On the critical role of martensite hardening behavior in the paradox of local and global ductility in dual-phase steels

The ductility of sheet metal is typically limited by either localized necking or by damage and fracture. A recent ductility classification refers to these failure modes respectively as ''global'' and ''local'' formability. The forming limit curve (FLC) and the uniaxial tensile test assess global formability, whereas the fracture forming limit (FFL), the true thickness fracture strain, hole expansion ratios (HER), etc. are indicators of local formability. Experimental hole expansion data in the literature for different dual-phase (DP) steel grades of similar strength and composition presents a paradox: grades which are found to be ductile in a tensile test and/or FLC show a low ductility in hole expansion, whereas other grades with a low ductility in conventional tests perform surprisingly well at cut edges. In this work, an in-depth systematic statistical analysis of idealized artificial two-phase microstructures is carried out to unravel the underlying mechanisms of the observed paradoxical trends. This is done by scaling the hardness of martensite and its volume fraction to generate virtual DP steels of the same strength but different strain hardening and mechanical phase contrast (hardness difference). The proposed micromechanical model adequately reproduces the experimentally observed trends. The results show that in DP steels, a higher global (necking-driven) ductility is obtained upon delaying martensite plasticity by increasing the mechanical contrast of the two phases. Consequently, the stress-strain distributions becomes more heterogeneous, resulting in a lower fracture limit of one of the phases or interfaces in shear loading, thereby, reducing the local ductility. Global ductility is improved by higher mechanical phase contrast and lower martensite volume fraction, whereas local ductility is improved by low phase contrast and higher martensite volume fraction. The hardening behavior of martensite is the key to avoiding the above trade-off between local and global ductility. It is shown that if the strain hardening capacity of martensite in the later stages of deformation (in high strains) can be increased, this would result in removing the observed paradoxical trends of local and global ductility in DP steels.