Analytical and numerical prediction of localized necking in sheet metal forming processes

The goal of this research is to investigate, develop and validate analytical and numerical tools that can accurately predict failure in sheet metal forming operations. The strain-based forming limit curve (FLC) is one of the tools to predict the maximum permissible strains of thin metallic sheets which are loaded in the plane of the sheet to different states of stress. It may be used to assess forming operations in the press shops as well as unintentional deformations, such as vehicle, aircraft, or train crashes. The accurate prediction of failure in sheet metal stamping can shorten product lead times, decrease tooling costs, and allow for overall more rigorous and robust designs. In the present work, three main analytical models are discussed: the modified Marciniak and Kuczynski (M-K) model which included a varying defect orientation with respect to the principal stress directions, the effective stress ratio model and the major strain ratio model. The M-K predictions of the FLC are demonstrated with several yield criteria for eight different materials. Furthermore, the stress-based FLC theory of the effective stress ratio model is described, and its extension to include varying defect orientation is presented. Also the original non-incremental FLC theory of the major strain ratio model is presented, and its extension to include varying defect orientation is described. In addition, numerical and experimental data are used to investigate the key assumption of the three analytical models and the results show that the parameters investigated to predict failure (i.e., the incremental strain ratio, critical stress concentration factor and critical strain concentration factor) were not constant for the various strain paths for three analytical models considered. Finally, finite element analysis (FEA) is used to predict the FLC with a stress-based failure criterion and a comparison between three different element types (shell, solid and solid-shell) is investigated in detail. The numerical results show that despite the differences in stress distribution assumptions, shell, solid and solid-shell elements would not provide differences in failure prediction for the uniform, in-plane stretching states examined when a stress-based failure criterion is used