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Advances in Mechanical Engineering

Volume 2013 (2013), Article ID 829379, 10 pages

http://dx.doi.org/10.1155/2013/829379

## The Effect of Process and Model Parameters in Temperature Prediction for Hot Stamping of Boron Steel

^{1}School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China^{2}Department of Mechanical Engineering, Imperial College London, London SW7 2AZ, UK^{3}IMRA Europe S.A.S. U.K. Research Centre, University of Sussex, Brighton BN1 9RS, UK^{4}Department of Mechanical Engineering, University of Birmingham, Birmingham B15 2TT, UK

Received 1 September 2013; Accepted 1 November 2013

Academic Editor: Dae-Cheol Ko

Copyright © 2013 Chaoyang Sun et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Finite element models of the hot stamping and cold die quenching process for boron steel sheet were developed using either rigid or elastic tools. The effect of tool elasticity and process parameters on workpiece temperature was investigated. Heat transfer coefficient between blank and tools was modelled as a function of gap and contact pressure. Temperature distribution and thermal history in the blank were predicted, and thickness distribution of the blank was obtained. Tests were carried out and the test results are used for the validation of numerical predictions. The effect of holding load and the size of cooling ducts on temperature distribution during the forming and the cool die quenching process was also studied by using two models. The results show that higher accuracy predictions of blank thickness and temperature distribution during deformation were obtained using the elastic tool model. However, temperature results obtained using the rigid tool model were close to those using the elastic tool model for a range of holding load.

#### 1. Introduction

Hot stamping of boron alloyed steels is a process for manufacturing high strength, lightweight, and sheet metal parts. It plays a major role in the automobile manufacturing industry, where the aim is to reduce vehicle weight while enhancing strength, particularly of safety-relevant parts [1]. In the process, a heated blank sheet is simultaneously formed and quenched by pressing it between unheated tools. The strong martensitic structure thus produced enables components of thinner gauge to be substituted for conventionally cold formed weaker parts. The process comprises coupled thermomechanical forming to obtain an intended phase transformation [2], which strongly depends on temperature history and mechanical deformation [3]. Therefore, the prediction of product properties arising from the manufacturing process requires detailed knowledge of heat transfer during the entire manufacturing process, which includes hot forming and cool die quenching from approximately 900°C to room temperature [4].

Coupled thermomechanical analysis has been used to predict material behaviour during the hot stamping process [5]. In the coupled system, interaction between mechanical and thermal fields must be considered. Knowledge of temperature and strain rate dependent material flow behaviour is also required to characterise the plastic deformation. Heat transfer between the blank and the tools as well as heat loss due to convection and radiation from the blank is essential for accurate FE thermomechanical analyses. Recently, FE simulation using proprietary software such as LS-DYNA, Auto-Form, PamStamp, and ABAQUS was used to analyse the hot stamping process. For example, analysis using the FE software LS-DYNA was performed using thermally coupled mechanical shell elements for the metal sheet [3].

Temperature distribution and history have a significant effect on microstructural evolution and hence mechanical properties [6–8], within a formed part therefore, accurate prediction of temperature in a blank plays a very important role in FE simulation. Temperature with a blank depends on starting temperature, temperature changes during transport, and temperature transfer at the tool interface. Therefore, knowledge of the value of the boundary condition, tool/workpiece heat transfer coefficient, is necessary for prediction of the temperature field [3]. An experimental procedure to estimate the thermal conductance at the blank to tool interface during a hot stamping procedure has been presented [9]. In their research temperature change of the dies was obtained, and the heat transfer coefficient between the steel blank and dies for different materials was identified. It has been found that heat transfer coefficient strongly depends on contact pressure at the interface [10].

With regard to tool definition in FE simulation, the hot stamping of a U-channel with 22MnB5 boron steel has been simulated using thermal shell elements to define the tools [4]. Due to the finite thickness of shell elements, the FE model with shell element tools cannot be used to describe the heat transfer phenomenon. Akerström et al. [5] have used rigid solid element tools to simulate the hot stamping process. However, the elastic deformation of tools cannot be predicted using rigid elements.

