Forming limit analysis of hemispherical-punch stretch forming

This paper combines elastic–plastic membrane finite elements and forming limit theory to determine the limiting dome height of axisymmetric stretch forming. The elastic–plastic finite element approach is based on the flow rule associated with Hill’s quadratic yield criterion for anisotropic material. The total Lagrangian formulation and virtual work theory are used to derive the stiffness equations and the relationship between displacement and strain. Using FE-calculation results and forming limit curves proposed by Storen and Rice, the limiting dome height and the rupture location were predicted for various materials. The calculated results are compared with available experimental data and existing numerical solutions. Furthermore, the influence of material properties (i.e., the strain-hardening exponent and anisotropy) and friction condition on the limiting dome height are presented.