Simulation of the Press Hardening Process and

Simulation of the Press Hardening Process and Prediction of the Final Mechanical Material Properties Bernd Hochholdingera, Pavel Horaa, Hannes Grassb and Arnulf Lippb a

Institute of Virtual Manufacturing, ETH Zurich, Tannenstrasse 3, 8092 Zurich, Switzerland b BMW Group, 80788 Munich, Germany

Abstract. Press hardening is a well-established production process in the automotive industry today. The actual trend of this process technology points towards the manufacturing of parts with tailored properties. Since the knowledge of the mechanical properties of a structural part after forming and quenching is essential for the evaluation of for example the crash performance, an accurate as possible virtual assessment of the production process is more than ever necessary. In order to achieve this, the definition of reliable input parameters and boundary conditions for the thermo-mechanically coupled simulation of the process steps is required. One of the most important input parameters, especially regarding the final properties of the quenched material, is the contact heat transfer coefficient (IHTC). The CHTC depends on the effective pressure or the gap distance between part and tool. The CHTC at different contact pressures and gap distances is determined through inverse parameter identification. Furthermore a simulation strategy for the subsequent steps of the press hardening process as well as adequate modeling approaches for part and tools are discussed. For the prediction of the yield curves of the material after press hardening a phenomenological model is presented. This model requires the knowledge of the microstructure within the part. By post processing the nodal temperature history with a CCT diagram the quantitative distribution of the phase fractions martensite, bainite, ferrite and pearlite after press hardening is determined. The model itself is based on a Hockett-Sherby approach with the Hockett-Sherby parameters being defined in function of the phase fractions and a characteristic cooling rate. Keywords: press hardening, thermo-mechanically coupled simulation, 22MnB5, final part properties PACS: 81.40.Gh, 81.40.Cd, 02.70.Bf, 81.40.-z

INTRODUCTION Today the press hardening process is well established for the manufacturing of body-in-white parts in the automotive industry. The number of parts in a new car generation that are manufactured by press hardening is still increasing. In general two variants of the press hardening process have to be distinguished. In the direct press hardening process (fig. 1a) the part is formed and quenched in one process step whereas in the indirect process (fig. 1b) the part is first classically cold-formed and afterwards heated and quenched in a separate operation.

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FIGURE 1. Principal process steps for the direct press hardening process (a) and the indirect press hardening process (b) as proposed by the steel company voestalpine AG.

The steel that is typically used for press hardening is the boron alloyed steel 22MnB5. It is available from different steel suppliers that offer 22MnB5 with different coatings. Depending on the actual chemical composition of the coating, the supplied 22MnB5 is either suited for the direct or the indirect process variant. With the upcoming of press hardening in the automotive industry the focus lay on the production of structural parts with ultra-high strength. Recently the press hardening process is enhanced to produce parts with tailored properties. Still the generation of ultra-high strength properties is the principal objective of press hardening but at the same time it is desired to get areas within a part that have lower strength but increased ductility. There are several ways to achieve this. A standard approach to realize different mechanical properties within a part is to use tailored blanks by joining two or sheets made of different steel. Another way to increase the ductility is to anneal the part after quenching as for example discussed by Laumann [1]. Instead of using different materials or annealing the part, the hardening process itself can be modified to generate different mechanical properties. In the so called tailored tempering process, as for example discussed by Lenze et al. [2], the tools are partially heated. This results in a locally reduced cooling rate. Instead of a solely martensitic microstructure, as it is the case for cooling rates faster than approx. 30 K/s, a mixture of ferrite, pearlite, bainite and martensite forms that has a lower strength but higher ductility than pure martensite. Another way to locally reduce the cooling rate is to insert grooves in the tool surface. Depending on the size and depth of the groove the heat flux from the hot part to the cold tools at the location of the groove is orders of magnitude smaller than in areas where part and tool are in direct contact. By the insertion of grooves the tool surfaces are not continuous anymore and cannot be used for forming a part. Therefore this approach may only be used in the indirect process variant, where the part is formed in a separate operation before the hardening takes place. For the virtual assessment of the press hardening process, thermo-mechanically coupled simulations have to be conducted, which require a variety of input parameters. Depending on which process variant is followed – direct or indirect press hardening – the relevance of the input parameters regarding the process simulation varies. As shown by Burkhardt [3], for the simulation of hot forming as part of the direct press hardening process, the accurate definition of the yield stress depending on strain, strain rate and temperature as well as temperature dependent friction are of major importance for a reliable prediction of the feasibility of the forming step and the geometrical properties, like sheet thickness and draw-in, of the part after forming. An experimental procedure for the determination of the yield stress and a comparison of the applicability of different mathematical models is given in Eriksson [4] and Hochholdinger [5]. Regarding the prediction of the final mechanical properties after the direct or the indirect process, the accurate prediction of the local temperature history within the blank is of major importance. The temperature history depends on various boundary conditions like thermal convection and radiation to the environment, but mainly on the timedependent contact situation between blank and tool. Especially for the generation of tailored properties by the insertion of grooves in the tool surfaces, the correct modeling of the interfacial heat flux is mandatory. Therefore the focus of this work regarding the determination of input parameters is set to the determination of the contact heat transfer coefficient as described in the following chapter.

