The Geometry of the Shear Zone in Metal Cutting

Abstract

The choice of a suitable trajectory shape and slip-line field for the shear zone must be influenced by the degree of work hardening and thermal softening, and is necessarily difficult. Although probably incorrect, the geometry of a polar slip-line field is described in terms of the properties of circular and logarithmic spiral trajectories, as this affords a suitable starting point. It is then assumed that the fundamental quantity is the trajectory shape, and it is shown that a slip-line field may be determined which corresponds to any given set of spiral trajectories. The choice of spirals is limited by the condition of volume continuity. The results of Kececioglu (1960) [4] are reexamined in the light of more recent theories of the shear zone and the experimentally determined strain-rate values are shown to be incorrectly derived. A suitable trajectory shape must first be adopted before calculating the value of the strain rate in terms of the width of the zone.