A plane-strain UBET analysis of material flow in a filled deep die cavity in closed-die forging

When a deep die cavity is filled in closed-die forging, further movement of the dies will reduce the extension of the plastic region, a part of the workpiece in the cavity becoming rigid and forming dead zones. Consequently the plastic deformation is localized within a particular region, where the plastic deformation imparted could be much greater than the average. In this work, the upper-bound elemental technique (UBET) is applied to analyze the material flow in a filled deep cavity for plane-strain conditions. The boundaries between the dead zones and the deforming material are determined together with the velocity field by minimizing the total power dissipation. The boundaries are analyzed and presented numerically. Strain-rate hardening and inhomogeneous deformation in the UBET element are taken into account. A detailed formulation of the analysis is presented in the paper. The influences of flash-height and the strain-rate hardening exponent of the deforming material are studied theoretically. The results are compared with those of model-material experiments and those of commercial FEM software, satisfactory agreement being obtained.