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*Corresponding author. E-mail address: bryan.macdonalddcu.ie (B.J. Mac Donald). Finite Elements in Analysis and Design 37 (2001) 107116 Three-dimensional nite element simulation of bulge forming using a solid bulging medium B.J. Mac Donald*, M.S.J. Hashmi School of Mechanical and Manufacturing Engineering, Dublin City University, Dublin 9, Ireland Abstract Bulge forming is an innovative manufacturing process which is used to manufacture many industrial components. Common products include T-branches, cross branches and angle branches. The understanding ofthe process to date has been rather limited.Finite elementanalysisof the processincorporatingthe contact phenomenon between the die and the tube reported in literature has been limited, with only very particular arrangements and liquid bulging media being considered. Three-dimensionalsimulation of the process using a solid bulging medium has not been reported. This paper presents a three-dimensional simulation of the manufacture of cross-branch components using a solid bulging medium. The e!ect of varying friction between the bulging medium and the tube is examined and the history of development of the bulge and stress conditions in the formed component are presented. The results of the simulation are compared to those previously obtained in simulation of the hydraulic bulging process. The explicit non-linear FE code LS-DYNA3D is used to perform the simulations. ( 2001 Elsevier Science B.V. All rights reserved. Keywords: Bulge forming; Simulation; Finite element method 1. Introduction Bulge forming is a widely used industrial process which is generally used to form complex componentsfrom tubular blanks. Componentsare formedby restraining the blank in a die bearing the desired shape and applying an internal hydrostatic pressure to the tube via a liquid or solid medium. Bulge forming by pressure load alone is limited in the type and quality of components it can produce. If a compressive axial load is applied to the ends of the tube in conjunction with the pressure load, then material can be pushed into the deformation zone during, forming thus 0168-874X/01/$-see front matter ( 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 8 7 4 X( 0 0 ) 0 0 0 2 3 - 8 Fig. 1. Bulge forming of cross branch components. preventing excessive thinning of the walls. Fig. 1 shows cross-sectional views of an arrangement for the manufacture of cross-branch tubular components. Experimental studies concerning bulge forming using a liquid bulging medium have been widely reported in literature, and recent numerical works 14 have contributed to a further understand- ing of the process. Bulge forming using a solid medium has been less widely reported. Al-Qureshi et al. 5 described an experimental process for axisymmetrically bulging thin-walled metal tubes. In a separate presentation, Al-Qureshi 6 compared bulge forming using a polyurethane rod with hydraulic bulge forming. It was concluded, due to the complexity of analysing the polyurethane forming technique, that the more highly developed hydraulic forming method gave better results. Filho and Al-Qureshi 7 presented an experimental method of forming tee joints from straight tubes using a urethane rod. The deformation was achieved by using repetitive loading and 108B.J. Mac Donald, M.S.J. Hashmi / Finite Elements in Analysis and Design 37 (2001) 107116 unloading cycles and by varying the length of the urethane rod between cycles. Thiruvarudchelvan and Travis 8 described experiments to axisymmetrically bulge copper tubes using a urethane rod. Thiruvarudchelvan 9,10 developed an approximate theory for predicting the initial yield pressure and nal forming pressure required for bulging a metal tube using a urethane rod. The theory made use of experimentally determined friction characteristics and was compared with experimental results. The above sources have investigated the bulge-forming process using a solid medium in several ways, and some understanding of the process has been accumulated. However, in order to optimise the design of the manufacturingprocess and hence the product, a deeper understandingis required, particularly of the internal stress distributions. In order to investigate the bulging and deformation mechanisms, a non-linear nite element analysis has been conducted to simulate the solid medium bulging process of cross-branch components. 