DETERMINATION OF THE CONTACT HEAT TRANSFER COEFFICIENT Depending on the actual contact situation during the hardening process the effective heat flux from the blank/part to the tools may vary by several orders of magnitude. The input parameter that determines the heat flux due to contact is the contact heat transfer coefficient (CHTC) h. In general the following two contact situations have to be distinguished: 1. Part and tool are in direct contact. The CHTC depends on the effective area in contact. Since the effort to model the effective contact area accurately with finite elements would be much too high, the CHTC is defined as a function of contact pressure h(p). It is obvious that for high contact pressures the effective contact area is larger than for small pressure values. 2. Part and tool are not in direct contact, but there is a small gap between the contact partners. Since part and tool are close to each other, there is heat transfer due to radiation and convection of the fluid in the gap. In this case CHTC is a function of the gap distance h(lgap). With the gap between part and blank getting larger, the heat flux due to the interaction between the contact partners is decreasing. For gaps with lgap>lgap,max the heat loss due to convection and radiation to the environment is dominant and the heat flux between the contact partners can be neglected.

Experimental Setup In order to determine the CHTC for the contact situations described above, simple experiments at the Chair of Manufacturing Technology of the University of Erlangen-Nuremberg have been conducted. The principle experimental setup is shown in fig. 2a.

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FIGURE 2. Experimental setup for determining the CHTC (a) and experimental and simulated temperature over time curves for an applied contact pressure of 30 MPa (b).

After heating up the blank it is quenched between upper and lower tool. In the closed configuration the closing force of the press can be adjusted such that the blank is clamped with a predefined pressure. In the experiments pressure values of 0, 5, 10, 20, 30 and 40 MPa have been used. Alternatively the blank can be placed on adjustable pins on the lower tool and the upper tool can be positioned at a specified distance away from the upper side of the blank. Like that the second contact configuration with a small gap between blank and tools is realized. In the experiments gap distances were set to 0.1, 0.3, 0.5, 1.0 and 2.0 mm. The temperature is measured through thermocouples in the middle of the blank thickness and in the upper and lower tool 1 mm underneath the tool surfaces. In order to ensure the same initial temperature of the tools when conducting a series of consecutive experiments, upper and lower tool can be water-cooled. Further details on the experimental setup can be found in Hoff [6].

Inverse Identification of the CHTC For the determination of the CHTC based on the measured temperature over time curves different approaches can be employed. A fairly simple, analytical approach is to use Newton’s law of cooling as e.g. done by Lechler [7]. When using Newton’s law of cooling it is assumed that the blank has a constant temperature over its thickness and that the tool temperature is constant over time. Especially for the test configurations with blank and tool being in direct contact, the measured tool temperatures showed that the assumption of constant tool temperatures is not appropriate (see fig. 2b). Instead of trying to employ an analytical formula, an inverse approach for the identification of the CHTC is chosen. For this purpose a simple simulation model of the experiment is set up, where the measured temperatures in the upper and lower tool are applied as boundary conditions at the nodes 1 mm underneath the tool surfaces. For each of the tested configurations with a specific pressure or gap distance applied, an optimization run was conducted. The objective of these optimization runs is defined as the mean square error (MSE) between simulated and measured blank temperature over time. In order to avoid a falsification of the results by the release of latent heat during the cooling process, only the temperature history prior to the occurrence of phase change was considered for the evaluation of the MSE. The effects of phase change could be included in the optimization process by specifying the latent heat and the phase change temperature as additional optimization variables. Since such an approach led to unstable results, solely the CHTC was defined as a variable within the optimization procedure. The dashed curve in fig. 2b shows the resulting blank temperature over time using the “optimal” CHTC for the configuration with applied contact pressure equal to 30 MPa. In fig. 3 the normalized values of the determined CHTCs over gap distance and pressure are shown.

