Keywords: hydroforming, welded tube, anisotropic plastic flow, nanoindentation, numerical simulation, reliability based design optimization.

As a result of the increasing demands for the manufacturing of complex and lightweight parts in various fields, the hydroforming process of welded tubes (WT), considered as an alternative to stamping for obtaining hollow tubular structures, occupies an increasingly significant place in automotive aircraft and aerospace industries [1]. However, the effective use of the hydroforming technology in the manufacturing industry has triggered new challenges in terms of the technological parameters specified for the forming process and particularly the material properties of the WT [2]. The latest studies are devoted to the mechanical and numerical modelling of the hydroforming processes using the finite element analysis, allowing the prediction of the material flow and optimisation of hydroforming parameters [3]. In addition, the accuracy of the numerical prediction remains linked to the fidelity models representing the behaviour of the WT and particularly the mechanical properties (plasticity metal flow, anisotropy effect and damage initiation and growth) of the base metal (BM) and the welded joint (WJ) zone [4]. The characteristic of the welded structures comes from the significant transformations (shaping, calibration, bending, rolling, welding) undergone by the tube throughout its production cycle. All these operations induce complex evolutions of hardening flow and material anisotropy; those are amplified by the presence of the WJ along the tube. This material imperfection is characterized by a heat affected zone (HAZ) singular by its geometry and properties. This fact shows that oriented tensile tests are not adapted to identify the total behaviour of the tubes with regard to the loading paths generated by the hydroforming process [5]

In this work, some variables of this process are taken randomly and we show the robustness of the coupling of the mechanical studies and the reliability analysis in the first step. The second step concerns the introduction of global optimization problem taking into account the structural optimization and the reliability index to perform the hydroforming process of welded tubes. Some numerical results are presented and also the comparison between experimental and numerical values are given.

1

Y.S. Shin, H.Y. Kim, B.H. Jeon, S.I. Oh, "Prototype tryout and design for automotive parts using welded blank hydro forming", J. Mater. Process Techno., 130-131, 121-127, 2002.

2

R.M. Natal Jorge, A.P. Roque, R.A.F. Valente, M.P.L. Parente, A.A. Fernandes, "Study of hydro formed tailor-welded tubular parts with dissimilar thickness", J. Mater. Process. Techno., 184, 363-371, 2007.

3

B. Radi, A. Cherouat, M. Ayadi, A. El Hami, "Optimization technics to identify the characteristics of an hydroformed structure", to appear in Inter. J. of Simul. Multidisci.Des. Optim., 2011. doi:10.1051/ijsmdo/2010006

4

A. Cherouat, K. Saanouni, Y. Hammi, "Numerical improvement of thin tubes hydroforming with respect to ductile damage", I. J. Mech. Sci., 44, 2427-2446, 2002. doi:10.1016/S0020-7403(02)00177-7

5

P. Bortot, E. Ceretti, C. Giardini, "The determination of ?ow stress of tubular material for hydroforming", J Mater Process Techno 203, 381-388, 2008.

6

J.J. Ye, "Nondifferentiable multiplier rules for optimization and bilevel optimization problems", SIAM J. Optim, 15(1), 252-274, 2004. doi:10.1137/S1052623403424193

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