**1. Introduction**

The increasing application of hydroforming techniques in automotive and aerospace industries is due to its advantages over classical processes as stamping or welding. Particularly, tube hydroforming with various cross sectional shapes along the tube axis is a well-known and wide used technology for mass production, due to the improvement in computer controls and high pressure hydraulic systems (Asnafi et al., 2000; Hama et al, 2006; Cherouat et al., 2002). Many experimental studies of asymmetric hydroforming tube have been examined (Donald et al., 2000; Sokolowski et al., 2000). Theoretical models have been constructed to show the hydroforming limits, the material and the process parameters influence on the formability of the tube without failure (buckling and fracture) (Sokolowski et al.,2000). Due to the complexity of the process, theoretical studies up to date have produced relatively limited results corresponding the failure prediction. As for many other metal or sheet forming processes, the tendency of getting a more and more geometric complicated part demands a systematic numerical simulation of the hydroforming processes. This allows modifying virtually the process conditions in order to find the best process parameters for the final product. Thus, it gives an efficient way to reduce cost and time.

Many studies have been devoted to the mechanical and numerical modelling of the hydroforming processes using the finite element analysis (Hama et al., 2006; Donald et al., 2000), allowing the prediction of the material flow and the contact boundary evolution during the process. However, the main difficulty in many hydroforming processes is to find the convenient control of the evolution of the applied internal pressure and axial forces paths. This avoids the plastic flow localization leading to buckling or fracture of the tube during the process. In fact, when a metallic material is formed by such processes, it

© 2012 Hami et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 Hami et al., licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

experiences large plastic deformations, leading to the formation of high strain localization zones and, consequently, to the onset of micro-defects or cracks. This damage initiation and its evolution cause the loss of the formed piece and indicate that the forming process itself should be modified to avoid the damage appearance (Cherouat et al.,2002). In principle, all materials and alloys used for deep drawing or stamping can be used for hydroforming applications as well (Koç et al,2002).

Hydroforming Process: Identification of the Material's Characteristics and Reliability Analysis 5

Many studies have been devoted to the mechanical and numerical modeling of the hydroforming processes using the finite element analysis, allowing the prediction of the material flow and the contact boundary evolution during the process. However, the main difficulty in many hydroforming processes is to find the convenient control of the evolution of the applied internal pressure and axial forces paths. This avoids the plastic flow localization leading to buckling or fracture of the tube during the process. In fact, when a metallic material is formed by such processes, it experiences large plastic deformations, leading to the formation of high strain localization zones and, consequently, to the onset of micro-defects or cracks. This damage initiation and its evolution cause the loss of the formed piece and indicate that the forming process itself should be modified to avoid the damage appearance. In principle, all materials and alloys used for deep drawing or stamping can be

Taking into account the ratio thickness/diameter of the tube, the radial stress is considerably small compared to the circumferential <sup>θ</sup> σ and longitudinal stresses σ<sup>z</sup> (see Figure 2). In addition, the principal axes of the stress tensor and the orthotropic axes are considered coaxial. The transverse anisotropy assumption represented through the yield criterion can

> ( ) θ θ σ = σ −σ + σ + σ 2 2 2 2

If the circumferential direction is taken as a material reference, the anisotropy effect can be

 σ = σ −σ +σ +σ <sup>+</sup> 2 2 2 2

<sup>ε</sup> ε= σ− σ σ +

<sup>ε</sup> ε= σ− σ σ +

where ε is the effective plastic strain and ( ) <sup>θ</sup> ε ε<sup>z</sup> , are the strains in the circumferential and the axial directions. The effective strain for anisotropic material can be derived from equivalent plastic work definition, incompressibility condition, and the normality condition:

( ) θ θ

1 R

1 R

( ) θ θ <sup>θ</sup>

θ

z

z z

with (F,G,H) are the parameters characterizing the current state of anisotropy.

<sup>1</sup> <sup>R</sup>

The assumptions of normality and consistency lead to the following equations:

θ θ

d R <sup>d</sup>

d R <sup>d</sup>

z z

+ + ε= ε + ε + ε − ε = γ + γ + ε + + +

1 R 2R 1 R <sup>d</sup> d d Rd d 1 d 1 2R 1 R 1 2R

2 2 2 2

z z

characterized by a single coefficient R and the equation (1) becomes:

z z F GH (1)

1 R (2)

(3)

with

θ ε γ = ε <sup>z</sup> d d (4)

used for hydroforming applications as well.

be written as:

**2.1. Mechanical characteristic of welded tube behaviour** 

This chapter presents firstly a computational approach, based on a numerical and experimental methodology to adequately study and simulate the hydroforming formability of welded tube and sheet. The experimental study is dedicated to the identification of material parameters using an optimization algorithm known as the Nelder-Mead simplex (Radi et al.,2010) from the global measure of displacement and pressure expansion. Secondly, the reliability analysis of the hydroforming process of WT is presented and the numerical results are given to validate the adopted approach and to show the importance of this analysis.
