A Few methods of analytical calculation of forming-limit curves

The main aim of the present work is the modification of analytical calculation methods for forming limit curves. The calculated curves were compared with experimental data for steel and aluminium sheets and the best modifications were chosen. The following modifications were analysed: combination of the Swift diffuse instability criterion developed by Lian with the localized necking M-K theory developed by Jalinier and co-workers. The initial calculation, to some degree of deformation, was performed using: the Swift model and then the Jalinier localized theory until fully localization of the strain was applied; the application of Hill's non-quadratic yield criteria for material with in-plane isotropy to the Jalinier theory; the application of the heterogeneity coefficient described by surface roughness to the Jalinier theory; and the development of the Gillis-Jones theory, which eliminates the necessity of the determination of the initial heterogeneity coefficient. The latter theory is based on the assumption that instability develops during successive cycles of deformation: uniform deformation, progressive strain localization, force drop and fully localized necking. Good correlation was found between theoretically calculated and experimentally determined curves for all modified methods, but the best agreement was for the Jalinier theory with the heterogeneity coefficient described by surface roughness and the Gills-Jones theory. The theories can be used successfully for the CAD of sheet forming processes.