Input measured value of temperature history at P1
Obtain simulation value of temperature history at P1
Adjust value of ECHTC
Calculate value of objective function
If E q.(1) is valid˛ Yes Output value of ECHTC End
No
Int J Adv Manuf Technol 6000
240
4000
3000
2
R =0.9914 2000
5MPa 10MPa 20MPa 30MPa 40MPa
220
7HPSHUDWXUH˄ć˅
'DWD )LWWLQJFXUYH
5000
(&+7&:Pg.
after the ith iteration, Tej the measured value of temperature at jth acquisition, and δ the accuracy of the objective function. The first-order algorithm in ANSYS was used as the optimization method, with which the number of iterations ranged from 4 to 11 for the inverse evaluation processes under various contact pressures. Figure 6 is the flow chart of inverse evaluation of the ECHTC.
200 180
1000 0
5
10
15
20
25
30
35
40
45
&RQWDFWSUHVVXUH03D
160
Fig. 8 Variation of ECHTC with pressure
140 120
3 Results and discussion
100 80
3.1 Temperature history in physical simulation of DQBS
60 0
(a)
5
10
15
20
25
30
7LPH˄V˅
7HPSHUDWXUH˄ć˅
140
120
5MPa 10MPa 20MPa 30MPa 40MPa
100
80
60
(b)
0
5
10
15
20
25
30
7LPH˄V˅
Figure 7 demonstrates the temperature history curves at measurement points under different pressures, in which the zero of time is the moment when the upper quenching die starts to contact with the sheet. In Fig. 7a, the temperatures at P1, which is closer to the sheet, increase sharply to peaks and then rapidly decrease under different pressures; the higher the pressure, the more quickly the temperature rises and the higher the peak. Figure 7b shows that the temperature at P2, which is far from the sheet, rapidly increases followed by a slow decrease under 40 MPa while quickly and then slowly increases under the other pressures; the higher is the pressure, the higher is the temperature. The temperatures at P3, which locates at the sheet canter, sharply decrease and subsequently tend to become steady under different pressures; the higher the pressure, the more quickly the temperature reduces, as shown in Fig. 7c.
800
600
/LHWDO[10] +XHWDO[9] 7RQGLQLHWDO[8] 0HUNOHLQHWDO[3] &DURQHWDO[6] 7KLVVWXG\
8000
(&+7&˄:Pg.˅
700
7HPSHUDWXUH˄ć˅
9000
5MPa 10MPa 20MPa 30MPa 40MPa
500 400 300
7000 6000 5000 4000 3000
200 2000
100
(c)
0
5
10
15
20
25
30
7LPH˄V˅
Fig. 7 Temperature history curves at measurement points under different pressures. a P1. b P2. c P3
1000 0
5
10
15
20
25
30
35
40
45
&RQWDFWSUHVVXUH˄03D˅
Fig. 9 Comparison between ECHTCs evaluated by different studies
50
Int J Adv Manuf Technol
3.2 ECHTC identified by inverse evaluation Figure 8 shows the ECHTCs identified by inverse evaluation under different pressures. It can be seen that the ECHTC increases exponentially with the pressure. This may be caused by the increased real contact area and thus the decreased
interface thermal resistance. The relationship between the ECHTC and pressure can be described by the following exponential function, with the correlation coefficient of 0.9914: y ¼ −63:62 þ 919:24expðx=22:38Þ where y is the value of the ECHTC and x is the pressure.
