Theoretical FLD Prediction Based on M-K Model using Gurson's Plastic Potential Function for Steel Sheets

The aim of this study is to develop a new analytical method for predicting localized necking in the plastic deformation of sheet metals with internal cavitation. This method is based on the model of Marciniak and Kuczynski (M-K) as well as Gurson's plastic potential function. 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 with globally convergence procedure, using MATLAB software. This new analytical method (M-K-Gurson) was used to predict the forming limit diagram (FLD) of different steel alloy sheets and the results were compared with those of other researchers. The results showed that the M-KGurson method predicted the FLD with good agreement.