Finite Element Simulations for Sheet Warm Hydroforming

Transcription

1 Finite Element Simulations for Sheet Warm Hydroforming A. Del Prete a, G. Papadia a, A.A. De Vitis a and T. Primo a a Department of Engineering for Innovation, University of Salento, Via per Arnesano, Building O, Lecce, Italy Abstract. The use of lightweight alloy offers significant potential to improve product performances. However, the application of formed lightweight alloy components in critical structures is restricted due to this material s low formability at room temperature and lack of knowledge for processing lightweight alloys at elevated temperature. Warm forming is becoming of great interest in order to increase the formability of these materials and many conventional processes are adapted including the temperature as a new parameter. In addition to this option, warm hydroforming technology for the lightweight materials is currently emerging to achieve reduced number of manufacturing steps and part consolidation. The warm hydroforming process makes use of the improved formability at elevated temperature and it also utilizes the fluid to transport the forming action as well as heat. In the present work, the authors have studied the warm hydroforming process using two different numerical approaches in order to simulate it. The first software is traditionally used in metal stamping simulations (also warm and hot) unlike the second. The analyzed material is an Al 6061 alloy 2,03 mm thick. Process responses such as: bulge height, thickness reduction and strain distribution have been evaluated different temperature levels (room temperature, equal to 23 C, 100 C and 200 C). The obtained results have been used to study the accuracy of the second software in sheet warm hydroforming simulation. The authors have also defined the more reliable numerical environment in order to develop material damage models in warm forming conditions. Keywords: Warm hydroforming, Bulge height, FEM Simulation. PACS: Bb Industrial and technological research and development INTRODUCTION The realization of lightweight structures for transportation vehicles (aerospace and automotive) is a prominent way of improving fuel efficiency and reducing emissions. Because of their low density, comparable strength, and stiffness, lightweight materials such as aluminum alloys offer great potential in replacing mild steel structures to reduce weight. However, cost-effective forming of lightweight sheet materials into desired functional complex shapes is extremely difficult with the conventional forming technologies (i.e. stamping) because of the formability limitations of these materials at room temperature. In fact, a certain number of aluminum alloys have poor formability limiting their potential application. When subjected to deformation at higher temperatures, they often exhibit very high tensile elongations and can undergo extensive thinning without fracture or necking [1,2]. From both thermal and deformation viewpoints, warm hydroforming of these materials has many advantages. Complex shapes can be readily formed, and less energy is required to achieve the forming due to lower flow strengths, thereby minimizing the equipment size needs. Warm forming is becoming of great interest in order to increase the formability of these materials and many conventional processes have been modified including temperature as a new parameter. On the other hand, hydroforming has become an increasingly attractive manufacturing process in steel applications during the last decades as it leads higher strength to weight ratios in comparison to the parts manufactured by stamping. Different studies show that it is possible to apply warm forming techniques to manufacture hydroformed aluminum products reaching the advantages of the both approaches [3-14]. Sheet warm hydroforming is one of the innovative methods currently being pursued by automakers worldwide because of the advantages of combining sheet hydroforming and warm forming. In the present work, the authors have studied the warm hydroforming process using two different numerical approaches in order to simulate it. The first software is Ls-Dyna, that is well known for its capability in metal stamping simulations, while the second is Deform 2D, less used than Ls-Dyna but with different capabilities in the development of material damage models, useful to be applied during the deformation process. Precisely warm bulge test was considered for Al 6061 alloy with 2,03 mm

