A Novel Approach in Manufacturing Two-Stepped ... - Springer Link

INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 15, No. 11, pp. 2343-2350

NOVEMBER 2014 / 2343

DOI: 10.1007/s12541-014-0599-z

A Novel Approach in Manufacturing Two-Stepped Tubes using a Multi-Stage Die in Tube Hydroforming Process Hamed Ziaei Poor1,#, Hossain Ghorbani Menghari1, Ricardo J. Alves de Sousa2, Hassan Moosavi1, Mahboubeh Parastarfeizabadi3, Mahmoud Farzin1, and Hamed Sanei4 1 Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran, 8415683111 2 Department of Mechanical Engineering, University of Aveiro, Portugal 3 Department of Biomedical Engineering, Isfahan University, Isfahan, Iran 4 Department of Mechanical Engineering, Kar University of Khoramdareh, Khoramdareh, Iran # Corresponding Author / E-mail: [email protected], TEL: +98-918 9633493, FAX: +98-311 3912628 KEYWORDS: Tube hydroforming, Stepped tubes, Finite element analysis, Thickness distribution, Corner filling

Optimization of operating conditions is one of the most signicant issues concerning hydroforming the tubular components, including stepped tubes, conical tubes, box shape tubes, and etc. Obtaining a sharp corner without any defects such as thinning and rupturing is one of the main goals in the production of these components. In order to manufacture tubes with filled corners, it is common to increase the imposed pressure to the tubes. However, it may result in rupturing and thinning at the die corner radius, especially when it is too small. In this paper, a new multistage die has been proposed for producing two stepped tubes. Numerical modeling has been conducted using Abaqus/Explicit code. The results of simulation were afterwards checked against experiments in which it is shown that a better thickness distribution could be obtained employing the proposed die set. There is no thinning in the final workpiece, particularly at the copper tube corners. Moreover, it could be possible to produce two stepped tubes with complete filled corners. Finally, comparing to other well-established methods, a lower pressure profile is required and a better thickness distribution can be achieved. Manuscript received: June 4, 2014 / Revised: July 2, 2014 / Accepted: July 15, 2014

NOMENCLATURE PY = Yielding Pressure PC = Calibration Pressure PB = Bursting Pressure D0 = Tube Diameter t0 = The Initial Tube Wall Thickness σu = Ultimate Tensile Strength σy = Yield Strength rb = The Smallest Die Corner Radius σf = Flow Stress of the Material DP = Protrusion Diameter Dmax = Maximum Diameter of Bulged Tube E = Young Modulus ν = Poisson Coefcient µ = Friction Coefcient ρ = Density

© KSPE and Springer 2014

1. Introduction Hydroforming process has been developing since a while before World War II. In recent years, hydroforming technology has gained an increasing interest in automotive, aircraft, and household applications .Hydroforming is a metal fabricating and forming process which allows the shaping of metals such as steel, stainless steel, copper, aluminum, and brass. This process is a cost-effective and specialized type of die molding that utilizes highly pressurized fluid to form metal. Generally there are two classifications used to describe hydroforming, sheet hydroforming and tube hydroforming. Sheet hydroforming uses one die and a sheet of metal; the blank sheet is driven into the die by high pressure water on one side of the sheet forming the desired shape. Tube hydroforming is the expansion of metal tubes into a shape using two die halves, which contain the raw tube. Hydroforming is used to replace the older process of stamping two part halves and welding them together. It is also used to make parts both more efficiently by eliminating welding as well as creating complex shapes and contours.

