Analytical model for tube hydro-bulging test, part I: Models for stress components and bulging zone profile

• The unified analytical model for stress components calculation is proposed.
• Same formulation for axial stress can be used for fixed and closed ends.
• The die-related ellipsoid model can give better description of bulging zone.
• Hydro-bulging test can be standardized based on the models presented.

Hydro-bulging test is an advanced method for characterizing the mechanical properties of tubular materials under bi-axial stress state, by measuring the bulging height, pole thickness and internal pressure. This method has been investigated and applied over the past decades. However, different testing conditions and analytical models have been used in practice, which makes the tested results incomparable. In this paper, hydro-bulging tests with different constraining are first analyzed and compared, and a unified analytical model for stress components calculation is proposed for closed-ends and fixed-ends conditions. Finite element analysis of tube hydro-bulging with closed-ends and fixed-ends shows that both the stress and strain responses of the tubular specimen, i.e., the stress and strain components under different internal pressures, are almost identical to determine the stress–strain relations. Geometrical models for bulging zone are analyzed and compared with special attention on the calculation of the radius of axial curvature, which is one of the key parameters for both stress and strain components determination. A die-related ellipsoid model is presented and is well verified by experimental results on extruded AA6061 tubes.