900
900
P2-measured value P2-simulation value P3-measured value P3-simulation value
700
800
7HPSHUDWXUH˄ć˅
7HPSHUDWXUH˄ć˅
800
600
Contact pressure=5MPa
500 400 300
500
Contact pressure=30MPa
400 300 200
100
100
0
5
10
15
20
25
30
7LPH˄V˅
0
10
15
20
25
30
7LPH˄V˅ 900
800
800
600
7HPSHUDWXUH˄ć˅
P2-measured value P2-simulation value P3-measured value P3-simulation value
700
Contact pressure=10MPa
500 400 300
600
P2-measured value P2-simulation value P3-measured value P3-simulation value
500
Contact pressure=40MPa
700
400 300
200
200
100
100
0
(b)
5
(d)
900
7HPSHUDWXUH˄ć˅
600
P2-measured value P2-simulation value P3-measured value P3-simulation value
700
200
(a)
ð2Þ
5
10
15
20
25
30
7LPH˄V˅
0
(e)
5
10
15
20
25
30
7LPH˄V˅
900
7HPSHUDWXUH˄ć˅
800
600
P2-measured value P2-simulation value P3-measured value P3-simulation value
500
Contact pressure=20MPa
700
400 300 200 100
(c)
0
5
10
15
20
25
30
7LPH˄V˅
Fig. 10 Comparisons between predicted and measured temperature histories under different pressures. a 5 MPa. b 10 MPa. c 20 MPa. d 30 MPa. e 40 MPa
Int J Adv Manuf Technol Fig. 11 Experimental dies and formed part of hot stamping of Ushaped beam
The comparison between ECHTCs evaluated by different studies is presented in Fig. 9. For different studies, the variations of the ECHTC with pressure follow a similar trend, but the discrepancy among them was found regarding the value of the ECHTC. Comparatively speaking, the difference between the result from Li et al. [10] and that from Tondini et al. [8] is smaller, while the result from Hu et al. [9] is closer to that from Merklein et al. [3]. The result obtained by this study lies roughly between the above two groups. Caron et al. [6] predicted an obviously greater result than other researchers. The discrepancy among these results may be due to the material property fluctuation and the differences in the coating state and oxide scale thickness on the sheet surface, the die material, the surface roughness of the sheet and dies, etc. 3.3 Verification of ECHTC 3.3.1 Verification by physical simulation of DQBS The relationship of the ECHTC with pressure expressed by Eq. (2) was embedded into the FE model for physical simulation of DQBS illustrated in Fig. 5. The simulation values of temperature histories at P2 and P3 are obtained and compared with the measured values presented in Fig. 7b, c under
Fig. 12 A quarter of FE model for hot stamping of U-shaped beam
different pressures, as shown in Fig. 10. Good agreement was observed between the simulation values and the measured ones, with the maximum relative error of 9.6 % appearing at about 6.5 s in the temperature history of P3 under the pressure of 5 MPa, which indicates the reliability of the ECHTC evaluated. The error may arise from solution algorithm for nonlinear FE heat transfer analysis and the temperature measuring system itself, including thermocouple temperature measurement, measurement positions, the dynamical data acquisition system, the heat loss in the transverse direction, etc.
3.3.2 Verification by HSBS experiment The experiment of hot stamping of U-shaped beam was conducted to further verify the ECHTC. The experimental dies and hot stamped part are presented in Fig. 11. The sheet and dies had identical material with that in the physical simulation of DQBS, and their initial temperatures were 900 and 20 °C, respectively. The velocity of the punch was 20 mm/s in the stamping stage. The dwell time was 10 s, and the flow velocity through the cooling water channel was 700 mm/s in the quenching stage. The temperature was measured at points A, B, and C, which were 5 mm distance from the surfaces of the side, round corner, and bottom of the punch, respectively, as
Fig. 13 Comparisons between predicted and measured temperature histories at measurement points in hot stamping of U-shaped beam
Int J Adv Manuf Technol
illustrated in Fig. 12. The temperature measurement method was the same as that in the physical simulation of DQBS. Figure 12 illustrates a quarter of the coupled thermomechanical FE model for the process. In order to improve computational efficiency, only a quarter of the model was established allowing for the symmetry in both the geometry and load. Besides, the region far away from the cooling water channel was removed from the die geometry. The coupled thermo-mechanical hexahedron element (C3D8RT) with eight nodes was selected to discretize the model, with five layers of element along the thickness of the sheet. Reduction integration and hourglass control were applied to save computational time and avoid the zero-energy mode caused by the bending mode of deformation, respectively. Four contact pairs were defined between the sheet and the ejector, punch, and die, respectively. There are contact heat transfer and friction at the interface of each contact pair. At each contact interface, the ECHTC was assumed to be defined by Eq. (2), and it was assumed that half of the heat dissipated as a result of friction is conducted into the sheet. Relative sliding existing at the interfaces contributes to describing the friction with the Coulomb friction model, with the friction coefficient of 0.4 [13]. The predicted temperature histories at measurement points are compared with the measured ones, as presented in Fig. 13. In Fig. 13, the three points have increasing temperatures in the stamping stage (0–2 s); during the die quenching stage (2– 12 s), the temperature at point A continues to rise slowly, while the temperatures at the other two points rise to peaks in 2–4 s and then drop; point C is between points A and B in temperature. Furthermore, simulation values are greater than measured ones for all three points, with the maximum relative error of 19.7 % occurring at about 0.2 s in the temperature history of point A, which suggests the reliability of the ECHTC for the more complex problem. The sources of the error may include the inverse evaluation error of the ECHTC, the nonuniform temperature distribution of the sheet caused by the transfer from the furnace to dies, the material property fluctuation of the sheet and dies, and the dynamic change in thermal friction state.