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Parts created in this method have a number of manufacturing benefits including seamless bonding, increased part strength, and the ability to maintain high-quality surfaces for finishing purposes.1 Various methods have been reported for hydroforming process such as rubber diaphragm hydroforming,2,3 hydro-mechanical deep drawing (HMDD),1 hydrodynamic deep drawing,2 hydro-rim deep drawing,3 sheet hydroforming with movable die,2 hydrodynamic deep drawing with radial pressure,4,5 and tube hydro-forming process. Thinning and rupturing are some of the most important defects that can occurring in both sheet hydroforming and Tube Hydro-Forming (THF) processes. Ziaei Poor et al.6-8 revealed that these defects mainly took place due to insufficient control during the forming process, excessive plastic deformation and improper forming mechanism. Tube hydroforming technology has been widely used to manufacture hollow tubular part with different sections so as to meet the demand of light-weight structures of automobile and aerospace industry.9-13 Bihamta et al.14 proposed an approach in which a three-part die is used instead of one with two-halves to produce complex tubes by the THF method. They showed that, without these modications, producing most of work pieces with complex geometries is difficult, if not impossible. Some researchers have focused on die corner filling in THF processes. Kridli et al.15 have studied the effects of some materials and die parameters on corner filling and wall thickness distribution of the hydro-formed parts. It has been concluded that wall thickness distribution is a function of die corner radius and strain-hardening behavior of material. It has been also stated that the thickness distribution could be reduced if a larger die corner radius was utilized. Hwang and Chen16 examined the corner filling in a square cross-sectional die by analytical, numerical, and experimental methods. They concluded that a higher pressure was required to fill the die corner in case the corner radius was decreased, and doing so would increase the internal pressure to a critical value, so it would cause the tube to be torn. Xu et al.17 studied the effects of friction coefficient, strain-hardening exponent, and anisotropic coefficient on thickness distribution of the tube in a square crosssectional die by analytical, numerical, and experimental methods. They finally reported that the increment of friction coefficient increases tube thickness variation, and as a result, the uniformity of the part is reduced. A study on hydroforming of aluminum alloy tube with rectangular sections carried out by means of experiment and numerical simulations using solid elements by Song et al..18 In this research, the stress and strain states of typical points were analyzed and the three-dimensional graphic representation of normal stress was investigated. Fluid pressure being increased during tube hydroforming process for the purpose of achieving a minimum amount of corner radius can be considered as cause of an excessive decrease of thickness in these regions of formed tubes. So, it seems production of a tube with complete filled corners is inaccessible using simple dies. Elyasi et al.19 used a new mechanics to produce a fully completed corner radius in single stepped tubes formed by the THF process. In their mechanism, two moveable bushes have been installed to push the initial tube into the die cavity. The obtained results in this paper illustrate the improvement of die corner lling mechanism in the proposed die-set. There is no sufficient research on the die corner lling in a two-stepped tube with a box shape, which can

Fig. 1 Conventional tube hydroforming (a), Tube hydroforming using 4 variable bushes (b) (current method)

be produced by traditional methods which do not work properly due to excessive friction between die and tube. In this article, it is shown that the conventional method in production of two stepped tubes leads to some defects such as thinning and wrinkling. Our main objective is to provide a new technique for producing two stepped tubes with complete corner areas. To validate the simulation results, they were compared with experimental tests which have been conducted for single stepped tubes. As illustrated in Fig. 1, the new die set contains 4 moveable bushes in comparison to conventional THF processes.

2. Experimental Procedure In this new technique, two punches and two moveable bushes are placed into the die structure to provide axial feeding of the tube in the die cavity. At first, the tube is put inside the die and the installed “O”rings are placed at the end of the punches to seal them. Then, the pressurized hydraulic oil is pumped inside the tube from the hydraulic unit, via the central hole of the upper punch (Fig. 2). After increasing the pressure to the maximum value and at the onset of tube bulge, the two punches are simultaneously moved forward with a constant velocity toward the die. As the result of this displacement, the two bushes which are placed at both ends of tube get close to each other and the first step is done. The value of fluid pressure must be constant when the punches are forming the tube. The next stage is to reduce the pressure to zero and move the two box-shaped bushes out to carry out the final feeding, simultaneously increasing the fluid pressure to its maximum value. Finally, the four defined bushes move toward each other, as the top punch gets closer to the bottom punch the second step is done. Different parts of the proposed die for production of two stepped tubes are illustrated in Fig. 2. To perform experimental tests, a multipurpose hydraulics press machine with capacity of 600 KN was employed as well as a computer to control the pressure profile value and registration of the results. Moreover, a 45 MPa pump was applied to provide an adequate maximum pressure. Working pressure was regulated by a pressure relief valve. In this study, a seamless pure copper tube was also utilized. To determine the mechanical properties of the copper, tube samples were provided according to ASTM-A370 standard. Also, an INSTRON universal test machine of 250 KN was used for tubes tensile test. The experimental



Fig. 4 The Stress-Strain diagram of the copper tube obtained from uniaxial tensile test

Fig. 2 The assembled model of the new die set

Fig. 5 Shape and dimensions of the required part, (Dimension in mm)

were computed based on a theoretical method proposed by Aue-ULan20 for one-stepped tubes. An initial guess could be possible using these parameters, reducing the number of trials. A path diagram of pressure loading is estimated by relating three different parameters which are (PY), (PB), and (PC). These parameters are shown by the following equations:20

