The range of permissible shear angles in orthogonal machining allowing for variable hydrostatic stress on the shear plane and variable friction angle along the rake face

Abstract The work of Hill [1] showed that for an ideal rigid-plastic material, a permissible range of shear plane inclinations could be obtained by excluding configurations which imply overstressing of material at the singularities of stress which exist at each end of the shear plane. However, in many cases [2, 3] experimental results tend to fall outside Hill's permissible range. It is shown that two possible causes of this lack of agreement are: (i) the assumption that the work material deforms with constant flow stress with the consequence that the hydrostatic stress on the shear plane is a constant, and (ii) the use of a constant friction angle, λ, to relate shear stress to normal stress at all points along the rake face. These restrictions are eliminated in the current theory and it is shown that without them, the range proposed by Hill is extended to include most experimental results.