To obtain maximum strength and hardness, a work-piece must be quenched in the tools rapidly and this requires the temperature of the tools to be low. In mass production frequent contact of workpiece and tools under pressure causes tool temperature to rise and thus quench rate to fall. Therefore, to ensure that tool temperature is always low enough for the quench rate to be sufficient to obtain the desired phase transformation, the tools are cooled normally using water flowing in subsurface cooling ducts [11]. More efficient cooling is obtained by increasing the total cross-sectional area of the cooling ducts and situating them as close as possible to the tool surface, and, in general, the size and disposition of the ducts are limited by tool strength considerations. However, the size and disposition of cooling ducts often are based on knowledge and intuition; hence the aim of the work described in this paper is to demonstrate a methodology using finite element modelling and simulation to study the effect of tools with cooling ducts and process conditions on tool/workpiece heat transfer and tool temperature when hot stamping boron steel.

Generally tools can be modelled as rigid or elastic parts and an FE model with rigid tools costs less computational time. However, elastic tool deformation will affect tool/workpiece contact pressure distribution and tool/workpiece clearance, which will affect heat conduction. Therefore the use of elastic tools is likely to result in greater accuracy, particularly for high forming loads. For comparison, forming with either rigid or elastic tools has been simulated. Heat loss prior to forming and during forming is calculated using mathematical models taken from the literature.

In order to determine the thermomechanical characteristics of 22MnB2 steel, a set of dislocation-based hardening constitutive equations was embedded in FE software. The FE model was validated by comparing experimental and FE results, for temperature distribution and workpiece thickness distribution. Also the effect of forming load on heat transfer was investigated.

#### 2. Experimental Setup and Method

The blank material was boron steel of initial thickness 1.6 mm. The length and the width of the blank were 120 mm and 100 mm, respectively. As shown in Figure 1, the tool set consisted of a punch and a die of constant dimensions along their length. Three cooling ducts were located in the punch, and four cooling ducts were located in the die. The material of the tools was H13 steel. The geometric dimensions of the die and the punch are as shown in Figure 1. By increasing the number and the size of the cooling ducts, the cooling rate of the blank during the cool die holding period could be increased. However, on the other hand, a smaller number and size of cooling ducts would reduce the elastic deformation of the tools, that is, die deflection, during the forming process and also tool stresses. In this study, the cooling ducts had a radius of 3.5 mm and the minimum distance between the nearest duct surface and tool surface was 10 mm. The ducts were filled with flowing water.

As shown in Figure 2, hot stamping tests for boron steel were performed in a hydraulic press with a nominal maximum load capacity of 25 MN. Blanks were heated in an electric furnace to 850°C and held for 300 s to ensure full austenitization, and then it was quickly transferred to the water-cooled die as shown in Figure 2(b) and deformed by the water-cooled punch. The deformed part was held under pressure in the tool for various time periods. Temperature distribution in a blank after hot stamping and cold die quenching was measured using a thermal camera situated at one side of the tool.

#### 3. Development of the FE Model

##### 3.1. Material Model

Various semiempirical and physical-based material models for boron steel have been proposed [1] and a set of unified material modelling equations, including phase transformation, was developed and utilised in finite element simulations by Oldenburg et al. [3]. In their equations, material hardening in the viscoplastic deformation was attributed to the accumulation of plastic strain only. Recently dislocation-based hardening constitutive equations have been developed by [12], in which the recovery of dislocations due to annealing and recrystallisation was included for hot forming boron steel. Also, Li et al. [13] developed a set of unified viscoplastic constitutive equations for boron steel in which damage was considered. In this paper damage accumulation was ignored to simplify the constitutive model. The constitutive equations are shown as where and are total and plastic strains. Equation (1) describes the viscoplastic material flow by power law. is internal stress due to isotropic hardening, and is the initial yield stress. Equation (2) is based on Hook’s law. is flow stress, and is the Young’s modulus of the material. The material hardening (3) is calculated according to the accumulation of dislocation density. Equation (4) calculates normalised dislocation density. The first term of (4) represents the dislocation accumulation due to plastic deformation and the second term is related to the static recovery of dislocation at hot forming conditions. The constants , , , , , and are temperature-dependent parameters and can be formulated by the Arrhenius equation as shown in Table 1. and are material constants. The determined material constants are given as shown in Table 2 [13].