Fig. 3 The experimental setup of the proposed Multi Stage Die

setup used in this research is shown in Fig. 3. Furthermore, an ultrasonic thickness gauge with the accuracy of 0.001 millimeters was used for the measurement of thickness distribution during the experiments. The result of stress-stress diagram obtained from uniaxial tensile test is shown in Fig. 4. A critical parameter in THF process is the magnitude of the chamber pressure. Excessive pressure may lead to tube tearing, while insufficient values may result in wrinkling or incomplete die corner filling. In this research, to predict the pressure profile, three significant pressure values

PYield = σy ( 2t0 ⁄ ( D0 – t0 ) )

(1)

PB = σu ( 4t0 ⁄ ( Dp – t0 ))

(2)

PC = ( 2/ 3 )σf Ln ( rb ⁄ ( rb – t ) )

(3)

The amount of different pressure parameters is shown in Fig. 5 according to the presented theoretical framework. Fig. 6 illustrates shapes and dimensions of the final product. The maximum diameter of the bulged tube and the initial diameter of the original tube are 50.05 mm and 35.05 mm, respectively. According to Eq. (4), the maximum allowable expansion ratio of this annealed tube will be 42.8%. Maxexpansion = ( Dmax ⁄ D0 ) × 100

(4)

Fig. 7 shows that rupturing occurs at the middle tube section approximately, when the pressure of 17 MPa is used for initial shaping of the tube in bulge stage.



Fig. 8 The initial pressure used in the Conventional THF (PC) and the proposed method Fig. 6 The calculated pressure values for initial guess20

Fig. 7 The ruptured tube in the initial bulge stage, pressure = 17 MPa

In order to study the effects of these four variable bushes on corner filling, the axial feeding for the first and second steps are assumed to be equal (length of 8mm for each one). As depicted in Fig. 8, Pc is the pressure of conventional THF process and Pn is the pressure profile implemented within the proposed method. Regarding FEM analysis and experimental tests, a general strategy has been utilized for all of the pressure profiles. As it can be seen in Fig. 8, at the beginning of the process, pressure just increases to the maximum level for the initial bulging. Then, it remains constant during the second stage. Following up, pressure value decreases to zero and finally, the maximum pressure value is elevated to its highest level (35.5 MPa). Regarding the theoretical values included in the provided theoretical method in Fig. 6, the minimum pressure for the initial bulging during the conventional hydroforming process is 10.5 MPa, and the maximum value is 38.1 MPa in the last stage.

3. Finite Element Analysis Undoubtedly, FEA is a powerful simulation means for analyzing a wide range of metal forming processes. Accordingly, a model of THF process was developed using Abaqus/Explicit. In order to compare the mechanism of corner lling in the conventional method with new hydroforming dies, the both dies were analyzed. All the simulation conditions, such as contact and friction conditions and type of elements,

Fig. 9 The sequence of forming the tube at various punch strokes

were similarly dened for both dies. Due to axial symmetry, axisymmetric models were used for the first step of numerical analysis. Fig. 9 shows the FE models of the die sets, in which it is seen that the tube was modeled as 2D axisymmetric with CAX4R 4-node bilinear axisymmetric elements with reduced integration and hourglass control. The 2D analytical rigid wire was implemented for other tools including die and bushes. In all the simulations, the number of elements was optimized and the number of nodes increased. The final mesh shown in Fig. 9 includes 350 elements along the length and 7 elements along the thickness of the tube. The coulomb friction model was used for simulation, while the friction coefficient is 0.06. The formulation of surface-to-surface contact was chosen to define the contact conditions between tubes and dies. To study the thickness distribution along the various regions of the final product, a different strategy in FE analysis was applied, and a shell model was used for all parts. In this simulation, two types of elements were applied. The S4R (4-node shell, reduced integrated) element was chosen for the copper sheet and R3D4 for rigid parts. The deformed tube profiles simulated at various punch strokes are shown in Fig. 9. The path of the counter-pressure was defined using “Amplitude” which employs forming-time as a variable. We assume that there are a same friction coefficient between all tools and the inner and outer surfaces of tube. The data provided in Table 1 are used in numerical analysis by Abaqus/ Explicit method.