FIGURE 3. Normalized values of the (CHTC) over gap distance (left) and contact pressure (right).

SIMULATION OF THE PRESS HARDENING PROCESS Depending on which answers and results are expected from the simulation, the model setup as well as the numerical strategy for the virtual assessment might differ significantly. If just the feasibility of the forming phase during the direct press hardening process is of interest, it is in most cases sufficient to simulate gravity, closing and hot forming of the blank without consideration of heat conduction or cooling within the tools. As can be seen from the results submitted for Benchmark 3 of the Numisheet 2008 Conference (Oberpriller [8]) the sheet thickness and the position of local necking after hot forming can be fairly well predicted by the use of finite element models that are quite similar to the ones employed for standard cold-forming simulations. If on the other hand the objective of the simulation is the prediction of the mechanical properties after hardening, the process steps that have to be considered as well as the requirements regarding the FE model are more comprehensive. In the following two chapters these issues are discussed.

Simulation of the Process Steps during Press Hardening In order to be able to predict the properties of the final part correctly all process steps that influence the thermal history of the part, have to be considered in the simulation. Fig. 4 shows the process steps for the indirect press hardening process.

FIGURE 4. Simulated process steps during the indirect press hardening process.

All process steps are simulated using a weak coupling of the mechanical and the thermal problem. Like that it is possible to use different time integration schemes with different time step sizes for both problems. Table 1 shows the chosen settings for the thermo-mechanical simulation of the process steps. The starting point for the coupled simulation is the trimmed part after cold-forming. During heating from room temperature up to an austenitization temperature of approx. 900 °C the volume of the part increases due to thermal expansion. The correct definition of the temperature dependent coefficient of thermal expansion (CTE) is essential to get the right dimensions after heating. The FE code LS-DYNA® that is used for the simulations utilizes the tangent CTE in contrast to the secant CTE that is e.g. used by the FE program Abaqus ®. After heating the part and holding it at a constant temperature for several minutes, it is assumed that residual stresses and the accumulated plastic strain that evolved during cold-forming are cancelled out. During transfer from the oven to the press the part

cools due to radiation and convection to the surroundings. The temperature drop depends on the effective duration of transfer, usually 3-8 seconds, and the values provided for the convection heat transfer coefficient and the emissivity of the blank surface. Reasonable values for these input parameters are stated in Shapiro [9]. In the subsequent gravity simulation the part is put on the lower tool. In this step there is a heat flux on the lower side of the part due to local contact with the cold tool and on the upper side due to convection and radiation. For the closing step a separate simulation is setup, since a different time integration scheme is used for the solution of the mechanical problem (see table 1). The experience has shown that the use of an explicit time integration scheme is more robust in handling the changing contact situations than the dynamic implicit Newmark integration. During the quenching step the part is tightly clamped between upper and lower tool. As discussed above, the effective heat flux depends on the local pressure or on the gap distance at the part-to-tool interface. Either the explicit or the implicit time integration may be used. If the explicit approach is chosen the application of mass and time scaling is recommended to reduce the computation time. A detailed description of the recommended settings for the explicit time integration scheme can be found in Lorenz [10]. To reduce the cycle times in serial production, the duration that the tools are held closed should be as short as possible. Accordingly the tools are usually opened when the part is still well above room temperature. In order to get the correct geometry at room temperature, it might therefore be necessary to conduct an additional simulation of opening the tools and cooling down of the part. The more or less free thermal contraction during that cooling phase on air might lead to geometrical distortion of the part. TABLE 1. Applied time integration schemes for the thermo-mechanically coupled simulation of the separate process steps. Process Step Mechanical Problem Thermal Problem heating static implicit implicit transfer static implicit implicit gravity dynamic implicit implicit closing explicit implicit quenching explicit or dynamic implicit implicit

