An improved strain gradient approach for determination of deformation localization and forming limit diagrams

The purpose of this study is to develop a methodology for prediction of the deformation localization and forming limit diagrams (FLD). The strain gradient approach is incorporated into the M–K method for deformation localization analysis and the prediction of forming limit diagram in sheet metal forming. This approach introduces an internal length scale into conventional constitutive equations and takes into account the effects of deformation inhomogeneity and material softening. To solve the non-linear second order boundary value problem collocation method has been used. In this solution, the neck evolution structure has been presented. Compared to the “Shooting Method” used by other researchers in the present work, the convergence and accuracy of solution is guaranteed with better speed. It thus overcomes the imperfection sensitivity encountered in the conventional M–K method and the neck evolution structure presented. Also the post-localization behavior of sheet metal presented. The comparison between the experimental and theoretical results for FLDs as predicted by different methods indicates that the present approach is quite successful.