Slip Line Field Solution for Orthogonal Cutting of Strain Rate Sensitive Materials

Abstract

The objective of this work to investigate the orthogonal cutting process J with the aim of determining the cutting forces analytically as a function of the cutting conditions and the properties of the material used. An analytical model of chip formation based on the theory of plasticity (slip-line field solution) was built. The model describes the case of orthogonal machining with continuous chip formation without built-up edge. The undeformed chip thickness t, was considered to be small compared with the width of cut, b, and thus a condition of plane strain deformation can be assumed. Rigid plastic material without work-hardening, but with flow stress sensitive to strain rate variation was considered. The cutting edge was considered extremely sharp so that the effect of ploughing was neglected. The model was solved and relationships to determine the cutting and thrust forces were derived. These relationships were found to be functions of the flow stress of the cut material, width of cut, rake angle and defonned chip thickness. In order to verify the proposed model a comparison between theoretical and experimental results was carried out. Three different workpiece materials namely, AISI C 1022 steel, ASTM B210 (Al 6061-F) and ASTM Bl35 (brass 70/30) were used for the verification. The flow stress data for the tested materials at high strain rate, equivalent to that encountered in metal cutting operations, has been determined using dynamic tensile test. This test was performed on a tensile split-Hopkinson bar. Dry orthogonal cutting tests were performed on a center lathe using tubular work• pieces made of the tested materials and high-speed steel cutting tools. A wide range of cutting speed, feed, and rake angle was used in these experiments. Cutting forces were measured using a two components tool force dynamometer, while the chip thickness was measured using an Abbe vertical