Theoretical Investigation of Internal Cavitation on the FLD of IF Steel Using M-K Model and Gurson Plastic Potential Function

The sheet metals formability can be restricted by localized necking and internal cavitation. On the one hand, nucleation and growth of cavities during plastic deformation can increase the inhomogeneity of sheet metal and accelerate the localized necking. On the other hand, localized necking at the intervals between the cavities can lead to accelerate the joining and coalescence of the internal cavities. In this paper an analytical model based on Marciniak-Kuczynski (M-K) model and Gurson plastic potential function in order to exert the internal voids effect on localization necking has been developed. Stowell’s model was used to illustrate void growth behavior during plastic deformation. In order to examine the effect of the voids on localized necking, the void volume fraction was considered in the imperfection factor and the plastic volume constancy principle. The nonlinear system of equations was solved with the modified Newton-Raphson method using MATLAB software. This new analytical method (M-K-Gurson) was used to predict the forming limit diagram (FLD) of IF steel alloy sheets and the results were compared with those of other researchers. The results showed that the M-K-Gurson method predicted the FLD with better agreement comparing with experimental results. Thereafter, the effects of strain hardening exponent, anisotropy coefficients, geometrical imperfection factor, the void volume fraction and the void growth rate parameter on the FLD were investigated.