The strain gradient approach for determination of forming limit stress and strain diagrams

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Abstract
The forming limit stress diagram (FLSD) has been reported as being much less path dependent and much more favourable than the forming limit diagram (FLD) in representing forming limits in the numerical simulation of sheet metal forming processes. Therefore, the purpose of this study was to develop a methodology for the prediction of the forming limits both in strain and stress forms. All simulations are based on strain gradient theory of plasticity in conjunction with the Marciniak—Kuczynski (M—K) approach. This approach introduces an internal length scale into conventional constitutive equations and takes into account the effects of deformation inhomogeneity and material softening. The non-linear second-order ordinary differential equation of the thickness of sheet metal has been solved using the collocation method. It is shown that this method overcomes the imperfection sensitivity encountered in the conventional M—K method. An evaluation of the theoretical results is carried out. The comparison between the experimental and theoretical results for FLDs and FLSDs as predicted by different methods indicates that the present approach is suitable for these problems.