Table 1 Material properties for copper tubular blank used in simulations Parameter Tube diameter, (mm) Tube length, (mm) sheet wall thickness, (mm) Yield stress, (MPa) Density, (kg/m3) Young modulus, (GPa) Poisson coefcient Friction coefcient

Value 35 180 1.35 109 8900 110 0.343 0.06

4. Results and Discussion 4.1 Die corner filling It is expected that the THF process produces parts fully formed into the die cavity without any defects or faults. Therefore, the maximum formability of tube during the forming process is assumed as a goal function. One of the most important features of the proposed method is that it causes the material to be forced into the die corner due to the compression made by the variable bushes. Uniform stretching, good compression, and appropriate feeding are the three determining parameters during the THF process. Figs. 10 and 11 illustrate the initial tube as well as the tube formed by conventional and this proposed method, respectively. As it can be seen, an excessive thinning occurred in the second step of the tube during traditional THF process. Results show an excessive friction between the die and the tube as well as nonuniform stretching during the forming process, which can be considered a cause of this problem. Hence, values of Von Mises stress increase near the corner areas and local thinning around this region becomes more severe due to the rise in the stretching force. The outcome of FE analysis shows that the wrinkling phenomenon took place around the corner areas during the first step of the conventional process. The main reason is the improper material flow into the die cavity, which depends on the forming process mechanism. Results also show a sound formed tube with a complete filled corner as well as a proper thickness distribution, achieved by the suggested method. 4.2 Wall thickness distribution In this section, experimental and numerical investigations of the thickness distribution are done considering different feedings. The results obtained from the current method are compared to the conventional one. Accordingly, five fluid pressure profiles; named Pc and P1 to P4 have been employed. As it is evident from Fig. 12, Pc is the pressure of the conventional THF process and all of the other profiles have been implemented for hydroforming through the new proposed method. All of the profiles applied for the current method follow a general pattern rendered from the results of the numerical and experimental works. In order to compare wall thickness distributions, the obtained results from FE analysis along two different paths, named A-B and C-B, have been studied. As the results of numerical analysis show, the primary reason to select these two paths was the severity of thinning in the regions around points B and C. The ideal is to producing a tube with uniform thickness distribution; however, this target is not actually realized because there are stretching forces in the corner regions and between die and tube

Fig. 10 The sequence of forming the tube at various punch strokes (conventional method)

Fig. 11 The sequence of forming the tube at various punch strokes (current method)

surfaces. To investigate the thickness variations, several FE simulations were performed and the thickness distribution was measured. These two paths are shown in Fig. 13. A comparison of the thickness distribution between the new THF process and the conventional THF process, according to different feeding profiles, is shown in Fig. 13. Generally, it can be seen in Fig. 13 that the thickness distribution at the corner regions raised dramatically. Naturally, the minimum thickness was obtained during the second forming step. Results demonstrate that P4 profile yields a higher thickness variation. Also, the maximum thickness at corners 1 and 2 increased around 21% and 33.3%, respectively. A comparison of



Fig. 12 Various fluid pressure profiles applied for consideration of thickness distribution

Fig. 14 Comparison of thickness distributions at various feeding profiles

Fig. 13 Two various paths for investigation of thickness distribution

the results from various feeding profiles reveals that thickness reduction in profile PC has decreased approximately 39.2% while the maximum thickness can be found around the corner 1. Furthermore, a better thickness distribution can be obtained by getting fewer slopes of the interpolated line. A brief look at Fig. 15 reveals that by increasing the feeding rate from PC to P3, the slope of the interpolated lines significantly decreases, which means a best uniform thickness distribution is obtained by employing P3. In addition, after reaching the lowest slope value, an increasing trend took place for profile P4. The main reason is that there is a well-balanced forming condition in P3 rather than P4 in terms of a better feeding rate as well as a lower friction between die and tube. It is important to mention that when the feeding rate is higher than the required amount, some areas of the tube will be unsupported and consequently an excessive stretching will occur. The bar chart of Fig. 15(a) shows that the interpolated line slope is improved around 47% for the current method in P3. Furthermore, as shown in Fig. 15(b) the value of Y-Intercept in case of PC is the highest in comparison to other profiles, which are approximately equal. It can be concluded that the high friction acting on the tube prevents the material flow towards the expansion zones, especially for conventional THF. That is why there is a clear difference between the profiles of Y-Intercept. In addition, it can be realize out that there is no noticeable change for the other profiles and the lowest Y-intercept value was obtained in the P3 profile pressure.

