Forming limit predictions with the perturbation method using stress potential functions of polycrystal viscoplasticity

Plastic potentials of polycrystalline materials are calculated for plane stress states using viscoplastic crystallographic slips and the Taylor approach. The derivation process of these potentials and their development during large plastic deformation of textured aluminium sheets are discussed. These potentials are then used to predict the forming limits of sheet metals. The approach employed was that of the perturbation technique developed by Dudzinski and Molinari [Int. J. Solids Struct. 27, 601 (1991)]. The perturbation method is analytic if Hill-type yield potentials are used. Therefore, to facilitate the use of the polycrystal plastic potentials in the perturbation approach, the polycrystal stress potentials were approximated locally at the loading point by Hill-ellipsoids. In this way even the development of anisotropy during stretching could be taken into account. The effect of initial texture as well as the changes in the anisotropy during deformation are discussed. It has been found that the development of anisotropy influences strongly the predicted limit strains in the vicinity of equibiaxial stretching.