Study on the influence of the yield surface shape in the hole expansion test

The hole expansion test has become popular since it allows to study the formability of metallic sheets, in particular the onset of necking in stretch flanging areas. The accurate prediction of strain localization and consequent fracture requires a proper description of the plastic behavior, particularly the anisotropic yield function. In the context of strain localization prediction, the yield criterion adopted plays an important role, particularly when using an associated flow rule, since the direction of the plastic strain tensor is modelled by the normal to the yield surface. In this work, the parameters of an advanced yield criterion are calibrated considering a wide set of experimental data, which includes results from uniaxial and biaxial tension tests. This enables establishing yield surfaces with similar shape in the plane defined by the stress components in the rolling and transverse directions and a null shear component in the same plane. However, their shape changes slightly when considering non-null values for that shear component. The numerical simulations of the hole expansion test demonstrate the impact of these slight differences on the thickness strain distribution and, consequently, in the instant and location of the necking.