A mesoscopic approach for predicting sheet metal formability

A mesoscopic approach for constructing a forming limit diagram (FLD) is developed. The approach is based on the concept of a unit cell. The unit cell is macroscopically infinitely small and thus represents a material point in the sheet, and is microscopically finitely large and thus contains a sufficiently large number of grains. The responses of the unit cell under biaxial tension are calculated using the finite element method. Each element of a mesh/unit cell represents an orientation and the constitutive response at an integration point is described by the single crystal plasticity theory. It is demonstrated that the limit strains are the natural outcomes of the mesoscopic approach, and the artificial initial imperfection necessitated by the macroscopic M–K approach is not relevant in the mesoscopic approach. The effects of strain-rate sensitivity, single slip hardening and latent hardening, texture evolution, crystal elasticity and spatial orientation distribution on necking are discussed. Numerical results based on the mesoscopic approach are compared with experimental data.