An optimization method is developed for the design of intermediate die
shapes needed in the plane strain and axisymmetric forging operations
. The approach is based on backward deformation simulation using nonli
near rigid viscoplastic finite element method and shape optimization t
echniques. The advantage of this optimization approach is that it has
the ability to determine the intermediate die shapes from the final pr
oduct shape by applying constraints on the plastic deformation of the
material. This paper presents axisymmetric disk and plane strain case
studies to demonstrate the new design procedures for minimizing variat
ions in deformation rates during a multistage forging operation.