Computational analysis of stress-based forming limit curves

This article, through computational analyses, examines the validity of using the stress-based and extended stress-based forming limit curves to predict the onset of necking during proportional loading of sheet metal. To this end, a model material consisting of a homogeneous zone and a zone that has voids (material inhomogeneity) is proposed and used to simulate necking under plane strain and uni-axial stress load paths. Results of the in-plane loading computations are used to construct a strain-based formability limit curve for the model material. This limit curve is transformed into principal stress space using the procedure due to Stoughton [Stoughton, T.B., 2000. A general forming limit criterion for sheet metal forming. International Journal of Mechanical Sciences 42, 1–27]. The stress-based limit curve is then transformed into equivalent stress and mean stress space to obtain an Extended Stress-Based Limit Curve (XSFLC). When subjected to three-dimensional loading, the model material is observed to display a variety of responses. From these responses, a criterion for the applicability of the XSFLC to predict the onset of necking in the model material when it is subjected to three-dimensional loading is obtained. In the context of straight tube hydroforming, to provide support for the use of the XSFLC, it is demonstrated that the criterion is satisfied.