##### 3.2. FE Model for Different Tool Properties

A three-dimensional finite element model of hot stamping and cool die quenching, which represents the tool geometry shown in Figure 1, is shown in Figure 3. Due to symmetry, only a half of the blank is used in the simulation for simplicity and efficient calculation. The planes of symmetry are shown in Figure 3.

In the FE model, the dimensions of the blank sheet were the same as those used for the practical tests. A shell element with seven integration points through the thickness was used for the blank, and an adaptive meshing technique was activated for an accurate representation of geometry. A key problem in all FE simulations is to ensure that material behaviour is correctly modelled. The unified viscoplastic damage constitutive equations determined by [13] were integrated with Ls-dyna/Explicit via a user defined material subroutine. For the thermal analysis, the thermal properties for boron steel published by Shapiro [14] were used; heat capacity and thermal conductivity were 6.5 × 108 J/(kg·K) and 30.0 W/(m·K), respectively.

In this paper hexahedral solid elements were used in the tools. To correctly capture the thermal contact between hot blank and cold tool surface, the element size in the tool close to the interface was less than 1 mm. To obtain an accurate representation of tool curvature, five to eight elements were used to define the radii. Estimation of the time step was based on the initial mesh and the material properties of the element in the FE model. A typical hot forming and cool die quenching process consists of essentially furnace heating, air cooling during the transport, hot forming, cool die quenching by conduction, and air cooling. The thermal time step during forming is relatively small due to the high cooling rate. Therefore a mass scaling factor for the thermal analysis was used in the process apart from the hot forming, to reduce computational time.

The locations of the cooling ducts can be seen in Figure 3. It is necessary to apply a high load to the tools during the dwell period, to ensure that the rate of heat transfer to the tools is maximised. Thus it is likely that significant distortion of the tool surface will occur. The distortion could affect heat transfer between blank and tools and for accurate prediction of workpiece mechanical properties, tool properties must be allowed for.

To understand the influence of elastic deformation of tool on temperature distribution in a blank, two finite element models were built: one with rigid tools, the other with elastic tools. For the rigid tool model solid elements were adopted. For the elastic tool model, a temperature-dependent Young’s modulus was assigned to the die and the punch. A dummy rigid mesh and a constant velocity of 50 mm/s were defined to control the displacement of the punch. Different loads with a range from 50 kN to 600 kN were applied on the top surface of the punch. The initial temperature of the blank was 850°C, and the initial temperature of tools was 20°C. Temperature within the cooling duct remained constant at 20°C.

##### 3.3. Simulation Parameters

The simulation stages mirrored those experienced in the practical tests. A heated blank was assumed to be fully austenitized when taken from the furnace and the hot forming and cold die quenching process was divided into three steps, as shown in Figure 4.

During transport time of 1.2 s cooling of the blank due to convection and radiation occurred. When the blank was placed in the die and during deformation, heat was lost mainly by conduction. In the forming stage, thermal-mechanical analysis was carried out. Mechanical contact between blank and tools was defined using a rate-independent friction model with a static friction coefficient of [15]. The heat transfer between the tools and the formed part and heat convection between the tools and air were simulated by using heat equations. During forming, the punch velocity was 50 mm/s and the forming stroke was 40 mm. Due to the temperature dependent mechanical properties of boron steel, the stress field is varied with the change of temperature during deformation; therefore thermomechanical analysis was conducted in the FE simulation. The third step was cold die quenching. After hot deformation, tools and the blank remained in contact under pressure, generated by the punch load of 500 kN, for a period of either 3 s, 5 s, or 7 s.