2. Finite element model The explicit FE code LS-DYNA3D is used in this paper to simulate the bugle forming process. Simulations were carried out to bulge a copper cylindrical tube of 1.03 mm wall thickness, 24.12 mm diameter and 107 mm length into a cross joint. The diameter of the branches was equal to that of the main tube. The length of the bulging medium was modelled slightly shorter than that of the tube. This accurately modelled the actual situation which facilitates insertion of the punch into the tube. By taking advantage of symmetry it was possible to model one-eighth of the problem. Fig. 2 shows the discretised model. Some points are indicated for further discussion in the results section. Both the die and the tube were modelled using eight-node solid elements. A total of 2875 elements describe the model. The interfaces between the die and the tube, and between the bulging medium and the tube, were modelled using an automatic surface to surface contact algorithm. The algorithm uses the material properties of both contacting surfaces to calculate the sti!ness of the contact elements. An elastic coulomb friction law was assumed and a coe$cient of friction of 0.15 was assigned between the die and the tube. This value is representative of values measured experimentally 11. The coe$cient of friction between the bulging medium and the tube was varied in order to determine its e!ect on the process. The tube material properties were determined from a compression test on annealed copper. A piecewise linear elasto-plastic material model was used with the following parameters: Youngs modulus124103 MPa, yield strength160 MPa, tangent modulus925 MPa, Poissons ratio0.3, density8.9106 kg/ mm3. The material parameters for the bulging medium were chosen to approximately represent lead. Soft metals such as lead are widely used as a bulging medium in industrial applications and are capable of producing far more deformation than elastomers. 3. Loading and solution As one-eighth of the problem was modelled by taking advantage of symmetry, the tube and bulging medium nodes were constrained in the appropriate directions. The die was constrained as B.J. Mac Donald, M.S.J. Hashmi / Finite Elements in Analysis and Design 37 (2001) 107116109 Fig. 2. The nite element model. Fig. 3. Loading pattern used. a rigid body. The internal pressure was generated by applying a prescribed displacement to the nodes at the end of the ller material. The axial deformation in the main tube was generated by applying a prescribed displacement to the nodes at the edge of the tube end. In the actual forming process the axial loads on the ller and tube are applied by a shoulderedpunch, where the length of the shoulder controls the amount of deformation of the ller material prior to axial deformation of the tube. In this case the punch was not modelled, instead the nodes of the tube under the punch were constrained in the radial and circumferential directions, which is equivalent to the punch being in place. The loading pattern used in all simulations is shown in Fig. 3. This pattern was developed in order to maximise branch height. 110B.J. Mac Donald, M.S.J. Hashmi / Finite Elements in Analysis and Design 37 (2001) 107116 Fig. 4. Distribution of Von-Mises stress in the tube at 20% of axial displacement. In order to gain a better understanding of the process, a number of simulations were carried out in which the process parameters were varied. In all simulations the axial load was applied simultaneously to the ller material and tube. The rst simulation was carried out using a zero coe$cient of friction between the bulging medium and the tube. In subsequent simulations the coe$cient of friction was varied between zero and 0.5. 4. Results and discussion 4.1. Development of the bulge In order to study the development of the bulge the loading case in which the value of friction between the ller material and tube was set as 0.3 was chosen. The case was taken as being a representativeof the values measured experimentally 11. Figs. 47 show the development of the bulge in the tube. It can be seen from the gures that the bulge initially develops as a hump just ahead of the die bend. As the pressure exerted by the bulging medium increases then the bulge begins to become more regular. By the time 40% of the axial displacement has been applied, the hump has disappeared and the branch top is almost #at, as shown in Fig. 5. From this stage, due to increasing internal pressure and axial displacement of the tube, the bulge develops in a regular fashion as illustrated in Figs. 6 and 7. It is interesting to note the developmentof stress in the tube as the bulge develops.At 10% of the loading the maximum stress is located at point A. As the process continues, the location of maximum stress does not move, but, the stress gradient around the area of maximum stress becomes more concentrated as loading increases. It can be seen from the deformation of the elements in this region that the high stress is due to a combination of compressive axial strain and tensile hoop strain. B.J. Mac Donald, M.S.J. Hashmi / Finite Elements in Analysis and Design 37 (2001) 107116111 Fig. 5. Distribution of Von-Mises stress in the tube at 40% of axial displacement. Fig. 6. Distribution of Von-Mises stress in the tube at 70% of axial displacement. 