Evaluation of forming limit by principal shear strain energies

In sheet metal forming, crack in the formed sheets is one of the serious defects, and it is tried to avoid the crack by use of numerical simulation. In the simulation, period and location of the occurrence should be quantitatively evaluated by the formulated criteria. For prediction of crack occurrence, various ductile fracture criteria have been proposed. These criteria are based on the void damage theory and include effect of void growth and coalescence at the late stage of the fracture. In sheet forming, however, not only crack but also necking is problems, and it is important to obtain forming limit of the uniform deformation. Although the forming limit has been examined by M-K theory etc., the criteria does not reach the sufficient level. We consider that the plastic deformation depend on the shear deformation and the criterion by three principal shear strain energies is proposed. In order to verify applicability of the criterion, flat-die drawing tests of aluminum sheets with proportional and non-proportional strain passes were carried out and the forming limit curves predicted by the proposed criterion comparatively agrees with the test results.