Hydraulic

This work aims to find forming limit diagram and mechanical properties experimentally to measure formability by hydraulic bulge test and tensile test, and determination the values of the bursting pressure and final thickness in the final stage at bursting experimentally and numerically by using program (ANSYS 11) to perform numerical simulation for copper and aluminum alloy (6060) tubes before and after heat treatment by hydraulic bulge test. In this work, used two types of tubes with dimensions for copper of (L 0 =150mm, d 0 = 41.275mm, t 0 = 1.06mm) and for aluminum alloy (6060) are (L 0 =150mm, d 0 = 60mm, t 0 = 2 mm). Applied heat treatment (annealing) of copper and aluminum tubes at temperature (450°C, 400°C).the holding time in the furnace was 1 hour and then cooled in the furnace. Has been printed square grid by screen method with dimensions (5x5 mm) for copper and aluminum tubes before and after heat treatment and with dimensions (2.5x2.5 mm) for tensile samples of copper and aluminum before and after heat treatment. Strain Measurement accomplished by using image processing technology using MATLAB by measuring the dimensions of the grid printed before and after the deformation and then measure the true strain on tensile samples and tubes used in the tensile test and hydraulic bulge test before and after heat treatment. The results show that, the values of the bursting pressure and final thickness in the final stage


INTRODUCTION
uring tube hydroforming, several forming parameters, including the loading path, material properties, die design, and friction at the tube-die interface, significantly influence the results.For example, Ahmed and Hashmi (1997) proposed a theoretical method to estimate the forming parameters required for hydraulic bulge forming of tubular components; in particular, they studied the factors of internal pressure, axial load and clamping load.Sokolowski et al. (2000) proposed a tooling and experimental apparatus to determine the material properties of tubes.Vollertsen and Plancak (2002) proposed a principle for the measurement of the coefficient of friction in the forming zone.Lei et al. (2002) used the rigid-plastic finite element method combined with a ductile fracture criterion to evaluate the forming limit of hydroforming processes.The present authors (Hwang and Lin, 2006) proposed a mathematical model considering the forming tube as an ellipsoidal surface for the pur pose of analyzing the forming pressure and maximum bulge height.The properties of tubular materials were additionally evaluated by hydraulic bulge tests combined with the above-proposed analytical model (Hwang and Lin, 2007).
The forming limit diagram (FLD) of tubular materials ought to be established, because it directly influences the formability of the hydraulic forming processes.A few studies concerning the loading paths or the forming limit of tubes and sheets have been reported.For example, Tirosh et al. (1996) explored an optimized loading path for maximizing the bulge strain between necking and buckling experimentally with aluminumA5052 tubes.Zhao et al. (1996) discussed analytically and experimentally the effects of the strain rate sensitivity of the sheet material on the FLD in sheet metal forming based on the M-K model and Graf-Hosford anisotropic yield function.They found that FLDs with different pre-strains are signif icantly influenced by the straining paths.However, the converted forming limit stress diagrams (FLSD) appear not to be strongly influenced by the straining paths.Xing and Makinouchi (2001) investigated the differences in forming limits of tubes under internal pressure, independent axial load or torque D based on Yamada's plastic instability criteria and Hill's quadratic yield function.The above theory coupled with an in-house finite element code ITAS3d was used to control the material flow and to prevent the final failure modes from occurring.Nefussi and Combescure (2002) used Swift's criteria for sheets and tubes and took into account the buckling inducedby axial loading inorder to predict plastic instability for tube hydroforming.They concluded that the two Swift's criteria are applicable to predict necking and that a special attention has to be paid to plastic buckling, because the critical strains corresponding to buckling are much smaller than the critical strains predicted by the necking criteria.However, experiments are required to validate their theoretical results.Yoshida and Kuwabara (2007) discussed the FLD of steel tubes subjected to a combined axial load and internal pressure.They proposed a FLSD, and concluded that the forming limit stress of the steel tube is not fully path-independent and that the path dependence of forming limit stress is strongly affected by the strain hardening behavior of the material for given loading paths.Korkolis and Kyriakides (2008) investigated the performance of Hosford and Karafillis-Boyce non-quadratic anisotropic yield functions in predicting the response and bursting of tubes loaded under combined internal pressure and axial load.They concluded that the predicted structural responses are generally, but not universally, in good agreement with the experimental results, while the predicted strains at the onset of rupture are somewhat larger than the values measured.So far, a consistent conclusion for forming limit theorems of tubular materials has not been established and the forming limit diagram for AA6011 tubes has not been found.

