Predicting the fracture initiation of dual-phase steels under different stress paths through an implicit stress update scheme

Dual-phase steels are extensively utilized materials in automotive parts to reduce the weight of the autobody and increase fuel performance. Since most of the parts in the autobody are subjected to different loading conditions, the fracture initiation limits of these steels have become significant in recent years. This study systematically investigates the effects of anisotropic plasticity modeling on the ductile fracture predictions and forming limit curves (FFLCs) of dual-phase steels (DP600 and DP800), commonly utilized in automotive applications. Experimental uniaxial tensile tests were performed in multiple material orientations to characterize anisotropic mechanical responses, and these data were used to calibrate the sixth-order polynomial-based anisotropic yield criterion (HomPol6). Additionally, tensile tests on four notched geometries were conducted to provide stress state-dependent fracture strains, facilitating calibration of the DF2016 ductile fracture model. Notably, the calibration procedures were separately conducted for isotropic (von Mises) and anisotropic (HomPol6) yield criteria to critically evaluate their effects on fracture prediction accuracy. A detailed theoretical discussion is provided regarding the discrepancies observed in equivalent plastic strain, stress triaxiality, and Lode parameters between isotropic and anisotropic constitutive models, highlighting the intrinsic dependence of stress state evolution on anisotropic plastic flow. Subsequently, Finite Element (FE) analyses of the Nakajima tests were implemented using an implicit Marc solver with user-defined material subroutines (Hypela2). The numerical FFLC predictions obtained using the anisotropic calibration demonstrated enhanced agreement with experimentally derived literature data compared to the isotropic approach, explicitly highlighting the importance of anisotropic constitutive modeling. Furthermore, this study elucidates how critical numerical factors, such as friction, contact mechanics, mesh discretization, and bending effects in the Nakajima tests, interact with anisotropy to influence FFLC predictions. Finally, clear recommendations are provided for future experimental and theoretical directions, emphasizing the necessity of developing fully anisotropic fracture criteria to comprehensively capture orientation-dependent fracture ductility in advanced high-strength steels.