##### 3.4. Heat Transfer Coefficient for Different Contact Conditions

Heat loss was considered to be due to air convection during transport and radiation and conduction between blank and tools during forming [16]. In this coupled thermomechanical process, heat conduction between blank and tools has the greatest effect on mechanical properties of the formed part. In this work, convection and radiation heat transfer coefficients were defined as 20 W/m^{2 }K and 4.536 × 10^{−8} W/m^{2} K^{4} by using standard empirical equations from the literature [14].

When the blank was placed on the bottom tool heat transfer coefficient was defined as a function of the gap between blank and tools. Gaps between blank and tools at different locations were calculated automatically by Ls-Dyna. A useful modelling technique to define heat transfer coefficient as a function of gap is described as where is defined as thermal conductivity between the contact surfaces, which equals 0.06 N/(s·K) [10]. When the gap is greater than the maximum value , of 2 mm, it was assumed that no heat was exchanged or radiated between the blank and the tools. Therefore, the effective heat transfer coefficient, , is defined as zero at the locations where the gap is larger than 2 mm. When the gap between the blank and tools ranges from the maximum value to the minimum value of 0.03 mm, the effective heat transfer coefficient, , is inversely proportional to the gap.

When the blank was held firmly in contact with the tools, the conductive heat transfer coefficient was defined as a function of pressure [17]. As shown in Figure 5, with increasing contact pressure, heat transfer between the blank and dies increases, as a consequence of the increased real contact area between blank and dies [16]. Taking these three types of heat transfer into account, the heat transfer coefficient was defined as (6) in the FE model:

#### 4. Experimental Validation of the FE Modelling Results

##### 4.1. Temperature Distribution in the Blank

In the practical stamping tests, temperature distribution in a blank after unloading was captured using a thermal camera. As shown in Figure 6(a), a further cooling stage was added to those shown in Figure 4. The procedure consisted of air cooling during transport (SA1), forming (SF), and cold die quenching (SH) and then cooling by air in open dies (SA2). The SA1 stage lasts for 1.2 s, SF stage lasts for 0.8 s, and SH stage lasts for either 3 s, 5 s or 7 s. Due to the fact that in the tests it took 8 s for the thermal camera to capture the temperature distribution, in order to compare the corresponding temperature distribution from the thermal camera with those from the FE simulation, an additional 8 s duration air cooling stage SA2 was included in the FE model.

In order to validate the FE model, the measured and calculated temperature distributions of the blank in the FE models with rigid tool property and elastic tool property have been compared. Figure 6 shows blank temperature distribution at a holding time of 3 s, 5 s, and 7 s, respectively.

From Figure 6(b), it can be seen that when holding time was 3 s, that is, total time 13 s, the highest experimental temperature of about 197°C was found in the straight wall area (area I in Figure 6(b)). It could be attributed to a lower interfacial workpiece/tool pressure in this region. The maximum temperatures near the bottom of groove (area II in Figure 6(b)) and the flange (area III in Figure 6(b)) were about 182°C and 140°C. When the holding time was 5 s, that is, total time 15 s, the maximum temperature at the bottom groove, straight wall, and flange were 142°C, 187°C, and 131°C, respectively. When the holding time was 7 s, that is, total time 17 s, the maximum temperature at the bottom groove, straight wall, and flange were 114°C, 129°C, and 90°C, respectively.

From Figures 6 and 6, it can be seen that the temperature distributions after different holding times predicted by the FE models with elastic tools and the rigid tools are very similar to those measured experimentally. The maximum temperature and the minimum temperature at three typical areas are in good agreement with the experimental temperature. For the rigid tool model maximum error between the predicted and measured temperatures was 19°C when the holding time was 7 s, while for the elastic tool model the maximum error between the predicted and the measured temperatures was 10°C when the holding time was 7 s. Therefore, it is assumed that the FE model developed in this paper can be used to predict the heat transfer behaviour for the blank and the tools. Moreover, the temperature predicted by elastic tool model is closer to experimental test results than that predicted using the rigid tool model.

