Slip-Line Field Analysis for Orthogonal Machining Based upon Experimental Flow Fields

Abstract

An experimental flow field for slow speed (0·5 in/min) orthogonal (plane strain) machining was analysed using slip-line field techniques. Although the experimental streamlines were not sufficiently accurate to determine a slip-line field directly by calculating the directions of maximum shear strain rate from the velocity gradients, they were found to give sufficient information together with the measured cutting forces for an approximate step-by-step method of constructing a slip-line field. In this way a slip-line field was constructed not only for the plastic zone in which the chip is formed but also for the plastic flow along the tool-chip interface. It is shown that for most of the flow the slip-line field is satisfactory for both stress and velocity. An interesting feature of the analysis is that at the start of plastic deformation where the work material enters the plastic zone in which the chip is formed the increase in flow stress caused by strain-hardening is appreciable and must be taken into account in analysing the stresses, that is, in the stress equilibrium equations. However, along the tool-chip interface where the material has been severely strained there is little strain hardening and the slip lines in this region are shown to be consistent with the Hencky stress equilibrium equations for a material of constant flow stress.