Predictions of forming limit diagrams using a rate-sensitive crystal plasticity model

Abstract

A rate-sensitive crystal plasticity model is applied directly in conjunction with the Marciniak-Kuczyński approach to predict forming limit diagrams (FLD's) for annealed FCC sheet metals having various initial textures. Sheets with ideal orientations are first analysed in order to investigate analytically the influence of microstructure and microscopic properties on the FLD. Two ideal orientations of rolling textures, (101) [010] (Goss) and (001) [OTO] (cube), are considered. In the limit of zero material strain-rate senstivity ( m → 0), a simple analytic expression for the localized necking strains is obtained. It indicates that localized necking occurs when the total accumulated shear over all slip systems in the band of localized deformation reaches a critical value. The FLD's of annealed sheets having arbitrary initial textures are then determined numerically. Three particular initial textures are considered. Among these, the predicted FLD for the R-type initial texture shows the best agreement with the experimental ones. Finally, the effects of various factors on the forming limit diagrams are discussed such as: slip hardening, strain-rate sensitivity, initial imperfections, initial texture and yield surface shape.