Improvement of stress evaluation equation on biaxial bulge test considering stress in thickness direction

The biaxial bulge test method (BBTM) is effective for accurately measuring the biaxial stress-strain curves of sheet metals subjected to arbitrary stress paths for a large plastic strain more than several percent. In BBTM, a sheet sample is bent and welded to fabricate a circular tube specimen, and an axial force T and internal pressure P are applied simultaneously to generate a biaxial stress state. In this study, finite element analysis (FEA) of BBTM is performed to evaluate the effect of internal pressure and the ratio of the initial sheet thickness to the tube diameter, a 0 / D 0 , on the accuracy of stress measurement. Solid elements with isotropic and anisotropic yield functions are used for the FEA. The distribution of the stress components along the thickness direction is calculated. Based on the FEA results, a new stress evaluation formula is proposed. It is found that for a tubular specimen having a relatively large thickness, the stress in the thickness direction, σ t , at the center of the thickness cannot be neglected but can be approximated by σ t = − P /2. By translating the triaxial stress state with non-zero σ t to the plane stress state with σ t = 0, the yield surface associated with the plane stress state can be identified with an error of less than 2% up to a reference plastic strain of 0.4.