Design of experiments and springback prediction for AHSS automotive components with complex geometry A. Asgari, M. Pereira, B. Rolfe, M. Dingle, and P. Hodgson* School ofEngineering and Technology, Faculty ofScience and Technology, Deakin University, Waurn Ponds 3217, Australia
[email protected] Abstract. With the drive towards implementing Advanced High Strength Steels (AHSS) in the automotive industry; stamping engineers need to quickly answer questions about forming these strong materials into elaborate shapes. Commercially available codes have been successfully used to accurately predict formability, thickness and strains in complex parts. However, springback and twisting are still challenging subjects in numerical simulations of AHSS components. Design of Experiments (DOE) has been used in this paper to study the sensitivity of the implicit and explicit numerical results with respect to certain arrays of user input parameters in the forming of an AHSS component. Numerical results were compared to experimental measurements of the parts stamped in an industrial production line. The forming predictions of the implicit and explicit codes were in good agreement with the experimental measurements for the conventional steel grade, while lower accuracies were observed for the springback predictions. The forming predictions of the complex component with an AHSS material were also in good correlation with the respective experimental measurements. However, much lower accuracies were observed in its springback predictions. The number of integration points through the thickness and tool offset were found to be of significant importance, while coefficient of friction and Young's modulus (modeling input parameters) have no significant effect on the accuracy of the predictions for the complex geometry.
development engineers in the automotive industry. For AHSS there is an inevitable lack of knowledge about forming complex automotive parts with regards to their springback and twisting effects. Nevertheless, AHSS including Dual Phase (DP) and Transformation Induced Plasticity (TRIP) steels, require a much greater degree of precision to answer the needs of forming simulation accuracy. The principal difference between AHSS and conventional steels is in their microstructures. AHSS are ferrite-phase matrix steels with varying percentages of hard martensite, bainite and retained austenite phases that give favorable combination of elongation and strength. A low ratio of yield strength (YS) to ultimate tensile strength (UTS) and high strain-hardening capacity increases the formability and elongation of AHSS. Meanwhile due to high YS and much higher UTS, higher press loads, greater springback and die wear are major issues with AHSS. Thus an accurate forming simulation is essential for the design of an efficient and consistent forming process for a complex automotive part with these new steel grades.
INTRODUCTION Not long ago the main usage of finite element software packages in sheet metal forming was limited to strain and thickness predictions. Nowadays integrated sheet metal stamping simulation software addresses die design feasibility, product formability and virtual die tryouts to develop robust and optimized production processing. Commercial software packages for sheet metal forming are fine tuned to provide the user with a detailed and accurate insight into stresses, strains, splits and wrinkles, blank shape, binder forces, locator pins, drawbeads, trim tools and even springback. The latter demands to capture all of the events involved during forming, trimming, flanging and springback stages. Generally, for conventional steels, such software packages are able to predict forming and springback results with accuracies up to 90% or more [1]. These steel grades, in contrast to AHSS, are generally the grades which are known to the press shop engineers, part designers and product
CP778 Volume A, Numisheet 2005, edited by L. M. Smith, F. Pourboghrat, l-W. Yoon, and T. B. Stoughton © 2005 American Institute of Physics 0-7354-0265-5/05/$22.50
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This paper investigates the accuracy of current commercial software packages when used to simulate forming and springback of AHSS complex components. A complex automotive component might have several forming modes as well as bending and unbending where the challenge for the current numerical techniques is to predict springback and twisting of the part with an AHSS material.
DESIGN AND ANALYSIS STRATEGY The accuracy of a numerical technique is assessed by comparing the predicted results of the simulation with the experimental results. The predicted results of a simulation depend on how accurately the model is configured. When configuring a computer model, depending on the solver method, several input parameters can affect the accuracy of the results. Given that experimental measurements always have a precision tolerance, the aim is to choose numerical parameters so that the simulation results correlate with the experiment, i.e. simulate the actual experiment.
