Investigation of the Transition From Plane Strain to Plane Stress in Orthogonal Metal Cutting

It is widely known that in practical orthogonal machining experiments, interior sections of the deforming material undergo plane strain deformation whereas material near the side faces of the workpiece undergoes plane stress deformation. This study is aimed at investigating the plane strain to plane stress transition using 3D coupled thermo-mechanical finite element analysis of orthogonal machining. The temperature, stress, strain and strain-rate distributions along different planes of the workpiece are analyzed to obtain estimates of the fraction of material undergoing plane strain deformation for different widths of cut. While it is found that the deformation in the mid-section of the workpiece is close to that observed in 2D plane strain simulations, the deformation along the side faces is quite different from that observed in 2D plane stress simulations, due to the constraint imposed upon the material along the sides by the material in the middle. Though the chip thickness along the sides is smaller than the chip thickness in the middle, the strain, strain-rate, and temperature fields along the side face and mid-section are quite similar. This study confirms that accurate maps of temperature, strain and strain-rate in plane strain deformation can be obtained by observing the side faces. It is found that for the cutting conditions used, a width to depth-of-cut ratio of twenty (not ten, as is commonly assumed) results in a close approximation to plane strain deformation through more than 90% of the width of the work material. For a width to depth-of-cut ratio of ten, significant deviations are observed in the stresses, with respect to their corresponding values in plane strain. Recommendations for the width of cut to depth of cut ratio to be used in experiments for other cutting conditions can be developed based upon similar studies.