2 thick. A comparison, in both virtual environments, of the following process responses has been made: bulge heights, thickness reductions and strain distributions have been evaluated at different temperature levels (23 C, 100 C and 200 C). The obtained results have been useful in order to define the more reliable numerical environment able to simulate such non conventional forming process. This work is a part of a research project, actually in progress, where the authors aim is to tune experimental and numerical models from which it could be possible to learn more about the warm hydroforming process and its control. The obtained results have been used to study the accuracy of Deform 2D by comparison with Ls-Dyna, in sheet warm hydroforming. The authors have also defined the more reliable numerical environment in order to develop material damage models in warm forming conditions. NUMERICAL SIMULATION Today many numerical codes are able to simulate deep drawing processes with a good accuracy. In the last decade these codes have been also used to simulate critical sheet forming processes like warm hydroforming. The aim of this paper is to evaluate and to compare the approaches adopted by two different commercial codes to simulate a warm bulge test. The analyzed commercial codes are: LS-Dyna and. LS-Dyna FE Model Set-up FE simulations have been performed using the commercial finite element code LS-Dyna [16]. HyperForm has been used to create the finite element mesh, to assign the boundary conditions and, finally, to build LS-Dyna input deck for the analysis. The Die and the Blank Holder have been modeled like rigid materials (*MAT_20 in LS- Dyna), while a strain rate sensitive elasto-plastic material with a power law hardening (*MAT_64 in LS-Dyna) has been used for the Blank. An adaptive meshing scheme has been performed to reduce the calculation time keeping an high accuracy. In the forming analysis, the Belytschko Tsai (ELFORM #2) formulation with five integration point has been used for the blank, that has been modeled through shell elements. In fact these elements deliver good results if the thickness to curvature ratio is sufficiently low and if there are no significant normal stresses. The blank diameter is 200 mm and the thickness is 2.03 mm. For symmetry reasons, only a quarter of the model has been simulated. To prevent flexure of the flange, the sheet has been clamped through 12 bolts, that have been simulated like constrains in the all degrees of freedom of the interested nodes (FIGURE 1a). FIGURE 1b shows the FE model of the tooling. Blankholder Blank FIGURE 1. Schematic view of: (a) clamping conditions; (b) FE model in Ls-Dyna As a general rule, when temperature increases flow stress decreases therefore formability improves. Material properties are one of the critical input parameters during a process design by FEM, thus, material characterization is essential in order to perform simulations with reliable data. In this paper experimental literature data have been used [15]. Thus, the material properties have been implemented under different temperatures and strain rates in the simulation environment. The material input parameters available by literature references [14] are: elastic module (E), poisson s ratio (ν) and mass density (ρ), (TABLE 1), while the material flow curves at different temperature levels have been modeled using Field Backofen equation (rate power law: σ = k ε n έ m ), as tabulated in TABLE 2. TABLE 1. Material parameters for Al6061 used in FEM models. Material Parameters Al6061 Elastic Module, E (MPa) Poisson s ratio, ν 0.33 Mass density, ρ (tons/mm 3 ) 2.70E-9 Die

3 TABLE 2. Material constants for Al6061 (σ = k ε n έ m ) from bulge test at different temperatures. Temp. ( C) K (MPa) n m σ 0 (MPa) For the simulation of the fluid pressure law (FIGURE 2) it has been used a card, created for other applications, but useful also for the case of interest. This card is called AIRBAG and, in particular, it has been used its LINEAR_FLUID option. Through this card, it is possible to define a control volume, thanks to which all the finite elements of the control volume are under the action of the fluid pressure. FIGURE 2. Bulge Forming pressure for the three examined temperature conditions. DEFORM-2D FE Model Set-up SFTC-DEFORM 2D V is a commercial FEM code based on the updated Lagrangian formulation and it is an implicit integration method. It is able to solve coupled thermo-mechanical physical problems through the following computation sequence: 1) Definition of Input Geometry & Processing Conditions; 2) Generation of Initial Guess of Velocity Field single step, 3) Calculation of Element Behavior Based on Velocity Field & other variables (strain, temp, etc), 4) Calculation of Force boundary conditions based on Velocity Field, 5) Assembly and solution of the matrix equation, 6) Calculation of the error, 7) If the error is too large, the code applies correction to the velocity field and go to step 3. Otherwise, the sequence continues to next steps, 8) Updating of Geometry, 9) Calculation of temperature change for this step, 10) Calculation of new press velocity if necessary, 11) If stopping criteria has been reached, END. Otherwise, the code goes to step 3 and it repeat the sequence. In this simulation environment, the geometry has been modeled over a unit radial about the Y-axis due to the axisymmetric deformation mode (FIGURE 1). The area clamped by bolts has been modeled through constrains around the whole perimeter of each hole. The sheet modeled as elastic-plastic has been meshed by means of 2500 iso-parametric fournode quadrilateral elements. The blank model is characterized by the presence of five elements in its thickness in order to simulate and to calculate the bending strains. The dies has been considered rigid and isothermal. The sheet material has been modeled using the same values and the same flow rule listed, respectively, in TABLE 1 and in TABLE 2. The Coulomb friction coefficient µ, used to define the friction conditions in the interfaces contacts, is equal to The fluid pressure law, that is the same used for the LS-Dyna model, has been assigned directly to the sheet as boundary condition. FIGURE 3. FE model in DEFORM 2D