THEORETICAL CONSIDERATIONS
Consider a tube which is subjected to an internal pressure, pi, and compressive axial forces, F,
In the analysis above, F is assumed to be equal to the forming force.In other words, the sealing and friction forces are not considered in the analysis above.17) and ( 18) predict that the tube yields at F = 0 under plane stress condition, When α = 1 (equal biaxial stress) Eqs. ( 17) became is piy = σy *

NUMERICAL SIMULATION
For simulating free bulge hydroforming process, commercial FEA software ANSYS 11 was used, in which the "Newton-Raphson" implicit approach was employed to solve nonlinear problem.
The 3-D 8-node plastic structural solid element of VISCO107 was used for work piece (blank).The tool set (die) was modeled as rigid bodies.
Automatic contact procedure in ANSYS 11 was used to model the complex interaction between the blank and tooling.For rigid (tool set)-flexible (blank) contact, 3D 8-node quadrilateral target elements of TARGE170 were used, to represent 3D target (tool set) surfaces which were associated with the deformable body (blank) represented by 3D 8-node contact elements of CONTA174.The contact and target surfaces constituted a "contact pair", which was used to represent contact and sliding between the surfaces of tool set and workpiece (blank).
free bulge hydroforming models were created.Due to the symmetry in the specimen geometry, constraints and boundary conditions, only a 1/8 portion of the tube blank had been shown in Figure (3).
The von Mises isotropic yield criterion was used in numerical simulation and their predictions compared against the experimental results of aluminum alloy (6060) tube and pure copper tube before and after heat treatment.A Coulomb friction law was employed to investigate the effect of friction at the tool-material interface.Elasto-plastic constitutive model with isotropic strain hardening was used to simulate the tube response.The elastic behavior was taken to be linear and the plastic response was modeled using the von Mises yield criterion (isotropic).Table (1) shows the mechanical properties for two materials before and after heat treatment.

RESULTS AND DISCUSSION strain measurement
The image processing technique can measure true strain of the tensile samples of copper and aluminum tubes before and after heat treatment by analysis of the grid which was printed on surface of the tensile samples in the failure region and then has been determine another variables in tables below depended on the equation (6).As already said the experimental campaign was carried out on copper and aluminum tubes before and after heat treatment.The experiments were conducted at different pressure levels in order to obtain the relationship between bulge height, thickness and pressure.A square grid was etched on each tube to measure the hoop and the longitudinal strain at the end of the process so to verify the deformations calculated by the analytical model.Figures ( 6) and ( 7) show the copper and aluminum tubes at the end of the process experimentally and numerically.The bulge area is plastically deformed.During the test the axial actuators are still and the tube is fully blocked.The experiments design starts from the observation of the tube bursting pressure and yield pressure.Within this range other different pressure levels have been investigated.For each tested tube the bulge height, the radius of curvature in the longitudinal direction and the wall thickness were measured.From these experimental values.The results show in the tables below.10), ( 11) and ( 12) show relationship between internal pressure and bulge height in the bulge test of copper and aluminum tubes before and after heat treatment , in tube hydroforming in square die must be not increase the bursting pressure value of bulge test as show in the Tables ( 7) to (10).13) shows thickness distributions and location of thinning in the bulge test of copper and aluminum tubes before and after heat treatment.The minimum simulated thickness of tube Aluminum tubes before and after heat treatment (1.7919, 1.4871) mm .While it is reduced from 2 mm to (1.7094, 1.35411) mm by experimental test at pressures (19,16) MPa.The variation between simulated and experimental tests results are (4.8,9.8) %, and the minimum simulated thickness of tube copper tubes before and after heat treatment (0.8918, 0.621) mm .While it is reduced from 1.06 mm to (0.853652, 0.571534) mm by experimental test at pressures (29, 27) MPa.The variation between simulated and experimental tests results are (4.4,8.6) %.

Determine hydraulic yield pressure
From Equation (2-17) and depended on mechanical properties and dimensions of the copper and aluminum tubes before and after heat treatment can determine yield pressure in the bulge test and determine yield pressure numerically and experimentally from the Tables (7) to (10) , the results show in the table below.From the figure above it can be noted that aluminum and copper tubes after heat treatment good formability comparison with aluminum and copper tubes before heat treatment.

2 Figure ( 2 )
Figure (2) The stresses acting on an element at the middle of the tube.[4]
Figure (8) numerical Von-Mises strain of final tubes at bursting a-cu tube without heat treatment b-Cu tube after heat treatment c-Al 6060 tube without heat treatment d-Al 6060 tube after heat treatment.
Figures (9) relationship between internal pressure and bulge height ofaluminum tube after heat treatment.
Figure (13)show the tube thickness along its bulged part at the end test a-Al 6060 tube without heat treatment b-Al 6060 tube after heat treatment c-Cu tube after heat treatment d-cu tube without heat treatment.
(n) by drawing strain paths data , and show in Figure (14forming limit diagram of a-cu tube without heat treatment b-Cu tube after heat treatment c-Al 6060 tube without heat treatment d-Al 6060 tube after heat treatment

Table ( 15) show values yield pressure in the bulge test Tube materials Yield pressure (Mpa) Experimentally numerically theoretically Al before heat treatment 4 4 4.83 Al after heat treatment 2 2 2.75 Cu before heat treatment 6 4 6.537 Cu after heat treatment 4 2 2.89 forming limit diagram
To find forming limit diagram of copper and aluminum tubes before and after heat treatment depended on tensile test and bulge test and strain hardening exponent