FIGURE I. Front cross member component
Design factors Design factors in this study were limited to those input parameters that are common in both solvers. When AHSS grades are being used for simulation, not all of the processing and material properties are always known or obtained easily. Table 2 shows four selected input parameters, which include the number of integration points through the thickness (NIP), offset or gap between tools (offset), Young's modulus of the blank material (E) and also coefficient of friction between the tools and the blank (Il).
In this paper, a what-if type of analysis of the accuracy of two forming simulation solvers is performed. These two solvers are commercial software packages: AutoForm (implicit solver) and DynaForm (explicit solver, LS-Dyna). The selected part is an automotive front cross-member component (Fig. 1).
These four parameters are selected with a high and low level for each. NIP was changed between 3 and 7 points. Since the blank thicknesses for SPHD and TRIP were 2.2mm and 2.0mm respectively, tool offset was changed between 10% and 21 % of the blank thicknesses. High and low values for Young's modulus were 186.3GPa-227.7GPa and 184.5GPa-225.5GPa for DynaForm and AutoForm models, respectively. This range of Young's modulus variation was based on plus or minus 10% of suggested values by common practice or by the software packages [2, 3]. Finally, the coefficient of friction varied between 0.125 and 0.175.
The objective is to investigate variations in the default input parameters when TRIP steel is being used in the simulation. The same input variations were applied to the conventional drawing quality low carbon steel (SPHD). Tabulated true stress-strain curves measured from conventional tensile tests of TRIP and SPHD steels were used in this study to represent the mechanical properties. Basic material data for these steels is given in Table 1.
TABLE 1. Properties of Steel Grades Used in This Study.
Parameter Thickness Tensile strength (MPa) Yield strength (MPa) n-Value (5-15 % Strain)
SPHD 2.2 344 241 0.18
Response selection
TRIP
2.0 790 569 0.21
In order to normalize the outputs and make them comparable, a single scalar correlation value (statistical R-value) between experiment and simulation was calculated for each single run. This correlation value refers to the strain measurements on a cross section of the drawn part where the plane strain forming mode was dominant (26 data points) indicated with (l in Table 2.
Four input factors (modeling input parameters) were selected and varied on 2 levels for each material. These simulations were performed in two stages of forming and springback using each solver. That means n (n=128) scenarios (combinations of factor levels/values, solvers, materials and simulation stage) were performed.
216
TABLE 2. Full factorial orthogonal array of DOE input parameters: NIP, Tool offset, Young's modulus and friction with corresponding outputs (correlation) for each run of 128 runs in forming (n) and springback (~) stage Run I 2
3 4 5 6 7
8 9
10 11
12
13 14 IS
16
NIP
Offset
3 3 3 3 3 3 3 3 7 7 7 7 7 7 7 7
10% 10% 10% 10% 21% 21% 21% 21% 10% 10% 10% 10% 21% 21% 21% 21%
E Low Low High High Low Low High High Low Low High High
Low Low High High
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0.125 0.175 0.125 0.175 0.125 0.175 0.125 0.175 0.125 0.175 0.125 0.175 0.125 0.175 0.125 0.175
87.36 87.86 87.87 88.00 82.84 82.42 82.36 82.99 94.32 94.16 94.02 94.86 91.43 91.29 91.18 91.42
81.40 86.72 86.45 84.71 81.31 82.41 80.50 80.82 89.07 91.65 93.85 89.83 78.97 80.24 81.20 83.94
As an example, 16 curves of major strain to experimental measurements compared measurements leads to 16 a1 correlation values. These 16 curves are plotted in Fig. 2 with the corresponding a1 values shown in Table 2. 0.30
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60.70 59.67 63.49 62.68 57.75 55.44 41.95 54.62 73.75 69.47 71.92 70.52 61.58 55.80 64.40 59.88
55.52 56.24 61.69 60.28 60.78 45.77 52.37 50.85 64.90 73.87 72.69 69.88 64.15 56.84 60.35 62.02
50.39 48.62 48.73 47.76 34.75 33.14 32.23 38.88 55.37 46.32 53.13 46.79 47.82 43.93 51.64 45.28
translation in Y and Z while P3 and P4 were both fixed for translation in the Z or drawing direction.