Fig. 15 The value of Slope (a) and the value of Y-intercept (b) obtained from interpolated line

Fig. 16 shows that the obtained results from conventional THF process and the developed method for two stepped tubes using the PC and P3 pressure profiles. As the results of Abaqus/CAE depict, there is a distinct difference between the results obtained from the current method and the ones obtained from conventional THF process, in terms of filling the corners and thickness distribution around various regions. The results show that corners filling during the developed THF process are much better than the conventional ones. As it can be understood from the Fig. 16, the copper tube formed by the developed method has a more uniform wall thickness distribution rather than the tube produced by the conventional method. To validate the above numerical results, the optimized feeding profile P3 was employed to produce a part. As it is shown in Fig. 17, there is reasonable correspondence between FEA and experiments. The wall thickness of the produced part was measured along A-B path. The copper tube was able to achieve the proper final shape without experiencing any failure, particularly at the critical areas around the corner 1 and corner 2 (which are placed on path A-B). Moreover, for additional verification of the experimental results with numerical



Fig. 17 Thickness distribution along the path A-B for P3 feeding profile

Fig. 18 Thickness distribution along path B-C using feeding profiles PC and P3

5. Conclusion Fig. 16 THF process of two steeped copper tubes using the conventional method (a); the results obtained from FEM analysis (b) and experimental work (c)

outcomes, another direction of the tube along path C-B was chosen. In the conventional case, it was noted from the FE analysis that if the internal pressure increased to the maximum level (38.5 MPa), then high thinning occurred at the tube corners. As it is indicated in Fig. 18, the maximum thinning took placed in corner 3 for all of the cases, and by 53% thickness reduction, the thinning is more severe than the one in the conventional kind. As it is discussed, Elyasi et al.19 used a similar mechanism in production of single stepped tubes. They showed, filling the corners in box shape tubes can be possible and in the current research it has been confirmed that using the proposed method producing the two stepped tubes with completed corner is achievable.

Producing two stepped tubes by utilizing the conventional THF method may lead to defects such as thinning, wrinkling, and rupturing. In this study, it was shown that the second step of forming using conventional dies is not feasible. Also, a mechanism to improve die corner filling and thickness distribution was proposed to manufacture two stepped tubes. From the experimental and FEM results, it can be concluded that in the new hydroforming die, the four additional bushes can play a determining role in the mechanism of tube formability improvement. As a result, the indicated change in the design of hydroforming dies led to a considerable improvement in the forming process. Using the proposed methodology, it was possible to employ more uniform pressure profiles; thickness reduction was maintained at acceptable levels (30%) compared to critical ones (circa 50%) using the conventional method, which will naturally bring benefits on the part usage and reliability. Moreover, stress levels around Corner 1 reached during forming process were reduced in 55% which is essential to



promote machine maintenance and reduce springback after forming. The experimental results show that in order to flow the material into the die cavity, it is required that the punch have a relative movement with respect to the die deviation relative to the tube. Furthermore, the formability of the material during the proposed strategy is much better than the conventional .The prime reason is that by using the current method, the tube surface experiences lower frictional forces; therefore, a better thickness distribution in both axial and radial directions can be achieved and a complete filled corner can be obtained. In spite of the above merits, other important aspect that should be considered in the final manufacturing process is that this method is not applicable for producing seamless tubes with a thick thickness.

ACKNOWLEDGEMENT This paper was financially supported by Mechanical Department of Isfahan University of Technology, Iran.