##### 4.2. Thickness Distribution in the Blank

The thickness distribution of the blank reflects material flow in the hot stamping process. Blank thickness was measured along a crosssection after the workpiece was taken out of the die. Relative thickness is used to describe the thickness change. Figure 7 shows comparisons of the relative thickness distribution obtained from FE results assuming rigid tools and elastic tools with experimental results at eight locations. It can be seen that predicted relative thicknesses of both models agree well with experimental results. The measured and simulated minimum relative thicknesses of rigid tool model and elastic tool model were 0.920, 0.916, and 0.925, respectively.

The relative thickness resulting from using elastic tools is larger than that from using rigid tools and is closer to the experimental results. This can be attributed to cavity enlargement due to elastic deformation. There is less tension stress at the second, fourth, fifth, and sixth locations, where smaller thinning can be found. It can be seen that maximum thinning occurred at location 2. Probably, this is because in the early deformation stage the sheet becomes trapped at location 3 and is stretched to fill the region between location 3 and location 1, the point of symmetry where no flow occurs.

The close match of predicted workpiece temperature and workpiece thickness, with practical experimental results, provides reasonable validation of the FE model.

#### 5. Predictions of In-Process Variables

##### 5.1. Temperature History at Typical Locations

Figure 8 shows temperature histories at four locations, under the holding load 50 kN. Locations A, B, C, and D can be found in the final shape of the workpiece. The temperature histories show the temperature at corresponding locations at different times. It can be seen that little difference in temperature arises between the use of rigid and elastic tool models after final air cooling.

The temperature at location C and location D decreased sharply to 780°C at time 1.2 s. The rate of temperature reduction was less at locations A and B, where temperature was approximately 839°C at 1.2 s. This is due to the fact that, in the first 1.2 s, the flat blank was placed on the lower die. As shown in Figure 3, the workpiece was supported by the water-cooled lower die. As a result, before the punch touched the workpiece, heat transfer for locations A and B was attributed to air convection; heat transfer for locations C and D was attributed to heat conduction with the lower die.

After 1.2 s, that is, during deformation local die/work-piece, contact pressures for elastic tools were lower, compared with those for rigid tools; therefore, heat transfer was lower and workpiece temperature generally was higher. However, on full closure, for the perfectly shaped modelled tools, firm contact occurred equally in both rigid and elastic tools and temperatures rapidly equalised.

In the quenching process, the microstructure of the blank varies corresponding to the cooling rate. According to the CCT diagram of boron steel when the cooling rate exceeds 35°C/s, the martensite microstructure can be obtained for the blank. In Figure 8 it is indicated that the average cooling rate was 97°C/s, 95°C/s, 75°C/s, and 95°C/s at locations A, B, C, and D, respectively. The cooling rate at location C was relatively smaller. It is due to the fact that the location C is in the wall region, and thus the contact pressure at location C was lower; therefore the less heat transfer occurred between the blank and dies.

##### 5.2. The Effect of Holding Load on the Temperature

Figure 9 is a comparison of temperature at four locations at the end of the 5 s holding process when the holding load varies between 50 kN and 600 kN. It can be seen that the predicted temperature for the elastic tool model was higher than that for the rigid tool model when the holding load changed between 50 kN and 150 kN. Due to the elastic deformation in the elastic tool model contact pressure on the blank is less than that for the rigid tool model. At locations A, B, and D, which are on horizontal or near horizontal surfaces, for loads above about 200 kN temperature is not reduced, whereas at location C, increasing load reduces temperature always. This is because, on horizontal surfaces, the increase of load results in the increase of surface contact pressure. According to Figure 5, the heat transfer coefficient increases to a maximum value with the increase of contact pressure until the surfaces between the workpiece and tools are completely in contact, and then it remains constant for further increases in pressure. Therefore temperature decreases with the increase of the load when the load is lower than 200 kN and is not decreased further with higher loads. However, tool surfaces at location C are nearly vertical and unless tool dimensions are perfect, lower pressures will arise on them. Lower temperatures exist for elastic tools because they can accommodate themselves and close gaps. This is more apparent on the near vertical surfaces than on the horizontal ones.

