Formability limit prediction of TRIP780 steel sheet using lode angle dependent gurson-based models with Thomason coalescence criterion and bifurcation analysis

For biaxial stretching strain paths, which are typically encountered in sheet metal forming, the stress triaxiality ranges from 0.33 to 0.67. At this low level of triaxiality, voids change their shape from spherical to general spheroidal shape. In the literature, unit cell studies show the dependency of void shape on the lode parameter, especially at low stress triaxiality. Several authors also pointed out the influence of lode parameter on ductile failure. In the current study, lode parameter dependent Gurson-based models are combined with bifurcation analysis for the prediction of formability limits of TRIP780 steel sheet. Moreover, Thomason’s coalescence criterion is considered for the prediction of critical porosity. For the anisotropic plastic behavior of the dense material, the quadratic Hill’48 yield surface is considered. Contribution to porosity evolution due to shear mechanism is also analyzed. In addition, the effect of lode parameter on the prediction of forming limit diagram (FLD) is investigated. It is observed that the accelerated evolution of porosity, due to the consideration of lode parameter, induces lower ductility limits for the modified Gurson-based model, as compared to the original Gurson model. The results also demonstrate that the use of the Thomason coalescence criterion for the determination of critical porosity plays an important role in the prediction of FLDs, as compared to fixed critical porosity used in the Gurson-Tvergaard-Needleman model