An analysis of plastic flow through polygonal converging dies with generalized boundaries of the zone of plastic deformation

Abstract

A generalized expression for the spherical flow field generated by plastic flow of metal through a converging die of regular polygonal cross-section is suggested. The expression is valid for all the possible boundary shapes of the zone of plastic deformation. The working stress for a rigid-perfectly plastic material is calculated by applying upper-bound techniques assuming that the boundaries of the zone of plastic deformation are exponential cylindrical surfaces. A constant frictional stress is assumed to be acting over the entire die-material interface. The working stress relation is minimized with respect to the shape of the boundaries of deformation zone, thus yielding a better upper-bound value of the working stress compared to the working stress for cylindrical boundaries. The effects of various process parameters on the working stress and the shape of the zone of deformation are given in graphical form. The analysis predicts optimum, dead zone and critical angles. Comparisons with earlier theories have been made and it is concluded that the theory presented is a more generalized theory and yields better results for large die angles.