Numerical simulation of hydroforming a double conical tube

Transcription

1 Numerical simulation of hydroforming a double conical tube S.J.Yuan, W.J.Yuan *, Z.R.Wang School of Materials Science and Engineering, Harbin Institute of Technology, Harbin150001, China Abstract. The hydroforming process of a double conical tube with the biggest difference of cross-section 75 percent is studied by means of FE simulation in this paper. The effects of loading paths during hydroforming process on the wrinkle shape and failure modes are analyzed. Thickness distribution and strain path of position with the biggest expansion rate on FLD diagram of this workpiece are given. The simulation results show that the part can be formed successfully with the feeding pressure selected in the range from 20 to 25MPa. When the feeding pressure is 23MPa, the preform with desirable wrinkle distribution and plenty storage of materials can be obtained. The maximum of thinning rate by the simulation is about percent, which is close to 19.54% that is obtained in experiment. INTRODUCTION Hydroforming process is an advanced technology to manufacture hollow variable section tube parts [1-2]. The hollow workpiece with varied sections along its axes can be formed in one operation. Although much research about hydroforming process has been devoted to various varying diameter tubes of circular section [3-6], rather less attention has been paid to double conical tubes. In later case one problem should be solved is to decrease thickness thinning in the position corresponding to the largest diameter. In this paper, the useful wrinkles were constructed during feeding period of hydroforming, then in the end of calibration period of hydroforming a sound double conical tube can be obtained if the wrinkles are desirable. The effects of loading paths during hydroforming process on the wrinkled shape, failure modes, thickness distribution and strain path on FLD diagram of this workpiece were compared both with numerical simulation and experiment. Finally, the maximum expansion of cross-sections has been reached 75 percent. * Corresponding Author. Tel: ; yuanwenjing@hit.edu.cn PART DRAWING AND ITS MATERIAL FIGURE1. Geometry of part The shape and the dimensions of the double conical part are shown in Fig.1. In the experiments, the SS304 stainless tube blank was used and it was 56mm in diameter, 2.5mm in thickness and 300mm in length. The mechanical properties were obtained through tension test. The elongation δ u is 58 percent; the strain hardening index n is 0.38; the yield strength σ 0.2 is 203 MPa; the tensile strength σ b is 720 MPa. Hydroforming difficulties for this part are as follows: 1) The largest expansion of cross-sections of this part is 75 percent, therefore, the thinning of thickness and bursting are easy to take place; 2) The feeding distance is longer in 595

2 order to accumulate enough material without dead wrinkle before final calibration. FINITE ELEMENT MODEL AND NUMERICAL SIMULATION CODE Finite Element Model In this paper, the numerical simulations are carried out with a dynamic explicit code LS-DYNA. The finite element model is shown in Fig.2. The tube blank is meshed by Barlat s 3-Parameter Plasticity Model, and there are 5500 quadrate elements. The die and the left and right punches are meshed by rigid elements. The material is considered homogenous and obeys Mises criterion. Coulomb friction model is used and the friction coefficient is adopted 0.1. The material mode of the tube blank is σ=800ε 0.38, based on the tensile test of specimen. Internal pressure (MPa) p0 A(p0=12MPa) B(p0=16MPa) C(p0=20MPa) D(p0=23MPa) E(p0=25MPa) F(p0=30MPa) Axial feeding (mm) FIGURE3. Loading paths Calibration pressure :100MPa ANALYSIS OF SIMULATION RESULT Shape change The biggest expansion is in the middle of this part, so the ideal distribution of wrinkled shape is that the diameter of wrinkle top in the middle of the workpiece is larger and longer than that in the two ends after feeding. It means that more storage of materials in the middle of the workpiece than that in the two ends. In this case, the thinning rate becomes lower. Also, the strain localization even fracture can be avoided after calibration. FIGURE2. Finite element model 1-left punch, 2-tube, 3-die, 4-right punch Loading Path of Numerical Simulation The loading path is shown in Fig.3. The first step is to give the constant feeding pressure p 0 into the tube. After feeding, the internal pressure is increased rapidly for finish calibration. The feeding pressures p 0 were adopted 12MPa, 16MPa, 20MPa, 23MPa, 25MPa and 30MPa respectively. After feeding, the internal pressure is increased to 100MPa to finish calibration. According to the shape of part shown in Fig.1, the tube thickness is supposed constant. Then the total axial feeding length (56mm) and the feeding length of each side (28mm) can be calculated. Fig.4 shows the hydroforming process of tube with different axial feeding length of loading path A. Three wrinkles have been formed when the axial feeding length exceeds 20mm. Because of the lower feeding pressure, the diameters of three wrinkles are all smaller, and difference of diameters between wrinkle tops in the middle and in the two ends of the workpiece is 8.9 percent after feeding. Storage of materials in the two ends are larger than that in the middle of the workpiece, and the distribution of wrinkles is undesirable, therefore, dead wrinkles are formed on the surface of the part after calibration, and serious thinning takes place in the middle of the part with the maximum of thinning rate about percent. The feeding pressure of loading path B is slightly higher than that of loading path A, so their simulation results are similar. 596

