A dislocation-based model of forming limit prediction in the biaxial stretching of sheet metals

In this paper, a dislocation-based model based on the rate-sensitive crystal plasticity is proposed for the prediction of forming limits diagrams (FLD) without assuming an initial geometry imperfection (the M–K approach). The misorientation of pairs of chosen crystal grains inside and outside the narrow band is assumed to be responsible for the initial formation of the band and its subsequent deterioration into localized necking. Analytical expressions for the calculation of forming limit strains are derived for several pairs of crystal grains with ideal orientations, such as Goss, Cube, Copper and Brass to evaluate the influence of microstructure on forming strain. The analysis demonstrates the feasibility of deriving and constructing the FLD of a polycrystalline sheet metal from a knowledge of the misorientation distribution of grain orientations.