Development of a heterogeneous microstructurally based finite element model for the prediction of forming limit diagram for sheet material

A heterogeneous finite element model with randomly distributed inhomogeneities has been developed for the determination of the forming limit diagram (FLD) for thin aluminum sheet material based on the prediction of localized necking. The strength difference between the inhomogencities and the matrix is ascertained either from the fluctuation of the experimental stress-strain curve or from a micromechanical analysis that uses a representative particle field. By changing the specimen geometry and friction conditions, different stress states (or strain paths) are achieved. A plot of the critical Oyane fracture parameter is used to identify the limit strain state. Also, a plot of equivalent plastic strain rate is used to distinguish the boundary of intense shear bands and hence to identify where to take the measurement point. Both a plane stress model and a three-dimensional (3-D) model are adopted to predict the shear banding phenomenon and hence the FLD. The predicted FLD agrees well with the measurements from a recent round robin experimental FLD involving several independent research laboratories. The Taguchi method is applied to assess how the various parameters involved in the heterogeneous model affect the calculated forming limit strain.