An Analytical and Experimental Study of the Flow of Sheet Metal Between Circular Drawbeads

Abstract

This paper describes an analytical model for determining the pulling and shear forces and bending moment required to form sheet metal subject to plane strain along its width. The model is based on simplifying assumptions widely accepted in the analysis of wide thin sheet: planes remain plane and normal to the mid-surface, and plane stress state across the thickness. During deformation, any bending, unbending and reverse bending of the strip is analyzed and the constitutive law for this cyclic process is discussed. The model consists of an iterative procedure which is ended when the equation of equilibrium and all boundary conditions are satisfied. The output of the model gives the geometry of the deformed shape, the forces and moments applied along the strip, the displacement field, thickness variations, and stress and strain history fields. The model can be applied to an arbitrary die geometry, and it is used here to analyze the specific case of sheet flow through a drawbead gap consisting of circular drawbeads. The calculated resultant forces, the theoretical surface strains and thickness reductions agree reasonably well with the experimental results.