Large Plastic Deformation of a Circular Sheet Caused by Punch Stretching

Abstract

The stress and strain distributions in a circular sheet caused by the stretching of the sheet with a hemispherical punch are analyzed in terms of an incremental theory of plasticity. The material of the sheet is assumed to have strain-hardening capacity and to be transversely isotropic with respect to the thickness direction. It is found that, at a certain stage in the stretching, a region of the sheet becomes rigid and, at the edge of this rigid region, a surface depression, or neck, having a V-shaped thickness profile is formed. These results are interpreted as a fracture mechanism for the sheet. Numerical results are calculated for the size of the rigid region, the thickness strain at the root of the neck, and the corresponding dome height. The dependence of these quantities on the interfacial friction between the punch and sheet and on the material properties of the sheet is also calculated and shown graphically.