Buckling in low pressure tube hydroforming
Introduction
Hydroforming is increasingly used in the automotive industry. High Pressure Tube Hydroforming (HPTH) uses an internal fluid pressure of 80–400 MPa [1] to expand the tube into a closed die cavity but due to the excessive fluid pressure and press tonnage that would be required application for the forming of Advanced High Strength Steels (AHSS) is limited. Thus a new technology called low pressure tube hydroforming (LPTH) has gained increasing attention in the automotive industry, for the forming of high strength steels to structural sections as shown in Fig. 1 [2], [3]. In this method, a fluid filled tube is crushed to the required shape by the action of a punch or a moving die. In LPTH the internal pressure is less than 10% and the die closing force is less than half [2], [3], [4], [5] of that required in HPTH. Thus the process is a promising alternative for the forming of high strength steels.
Analytical and experimental studies on the process parameters and the material behavior during HPTH can be found in the literature. A diffuse necking criterion was proposed by Boumaiza et al. [6], [7] for the prediction of neck formation and strain gradients in the HPTH of cylindrical tubes, while the bursting failure diagram for tube hydroforming was developed and analyzed by Kim et al. [8]. This was based on the incremental theory of plasticity and the assumption of anisotropic material behavior. The study observed that the bursting pressure increases with decreasing r0-value and reduces with the r90-value. Another study adopted the Swift criterion for diffuse plastic instability based on Hill’s general theory and applied it for the numerical and analytical prediction of fracture locations and of the bursting pressure for HPTH of a cylindrical tube [9]. In addition previous studies reported that in HPTH the forming results depends on the loading path and material parameters such as the strain hardening exponent and material anisotropy [10], [11], while an analytical model for the prediction of bursting was proposed by Song et al. [12] that considered the combined effect of internal pressure and axial feed. The working window with failure modes and loading paths can be seen in [13], [14], [15], [16], [17]. Additionally an analytical model for planar tube hydroforming was proposed by Yang and Ngaile [18] and used to predict the final shape of the formed tube as well as the corner filling conditions, wall thinning and the required internal pressure. Some other analytical studies have focused on the effect of interface friction and material properties on the thickness distribution in the tube after forming and the dissipation of tension forces along the tube/die interface [19]. Based on the deformation theory a model for planar tube hydroforming was created [20], [21], [22].
In contrast to the HPTH process which has been investigated in detail by the numerous investigations stated above only a limited amount of literature has focused on the LPTH process. These were limited to the effect of material properties on part quality in the LPTH of triangular [23] and rectangular [24] shapes. Due to the low pressure in the process, the tube in the straight wall region in contact with the die is prone to buckle. Previous studies are limited to identify specific internal pressures for particular forming cases [2], [3] but no empirical relation has yet been developed to estimate the pressure required to prevent buckling in LPTH. Thus, in this study, first a simplified analytical model is developed to determine the minimum pressure required to avoid buckling during a simple low pressure tube hydroforming operation. After that the model is validated by numerical analysis and used to perform a sensitivity analysis to investigate the effect of process and material parameters on the minimum pressure required to avoid buckling.
Section snippets
Low pressure tube hydroforming
In low pressure tube hydroforming, a round tube is first pressurized using a fluid and then forced into a die by a moving punch (Fig. 2). The outer perimeter of the un-deformed and the formed tube stays approximately the same and Eq. (1) is assumed to apply.Pf = Piwhere,
Pf − Perimeter of the formed tube (2L + 2W + 2лr)
Pi − Perimeter of the initial tube (лDo)
If the fluid pressure is too low the tubes are prone to buckle which is considered as a geometrical defect (Fig. 3). It is therefore important to
Analytical model
As mentioned above the tube material buckles due to insufficient pressure and this generally occurs on the tube side wall. To start with an analytical model the deformed wall section of the tube is considered to be a vertical column and its length is measured from the end of the two corner radii as shown in Fig. 4.
During forming, the column is loaded with a vertical force (Fig. 5(a)) in the axial direction leading either to compression or buckling as shown in Fig. 5(b) and (c) respectively.
The
Validation of the analytical model
To validate the analytical model, numerical analysis was performed and the results compared with those of the analytical solution. The numerical model used for this has been experimentally validated in previous work [26]. To simulate the process the FEA package ABAQUS/Explicit 6.13-2 was used. In the model the tube was assumed to be a cylinder and variations in wall thickness and material properties were neglected. The die is considered to be rigid while the tube is defined as a deformable body
Robust design technique
To understand the most influencing variable which would provide the minimum pressure required to prevent buckling in low pressure tube hydroforming, the analytical equation given in Eq. (24) was considered. Eq. (24) shows that the minimum pressure, p, required to prevent buckling depends on three variable which are the yield strength, σy, of the considered tube material, the wall thickness, t, of the considered tube material and the desired length, L, of the hydroformed tube wall. These
Discussion and conclusion
The proposed analysis to determine a minimum internal pressure to avoid buckling during low pressure tube hydroforming shows an analogy with the analytical solution for pressure during high pressure tube hydroforming, i.e.; where R is the corner radius [1]. High pressure tube hydroforming is limited by splitting of the tube wall (tensile instability) and thus the tube wall stress cannot exceed the ultimate tensile strength.
Low pressure tube hydroforming is limited by buckling of
Acknowledgement
This research was supported by Deakin University and AUTOCRC. The authors gratefully extend their gratitude to Professor Emeritus John L Duncan from The University of Auckland, New Zealand for his assistance with this work. One of the authors (PDH) acknowledges the support of the Australian Research Council through his federation fellowship.
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