Analytical modelling of drawbeads in sheet metal forming

An analytical model is developed to account for the bending/stretching process experienced by a metal sheet passing along a drawbead. The geometrical evolution of an elementary length of the sheet is described by the Love–Kirchhoff assumption. The material is assumed to be elastic–plastic, and the assumptions of either isotropic or non-linear kinematic hardening are considered. First, the stress–strain history for any point within the thickness of the sheet is derived from the evolution of curvature imposed by the tooling, together with the evolution equations relating the tensile force N and the bending moment M. The external forces exerted by the tools are then estimated from equilibrium equations expressed for different parts of the sheet along the tooling. The results are compared with the predictions of finite element simulations and with experimental results of the literature. A detailed analysis is finally performed to delineate the influence of geometry, material parameters and friction on the restraining force, the thickness strain and effective strains at the exit of the tooling.