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FIGURE 3. Springback measurement locations and rigid body elimination constraints on the trimmed part
A summary of the simulation output variables a and ~ achieved from combinations of different solvers, materials and simulation modes is given in Table 3.
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X along section (mm)
FIGURE 2. Major strain predictions generating 16 values for case n1
In the springback simulation, the correlation values indicated in Table 2 with ~ refer to the correlation of springback at 10 different positions on the sprung part shown on Fig. 3, with letters A to E. The normal displacement (drawing direction) of these points was measured from scan data obtained using a FARO arm scanner. The correlation (statistical R-value) was measured by comparing experimental values to the simulation values (10 data points: A to E).
TABLE 3. Summary of the simulation output definitions Material
Figure 3 also shows the constraint points (pI to P4) that have been used for elimination of rigid body motion in the springback stage. PI was fixed for translation in X, Y and Z directions; P2 was fixed for
217
Solver
Mode
Number of runs
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SPHD
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Fonning
16
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Dyna
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112 83 114
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16
RESULTS AND DISCUSSION
80.00
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Correlation values for the forming stage a and springback stage p are plotted in Figs. 4 and 5, respectively. Changing NIP to 7 gives a sudden increase in the correlation for both the springback and the forming stages.
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In the forming stage of a complex geometrical model, increasing NIP would help to capture the bending effects. This is true for both the AutoForm and DynaForm solvers, even though they use different element formulations. In a sensitivity study using DynaForm solver, Shi et al. showed that in the forming simulations 5, 7 and 9 NIP resulted in similar thinning distribution in a rectangular pan and automotive rail [4]. However, increasing NIP to 9 in a complex model, like the one in this paper, causes the model size to increase by a factor of 4 or 5, demanding higher memory requirements and higher simulation costs.
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The main effect of tool offset shows that the increase of the gap between tools from 10% to 21 % reduces the correlation values for both software packages. For the TRIP steel (cases P3 and P4) both software packages show higher sensitivity to the tool offset value. It should also be noted that an increase in tool offset value of more than approximately 21 % of the sheet thickness in a complex automotive geometry may lead to unrealistic radii in the bend areas.
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Figure 6 shows that both software packages predict springback results with much less accuracy for SPHD and TRIP than the forming predictions; and in comparison of their performance for the two materials, lower correlations are obtained for the TRIP steel (cases P3 and P4). It is also shown that NIP is much more effective in the springback stage (P) compared to the forming stage (a.) for both packages and materials.
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FIGURE 5. Correlation plot for outputs ofthe springback stage
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Run Number
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Run Nurrmer
FIGURE 4. Correlation plot for outputs of the forming stage
Figure 6 shows that a change in the coefficient of friction and the Young's modulus does not have a strong effect on the accuracy of the predictions. This is true even though a change in these parameters causes an inconsistent change in the major strain and springback measurements in numerical models. The effects of f.l and E on springback measurements on 10 points (A to E) for TRIP steel (cases P4) are plotted in Figs. 7 and 8. The amount of springback is proportional to the elastic part of stress-strain curves of the steel. An increase in the yield stress produces an increase in the elastic stresses and, therefore, an increase in springback. It is expected that a decrease in E would result in higher springback measurements. In a complex geometry like that in this paper, some variations in the measured numerical springback were observed with the change in the input parameter E in the models.
The differences between AutoForm and DynaForm solvers were apparent in the springback stage with inconsistent predictions by both solvers. The level of accuracy of the springback simulations generally ranges from 30% to 80% for TRIP and SPHD steels (cases PI, p2, P3 and P4). To analyze these correlation plots, the simplest technique is to look at the response values and select the response that best satisfies the experimental target. Despite its simplicity, the design factor (input parameters) importance becomes unknown [5]. Therefore, the main effect of each selected input parameter or factor is plotted in Fig. 6.
