Forming limit predictions with the perturbation method using stress potential functions of polycrystal viscoplasticity
Plastic potentials of polycrystalline materials are calculated for plane stress plates using viscoplastic crystallographic slips and the Taylor approach. The derivation of these potentials and their development during large plastic deformation of textured aluminum 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 \textit{D. Dudzinski} and \textit{A. Molinari} [Int. J. Solids Struct. 27, No. 5, 601-628 (1991; Zbl 0734.73032)]. 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 are 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.
scientific article; zbMATH DE number 955115