comparison of the predicted with measured temperature histories at measurement points in physical simulation of DQBS, the maximum relative error of 9.6 % was observed, which indicates the reliability of the ECHTC evaluated. In order to prove its reliability for the more complex problem, the HSBS experiment was performed and the maximum relative error of 19.7 % was found between the predicted and measured temperature histories at measurement points. The study has great significance for controlling the local cooling rate of the sheet in HSBS and hence obtaining components with tailored microstructure and properties. In addition, it can provide a reliable thermal boundary condition for numerical simulation of the HSBS process. Acknowledgments The authors would like to thank the National Nature Science Foundation of China (51205116), the Natural Science Foundation of Hubei Province (2014CFB628), the Outstanding Young Scientific & Technological Innovation Team Plan of Colleges and Universities in Hubei Province (T201518), the Open Fund of State Key Laboratory of Materials Processing and Die & Mould Technology (2012-P12), and the PhD Scientific Research Fund of Hubei University of Automotive Technology (BK201102) for the support given to the research.
References 1. 2.
3.
4.
5.
6.
7. 8.
4 Conclusions 9.
A simple and effective experimental setup for physical simulation of DQBS was developed, where the temperatures at measurement points are related only to the ECHTC so as to lay foundation for the accurate evaluation of the ECHTC. A FE-based optimization model for inverse evaluating the ECHTC was established, and thus the ECHTCs under various pressures (5–40 MPa) at B1500HS sheet-H13 die steel interface were identified. It was found that the ECHTC increases exponentially with the pressure increasing, and the relationship between them was modeled analytically. Through the
10. 11.
12. 13.
Karbasian H, Tekkaya AE (2010) A review on hot stamping. J Mater Process Technol 210:2103–2118 Lim WS, Choi HS, Ahn SY, Kim BM (2014) Cooling channel design of hot stamping tools for uniform high-strength components in hot stamping process. Int J Adv Manuf Technol 70(5):1189–1203 Merklein M, Lechler J, Stoehr T (2009) Investigations on the thermal behavior of ultra high strength boron manganese steels within hot stamping. Int J Mater Form 2(Suppl 1):259–262 Hung TH, Tsai PW, Chen FK, Huang TB, Liu WL (2014) Measurement of heat transfer coefficient of boron steel in hot stamping. Procedia Eng 81:1750–1755 Abdulhay B, Bourouga B, Dessain C (2011) Experimental and theoretical study of thermal aspects of the hot stamping process. Appl Therm Eng 31:674–685 Caron E, Daun KJ, Wells MA (2014) Experimental heat transfer coefficient measurements during hot forming die quenching of boron steel at high temperatures. Int J Heat Mass Tranf 71:396–404 Beck J, Bleckwell B, Clair C (1985) Inverse heat conduction. Wiley, New York Tondini F, Bosetti P, Bruschi S (2009) An experimental numerical procedure to identify heat transfer coefficient in hot stamping processes. Proc. of 7th Euromech Solid Mechanics Conf., Lisbon, Portugal Hu P, Ying L, Li Y, Liao ZW (2013) Effect of oxide scale on temperature-dependent interfacial heat transfer in hot stamping process. J Mater Process Technol 213:1475–1483 Li HP, He LF, Zhao GQ (2013) Research on the surface heat transfer coefficient depending on surface. J Mech Eng 49(16):77–83 Salomonsson P, Oldenburg M, Akerstrom P, Bergman G (2008) Experimental and numerical evaluation of the heat transfer coefficient in press hardening. In: Steihoff K, Oldenburg M, Prakash B (eds) Hot sheet metal forming of high-performance steel. Proceedings, CHS2: 1st International Conference: 267–274 Holman JP (2010) Heat transfer. McGraw-Hill, New York Naganathan A (2010) Hot stamping of manganese boron steel. Dissertation, The Ohio State University