4 Numerical Post-Processing and Results Comparison The first type of comparison among the numerical results of the two analyzed codes is the evaluation of the thickness percentage reduction corresponding to different dome heights equal to: 19.6mm, 25mm, 30mm and 36mm at different temperatures (100 C and 200 C) (FIGURE 4). Since the maximum bulge height at 23 C is 19.6 mm, it has not been possible to reach the other dome heights (25mm, 30mm and 36mm) at this temperature. Analyzing FIGURE 3, it is evident an increase in the thickness percentage reduction corresponding to an increase in the dome height and a good agreement between Ls-Dyna and Deform results. Furthermore, taking into account the different dome heights values one-by-one, it can be said that if the temperature increases (from 100 C to 200 C), the thickness percentage reduction decreases, as expected. Thinning T=100 C 45,00 40,00 35,00 30,00 25,00 20,00 15,00 10,00 5,00 0,00 19,6 24,6 29,6 34,6 39,6 Hd (mm) Deform Thinning 45,00 40,00 35,00 30,00 25,00 20,00 15,00 10,00 5,00 0,00 T=200 C 19,6 24,6 29,6 34,6 39,6 Hd (mm) FIGURE 4. Thickness percentage reduction (%) versus dome heights The second type of comparison among the numerical results of the two analyzed codes is the evaluation of the effective plastic strain versus x-distance at fixed bulge heights, where the x axis is the radial axis in the analyzed geometry. FIGURE 5 shows the effective plastic strains at different temperatures (23 C, 100 C and 200 C). The bulge height is fixed and it is equal to 19.6mm. In particular, if the temperature increases, the effective plastic strain decreases. Also in this case the agreement between the two different numerical approaches, implemented through Ls-Dyna and Deform, is very good. 1,60E- 01 1,40E- 01 1,20E- 01 8,00E- 02 6,00E- 02 4,00E- 02 2,00E- 02 T=23 C, Hd= 19.6mm 1,40E- 01 1,20E- 01 8,00E- 02 6,00E- 02 4,00E- 02 2,00E- 02 T=100 C, Hd=19.6mm 1,40E- 01 1,20E- 01 8,00E- 02 6,00E- 02 4,00E- 02 2,00E- 02 T=200 C, Hd=19.6mm FIGURE 5. Effective plastic strain versus x distance at temperatures of 23 C, 100 C and 200 C and fixed bulge height equal to 19.6 mm

5 Since the maximum bulge height at 23 C is 19.6mm, in the next plots only the temperatures of 100 C and 200 C have been taken into account. In FIGURE 6 there are the effective plastic strains at the temperature of 100 C and 200 C versus x-distance. The bulge height is fixed and it is equal to 25 mm. Like expected, if the temperature increases the effective plastic strain decreases and, also in this case, the agreement between the two different numerical approaches is very good. 2,50E- 01 1,50E- 01 5,00E- 02 T=100 C, Hd=25mm T=200 C, Hd=25mm 1,50E- 01 5,00E- 02 FIGURE 6. Effective plastic strain versus x distance at temperatures of 100 C and 200 C and fixed bulge height equal to 25mm In FIGURE 7 there are the effective plastic strains at the temperature of 100 C and 200 C versus x-distance and the fixed bulge height, equal to 36 mm. Also in this case, if the temperature increases the effective plastic strain decreases and the agreement between the two different numerical approaches is very good. T=100 C, Hd=36mm 5,00E- 01 4,00E- 01 3,00E- 01 T=200 C, Hd=36mm 5,00E- 01 4,00E- 01 3,00E- 01 FIGURE 7. Effective plastic strain versus x distance at different temperatures and fixed bulge height equal to 36 mm For all the analyzed forming conditions, it is clear that a uniform effective plastic strain distribution in the part was achieved after forming characterized by a concentric zone with higher values in the bulging direction. Finally, it has been measured the maximum bulge heights of the deformed shapes that are 19.6 mm, 36.4 mm and 37 mm at the different temperatures, respectively: 23 C, 100 C and 200 C. It is evident the increase of the bulge height with the increase of the temperature.