FE-Model for the Simulation Press Hardening In general there are several approaches to model blank/part and the tools in a forming simulation. In standard cold-forming simulations of deep drawing processes, the tools are usually modeled as rigid contact surfaces providing the reference geometry for the part to be formed. For the simulation of press hardening, as discussed in this paper, it is as well assumed that the tools do not deform and therefore can be considered as rigid for the mechanical part of the problem. For the thermal problem the assumption of tools having a constant temperature over time is in most cases not adequate. When just the hot forming phase of the direct process has to be evaluated then the error of “thermally rigid” tools is probably acceptable as shown by Lorenz [10]. However if the final mechanical properties of the part are to be predicted, which requires an accurate simulation of quenching and cooling, then the tools have to be modeled with continuum or at least boundary elements. Only if heat conduction within the tools is considered in the simulation, the time dependent distribution of the tool surface temperatures can be captured, which is a prerequisite for the correct evaluation of the heat flux. TABLE 2. Recommended modeling of tools and blank for the thermo-mechanically coupled simulation of press hardening. Process Step Mechanical Problem Thermal Problem modeling of the tools rigid: no stresses, no strains thermal tetra- or hexahedron modeling of the blank/part elasto-viscoplastic shell 12 node thick thermal shell

For the structural (mechanical) problem, the blank/part is modeled with the same fully integrated shell elements that are usually employed for the simulation of cold-forming. Of course the material model that is used for the simulation of press hardening has to be capable of considering the temperature dependency of the mechanical input parameters, like e.g. Youngs modulus E(T) and yield stress y(, d/dt, T). For the thermal part the blank is modeled with a 12 node thick thermal shell element (red nodes in fig. 5b) as proposed by Bergman and Oldenburg [11]. The shell element is defined by the 4 nodes of the mechanical shell (black nodes in fig. 5b). The nodes defining the upper and lower surface of the thick shell are generated internally by LS-DYNA. The shell uses linear shape functions in plane and quadratic ones in the thickness direction. This offers several advantages. Like that it is possible to apply and model different boundary conditions on the upper and lower side of the shell, as for example during the gravity step (see fig. 4), and to accurately capture the resulting temperature gradient through the thickness.

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FIGURE 5. Solid model of the tools (a) and thick thermal shell element used for modeling the blank (b).

PREDICTION OF THE FINAL MECHANICAL MATERIAL PROPERTIES For the prediction of the mechanical properties after press hardening a post processing procedure was developed that automatically evaluates the temperature history of all nodes in the quenched part over all process steps after heating. The CCT diagram shown in figure 6 is used to evaluate the phase fractions that result after hardening at the nodes of the blank. Fast cooling rates result in a purely martensitic microstructure with a yield stress of more than 1500 MPa and Vickers hardness above 480. For intermediate cooling rates the austenite changes to a mixture of martensite, bainite, ferrite and pearlite. Rather slow cooling rates result in a microstructure that consist of ferrite and pearlite which is quite similar to the unquenched state of the 22MnB5.

FIGURE 6. CCT diagram of 22MnB5 from Naderi [12] for an austenitization temperature of 900 °C.

For the prediction of the yield curves after hardening a simple model based on the well-known Hockett-Sherby yield curve approximation is developed.

 y  pl   Ax, dT  ( Ax, dT  Bx, dT ) exp  M x, dT plN 

(1)

Where Ax,dT is the saturation stress, Bx,dT is the initial yield stress, Mx,dT is the saturation rate and N the hardening exponent. As indicated by the subscripts, the Hockett-Sherby parameters A, B and M are defined as functions of the phase fractions x and a characteristic cooling rate dT/dt at 700 °C (973 Kelvin), while the same hardening exponent N, which is unequal to one, is used for all configurations, independently of the specific microstructure or cooling rate. As can be seen from equation (2) each of the parameters Ax,dT, Bx,dT and Mx,dT is defined as linear combination of the phase fractions martensite xmart, bainite xbain, ferrite and pealite xferr-perl and the natural logarithm of the cooling rate at 973 K. As inspiration for this approach served the mixture rule developed by Maynier et al. [13], which uses the chemical composition of the steel to predict the Vickers hardness. The coefficients ax, bx and mx in equation (2) are determined by multi-linear regression. For this purpose tension tests of specimens with different cooling rates have been conducted. The resulting stress-strain curves are fitted employing the mentioned Hockett-Sherby approximation. The phase fractions for each tension test specimen are evaluated with the CCT diagram shown in fig. 6.