218
Main Effect of Youngs Modulus
Main Effect of Coefficient of Friction
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FIGURE 6. Collective main effect plots of different factors on both forming and springback outputs
For different cases of a and ~ with changes in E both software packages were able to pick up the trend of major strain and springback for SPHD material but not for the TRIP steel shown in Fig. 7. However, Fig. 6 implies that as long as E for the TRIP steel varies in a range of approximately 10% below or above of the known values of E for the conventional steel, the effect of this change in the accuracy of springback or forming predictions is negligible. This range corresponds to 188 to 213GPa documented by Lee et al. and Doege et al. for TRIP steel [6, 7].
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The effect of 1.1 on the accuracy of software packages when TRIP steel is modeled is again similar to that of E. Figure 8 shows that changes in 1.1 from low to high level causes variations in the springback measurements of TRIP steel.
FIGURE 7. The effect ofE on the springback predictions, case 134
219
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account the microstructure evolution with the proper yield criteria and the actual work hardening of these new steel grades are a necessary step to accurately simulate forming process of complex parts and capture the correct springback and twisting mode of final products.
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FIGURE 8. The effect of I.l. on the springback predictions, case 134
ACKNOWLEDGEMENTS
Such an effect of ~ was also observed in the fonning simulation of TRIP steel. Again, both software packages failed to predict the correct trend of springback for TRIP steel but they predicted the correct trends for SPHD material, although with a low correlation value in general. With these low correlations, changes of ~ from low to high level do not significantly affect the accuracy of the results.
The authors would like to thank Professor John Duncan from Auckland University, New Zealand for his help and support. This research was funded by Ford Australia and Deakin University and partially carried out using the APAC supercomputing facilities at ANU, Australia.
Not much twisting was observed in the experimental measurements of this complex component (indicated by positive springback values for all locations A to E). This could be due to the geometrical stiffness and/or relatively symmetrical shape of the component. However, poor predictions of springback modes for the TRIP steel, shows some large twists in the predicted sprung shape by both software packages. This was highlighted when TRIP steel was modeled with AutoForm software (case ~4). Selected constraint points (PI to P4) could be responsible for the error in the twisting effect predictions. Investigation of the different strategies to select these constraint points is the next step in the development of the successful prediction of the twist effects in the complex automotive geometries.
REFERENCES 1. A. Asgari, M. Pereira, B. Clark, M. Dingle, P. Hodgson, "Sheet metal forming simulation of Advanced High Strength Steels automotive components" in the NUMIFORM2004 conference, Ohio, 2004, pp. 977-982 2. AutoForm Users Manual, AutoForm v3.2 (AutoForm Engineering GmbH, 2002). 3. LS-Dyna Users Manual, LS-Dyna version 970 (LSTC, 2003). 4. M. F. Shi, D. G. Prince, and W. Song, "A sensitivity study of simulation parameters in sheet metal fonning and springback simulation using LS-Dyna." in the Proceedings of the 5th
LS-Dyna Users conference, 1998. 5. S. R. Schmidt and R. G. Launsby, Understanding industrial designed experiments, 4th ed., Air Academy Press & Associates, Colorado Springs, 1998. 6. S. S. Lee, U. S. Min, and B. Ahn, J of Mat. Sci. 33,687-692 (1998). 7. E. Doege, S. Kulp, and C Sunderkotter, "Properties and application of TRIP-steel in sheet metal forming." in the Int. Can! on TRIP-Aided High Strength Ferrous Alloys, 2002, pp. 347-351.
CONCLUSION The development of AHSS with better formability opens the way for more complicated geometries to be formed in the automotive industry. The increased complexity, introduces higher geometrical tolerance concerns for these materials. The current sheet metal forming software packages are powerful enough to predict accurate results for conventional steels, but there is plenty of room to fine tune simulations for AHSS grades such as TRIP steel. Specialized material models that take into
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