Generally when the holding load is between 150 kN and 300 kN the difference in temperature predictions using elastic and rigid tool is small. Since the simulation time for elastic tools is four to five times longer than that for rigid tools, the rigid tool model is recommended for FE simulation when the holding load is between 150 kN and 300 kN, as it takes less computer CPU time.

##### 5.3. The Effect of a Cooling Duct on the Temperature

Figure 10 shows the temperature at location C with different loads when the radius of the cooling duct was either 3.5 mm or 6 mm. For the smaller cooling duct and a lower load, the temperature predicted by the elastic tools was similar with that by rigid tools. For the larger cooling duct and higher load, the temperature predicted for elastic tools was lower than that for rigid tools. This is attributed to the fact that with the large cooling duct radius, a larger elastic deformation of tools occurred when the applied holding load was increased. It can be seen in Figure 11, with a 6 mm radius of cooling duct, the horizontal displacement of the tool surface was larger; therefore it resulted in a smaller gap between the punch and the die, and thus contact pressure increased.

#### 6. Conclusions

FE models, utilising both rigid and elastic tools, have been created to predict workpiece/tool heat transfer in hot stamping cold die quenching of a boron steel beam part. Corresponding practical tests were carried out and the numerical prediction results were validated by the comparison of empirically obtained temperature and thickness distribution of the formed parts. Results from this work result in the following conclusions.(1)Temperature prediction using the elastic tool model is more accurate than that predicted using the rigid tool, in comparison with experimental results. The difference in temperature predictions using elastic and rigid tool varies with location in the workpiece, holding time and holding pressure. When the holding load is between 150 kN and 300 kN the difference is small and the rigid tool model is recommended for FE simulation, as it takes less computer CPU time.(2)For various workpiece locations investigated, predicted temperature using the elastic tool model is lower than that using a rigid tool model. However, as the holding load and cooling duct size increase, the predicted temperature using the elastic tool is lower than that of rigid tool on the near vertical side wall. This is due to the fact that the deformation of the elastic tool increases the pressure at the side wall locations during pressure holding period, which increases the heat transfer coefficient. This effect is enhanced by increasing in size of cooling duct.(3)To study the effect of cooling ducts on temperature, it is important to use elastic tools in the FE model since the effect of a duct on tool elastic deflection can affect the blank temperature greatly.

#### Acknowledgment

The authors thank IMRA Europe S.A.S. U.K. Research Centre for financial support and the experimental data for this work.

