Experimental and numerical failure criteria for sheet metal forming

For sheet metal forming, often the forming limit diagram (FLD) is used as failure criterion as it can be derived easily in experiments. It is based on the assumption that localization of strain in the sheet plane is responsible for crack initiation, but application of FLD is limited to linear strain paths. Hence, only forming processes with approximately the same deformation history as the experiments carried out for FLD determination should be evaluated by this criterion. Forming limit stress diagrams (FLSD) do not exhibit such strict limitations. They are based on the assumption that principal stresses in the sheet plane are responsible for crack initiation. As these stresses are usually calculated by FE analysis using elastic plastic material laws, strain hardening is considered. Two-step forming tests as application examples prove the FLSD to be adequate for evaluation of non-linear forming processes with alternating forming directions. Nevertheless, FLSD are derived in extensive investigations which makes them unattractive for most industrial applications. Furthermore, both FLD and FLSD do not consider the physical background of ductile crack initiation which is provoked by an interaction of local stress triaxiality and equivalent plastic strain. Hence, a reliable failure criterion should concentrate on these two parameters. The Gurson-Tvergaard-Needleman- (GTN-) damage model can predict crack initiation during sheet metal forming. Application of the GTN model to 2 step forming tests with the bake hardening steel H220BD+Z showed good agreement to experimental results although a sensitivity of the model to mesh size and stress triaxiality is observed.