A theoretical prediction framework for the construction of a fracture forming limit curve accounting for fracture pattern transition

It has been accepted that the formability of a sheet metal with a moderate ductility can be limited by not only localized necking (LN), but also ductile fracture (DF). In this study, a theoretical prediction framework is developed for a comprehensive formability characterization, in which forming limit curves at LN (FLCN) and DF (FLCF) are elaborately correlated by considering strain path evolution. A dual-phase steel material (DP590 sheet metal) is selected with a series of DF and Nakajima tests performed. A newly proposed DF model (uncoupled type) is calibrated by implementing a hybrid experiment-simulation method in line with the DF tests, which are designed to achieve DF under distinct stress states, such as simple shear (SS), uniaxial tension (UT), plane strain tension (PST), and balanced biaxial tension (BBT). The resulting three dimensional (3D) fracture surface demonstrates a good agreement with the tested data. The modified maximum force criterion (MMFC) is selected for the theoretical identification of strain path evolution. The calibrated MMFC results in a FLCN exhibiting a certain level of underestimation as compared to the tested data in the range of positive minor strain. The MMFC is improved (iMMFC) by incorporating with an initial strain path-based function for a higher accuracy in characterizing evolutive strain paths; the resulting FLCN is observed to have a better performance than that of MMFC. Theoretical FLCFs are determined by the integral of ductile damage increment (defined by the DF model calibrated) over each identified strain path from UT to BBT. After considering strain path evolution, different deformation stages are added into the finalized forming limit diagrams including both FLCF and FLCN. It is found that the FLCF based on iMMFC model demonstrates acceptable deviations as compared to all the tested cracking data. Moreover, this FLCF intersects with the corresponding theoretical FLCN as load path approaches from UT to BBT, representing a fracture pattern transition from a LN band-accompanied DF to the one without LN band; this prediction is further validated by experimental observations. The FLCF based on MMFC fails to predict this transition behavior. The current study confirms the presence of a competition between LN-induced failure and DF-induced failure for sheet metals. Moreover, all of these findings advance the insight into the importance of performing a DF prediction aside of a FLCN prediction, especially for the case where a sheet metal with a moderate ductility shows a fracture pattern transition behavior.