The effect of the through-thickness normal stress on sheet formability

Sheet formability is limited by the onset of localized necking or fracture, and the limit strain is important to measuring sheet formability. The forming limit curve (FLC), which maps the limit strain under different strain paths into the strain space, provides a convenient and useful way to predict material failure in the sheet forming process. The FLC is closely related to many factors, such as the material mechanical properties, stress state, temperature and forming speed. This paper focuses on the influence of the through-thickness normal stress on the FLC, in which a modified M-K model with a corresponding algorithm under the 3D-stress state is proposed. The through-thickness normal stress is obtained by analyzing the Nakazima test and simplifying it. Both experimental and reference data are applied to the model validation, which indicates a higher prediction accuracy when the sheet thickness is introduced into the model. Theoretical FLCs under different ratios of t₀/D show a linear relationship between the sheet thickness and the limit strain increment in tension-tension states.