#### References

- H. Karbasian and A. E. Tekkaya, “A review on hot stamping,”
*Journal of Materials Processing Technology*, vol. 210, no. 15, pp. 2103–2118, 2010. View at Publisher · View at Google Scholar · View at Scopus - K. Ikeuchi and J. Yanagimoto, “Valuation method for effects of hot stamping process parameters on product properties using hot forming simulator,”
*Journal of Materials Processing Technology*, vol. 211, no. 8, pp. 1441–1447, 2011. View at Publisher · View at Google Scholar · View at Scopus - M. Oldenburg, P. Åkerström, G. Bergman, and P. Salomonsson, “Simulation and evaluation of phase transformations and mechanical response in the hot stamping process,” in
*Proceedings of the 9th International Conference on Numerical Methods in Industrial Forming Processes (NUMIFORM '07)*, vol. 908 of*AIP Conference Proceedings*, no. 1, pp. 1181–1186, June 2007. View at Publisher · View at Google Scholar · View at Scopus - D. Kan, L. Liu, P. Hu et al., “Numerical prediction of microstructure and mechanical properties during the hot stamping process,” in
*Proceedings of the 8th International Conference and Workshop on Numerical Simulation of 3D Sheet Metal Forming Processes (NUMISHEET '11)*, vol. 1383 of*AIP Conference Proceedings*, no. 1, pp. 602–609, August 2011. View at Publisher · View at Google Scholar · View at Scopus - P. Akerström, G. Bergman, and M. Oldenburg, “Numerical implementation of a constitutive model for simulation of hot stamping,”
*Modelling and Simulation in Materials Science and Engineering*, vol. 15, no. 2, article 007, pp. 105–119, 2007. View at Publisher · View at Google Scholar · View at Scopus - J. B. Leblond, G. Mottet, and J. C. Devaux, “A theoretical and numerical approach to the plastic behaviour of steels during phase transformations-I. Derivation of general relations,”
*Journal of the Mechanics and Physics of Solids*, vol. 34, no. 4, pp. 395–409, 1986. View at Scopus - J. B. Leblond, J. Devaux, and J. C. Devaux, “Mathematical modelling of transformation plasticity in steels I: case of ideal-plastic phases,”
*International Journal of Plasticity*, vol. 5, no. 6, pp. 551–572, 1989. View at Scopus - M.-G. Lee, S.-J. Kim, and H. N. Han, “Finite element investigations for the role of transformation plasticity on springback in hot press forming process,”
*Computational Materials Science*, vol. 47, no. 2, pp. 556–567, 2009. View at Publisher · View at Google Scholar · View at Scopus - B. Abdulhay, B. Bourouga, and C. Dessain, “Experimental and theoretical study of thermal aspects of the hot stamping process,”
*Applied Thermal Engineering*, vol. 31, no. 5, pp. 674–685, 2011. View at Publisher · View at Google Scholar · View at Scopus - F. Tondini, P. Bosetti, and S. Bruschi, “Heat transfer in hot stamping of high-strength steel sheets,”
*Proceedings of the Institution of Mechanical Engineers B*, vol. 225, no. 10, pp. 1813–1824, 2011. View at Publisher · View at Google Scholar · View at Scopus - H. Liu, C. Lei, and Z. Xing, “Cooling system of hot stamping of quenchable steel BR1500HS: optimization and manufacturing methods,”
*The International Journal of Advanced Manufacturing Technology*, vol. 69, no. 1–4, pp. 211–223, 2013. View at Publisher · View at Google Scholar - J. Lin and Y. Liu, “A set of unified constitutive equations for modelling microstructure evolution in hot deformation,”
*Journal of Materials Processing Technology*, vol. 143-144, no. 1, pp. 281–285, 2003. View at Publisher · View at Google Scholar · View at Scopus - N. Li, M. S. Mohamed, J. Cai, J. Lin, D. Balint, and T. A. Dean, “Experimental and numerical studies on the formability of materials in hot stamping and cold die quenching processes,” in
*The 14th International Conference on Material Forming (ESAFORM '11)*, vol. 1353 of*AIP Conference Proceedings*, no. 1, pp. 1555–1561, April 2011. View at Publisher · View at Google Scholar - A. Shapiro, “Finite element modeling of hot stamping,”
*Steel Research International*, vol. 80, no. 9, pp. 658–664, 2009. View at Scopus - A. Azushima, K. Uda, and A. Yanagida, “Friction behavior of aluminum-coated 22MnB5 in hot stamping under dry and lubricated conditions,”
*Journal of Materials Processing Technology*, vol. 212, no. 5, pp. 1014–1021, 2012. View at Publisher · View at Google Scholar · View at Scopus - F. Tondini, P. Bosetti, and S. Bruschi,
*Heat Transfer in Hot Stamping of High-Strength Steel Sheets*, Sage, London, UK, 2011. - B. Abdulhay, B. Bourouga, C. Dessain, G. Brun, and J. Wilsius, “Development of estimation procedure of contact heat transfer coefficient at the part-tool interface in hot stamping process,”
*Heat Transfer Engineering*, vol. 32, no. 6, pp. 497–505, 2011. View at Publisher · View at Google Scholar · View at Scopus