Effect of through-thickness normal stress on forming limits under Yld2003 yield criterion and M-K model

Forming limit curve considering through-thickness normal stress is theoretically obtained based on Yld2003 yield criterion and M-K model with the assumption that hydrostatic stress has no effect on plastic deformation. The suitability of Yld2003 yield criterion to describe the yield surface and forming limit under plane-stress condition for aluminum alloy AA6111-T43 is verified by the experimental data obtained from the literature. Then the effect of through-thickness normal stress on forming limit is analyzed. Different forms of forming limit presentation including traditional strain-based forming limit curve (FLC), forming limit effective strain curve (eFLC), stress-based forming limit curve (FLSC) and extended stress-based forming limit curve (XSFLC) are investigated in detail. It is found that forming limit curves in strain-space enhance with increased through-thickness normal stress under both linear and nonlinear strain paths with different pre-strains. However, the variation of forming limit curves in stress-space does not show single trend but depends on the variables of the coordinate plane. A new form of forming limit presentation named correcting FLSC is proposed. The correcting major stress enhances with through-thickness normal stress increase, and the floating range of the correcting FLSC due to through-thickness normal stress is much less than that of the traditional FLSC. The correcting FLSC can be taken as a steadier criterion for sheet metal forming limit prediction under three-dimensional stress state.