3 (a) (b) (c) (d) ( e) FIGURE4. Wrinkle shape and the wall thinning (%) of the part for loading path A (a) Axial feeding=20mm (b) Axial feeding=32mm (c) Axial feeding=45mm (d) Axial feeding=56mm (e) formed part Fig.5 shows the hydroforming process of tube with different axial feeding lengths of loading path D. Three wrinkles are formed during hydroforming process after feeding. The differences between the top and bottom of the wrinkles in the middle and in the two ends of the workpiece are 18.3 percent and 27.2 percent respectively. The distribution of wrinkles is desirable and storage of materials is plenty. The maximum of thinning rate of the final part is percent and the thickness thinning is smaller than others. The feeding pressures of loading path C, D and E are appropriate, so the outer shape of final part is acceptable but the thickness thinning rates are different. (a) (b) (c) (d) (e) FIGURE5. Wrinkle shape and the wall thinning (%) of the part for loading path D (a) Axial feeding=20mm (b) Axial feeding=32mm (c) Axial feeding=45mm (d) Axial feeding=56mm (e) formed part Fig.6 shows the hydroforming process of tube with axial feeding lengths of 20mm and 32mm according to the loading path F. No wrinkles were formed during the hydroforming because of the higher feeding pressure, and the tube burst when the axial feeding length is 32mm. It is known that better feeding and preforming can be realized by using optimized loading path, as well as the desirable distribution of wrinkle shape and thickness thinning rate. At last, an ideal final part with larger diameter difference and smaller thickness thinning rate can be obtained. 597

4 (a) FIGURE6. Wrinkle shape and the wall thinning (%) of the part for loading path F (b) a) Thickness distribution in the longitudinal direction of the part according to loading path D (a) Axial feeding=20mm (b) Axial feeding=32mm Distribution of Thickness Fig.7a) is the thickness distribution curves along axial direction of formed part according to loading path D. The positions corresponding the wrinkle tops and wrinkle bottoms are shown, and it is shown that in middle wrinkle top the thickness changes rapidly. Fig.7b) shows the wrinkle shape and the positions after feeding during simulation. It is known from Fig.7a) that the thickness increases at the entrance of conical surface, and then decreases continuously. Fig.8 shows that the thinning of thickness from top1 to bottom is small and a platform appears because that expansion rate of this area is small and storage of materials is plenty, while the expansion rate of area from bottom to top2 increases but the storage of materials is relatively less, so the thickness is decreased rapidly as shown in Fig.7a). b) Wrinkle shape after axial feeding FIGURE7. Thickness distribution Strain Path in FLD Fig.8 shows the strain path corresponding to loading path D, E and F of the point with maximum expansion rate. The feeding pressure of loading path D is 23MPa, and it is appropriate that the strain path is in the safe range, so ideal formed part with smaller thickness thinning is obtained. The feeding pressure of loading path E is lager, and its strain path is above the loading path D, so the thickness thinning is bigger. Moreover, the feeding pressure of loading path F is very large that the tube burst when the axial feeding length is only small. It means that when the axial strain is very small, the hoop strain is already very big, so the failure caused by the strain path exceeding the forming limit of localized instability and damage. 598

