An Analytical Model for Long Tube Hydroforming in a Square Cross-Section Die Considering Anisotropic Effects of the Material

Document Type: Original Article


Mechanical Engineering Department, Razi University, Kermanshah, Iran.


In this paper, a mathematical model was developed to analyze the hydroforming process of a long anisotropic circular tube into a square cross-section die. By using the thickness variation in two extreme cases of friction between the tube and die wall, namely no friction and sticking friction cases, thickness variation in the case of sticking friction was captured in the model. Then by using equilibrium equation for contact length segment, thickness distribution was determined and corresponding forming pressure is predicted. It was shown that in a plane strain state, anisotropic value has no influence on thickness variation of the deformed tube and the forming pressure will increase when the anisotropic value increases. The analytical results of forming pressures and thickness distributions were compared with the results available in the
literature to verify the validity of this simple analytical proposed model.


[1] J. Chen, Z. Xia, S. Tang, Corner fill modeling of tube hydroforming. Proceedings of the ASME, Manufacturing in Engineering Division, 11 (2000) 635-640.
[2] G. Kridli, L. Bao, P. Mallick, Two-dimensional plane strain modeling of tube hydroforming. Proceedings of the ASME, Manufacturing in Engineering Division, 11 (2000) 629-634.
[3] Y. Hwang, T. Altan, Finite element analysis of tube hydroforming processes in a rectangular die, Finite. Elem. Anal. Des., 39 (2002) 1071-1082.
[4] F. Vollertson, M. Plancak, On the possibilities for the determination of the coefficient of friction in the hydroforming of tubes. J. Mater. Process. Technol., 1125/1126 (2002) 412-420.
[5] G.T. Kridli, L. Bao, P.K. Mallick, Y. Tian, Investigation of thickness variation and corner filling in tube hydroforoming, J. Mater. Process. Technol., 133 (2003) 287-296.
[6] G. Liu, S. Yuan, B. Teng, Analysis of thinning at the transition corner in tube hydroforming, J. Mater. Process. Technol., 177 (2006) 688-691.
[7] Y.M. Hwang, W.C. Chen, Analysis and finite element simulation of tube expansion in a rectangular cross-sectional die, Proceedings of the Institution of Mechanical Engineers, Part B: J. Eng. Manufact., 217 (2003) 127-135.
[8] Y.M. Hwang, W.C. Chen, Analysis of tube hydroforming in a square cross-sectional die. Int. J. Plasticity., 21 (2005) 1815-1833.
[9] J.H. Orban, S.J. Hu, Analytical modeling of wall thinning during corner filling in structural tube hydroforming, J. Mater. Process. Technol., 194 (2007) 7-14.
[10] J.E. Miller, S. Kyriakides, A.H. Bastard, On bendstretch forming of aluminum extruded tubes I: experiments, Int. J. Mech. Sci. 43 (2001) 1283-1317.
[11] J.E. Miller, S. Kyriakides, E. Corona, On bendstretch forming of aluminum extruded tubes II: analysis, Int. J. Mech. Sci., 43 (2001) 1319-1338.
[12] E. Corona, A simple analysis for bend-stretch forming of aluminum extrusions, Int. J. Mech. Sci., 46 (2004) 433-448.
[13] Y. Guan, F. Pourboghrat, Fourier series based finite element analysis of tube Hydroforminggeneralized plane strain model, J. Mater. Process. Technol., 197 (2008) 379-392.
[14] Y. Guan, F. Pourboghrat, W. Yu, Fourier series based finite element analysis of tube hydroformingan axisymmetric model, Eng. Computations., 23 (2008) 697-728.
[15] L.M. Smith, J.J. Caveney, T. Sun, Fundamental concepts for corner forming limit diagrams and closed-form formulas for planar tube hydroforming analysis, J. Manufact. Sci. Eng., 128 (2006) 874-883.
[16] L.M. Smith, T. Sun, A non-finite element approach for tubular hydroforming simulation featuring a new sticking friction model, J. Mater. Process. Technol., 171 (2006) 214-222.
[17] C. Yang, G. Ngaile, Analytical model for planar tube hydroforming: Prediction of formed shape, corner fill, wall thinning, and forming pressure, Int. J. Mech. Sci., 50 (2008) 1263-1279.
[18] Z. Marciniak, J.L. Duncan, S.J. Hu, Mechanics of Sheet Metal Forming, second ed., Butter- worth Heinemann, 2002.