4.2. Ewect of friction The e!ect of varying the friction between the bulging medium and the tube was investigated by carrying out four simulations which used friction factors of 0, 0.15, 0.3 and 0.5, respectively. The maximum branch height produced in each case was around 11 mm and decreased with increasing friction, with a di!erence of only $1 mm between each simulation. The maximum stress at point A in each case varied between 300 and 328 MPa with the level decreasing with increasing friction. The maximum stress in the branch top varied between 185 and 200 MPa and again decreased with increasing friction. An examination of the thinning behaviour of the branch top showed that for 112B.J. Mac Donald, M.S.J. Hashmi / Finite Elements in Analysis and Design 37 (2001) 107116 Fig. 7. Distribution of Von-Mises stress in the tube at 100% of axial displacement. Fig. 8. Development of stress in the top central node of the cross branch during simulation 2 (Friction0.15). a friction factor of 0 the branch top had thinned to 90%, of the original thickness. The simulations for increased friction exhibited almost no thinning of the branch top. The thickening behaviour of the main tube, ahead of the punch, varied from 120% to 102% of the original thickness. Lower friction values produced less thinning of the branch top and more thickening of the main tube. B.J. Mac Donald, M.S.J. Hashmi / Finite Elements in Analysis and Design 37 (2001) 107116113 Fig. 9. Development of stress in the top central node of the cross branch during simulation 3 (Friction0.3). The development of stress was also in#uenced by the level of friction between the bulging medium and the tube. Fig. 8 shows the development of stress in the top central node of the cross branch during simulation 2 (friction0.15). The stress development is quite erratic indicating some stickslip behaviour between the bulging medium and the tube. When compared with Fig. 9, which shows the development of stress by simulation 3 (friction0.3) it can be seen that increasing friction results in a much smoother development of stress in the bulge. 4.3. Comparison with hydraulic bulging The authors in a previous work 4 have simulated hydraulic bulge forming of cross-branch components using the same blank geometry and material properties as used in this analysis. In order to compare the solid medium bulging process with the hydraulic bulging process, results from 4 were compared with results here. Clearly, the use of a solid medium allows for greater branch heights and less thinning of the branch top. In order to compare stress conditions a further simulation was run to bulge a compon- ent to the same height as that experienced in the simulation of the hydraulic process (11.5 mm). Figs. 10 and 11 show the distribution of Von-mises stress in the formed components using hydraulic and solid bulging processes, respectively. When the stress distributions were compared it was noticed that the solid medium bulging process produced less stress in the formed component. The distributionof stress in the formedcomponentwas quitesimilarin the area aroundthe pointof 114B.J. Mac Donald, M.S.J. Hashmi / Finite Elements in Analysis and Design 37 (2001) 107116 Fig. 10. Distribution of Von-Mises stress in hydraulically bulged cross branch 4. (height11.5 mm). Fig. 11. Distribution of Von-Mises stress in solid medium bulged cross branch. (height11.5 mm). maximum stress for both simulations. The main tube has stressed a great deal in the simulation for solid medium bulging. This is due to friction between the bulging medium and the tube causing greater axial stress to be imparted on the tube than was present in the hydraulic simulation. An important advantage of the solid medium process noticed during the comparison was that it can produce the same branch height as the hydraulic process but with far less reduction in length of the unbulged tube. This is again due to friction between the bulging medium and the tube causing material to be pulled into the bulging zone 57. B.J. Mac Donald, M.S.J. Hashmi / Finite Elements in Analysis and Design 37 (2001) 107116115 5. Conclusion This paper presents the results from the nite element simulation of solid medium bulge forming of cross-joint components. The simulation results indicate that (1)The use of a solid bulging medium allows for greater branch height, less thinning of the branch top and less stress in the formed component when compared to the hydraulic bulging process. (2)Increasing friction between the bulging medium and the tube results in less stress in the formed component, more thinning of the branch top, less thickening of the main tube and a smoother stress development during the forming process. (3)Increasing friction between the bulging medium and the tube has little e!ect on the resulting branch height in the formed component. (4)When compared to a cross branch of similar height obtained by the hydraulic bulging process, it is clear that the solid medium bulging process results in far less reduction in the length of the tube. References 1 H. Bauer, FE simulation of the production process of builder camshaft, O.C. Zienkievicz, J.L. Chenot, R.D. Wood (Eds.), in: Numerical Methods in Industrial Forming Processes, Balkema, Rotterdam, 1992, pp. 585600. 2 M. Ahmed, M.S.J. Hashmi, Three-dimensionalnite element simulation of a