5 a) Bursting workpiece during axial feeding FIGURE8. Changing locus of strain paths for maximum expanding point in the FLD EXPERIMENTAL The experiments were carried out on the IHPF machine in HIT. The experimental die set is shown in Fig.9. The tube blank is 56mm in outer diameter, 2.5mm in the thickness and 300mm in the length. b) Bursting workpiece during the calibration FIGURE10. Bursting Workpiece a) Middle shape after feeding FIGURE9. Experimental die set The tube burst will take place if the feeding pressure is too high, as shown Fig.10a). If the feeding pressure is too low and the feeding length is larger, the dead wrinkle will occur, and the fracture will also take place under high calibration pressure as shown in Fig.10b). When the feeding pressure is appropriate, the distribution of wrinkles is desirable and storage of materials is plenty after feeding, and successful part was obtained after calibration, shown as Fig.11. The thickness distribution along axial direction was measured. It is similar to the simulation results, as shown in Fig.7a). The maximum of thinning rate of the final part is percent. b) Final shape after calibration FIGURE11. Shapes of successful part during hydroforming CONCLUSIONS The hydroforming process of a double conical tube with the biggest difference of cross-section 75 percent is studied in this paper. The effects of loading paths during hydroforming process on the wrinkle shape and failure modes are analyzed. The conclusions are as follows: 1) The loading paths have a big effect on the wrinkle shape, size and thinning rate during hydroforming process. The parts can be formed successfully with the feeding pressure selected in the range from 20 to 25MPa. When the feeding pressure is 599

6 23MPa, the preform with desirable wrinkle distribution and plenty storage of materials can be obtained after feeding. After calibration, the maximum of thinning rate is about percent. When the feeding pressure is selected from 12 to 16MPa, storage of materials in the two ends are larger than that in the middle of the workpiece, therefore, dead wrinkles are formed on the surface of the part after calibration, and serious thinning takes place. When the feeding pressure exceeds 30MPa, the tube has burst before finishing the feeding. 2) The thickness of the part is not uniform. The expansion of the area between the middle wrinkle top and the wrinkle bottom is bigger after feeding, so the thinning rate of this area is bigger after calibration; while expansion of the middle area of the part is the biggest, so the thinning rate of this area is also the biggest. 3) Strain path of the area with the biggest expansion rate on FLD diagram for various loading paths of this workpiece are given. The strain path of loading path D is in the safe range, and it proved that the internal high pressure forming of a conical tube with bigger difference of cross-section is feasible. It is found from the experiments that when the feeding pressure is higher, the tube burst takes place before finishing the feeding; when the feeding pressure is lower, dead wrinkles are formed on the surface of the part after feeding and the tube burst after calibration; when the feeding pressure is appropriate, the preform with desirable wrinkle distribution and plenty storage of materials can be obtained and the part with the maximum of thinning rate about percent are obtained. The results of numerical simulation and experimental study are coincident. ACKNOWLEDGMENTS This paper was financially supported by National Natural Science Foundation of China (Project Number: ). The authors would like to take this opportunity to express their sincere appreciation. REFERENCES 1. F. Dohmann, C. Hartl., Journal of Materials Processing Technology, (1996). 2. K. Brewster, K. Sutter, M. A. Ahmetoglu, T. Altan, The Tube and Pipe Quarterly, 34-40(1996). 3. F. Dohmann, C. Hartl., Journal of Materials Processing Technology, (1997). 4. S. J. Yuan, L. H. Lang, X. S. Wang, Z. R. Wang, Hydroforming of Tubes, Extrusions and Sheet Metals, edited by Klaus Siegert, Proceedings of the Second International Conference on Hydroforming, Fellbach, Germany, 2001, pp S. J. Yuan, G. Liu, X. S. Wang, Z. R. Wang, Hydroforming of Tubes, Extrusions and Sheet Metals, edited by Klaus Siegert, Proceedings of the Third International Conference on Hydroforming, Fellbach, Germany, 2003, pp S. J. Yuan, G. Liu, X. R. Huang, X. S. Wang, W. C. Xie, Z. R. Wang, Journal of Materials Processing Technology, (2004). 600