6 CONCLUSIONS In the present paper, the authors have studied the warm bulge process using two different numerical approaches, Ls-Dyna and Deform 2D. The first software is traditionally used in metal stamping simulations (also warm and hot) unlike the second. Through this work the authors have studied the reliability of Deform 2D by comparison with Ls- Dyna. Process responses such as: bulge height, thickness reductions and strain distributions have been evaluated at different temperature levels (23 C, 100 C and 200 C). The obtained results show that there is not a great difference in the numerical calculations between the two software. In fact, related to the effective plastic strain, Deform 2D underestimates the Ls-Dyna effective plastic strains of about the 4% while, taking into account the thickness percentage reduction, Deform 2D overestimates the Ls-Dyna thickness percentage reductions of about the 3%. The previous results, together with some considerations about the more or less difficulty in the use of the software and the possibility to develop material damage models in Deform 2D, have persuaded the authors to use Ls-Dyna for bulging tooling design purposes and Deform 2D in the warm bulge numerical campaign. In fact further developments of this work, related also to the realization of the already mentioned research project, should be the bulging tooling design and the simulation of the warm bulge process taking into account Continuum Damage Model (CDM), that should be implemented in Deform 2D. ACKNOWLEDGMENTS Authors are very grateful to MUR: Ministero dell Università e della Ricerca for funding this work recognized as DAMEN: Formability and Damage in Sheet Metal Forming at Elevated Temperatures: New Experimental Procedures and Models. Special thanks are addressed to other research units of the project: University of Padova, Brescia and Trento. REFERENCES 1. J. Van Rijkan, Method of Hydroforming a Structural Member, European Patent, EP A1 (2001). 2. J. Kleinschmidt, T. Dieter, G. Elmar, Method and device for Hydroforming Hollow Workpiece, European Patent, EP B1 (2000). 3. S. Novotny, M. Geiger, Process design HF for lightweight metal sheets Hydroforming at elevated temperatures, JMPT, 2003, vol. 138, pp M. Prier, M. Geiger, Sheet and Tube Hydroforming at elevated temperatures, Proceedings of Hydroforming Conference, Felbach, 2003, p P. Groche, et al. Hydromechanical deep drawing of aluminum alloys at elevated temperatures, Annals of the CIRP 2002, vol. 51/1/2002, p T. Altan, Hydroforming of light weight components from Al-Mg tubes at elevated temperatures, internet comunication, R&D Update, oct. 2003, Columbus, Ohio. 7. M. Geiger, et al., Process strategies for sheet metal hydroforming of lightweight components, IMechE 2001, vol. 215 Part B, pp M. Kleiner, M. Geiger, A. Klaus, Manufacturing of Lightweight Components by Metal Forming. 9. J. Dörr, Innenhochdruck-Umformen mit lokaler erwärmung, Ptu presentation IHU Forum, R. Neugebauer, M., Seifert, Results of Tempered Hydroforming of Magnesium Sheets with Hydroforming Fluids, Proc.6th International Conference Magnesium Alloys and Their Applications, 2004, p J. Dörr, IHU mit Werkzeug- bzw. Medienerwärmung, internet comunication, B.J. Kim, K.S. Park, J.S Ryu, YH, Moon, Experimental analysis for the Tubular Hydroformability of Aluminum Alloys at Elevated Temperature, Materials Science Forum, 2005, Vol , p D. Banabic, M. Vulcan, Bulge Testing under Constant and Variable Strain Rates of Superplastic Aluminium Alloys, Annals of the CIRP, 2005, STC F, 54/1/2005, p M. Keigler, et al., FE-Simulation of the Thermal Hydroforming Process, LS-DYNA Anwerderforum, Bamberg, S. Mahabunphachai, M. Koç, Investigations on forming of aluminum 5052 and 6061 sheet alloys at warm temperatures, Materials and Design 31 (2010) Ls-Dyna User s Manual, Livermore Software Technology Corporation, 2007.