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In this paper, we try to prove the ability of this strategy to optimize loading path in the case of THP where different kind of nonlinearities exist (material, geometries and boundary conditions). The aim of this study is to obtain a free defects part with a good thickness distribution, decrease the risk of potential failures and to let the process insensitive to the input parameters variations. For more detailed description of the RBDO methodology and variety of frameworks the reader can be refer to the following references [27,28].

Workpiece behaviour's models used to simulate the expansion tests, made it possible to highlight the combined effects of the inhomogeneous behaviour of basic material and heat affected zone, as well as the geometrical singularities found in the welded tubes. From the simulations carried out, it is clear the influence of the plastic flow behaviour of the welded tube in the final results (thickness distribution, stress instability, tube circularity, critical thinning and rupture). Introduction Due to 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 the hollow tubular structures, occupies an increasingly significant place in automotive aircraft and aerospace industries [1,3].

Neffussi and A. Combescure: I. J. Mech. Science Vol. 44 (2002), p. I. N. W. J. A. Khaleel: I. J. Plasticity 20 (2004), p. 1111-1137 [15] S. Yuan, W. Yuan and X. Wang: J. Mater. Process. Techno. Vol. 177 (2006), p. 668-671 [16] M. KoƧ: J. Mater. Process. Techno. Vol. 133 (2003), p. J. Y. Hsiao: J. Mater. Process. Techno. Vol. 140 (2003), p. 520-524 52 Innovating Processes [18] K. Manabe, M. Suetake, H. Koyama and M. Yang: I. J. Machine Tools & Manuf. Vol. 46 (2006), p. 1207-1211 [19] T. Hama, T.

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