 dT  Ax , dT  amart xmart  abainxbain  a ferr  perl x ferr  x perl   adT ln  973   dt   dT  Bx , dT  bmart xmart  bbainxbain  b ferr  perl x ferr  x perl   bdT ln  973   dt   dT  M x , dT  mmart xmart  mbainxbain  m ferr  perl x ferr  x perl   mdT ln  973   dt 

(2)

Based on this model the following post processing is developed, that allows predicting the yield curves in the part after press hardening: 1. Extract temperature history from all process steps starting with the transfer simulation until the end of the hardening process. 2. Evaluate the resulting microstructure with the CCT diagram shown in fig. 6. 3. Employ the developed model (eq. (2)) to calculate an individual yield curve for each finite element in the simulation model. 4. Sort elements with similar yield curves in different groups. For this purpose the plastic potential of each yield curve is calculated. Calculate representative yield curve for each group of elements. 5. Output of the post-processed part including the determined yield curves. Fig. 7 shows two small sample press hardening setups and the corresponding results using the described post processing procedure. Fig. 7(a) shows a standard hardening tool. In fig. 7(b) the part after hardening is shown. The different colors represent different yield curves that are shown in fig. 7(c). The figures 7(d) to (f) show tools, the part after quenching and normalized yield curves for a setup, where grooves have been inserted in the surfaces of upper and lower tool. At the location of the grooves the cooling rates are slower than in areas where the tools and the part are in full contact. The yield curves at the location of the grooves are accordingly lower than in areas with higher cooling rates.

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(b)

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FIGURE 7. Figure (a) shows the tools, (b) the hardened part with areas having different properties and (c) the corresponding normalized yield curves for standard press hardening setup. In figures (d), (e) and (f) the tools, the quenched part and the corresponding normalized yield curves for a setup, where grooves have been inserted in the tool surfaces are shown.

SUMMARY AND CONCLUSIONS The intention of this work was to discuss the most relevant issues that are necessary to predict the yield curves of a part after press hardening. The preliminary for an accurate simulation is the knowledge of the input parameters for the thermo-mechanically simulation. The basic idea of press hardening is to quench a sheet metal blank or part made of hardenable steel, as for example the boron alloyed steel 22MnB5, by bringing it into contact with cold tools. The simulation of this process requires the definition of a large variety of input parameters. When the objective of the simulation is to predict the final part properties the by far most important parameter is the contact heat transfer coefficient. An inverse approach was chosen to determine the pressure and gap dependent CHTC from the experimental temperature over time curves. Furthermore a strategy for the simulation of the subsequent steps that are

involved in the press hardening process was presented. Since the mechanical and the thermal solution are just weakly coupled, different time integrations schemes for the mechanical and the thermal part may be used for solving the initial boundary value problem. In order to get the correct spatial and time-dependent temperature distribution the tools are modeled with volume elements. For the part a thick thermal shell is employed that allows capturing the temperature gradient over the sheet thickness and to apply different boundary conditions on top and bottom surface of the blank. For the prediction of the yield curves of the final part a phenomenological model was developed. This model requires the input of the microstructure in form of the phase fractions martensite, bainite, ferrite and pearlite. The phase fractions are determined by employing a CCT diagram from literature. The model itself is based on a Hockett-Sherby approach. The Hockett-Sherby parameters are defined in function of the phase fractions and a characteristic cooling rate. The evaluation and output is automatically done during post processing of the subsequent simulations. In order to determine the parameters for the presented model tension or compression tests of specimen that have been quenched with different cooling rates have to be conducted. As an alternative to the determination of the phase fractions by using the CCT diagram the material model developed by Åkerström and Oldenburg [14] could be used. This model employs transformation kinetics based on Kirkaldy’s rate equation to predict the phase fractions after quenching. Disadvantages of this model are the required input parameters, like the chemical composition, the austenite grain size and the activation energies of the diffusion driven transformation reactions, and the fact that the time-scaling cannot be applied to the simulation.

ACKNOWLEDGEMENTS The kind support of this work by the BMW Group is gratefully acknowledged. Also many thanks to Dr. A. Shapiro from LSTC for the implementation of many new features into the FE software LS-DYNA without which the virtual assessment of the press hardening process would not have been possible.

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