A new methodology for determining the stress state of the plastic region in machining with restricted contact tools

In rigid-plastic slip-line theory, once the geometry of the slip-line field is established, the stress state of the plastic region (including the primary and secondary deformation zones) in restricted contact machining is governed by the hydrostatic pressure P_A (at a point on the intersection line of the shear plane and the work surface to be machined) and the frictional shear stress τ on the tool rake face. Based on the recently established universal slip-line model and a detailed study of six representative machining cases, a new methodology for determining the stress state of the plastic region, i.e. maximum value principle, is presented in this paper. According to this principle, the stress state of the plastic region can be determined by giving both P_A and τ their theoretical maximum permissible values. The theoretical maximum permissible values of P_A and τ can be found by satisfying four mechanical and geometrical constraint conditions under which the universal slip-line model applies. A comprehensive assessment factor is introduced in this paper. It is shown that the three machining parameters investigated in this present study, i.e. cutting force ratio, chip thickness ratio, and chip back-flow angle can be simultaneously considered to form a comprehensive criterion to compare predicted and experimental results. The applicable range of the maximum value principle is also discussed.