Plane Stress Deformation of Anisotropic Sheet Metals

A mathematical model is presented to help understand sheet metal deformation during forming. The particular purpose of this model is to predict the forming limit diagram (FLD). The present model is an extension of a previous analysis by Jones and Gillis (JG) in which the deformation is idealized into three phases: (I) homogeneous deformation up to maximum load; (II) deformation localization under constant load; (III) local necking with a precipitous drop in load. In phase III the neck geometry is described by a Bridgman type neck.

The present model extends the JG theory which was applied to the right hand side of the FLD only. The main difference in treating the two different sides of the FLD lies in the assumptions regarding the width direction deformations. For biaxial stretching, the right hand side, the minor strain rate is assumed to be homogeneous throughout the process. However, for the left hand side of the FLD, in the critical cross-section, the minor strain rate is taken to be proportional to major strain rate. This is a critical difference from the JG approach and permits the left hand side to be computed with good accuracy.