REFERENCES 1. Zhang, S. H., “Developments in Hydroforming,” Journal of Materials Processing Technology, Vol. 91, No. 1, pp. 236-244, 1999. 2. Zhang, S., Wang, Z., Xu, Y., Wang, Z., and Zhou, L., “Recent Developments in Sheet Hydroforming Technology,” Journal of Materials Processing Technology, Vol. 151, No. 1, pp. 237-241, 2004. 3. Thiruvarudchelvan, S. and Travis, F., “Hydraulic-Pressure-Enhanced Cup-Drawing Processes-an Appraisal,” Journal of Materials Processing Technology, Vol. 140, No. 1, pp. 70-75, 2003. 4. Lang, L., Danckert, J., and Nielsen, K. B., “Investigation into Hydrodynamic Deep Drawing Assisted by Radial Pressure: Part I. Experimental Observations of the Forming Process of Aluminum Alloy,” Journal of Materials Processing Technology, Vol. 148, No. 1, pp. 119-131, 2004. 5. Lang, L., Danckert, J., and Nielsen, K. B., “Investigation into Hydrodynamic Deep Drawing Assisted by Radial Pressure: Part II. Numerical Analysis of the Drawing Mechanism and the Process Parameters,” Journal of Materials Processing Technology, Vol. 166, No. 1, pp. 150-161, 2005. 6. Ziaei Poor, H. and Moosavi, H., “An Investigation of Wrinkling and Thinning in Hydroforming Deep Drawing Process with Hemispherical Punch,” International Journal of Mechanic Systems Engineering, Vol. 3, No. 2, pp. 89-96, 2013. 7. Ziaei Poor, H. and Moosavi, H., “Prevent of Wrinkling and Rupturing Using a New Method Based on Punch Force in HydroMechanical Deep Drawing Process,” International Journal of Mechanic Systems Engineering, Vol. 3, No. 3, pp. 125-128, 2013. 8. Ziaei Poor, H., Moosavi, H., Menghari, H. G., and de Sousa, R. A.,

“Investigation of Punch Nose Radius and Punch-Die Clearance on Thinning and Puckering in Hydro-Mechanical Deep Drawing Process,” International Journal of Mechanic Systems Engineering, Vol. 4, No. 2, pp. 16-21, 2014. 9. Ahmetoglu, M., Sutter, K., Li, X., and Altan, T., “Tube Hydroforming: Current Research, Applications and Need for Training,” Journal of Materials Processing Technology, Vol. 98, No. 2, pp. 224-231, 2000. 10. Dohmann, F. and Hartl, C., “Hydroforming-a Method to Manufacture Light-Weight Parts,” Journal of Materials Processing Technology, Vol. 60, No. 1, pp. 669-676, 1996. 11. Dohmann, F. and Hartl, C., “Tube Hydroforming-Research and Practical Application,” Journal of Materials Processing Technology, Vol. 71, No. 1, pp. 174-186, 1997. 12. Yuan, S. J., Han, C., and Wang, X. S., “Hydroforming of Automotive Structural Components with Rectangular-Sections,” International Journal of Machine Tools and Manufacture, Vol. 46, No. 11, pp. 1201-1206, 2006. 13. Yuan, S. J., He, Z. B., Liu, G., Wang, X. S., Han, C., “New Developments in Theory and Processes of Internal High Pressure Forming,” The Chinese Journal of Nonferrous Metals, Vol. 21, No. 10, pp. 25232533, 2011. 14. Bihamta, R., D’Amours, G. D., Bui, Q.-H., Guillot, M., Rahem, A., and Fafard, M., “Numerical and Experimental Studies on the New Design Concept of Hydroforming Dies for Complex Tubes,” Materials & Design, Vol. 47, pp. 766-778, 2013. 15. Kridli, G. T., Bao, L., Mallick, P. K., and Tian, Y., “Investigation of Thickness Variation and Corner Filling in Tube Hydroforming,” Journal of Materials Processing Technology, Vol. 133, No. 3, pp. 287-296, 2003. 16. Hwang, Y. M. and Chen, W. C., “Analysis of Tube Hydroforming in a Square Cross-Sectional Die,” International Journal of Plasticity, Vol. 21, No. 9, pp. 1815-1833, 2005. 17. Xu, X., Li, S., Zhang, W., and Lin, Z., “Analysis of Thickness Distribution of Square-Sectional Hydroformed Parts,” Journal of Materials Processing Technology, Vol. 209, No. 1, pp. 158-164, 2009. 18. Wang, X. S., Yuan, S. J., Song, P., and XIE, W. C., “Plastic Deformation on Hydroforming of Aluminum Alloy Tube with Rectangular Sections,” Transactions of Nonferrous Metals Society of China, Vol. 22, pp. s350-s356, 2012. 19. Elyasi, M., Bakhshi-Jooybari, M., and Gorji, A., “Mechanism of Improvement of Die Corner Filling in a New Hydroforming Die for Stepped Tubes,” Materials & Design, Vol. 30, No. 9, pp. 3824-3830, 2009. 20. Aue-U-Lan, Y., Ngaile, G., and Altan, T., “Optimizing Tube Hydroforming using Process Simulation and Experimental Verification,” Journal of Materials Processing Technology, Vol. 146, No. 1, pp. 137-143, 2004.